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Interfacial diffusional theoretical, and clinical aspects of topical local anesthetic formulation

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Interfacial diffusional theoretical, and clinical aspects of topical local anesthetic formulation
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Interfacial diffusional theoretical, and clinical aspects of topical local anesthetic formulation
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Miller, Kenneth James.
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Diffusion coefficient ( jstor )
In vitro fertilization ( jstor )
Micelles ( jstor )
pH ( jstor )
Propylene glycols ( jstor )
Receptors ( jstor )
Skin ( jstor )
Solubility ( jstor )
Solvents ( jstor )
Transdermal application ( jstor )

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University of Florida
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Copyright Kenneth James Miller. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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INTERFACIAL, DIFFUSIONAL, THEORETICAL,
AND CLINICAL ASPECTS OF TOPICAL,
LOCAL ANESTHETIC FORMULATIONS















By

KENNETH JAMES MILLER II


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1991





























Copyright 1991

by

Kenneth James Miller II
































For everyone who's wondered what I've been doing lately.














ACKNOWLEDGEMENTS


There are so many people and organizations without whom much of this work

would not exist that it is difficult to acknowledge them without creating a second

dissertation. Chief among these is, of course, Professor Shah. Professor Shah and

I have now worked together some three and a half years and I am convinced that no

one has a better "feel" for the subject of surface science. Professor Westermann-

Clark has also been invaluable in this work, and I will always remember him as the

ingenious, "chewing gum and bailing wire" influence. Professor Goodwin has been

instrumental in helping me understand much of the medical jargon permeating this

field and will always remain for me, a selfless individual who manages to wear more

hats than I can count. Professor Sloan has taught me much more than the procedure

of in vitro diffusion and is another tireless researcher whom I can never hope to

mimic. When Professor Park and I were introduced, I was amazed that he knew so

much about my work at West Virginia and impressed that he took such an interest

in me so early in my graduate career. Thank you all.

I am also immensely grateful to the members of my family (whom I have not

seen in a long time). To my mother, I can finally say "now" for all the times she has

asked, "When will you be graduating?". To my father, I can say, "Thank you for your









support." (monetary and otherwise). To my sister, I can say, "Let's go for a ride."

And, to my niece, I can finally say, "Hello, I'm Uncle Ken."

This is the second time I have tried to thank Donna for her help in the

acknowledgements of a thesis. Even now, I sit at her computer typing what will be

the last few words of my dissertation. Words, however, cannot acknowledge the help

she has given me or my gratitude to her, but now it's my turn to help her.















TABLE OF CONTENTS



ACKNOWLEDGEMENTS ...................................... iv

LIST OF TABLES ............................................. x

LIST OF FIGURES ............................................ xi

ABSTRA CT ............................................... xvii

CHAPTERS

1 INTRODUCTION ........................................ 1

Literature R eview ........................................ 1
Theoretical Development ............................. 1
Diffusion Through Synthetic Barriers ................... .. 7
Transport Through Biological Membranes ................ 10
Differences between in vitro and in vivo systems ........... 22
Specific Objectives ....................................... 29
Topical Local Anesthetic ............................. 29
Theoretical M odelling ............................... 30

2 MATERIALS AND METHODS ............................ 33

M materials .................................. ........... 33
Solvents ......................................... 33
Local Anesthetics .................................. 34
M ethods .............................................. 37
Solubility ......................................... 38
Titration ...................................... ... 38
Thermal Breakdown of Tetracaine ...................... 38
Drug Partitioning .................................. 38
Surface Tension .................................... 39
Skin Sw selling ...................................... 40
Conductivity ....................................... 40
Ultraviolet Spectrometry ............................. 41









High Pressure Liquid Chromatography (HPLC) ............ 41
Quasi-elastic Light Scattering .......................... 44
In Vitro Diffusion Through Mounted Mouse Skin .......... 45
In Vivo Diffusion .................................. 51

3 PHYSICAL PROPERTIES OF DRUG FORMULATIONS ........ 57

Tetracaine Solubility in Propylene Glycol-water Solvents .......... 57
Partition Coefficient of Tetracaine from Propylene Glycol-Water
Solvents ......................................... 59
Partitioning into 1-octanol ............................ 60
Partitioning into N-octane ............................ 61
Surface Tension of Tetracaine Formulations .................... 63
C onductivity ........................................... 68
Ultraviolet Spectroscopy .................................. 71
Chrom atography ........................................ 74
Equilibrium Phenomena .................................. 76
Quasi-elastic Light Scattering ............................... 82
Thermal Breakdown of Tetracaine ........................... 84

4 DRUG DIFFUSION IN VITRO ............................ 86

C alibration ............................................ 86
Stirring Effects Using Synthetic Membranes ............... 86
Temperature Behavior of Diffusion Apparatus ............. 89
Skin Sw selling ...................................... 92
Scopolamine Diffusion ............................... 93
Transdermal Diffusion of Local Anesthetics ................... 96
Theoretical Considerations ........................... 96
Lidocaine Salt ..................................... 97
Diffusion of Tetracaine .............................. 99

5 DRUG DIFFUSION IN VIVO ............................. 111

R at Tail-flick Test ....................................... 111
Clinical Trials .......................................... 113
Lidocaine ........................................ 113
T etracaine ........................................ 113

6 TH EO RY ............................................. 121

Idealized System ........................................ 122
M odel D erivation ....................................... 124
Inclusion of Skin Swelling In Vitro ........................... 130









R results ............................................... 131
General Behavior of Model ........................... 132
Tetracaine Diffusion Through Hairless-mouse Skin ......... 133
Diffusion of Hydrocortisone Through Synthetic Membranes . 141
Concentration Profile Within the Skin ................... 143

7 CONCLUSIONS ........................................ 145


Physical Properties of Drug Formulations ...........
Solubility ..............................
Partitioning and Solubility .................
Surface Activity .........................
M icelle Size ...........................
Thermal Breakdown .....................
Drug Diffusion In Vitro ........................
Stirring ...............................
Temperature Behavior of Franz Diffusion Cells .
Skin Swelling ...........................
Skin Longevity ..........................
Effect of Propylene Glycol .................
Effect of Age ..........................
Effect of Formaldehyde ...................
Effect of Concentration ...................
Effect of pH ...........................
Drug Diffusion In Vivo ........................
Rat Tail-flick Test .......................
Clinical Trials ..........................
T heory ....................................
Quasi-steady State Model .................
Full Numerical Routine ...................


8 RECOMMENDATIONS FOR FUTURE WORK ...............

Physical Properties .......................................
Diffusion Experim ents ....................................
Theoretical M odelling ....................................
Clinical Studies .........................................

APPENDICES

A DERIVATION OF THE FULL NUMERICAL ROUTINE ........


145
145
145
146
147
147
148
148
148
149
150
150
151
151
152
152
153
153
153
154
154
154

156

156
157
158
159


B COMPUTER PROGRAMS ........................


....... 169









VARFIT.BAS ...
ENDVALUS.BAS
PROFILE.BAS ..
FNR.BAS ......


. . . . . . . . . . . . . . . . . . . . 170
. . . . . . . . . . . . . . . . . . . . 179
. . . . . . . . . . . . . . . . . . . . 183
. . . . . . . . . . . . . . . . . . . . 19 1


REFERENCES .............................................. 202

BIOGRAPHICAL SKETCH .................................... 212














LIST OF TABLES


Table 1: Tetracaine (60% free base, 40% acid salt w/w) equilibrium
concentrations and partitioning into 1-octanol ................... 60

Table 2: Tetracaine (60% free base, 40% acid salt w/w) equilibrium
concentrations and partitioning into n-octane ................... 62

Table 3: Tetracaine (60% free base, 40% acid salt w/w) solubility in
propylene glycol-saline and partitioning between propylene glycol-
saline and 1-octanol ...................................... 64

Table 4: Tetracaine (60% free base, 40% acid salt w/w) solubility in
propylene glycol-saline and partitioning between propylene glycol-
saline and n-octane ...................................... 65

Table 5: Critical micelle concentrations of tetracaine (60% free base,
40% acid salt w/w) in propylene glycol and saline as measured by
surface pressure ......................................... 70

Table 6: Critical micelle concentration of tetracaine (60% free base, 40%
acid salt w/w) in propylene glycol and saline as measured by
conductivity ............................................ 73

Table 7: Ultraviolet absorbance maxima of drugs .................. 74

Table 8: Approximate HPLC retention times of drugs .............. 77

Table 9: Critical micelle concentration of tetracaine (60% free base, 40%
acid salt w/w) in propylene glycol and saline as measured by pH .... 82

Table 10: Best rat tail-flick test results .......................... 112

Table 11: Clinical trials of lidocaine preparations ............... .. .114

Table 12: Full numerical routine summary and comparison to quasi-steady
state model............................................. 167















LIST OF FIGURES


Figure 1:

Figure 2:
and

Figure 3:

Figure 4:

Figure 5:

Figure 6:

Figure 7:

Figure 8:

Figure 9:

Figure 10:

Figure 11:

Figure 12:

Figure 13:

Figure 14:

Figure 15:


General schematic of skin structure .....................

Molecular structure of hydrocortisone, scopolamine, lidocaine,


tetracaine .


Schematic of high pressure liquid chromatograph ...........

Sacrifice of hairless mouse ............................

Securing hairless mouse ..............................

First incision ......................................

Second incision ....................................

M counting skin to cell cap ............................

Franz diffusion cell .................................

Schematic of rat tail Flick-o-meter ......................

Application of drug formulation to skin patch .............

Skin patch on arm of volunteer ........................

Testing response of volunteer to pain stimulus .............

Tetracaine solubility in propylene glycol and saline .........

Tetracaine (60% free base, 40% acid salt w/w) partitioning into


.............. 35


1-octanol ..............................................

Figure 16: Tetracaine (60% free base, 40% acid salt w/w) partitioning into
n-octane ..............................................

Figure 17: Product of 1-octanol partitioning and solubility data .........









Product of n-octane partitioning and solubility data .........


Figure 19: Surface tension of aqueous tetracaine acid salt ............ 67

Figure 20: Surface tension of aqueous tetracaine free base ........... 68

Figure 21: Surface pressure of tetracaine (60% free base, 40% acid salt
w/w) in propylene glycol and saline .......................... 69

Figure 22: Conductivity of aqueous tetracaine acid salt ............... 70

Figure 23: Conductivity of aqueous tetracaine free base .............. 71

Figure 24: Conductivity of tetracaine (60% free base, 40% acid salt w/w)
in propylene glycol and saline .............................. 72

Figure 25: Ultraviolet absorbance spectrum of hydrocortisone .......... 73

Figure 26: Ultraviolet absorbance spectrum of scopolamine ........... 74

Figure 27: Ultraviolet absorbance spectrum of lidocaine .............. 75

Figure 28: Ultraviolet absorbance spectrum of tetracaine ............. 76

Figure 29: HPLC chromatogram of scopolamine ................... 77

Figure 30: HPLC chromatogram of lidocaine ...................... 78

Figure 31: HPLC chromatogram of tetracaine ..................... 79

Figure 32: NaOH titration of aqueous tetracaine ................... 80

Figure 33: NaOH titration of tetracaine in propylene glycol and saline ... 81

Figure 34: pH of tetracaine in propylene glycol. ................... 81

Figure 35: pH of tetracaine in 80% propylene glycol and 20% saline
(v/v). ................... ............................. 81

Figure 36: pH of tetracaine in 60% propylene glycol and 40% saline
(v/v) ....... ... .. ................................... 82

Figure 37: pH of tetracaine in 40% propylene glycol and 60% saline
(v/v) ................................................ 82


Figure 18:









Figure 38: pH of tetracaine in 20% propylene glycol and 80% saline
(v/v) ................................................. 83

Figure 39: pH of tetracaine in saline ............................ 83

Figure 40: Micelle diameter of tetracaine (60% free base, 40% acid salt,
0.36 M) in propylene glycol and saline by QELS ................ 83

Figure 41: Thermal breakdown of tetracaine (60% free base, 40% acid salt
w/w) in 40% propylene glycol, 60% saline (v/v) ................. 85

Figure 42: Effect of stirring device on the diffusion of aqueous
hydrocortisone through synthetic membranes ................... 88

Figure 43: Effect of stirring rate on the diffusion of aqueous hydrocortisone
through synthetic membranes ............................... 89

Figure 44: Dynamic receptor phase temperature in Franz cell .......... 90

Figure 45: Dynamic donor-phase temperature in Franz cell (VD = 2 ml) 91

Figure 46: Dynamic swelling of excised hairless-mouse skin immersed in
w after ................................................. 92

Figure 47: Diffusion of aqueous scopolamine through fresh and chemically
preserved hairless-mouse skin .............................. 94

Figure 48: Comparison of experimental scopolamine diffusion data to data
of Chandrasekaran et al. .................................. 95

Figure 49: Long-term diffusion of aqueous lidocaine salt through untreated
hairless-m house skin ...................................... 98

Figure 50: Effect of propylene glycol on the diffusion of lidocaine salt
through untreated hairless-mouse skin ........................ 99

Figure 51: Effect of propylene glycol on the diffusion of tetracaine HCI
through hairless-mouse skin ................................ 100

Figure 52: Effect of propylene glycol on the diffusion of tetracaine (60%
free base, 40% acid salt w/w) through synthetic polycarbonate
m em branes ............................................ 102








Figure 53: Cumulative flux of tetracaine (60% free base, 40% acid salt
w/w) in propylene glycol and saline through hairless-mouse skin
(young m ice) ................... ....................... 103

Figure 54: Cumulative flux of tetracaine (60% free base, 40% acid salt
w/w) in propylene glycol and saline through hairless-mouse skin (old
m ice) ................................................. 105

Figure 55: Effect of 0.1 % (w/w) formaldehyde on the diffusion of
tetracaine (60% free base, 40% acid salt w/w, 0.36M tetracaine
overall) in 40% propylene glycol and 60% saline (v/v) through old
hairless-m house skin ...................................... 106

Figure 56: Effect of formaldehyde location on the diffusion of tetracaine
(60% free base, 40% acid salt w/w, 0.36M tetracaine overall) in 40%
propylene glycol and 60% saline (v/v) through old hairless-mouse
skin .................................................. 108

Figure 57: Effect of drug concentration on the diffusion of tetracaine (60%
free base, 40% acid salt w/w) in 40% propylene glycol and 60% saline
(v/v) through hairless-mouse skin ............................ 109

Figure 58: Effect of pH on the diffusion of tetracaine (60% free base, 40%
acid salt w/w, 0.36M tetracaine overall) in 40% propylene glycol and
60% saline (v/v) through young hairless-mouse skin .............. 110

Figure 59: Effect of alcohol cleansing on the diffusion of tetracaine (60%
free base, 40% acid salt w/w) in 40% propylene glycol and 60% saline
(v/v) through human skin in vivo ............................ 115

Figure 60: Dose response for tetracaine free base in 75% propylene glycol
and 25% saline (v/v) through human skin in vivo ................ 116

Figure 61: Dose response for 50% tetracaine free base and 50% acid salt
(w/w) in 40% propylene glycol and 60% saline (v/v) through human
skin in vivo ......................................... J.. 117

Figure 62: Dose response for 60% tetracaine free base 40% acid salt
(w/w) in 40% propylene glycol and 60% saline (v/v) through human
skin in vivo .......................................... . 118

Figure 63: Time response for in vivo analgesia by tetracaine (60% free
base, 40% acid salt w/w in 40% propylene glycol and 60% saline (v/v)
(1.1 M 1.8 M ) ...................................... ... 119









Figure 64:
base,
(v/v) (

Figure 65:

Figure 66:
(F1/02

Figure 67:

Figure 68:

Figure 69:

Figure 70:

Figure 71:

Figure 72:

Figure 73:

Figure 74:

Figure 75:

Figure 76:

Figure 77:

Figure 78:

Figure 79:

Figure 80:

Figure 81:

Figure 82:

Figure 83:

Figure 84:


Time response for in vivo analgesia by tetracaine (60% free
10% acid salt w/w) in 40% propylene glycol and 60% saline
0.036 M 1.004 M ) .................................

Schematic of idealized system .........................

Predicted donor- and receptor-phase concentrations
= 7) . . . . . . . . . . . . . . . . . . . . . .


Predicted concentration profile within skin ......

Model fits for saline (old mice) ..............


Model

Model

Model

Model

Model

Model

Model

Model

Model

Model

Model

Model

Model


for 5% propylene g

for 10% propylene

for 20% propylene

for 20% propylene

for 30% propylene

for 40% propylene

for 40% propylene

for 50% propylene

for 50% propylene

for 60% propylene

for 60% propylene

for 70% propylene


glycol (old mice) ...

glycol (young mice)

glycol (young mice)

glycol (old mice) ..

glycol (old mice) ..

glycol (young mice)

glycol (old mice) .

glycol (young mice)

glycol (old mice) .

glycol (young mice #

glycol (young mice i

glycol (young mice i


fits for 70% propylene glycol (young mice #


Model variance for saline (old mice) ..........

Model variance for 5% propylene glycol (old mice)

Model variance for 10% propylene glycol (old mic


120

123


129


.......... 130

.......... 134

.......... 134

.......... 134

.......... 134

.......... 135

.......... 135

.......... 135

.......... 135

.......... 135

.......... 135

K1) ....... 136

'2) ....... 136

)1) ....... 136

'2) ....... 136

.......... 137

...... ... 137

) ........ 137









Figure 85:

Figure 86:

Figure 87:

Figure 88:

Figure 89:

Figure 90:

Figure 91:

Figure 92:

Figure 93:

Figure 94:

Figure 95:

Figure 96:

Figure 97:

Figure 98:

Figure 99:

Figure 100:

Figure 101:


Model variance for 20% propylene glycol (young mice) ...... 137

Model variance for 20% propylene glycol (old mice) ........ 137

Model variance for 30% propylene glycol (old mice) ........ 137

Model variance for 40% propylene glycol (young mice) ...... 138

Model variance for 40% propylene glycol (old mice) ........ 138

Model variance for 50% propylene glycol (young mice) ...... 138

Model variance for 50% propylene glycol (old mice) ........ 138

Model variance for 60% propylene glycol (young mice #1) ... 138

Model variance for 60% propylene glycol (young mice #2) . 138

Model variance for 70% propylene glycol (young mice #1) ... 139

Model variance for 70% propylene glycol (young mice #2) . 139

Model fits for hydrocortisone in a stagnant cell ............ 141

Model fits for hydrocortisone in a poorly stirred cell ........ 141

Model fits for hydrocortisone in a well-stirred cell .......... 142

Model variance for hydrocortisone in a stagnant cell ........ 142

Model variance for hydrocortisone in a poorly-stirred cell .... 142

Model variance for hydrocortisone in a well-stirred cell ...... 142














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

INTERFACIAL, DIFFUSIONAL, THEORETICAL,
AND CLINICAL ASPECTS OF TOPICAL,
LOCAL ANESTHETIC FORMULATIONS

By

Kenneth James Miller II

December 1991

Chairperson: Dinesh O. Shah
Major Department: Department of Chemical Engineering

In general, local anesthetics do not penetrate the skin. There is considerable

need for a formulation that can allow the transdermal delivery of local anesthetics.

Using a combination of the salt and base forms of tetracaine as well as mixed

solvents of saline and propylene glycol, several compositions were developed that are

effective in the transdermal delivery of local anesthetics. Solubilization behavior and

diffusion through excised hairless-mouse skin of the salt and base forms of tetracaine

were studied in detail. The permeability behavior of the drug through the skin as a

function of several variables such as time, stirring rate, drug concentration, and

propylene glycol concentration were investigated. The results show that the mixed

solvents intricately influence the solubilization of the base form of the drug as well

as its partitioning into the skin.









There have been many models proposed which attempt to predict the

diffusion of substances through the skin. The major assumption made in most of

these models is a steady state or linear concentration profile within the skin. A new

model was developed which avoids the limiting assumptions of previous work and

allows the prediction of concentration within the skin as well as flux through the skin

at any time. This model has been successfully used for the prediction of tetracaine

diffusion from topical preparations through mounted hairless-mouse skin. In

addition, this model can account for the swelling of the excised skin as a function of

time immersed in saline. This model could also be easily adapted, through minor

modifications, to predict diffusion through skin in vivo.


xviii














CHAPTER 1
INTRODUCTION



This chapter has two sections: literature review and specific objectives. The

literature review discusses current transdermal research. The latter section of this

chapter is a list of specific objectives for this project.


Literature Review


The literature review for this project covers theoretical background, diffusion

through synthetic barriers, and diffusion through biological membranes. The

theoretical background discusses diffusion through membranes in general, and then

transdermal diffusion specifically. Diffusion through synthetic barriers discusses both

unsupported and supported barriers as analogues of skin's resistance to diffusion.

Diffusion through biological membranes discusses the use of skin to study

transdermal diffusion.


Theoretical Development


The review of past theoretical work pertaining to transdermal diffusion is

divided into two parts. The first section reviews the theory surrounding diffusion

through membranes. Readers familiar with Fick's laws of diffusion may skip this









2

material. The second section is a more detailed account of theoretical transdermal

diffusion.

Diffusion through membranes

Membrane diffusion is controlled by three basic effects: osmotic pressure,

solute diffusion, and fluid flow.20 In transdermal diffusion there are no osmotic

pressure effects because all species can diffuse through the membrane. Equilibrium

is approached through solute diffusion and solvent flow through the membrane

(solvent diffusion). Consequently, there is diffusion in both directions as the system

approaches equilibrium, with all components moving from higher concentration to

lower concentration.

This process can be described mathematically by Fick's laws of diffusion.

Fick's first law of diffusion states that flux is proportional to the concentration

gradient and the constant of proportionality is defined as the diffusivity.7


JA = -DAB VCA 1


JA = Molar flux of component A

DAB = Molar diffusivity of component A in B

CA = Molar concentration of component A


A special case of this law occurs when the gradient is constant. In such circumstanc-

es, the flux is constant (steady state). In a closed system, this occurs after long times,

but does not imply equilibrium.









3

Fick's second law of diffusion incorporates the time rate-of-change of

concentration to the flux with a mass balance.7


aC
A -v.J =DAB v2C 2
at vA AB A
at

Difficulty in analyzing diffusion data is usually encountered when the second

or combined law of diffusion (Equation 2) is integrated. The boundary and initial

conditions imposed by the system geometry and experimental apparatus often

complicate integration despite simplifying assumptions.

Transdermal diffusion theory'

Transdermal diffusion consists of many phases; including, release of the solute

from the solvent, diffusion of the solute through the solvent to the membrane,

partitioning of the solute into the membrane (establish equilibrium across the phase

boundary), diffusion through the membrane, partitioning out of the membrane,

reaction, and removal by the circulatory system.

For drug diffusion through the skin, some models assumed that the

concentration gradient and, consequently, the flux were constant. One of the earliest

theoretical models for transdermal diffusion was developed by Michaels et al.60

Their model described diffusion through a homogeneous barrier with a steady state

(linear) concentration profile within the skin and negligible receptor-phase drug




*An excellent and much more complete description of the mechanics of diffusion
as they relate to transdermal diffusion can be found in B.W. Barry's Dermatological
Formulations. Percutaneous Absorption Chapter 2.4









4
concentration. These simplifications yielded a model in which the flux was

proportional to the donor phase concentration.

Another model that assumed a steady state profile was that of Fleming et

al.25'42 They treated transdermal diffusion in a closed system as a first-order kinetic

process (J = kaC where J = flux, k = overall rate constant or mass transfer

coefficient, and AC = concentration difference across the membrane). The overall

rate constant (k) was assumed to be the result of diffusion through a series of

resistances (stagnant boundary layer/membrane/stagnant boundary layer). This

model predicted an exponential decay of concentration scaled by the ratio of the

compartment volumes.

McDougal et al. used a similar approach to model the absorption of vapors

in the lungs57 and in the skin56 of rats in vivo. Permeability (mass transfer)

coefficients, partition coefficients, and blood flows from experimental data were used

in the model. The use of experimentally measured partition and permeability

coefficients required no theoretical understanding of phase equilibrium or diffusion.

Consequently, the model was able to emulate experimental data, but provided little

insight into the mechanics of percutaneous absorption.

Zatz97 also developed a model that assumed a steady state concentration

profile, but increased its complexity by using multiple resistances in series to

represent the membrane. These additional resistances allowed the model to more

closely fit experimental data, but did little to increase the fundamental understanding

of transdermal diffusion.








5

Sloan et al.78'79 expanded on the model of Fleming et al.25'42 by describing the

phenomenon of partitioning across a membrane. Using the Gibbs-Duhem equation

(equivalent activities between phases in equilibrium), they related the drug

permeability to the theoretically determined partition coefficient and were able to

estimate permeability from theoretical solubility parameters.

Others have attempted to solve both Fick's first and second laws without

assuming a steady state profile. In 1979, Hadgraft41 attempted to derive rigorous

expressions for diffusion through the stratum corneum (hydrophobic outer layer of

keratinized cells), the epidermis, and the capillary bed. His derivation began with

Fick's second law and a solution was sought through Laplace transformation. To

simplify the mathematics, only solutions at long times were considered. Assumptions

about the relative values of the parameters and simplification by single term

expansions of transcendental functions permitted the Laplace solution to be inverted.

The effects of diffusion routes (transcellular versus intercellular), partition

coefficients, and skin binding were simulated by the model. Our quasi-steady state

model does not require these types of assumptions or simplifications and is valid for

all stages of diffusion in vitro.

In 1983, Guy and Hadgraft35 expanded their non-steady state model to include

transport from the vehicle to the membrane and from the membrane to the

capillaries. Transport between phases of the model was assumed to follow first-order

kinetics. They give few details of the mathematics, but the relative magnitudes of









6
their dimensionless groups and limiting cases were used to get expressions for the

amount of drug removed from the skin.

In 1983, Guy et al.39 examined the release of drug from liposomes in a topical

formulation. This theoretical treatment was based on Fickian diffusion in a spherical

geometry. To get an analytical solution, infinite sink conditions were adopted at the

boundary. Short and long times were used as limiting cases. The result was

expanded to account for multilamellar vesicles by assuming that a first-order rate

constant accounts for diffusion through the interface.

In 1985, Guy and Hadgraft34 derived equations for diffusion through skin

modelled as a bilaminate structure with layers of different dimensions, diffusivities,

and partition coefficients. The path through the stratum corneum was assumed to

be intercellular and tortuous. They also presented an expression for the concentra-

tion profile within the stratum corneum,33 but they gave no details of the derivation

or the boundary conditions the equation represented.' Results were plotted to

illustrate the ability of the model to simulate experimentally observed phenomena.

Most recently, Hadgraft42 built upon previous work25 by adding the resistances of a

drug reservoir and an adhesive layer to diffusion. These additional resistances are

supposed to represent those of a commercial transdermal therapeutic system (TTS).




'The equation presented by Guy and Hadgraft represents the concentration
within a finite slab as a function of time and position with constant boundary
conditions and no drug present initially. The model presented in this work (Chapter
6: Theory page 131) also made use of this solution to Fick's second law. For our
model, however, additional modifications were used to account for the changing
concentrations at the boundaries and the swelling of the skin.











Diffusion Through Synthetic Barriers


The study of diffusion through skin is complicated by the complex structure

of the skin. Inter- and intra-species variability in skin leads to differing diffusive

barrier properties. Because of this variability, many researchers substitute synthetic

membranes for biological membranes to more accurately determine differences

between transdermal formulations and avoid complex statistical analyses.

The advantages of synthetic barriers to diffusion are their consistency and well

characterized properties. The use of synthetic barriers requires several assumptions

about transdermal diffusion. It must be assumed that the skin does not metabolize

the drug significantly, which may or may not be true depending upon the drug

involved.81 Secondly, diffusion is assumed to be passive and the drug is assumed to

have an equivalent (or at least similar) affinity for the synthetic medium as for

biologically viable skin. These assumptions are violated to some extent simply

because the skin is an active medium and the chemical content of the synthetic

medium differs from that of skin. Provided one is prepared to make such

assumptions, synthetic media can be used to evaluate transdermal formulations

qualitatively.

Two main systems are used to simulate the barrier properties of skin:

unsupported barriers (usually two immiscible liquids in contact) and supported

barriers (usually two phases separated by a solid, but permeable barrier).

Unsupported barriers can be used to measure partition coefficients (equilibrium) or









8
diffusion coefficients. However, unsupported barriers usually assume that the

controlling resistance to diffusion is the hydrophobic stratum corneum (represented

by the lipid or hydrophobic, liquid phase). Supported barriers provide a mechanical

barrier that allows the testing of miscible solutions since the liquids are prevented

from mixing by a physical barrier. Supported barriers also allow the addition of a

hydrophilic barrier (the membrane or another liquid phase) to more closely resemble

the layered structure of skin.4

Unsupported barriers

Unsupported barriers are usually prepared by putting two immiscible liquids

in some sort of vessel. The barrier to diffusion in such a system in the phase

boundary between the two liquids. Unsupported barriers can be used to study the

release of a drug from a formulation as a function of time. They can also be used

to estimate the skin-vehicle partitioning behavior of substances.4 The partitioning of

alkyl homologs between water and an immiscible lipid phase was studied to develop

a correlation between partitioning and alkyl chain-length.26 The relationship is linear

when plotted on semi-log axes (i.e., log[partition coefficient] oc chain length).

Poulsen and Flynn66 reviewed a study on the release of steroids from water-

propylene glycol gels and creams into a receptor phase of stirred isopropyl myristate.

It was determined that, for all systems, the fraction of propylene glycol that produced

a saturated solution maximized the release rate.

The use of unsupported barriers provides some benefits for the study of

transdermal diffusion. However, the difficulties associated with the technique often









9

make supported membranes more attractive. Unsupported barriers do not accurately

represent the properties of skin because they can only be used when they are

immiscible with the formulation and they are subject to convection currents. For

these reasons, synthetic polymer membranes are often used with or without

hydrophobic liquids.

Supported barriers

Micro-porous membranes have been used to study many systems. Semi-

permeable membranes are routinely used to measure diffusion coefficients, osmotic

pressures, and streaming potentials in aqueous systems. Semi-permeable membranes

are also used for separations (ultra-filtration, reverse osmosis, dialysis, etc.). Johnson

studied the diffusion of steroids through microporous membranes in aqueous

systems.49 His experiments determined the diffusion coefficients for steroids diffusing

in porous polycarbonate membranes and provided the basis for the stirring-rate

studies in Chapter 4: Drug Diffusion In Vitro.

Silicone-rubber membranes have been used as diffusion barriers for a variety

of penetrants.4'26'46'48'55'68 These rubber membranes are very hydrophobic and a

comparison to studies using skin helped to establish that the primary diffusive barrier

of skin is lipophilic.26 Neubert modified an in vitro system using a silicone rubber

membrane by utilizing a non-polar receptor phase to study the diffusion of

hydrophobic drugs.62

A synthetic membrane and a hydrophobic liquid phase can be combined to

simulate the behavior of skin as a barrier to diffusion. The synthetic membrane









10

mechanically supports and confines the lipid phase in a well defined region.

Hadgraft and Ridout43 used a cellulose nitrate membrane saturated with isopropyl

myristate as the barrier to diffusion for a wide range of drugs. Isopropyl myristate

showed diffusive properties similar to those of the stratum corneum. The correlation

was very good, but the magnitude of the barriers differed by three orders of

magnitude (true skin being the more effective barrier). They later expanded their

experiments to include dipalmitoyl phosphatidylcholine, linoleic acid, and tetradecane

as model barriers.44 Tetradecane imitated the stratum corneum barrier properties

best. Hadgraft et al.45 also used this barrier to study the effect of azone (1-dodecyl-

azacycloheptan-2-one, a penetration enhancer) on the diffusion of salicylate and

determined that azone may form ion pairs with salicylate. Although synthetic

membranes can greatly reduce the difficulties associated with biological variability,

they can only estimate relative effects in transdermal diffusion. Experimental data

on transdermal diffusion must ultimately be obtained using real skin. It is more

difficult to discern trends because of scatter, but it is more likely that these trends

are relevant to a clinical setting.


Transport Through Biological Membranes


Recent developments in transdermal diffusion are organized into the following

groups: system effects, vehicle effects, solute effects, penetration enhancement,

differences between in vitro and in vivo systems, and topical local anesthesia. The









11

literature is organized in this way to present general findings first and then focus

more closely on aspects directly related to this study.

In vitro cell geometry

The design of an in vitro transdermal diffusion cell affects not only its ability

to mimic in vivo conditions, but also the ease of using the device. Almost all in vitro

transdermal diffusion experiments are done with either vertical or horizontal

transdermal diffusion cells31 (orientation refers to the direction of diffusion).

Gummer31 states that horizontal cells are easier to stir than vertical cells. The upper

phase in a vertical cell is open to the atmosphere and the skin forms its base so a

stirring magnet in the upper phase would rest on the skin. The donor-phase volume

in a vertical cell can be varied from bare coverage of the skin to the capacity of the

upper compartment. The use of the horizontal cell, however, requires the skin to be

fully immersed in a liquid phase and thus fixes the volumes of both receptor and

donor phases. The fact that the donor phase in a vertical cell is not usually jacketed

also complicates any attempt at temperature control.

Membrane effects

Variation in the experimental system such as the source of the membrane and

degree of hydration can profoundly affect transdermal diffusion. Figure 1 is a very

general schematic of skin structure for reference to the following material. The

permeability of human skin can vary as much from person to person as from place

to place on a given individual.4 The structure and physical properties of the stratum

corneum have been studied and described in detail.24'2863'77'84 Variation in stratum











Stratum Corneum (15 pru)


Viable Epidermis (150 pm)








,- Dermis (2000 rnm)







Figure 1: General schematic of skin structure

corneum thickness, number of sweat glands, number of hair follicles, and blood

supply will affect the routes and overall resistance of skin to diffusion.4'74'75'88 Some

of these parameters have been systematically studied and the results are reviewed

below.

Age. The effect of subject age on transdermal diffusion has been studied in

detail under a variety of conditions. In 1962, Marzulli53 identified a trend of

decreasing permeability with age of human skin in vitro. Since that time, other

researchers have confirmed this trend.4'6'34'89 There is some evidence that the general

permeability increases in elderly subjects4 or is dependent on the substance

investigated.6'34 The general trend of decreasing permeability with age is attributed

to the progressive decrease in moisture content in the skin of the elderly.34









13

Skin components. Marzulli53 separated human skin into its components to

measure their barrier properties individually. Statistical significance was only

detected between full thickness skin and the dermis, however, the sectioned skins

were generally more permeable than intact skin. Scheuplein76 found that the water

permeability of the outer layer of human skin was approximately one order of

magnitude lower than that of deeper tissue. Much later, Anderson et al.2 compared

the barrier properties of full thickness human skin to isolated stratum corneum.

They found that the isolated stratum corneum resembled the behavior of the full

thickness skin for both partitioning and diffusion. Findings such as these were

instrumental in identifying the stratum corneum as the primary resistance to

transdermal diffusion.

Damage and disease. Barry4 describes experiments investigating transdermal

diffusion as a function of skin condition. Permeability of mouse skin to hydrocorti-

sone was found to increase when the mice were deficient in essential fatty acids,

exposed to UV light, exposed to vitamin A acid, exposed to 10% acetic acid in

acetone, or exposed to solvents that fluidized or extracted the stratum corneum lipids.

Abraded skin was found to be equally permeable to steroids as unabraded skin in

rats, but more permeable in monkeys.4 Tape stripping* increased the rate of water

loss to approximately that of a free water surface and also increased the permeability

of the skin to most substances. Shaving of hair from both humans and laboratory




*Tape stripping refers to the removal of outer skin cells by applying and removing
adhesive tape.









14

animals is assumed to damage the stratum corneum and increase the diffusion rate.4

In general, it was determined that the permeability of the skin could be increased by

damaging the stratum corneum barrier.

Anatomical Region. Barry describes experiments in which human skin is

evaluated as a barrier to diffusion of hydrocortisone from various anatomical sites.4

Permeability was ranked as follows: scrotum > forehead > scalp > back >

forearms > palms > plantar surface of the foot arch. Wester et al.93 also determined

that the permeability of the skin of the scrotum is greater than that of the abdomen

for both adult and newborn skin.

Rougier et al.72 ranked human stratum corneum permeability as: forehead >

abdomen > thigh > chest > arm > back. Subsequent experiments73 established that

relative absorption depended not only on anatomical region, but also the chemical

nature of the penetrant. The authors did, however, reassess the general permeability

of human stratum corneum as: forehead > postauricular > abdomen > arm. The

forehead was found to be more than two times more permeable than the arm or

abdomen regardless of the substance tested.

Race. Differences in the permeability of skin were also measured between

different races of humans.4 Black skin was found to be less permeable than

caucasian skin, people of Celtic ancestry were more often irritated by toxic chemicals

than people of Mediterranean ancestry, and fair skinned people were found to be

more susceptible to contact dermatitis.









15

Animal models. In 1980, Durrheim et al.23 concluded that hairless-mouse skin

was a reasonable model for human skin through comparison of their data on the

diffusion of n-alkanols through hairless-mouse skin in vitro and previously published

data using human skin in vitro. The measured permeability of hairless-mouse skin

differed significantly from human skin for many substances,22'67 but the trends were

similar.

Hairless-mouse skin has been criticized as a model for human skin based upon

its reaction to long-term hydration,9 acetone attack,10 and penetration enhancers.11

Under such conditions, hairless-mouse skin cannot confidently mimic the trends of

human skin.

Barry5 has suggested the use of shed snake skin (Indian python or American

black rat snake) as a model for the permeability of human skin. Shed snake skin is

plentiful, can be collected without harm to the snake, and can be stored at room

temperature. Snake skin was found to be less susceptible to hydration and acetone

damage than mouse skin and performed more like human skin under these

circumstances. The effects of penetration enhancers were less dramatic for snake

skin than for mouse skin, but did not model human skin any better. The damage

caused by a number of pesticides was also investigated. The results indicated that

snake skin and human skin do not react similarly to the attack of the pesticides.

Overall the author suggested that snake skin is no better as a model for human skin

than other biological membranes like collagen, egg shell membranes, etc.









16

Many animal models have been investigated. The general trend of

permeability can be summarized: rabbit > rat > monkey = swine = man.4'37

Pigskin has been suggested as an in vitro model for human skin4 and the rhesus

monkey has been suggested as an in vivo model for human skin.34

Hydration. Excessive absorption of water increases the skin's thickness and

changes its relative chemical composition. These effects result in changes in the

skin's ability to act as a barrier to diffusion. Barry4 reviews much of the literature

concerning skin hydration and concludes that hydration increases the permeability

of the skin to all substances except small, polar molecules.

Blank8 treats hydration and skin permeability as the subject for an entire

chapter. He and co-workers measured the diffusion of water through stratum

corneum as a function of time and degree of hydration. They use this information

to calculate the thickness of the skin and the flux of water through the skin as a

function of the surface concentration of water (or relative humidity).

Vehicle effects

The subject of vehicles has received more attention than receptor phases in

transdermal diffusion. The receptor phase can only be altered in in vitro experiments

while the donor phase can be altered either in vitro or in vivo. The donor phase can

be altered to affect either the drug itself or the skin.* There are many reasons for

varying the donor phase composition to affect the drug (particularly its




'Vehicles that affect the permeability of the skin are known as penetration
enhancers. These effects are reviewed in another section (page 20).









17

thermodynamic activity) in solution. The effects of drug solubility, drug partitioning

(the ratio of equilibrium concentrations in the skin and vehicle respectively),

emulsification, and pH control are summarized below.

Solubility and partitioning." Roberts et al.70 correlated the permeability of

phenolic compounds, aromatic alcohols, and aliphatic alcohols with their partitioning

behavior in octanol. The log-log plot is linear up to a partition coefficient of about

100, but decreases in slope at higher partition coefficients.

Bronaugh and Franz13 determined that partitioning into the stratum corneum

was the determining factor for skin permeability in the absence of overriding

solubility constraints in the system. Other researchers have also demonstrated

this.11'23'26 Gummer32 concluded that, for a given concentration, the rate of diffusion

is inversely proportional to the saturation concentration (saturation implies maximum

thermodynamic activity in the vehicle) and proportional to the partition coefficient

of the drug (large partition coefficient implies low activity in skin).

Ward86 discusses the use of surfactants as a means of increasing the solubility

of the penetrant. A comprehensive algorithm is presented to optimize the vehicle

based on structure, interfacial properties, and phase behavior. In general, it was

found that increasing partitioning into the skin and approaching the solubility limit

aid transdermal diffusion.

Emulsions, liquid crystals, and liposomes. Emulsification of the drug in the

vehicle can be of benefit for a poorly soluble drug. Osborne et al.64 state that the



'Solubility and partitioning are, of course, properties of both solvent and solute.









18

use of a microemulsion or a lyotropic liquid crystalline system can increase the

thermodynamic stability of the drug in the formulation and its penetration into the

skin. There are exceptions which point up the fact that more information on the

effects of these systems is needed.

Uster82 discusses the use of liposome vehicles for topical delivery of drugs.

Liposomes differ from micelles in that the vesicles are defined by bilayers of lipids

(much like cell membranes) and separate the bulk aqueous phase from an entrapped

aqueous phase. Their advantage seems to be their ability to increase the concentra-

tion of drug in the skin without increasing the amount of drug entering the receptor

phase or the circulatory system. This effect could be caused by liposomes binding

to the skin surface and releasing their contents there. For small, water soluble

molecules, diffusion through lipid bilayers constitutes the rate-limiting step and the

additional bilayers formed by liposomes significantly inhibit their diffusion.

pH. Diffusion through skin can be affected by pH if the solute is a weak

electrolyte. Changes in pH shift the fractions of acid and base in solution. Since

these two forms of the solute have different properties, they will differ in their ability

to cross the skin barrier.60 Flynn26 hypothesizes that in lipoidal membranes (e.g.,

skin) ionic species will be less favorable in the membrane as compared to the

unionized species. Flynn later confirms this hypothesis experimentally. Therefore,

manipulation of the pH of the vehicle can have a profound effect on the transdermal

diffusion of ionizable substances.










Solute concentration

Concentration refers to molecularly dispersed substances; literature on the

effects of emulsification (i.e., systems in which the solute is not molecularly

dispersed) is reviewed on page 17. The theoretical response to increased concentra-

tion is a proportional increase in flux (according to Fick's first law). Chandrasekaran

et al.7 found that the diffusion of scopolamine through human epidermis followed

such a trend. There are also accounts of deviation from this expected response (both

positive and negative).13'32'70'91 Many of these effects appear to be due to confusion

between the overall concentration and the concentration of drug molecularly

dispersed in the medium.

Effect of temperature

The thermal motion of molecules is the driving force for diffusion. Increasing

the amplitude of thermal motion (temperature) should increase the rate of diffusion

of drugs through the skin just as it increases the rate of diffusion of other solutes in

other systems. The difference in the barrier properties of skin at different

anatomical sites may at least be partially due to differences in temperature.4 Barry

also states that the effect of temperature on transdermal diffusion is usually studied

by an Arrhenius plot (log of drug permeability versus the inverse of temperature).

Such analysis has determined that the activation energies of n-alkanols (ethanol to

pentanol) are constant (= 16.5 kcal/mol) between ambient and body temperature.

Heavier n-alkanols do not yield constant activation energies. It is suggested that this

may be caused by the melting or extraction of some lipids in the stratum corneum









20

at elevated temperatures. Durrheim et al.23 also measured the diffusion of n-alkanols

through skin as a function of temperature (Arrhenius plot) and got a similar value

of approximately 19 kcal/mol.

Scheuplein76 measured the diffusion of water and ethanol through human

stratum corneum as a function of temperature and found that the results depended

on whether the temperature was increasing or decreasing (hysteresis effect). This

effect was attributed to the fluidization and partial dissolution of the lipids in the

membrane (permanent damage to the barrier at elevated temperatures).

Raising the temperature can also affect the barrier properties of the stratum

corneum. Poulsen and Flynn66 found that the barrier properties of human and

hairless-mouse stratum corneum remain relatively constant up to approximately 800C.

Above this temperature there is a rapid, dramatic, and permanent loss of barrier

function.

In summary, the literature indicates that there are two effects of temperature:

a conventional thermal motion effect and a stratum corneum dissolution effect.

Penetration enhancers

Knepp et al.50 summarize the ideal features of a penetration enhancer as:

1: No pharmacological response

2: Specific in its action

3: Acts immediately and reversibly with predictable duration

4: Chemically and physically stable and compatible in formulation










5: Odorless, colorless, tasteless

6: Nontoxic, nonallergenic, nonirritant

Brown and Langer14 describe penetration enhancers as "vehicles that reduce the

barrier properties of the stratum corneum in such a way as to increase the

penetration of the drug of interest." Many substances have been investigated as

potential penetration enhancers. Chien18 lists the following as representative classes

of penetration enhancers: alkyl methyl sulfoxides, surfactants, and azones

(1-alkyl azacycloheptan-2-ones).

One mechanism for penetration enhancement seems to be disruption of the

stratum corneum lipids and proteins.19'85 Fluidization and extraction of stratum

corneum lipids by some proven penetration enhancers has been shown experiment-

ally.27'29'4 These same authors have also noted that some established penetration

enhancers (N-methyl-2-pyrrolidone, n-alkanols) do not affect the stratum corneum

and must act through some other mechanism.

Another process by which some penetration enhancers cationicc amines) may

increase drug flux is by forming ion pairs with the drug. Briefly, the mechanism of

facilitated transport by ion pairs at the skin surface is:85 long chain cationic amines

ionize and may pair with ionized permeant; the uncharged pair diffuses through the

stratum corneum; within the skin the pH rises, causing the amine to deprotonate and

freeing it to diffuse back through the skin.










Differences between in vitro and in vivo systems

Studying transdermal diffusion on living, intact organisms is more difficult than

studying diffusion in vitro. The difficulties of sample collection, sample analysis,

consistent dosing, variations between individuals, and effects of metabolism

complicate in vivo studies. Despite the experimental difficulties, topical formulations

must pass through a clinical in vivo testing phase before being approved for

widespread use. For some variables the effects are the same for in vitro and in vivo

studies; for others, such as metabolism, circulation, and radial diffusion, there are no

in vitro parallels.

Metabolism. Barry4 states that drug metabolism has been neglected in past

studies. Both inactive and active metabolites may form in the skin and can affect the

results of a transdermal diffusion experiment if not accounted for properly. Tdiuber81

details the effects of in vivo metabolism in detail.

One potential benefit of in vivo drug metabolism is the ability to specifically

engineer drug precursors (prodrugs) to improve their percutaneous absorption.

Prodrugs have little or no therapeutic activity, but are metabolized after absorption

into an active drug.36'37

Circulation. Blood flow in vivo creates an open system while an in vitro

system is usually closed. Blood flow carries drug from the skin and distributes it

throughout the body preventing equilibrium. In a closed, in vitro system, the drug

builds up in the receptor phase and the concentration difference across the

membrane decreases with time.









23

Radial diffusion. For a topically applied formulation in vivo, diffusion is not

limited to one direction. Radial diffusion can be a significant factor.38 In an in vitro

diffusion cell, radial transport is impossible since the drug cannot diffuse through the

walls of the diffusion cell or laterally through the skin.

Receptor phase. The choice of receptor phase can affect the ability of the

diffusing substance to partition from the skin into the receptor compartment. In

addition, the solubility of the diffusing substance in the receptor fluid can affect

interpretation of results if an infinite sink is assumed. Bronaugh and Stewart12 varied

the receptor fluid for the diffusion of two lipophilic fragrance chemicals. They found

that increasing the lipophilicity of receptor phase increased the flux of the fragrances

through the skin.

Recommendations. Wester and Maibach90 suggested ways to help match in

vivo conditions of humans using an in vitro diffusion cell.


Membranes Human skin should be used if possible


Cell design A large receptor volume minimizes the effects of

low solubility in the receptor phase


Temperature Circulating temperature should be 37C (results

in a skin temperature of 32C, average for skin in

vivo)









24
Receptor phase Buffered saline or as necessary to keep drug

thermodynamic activity below 10% that in the

donor phase


Miscellaneous Emulate in vivo or clinical system

Topical local anesthesia

The transdermal diffusion of local anesthetics has been more often studied in

vivo than in vitro. Many drugs have been tested, although the results have always

fallen short of expectations because of poor diffusion through the skin.

McCafferty et al.55'96 formulated local anesthetic bases in oil/water creams and

monitored their diffusion through silicone-rubber membranes. Based on their

observations, lignocaine (lidocaine) and amethocaine tetracainee) were the best

candidates for clinical study.

Adriani and Dalili' tested the bases and salts of dibucaine, tetracaine,

mepivacaine, prilocaine, lidocaine, procaine, benzocaine, and butesin for anesthetic

effect on more than 150 volunteers. The bases were dissolved in a solvent of 50%

water, 40% ethanol, and 10% glycerol. The salts were applied as aqueous solutions.

After the anesthetic preparations were on the skin for 30 minutes, their effectiveness

was measured by their ability to block itching and burning sensations induced by

electrical current. The time of 30 minutes was established after observations that

effective preparations established a block within 15 minutes. No other investigator

has claimed to produce an anesthetic effect so quickly. Other investigators, however;

have used much more stringent tests for efficacy than the relief of electrically









25

induced itching. Saturated solutions of the bases were found effective in most cases

and the order of decreasing efficacy was: tetracaine, mepivacaine, lidocaine,

benzocaine, and procaine. None of the anesthetic salts were effective. Adriani and

Dalili also tested 30 commercially available topical anesthetic preparations and found

that none could relieve the experimentally induced itching and burning except

Americaine (containing 20% benzocaine base). Adriani and Dalili stated that the

anesthetic effect of all topically applied formulations dissipated only 10 to 60 seconds

after being removed from the skin. Again, this result contradicts all other reports on

topical application of anesthetics. The rapid onset and subsidence of anesthetic

effect as measured by Adriani and Dalili could be a result of the electrical

conductivity of the anesthetics themselves or some other surface effect. The inability

of other investigators to even approach these results indicates that the anesthetics,

in fact, never reach the nerve endings.

Campbell and Adriani'5 studied the systemic levels of local anesthetics

administered by three routes (infusion, infiltration, and topical application) in both

human volunteers and dogs. The drugs tested were tetracaine, cocaine, procaine, and

benzocaine. Intravenous injection was used as the control. Absorption of the

anesthetics from the mucous membranes of the pharynx and trachea was comparable

to the absorption when administered intravenously. Transdermal diffusion was

detectable only when the skin was abraded or suffered third degree burns prior to

application. The authors' concern was avoiding toxic systemic levels of the drugs and

there was no assessment of analgesia.









26

Gesztes and Mezei30 studied the release of 0.5% tetracaine base from

multilamellar phospholipid vesicles. The anesthetic preparation was evaluated in

adult volunteers using the pinprick method.* The preparation was applied for one

hour and reportedly provided at least four hours of topical anesthesia. Pontocaine

cream, used as a control, was found to be ineffective. Despite clear details about the

anesthetic preparation and its administration, our attempts to reproduce the

published results were unsuccessful. The performance of their liposomal formulation

was also compared to the tetracaine preparation developed in our laboratory and

found to be less effective clinically. Their preparation was less concentrated,

however; and their comments about the benefits of low concentration for self-

administration by outpatients are important.

Kushla and Zatz,51 using an approach similar to that of Campbell and Adriani

for evaluating local anesthesia, induced pain electrically. Their anesthetic

formulation was lidocaine base (5%) in vehicles of either an aqueous gel containing

40% propylene glycol or an oil-in-water emulsion cream (77.5% water). Placebos of

the vehicles were used as controls. Tests of the topical formulations revealed that

the gel was not effective, but the cream was. Maximum effect was observed two to

three hours after application and lasted up to six hours.

Monash61 studied the diffusion of anesthetic salts and bases through both

mucous membranes and skin in vivo in human volunteers. The anesthetic bases were

dissolved in a solvent of 45% alcohol (probably ethanol), 45% water and 10%



'The subjects are asked to rate the pain level produced by a pin prick.









27

glycerine. The salts were dissolved either in the same solvent as the base or in water.

The bases of tripelennamine, lidocaine, tetracaine, phenacaine, and benoxinate

produced anesthesia after 45 to 60 min contact under occlusion at concentrations of

2%. The salts required at least two hours to produce anesthesia.

The use of ethanol and water as solvents for tetracaine was investigated in our

laboratory. These solvents were not compatible with tetracaine because the drug

broke down into a variety of aromatic aldehydes. Neither water nor ethanol alone

caused tetracaine to decompose. Therefore, even though the results of Monash were

equal to the current state-of-the-art in transdermal local anesthesia; we found his

system to be unstable.

McElnay et al.58 investigated the use of ultrasound to promote the in vivo

transdermal diffusion of lidocaine from a cream base. No statistical difference was

detected using volunteers, although the trend of the data suggested that ultrasound

decreased the onset time of anesthesia.

McCafferty et al.55 compared in vitro and in vivo percutaneous absorption of

several anesthetic bases in an oil-in-water emulsion cream (77.5% water). The

anesthetic concentration was 0.35 mmol/g. Drug diffusion was evaluated either in

vitro through a silicone rubber membrane or in vivo by the pinprick method. Of the

drugs tested, tetracaine (amethocaine) was the most effective both in vitro and in

vivo.

Woolfson et al.95 characterized the concentration response of three tetracaine

free base formulations: water, and two aqueous systems gelled with either 1.5%









28

carbomer wax or 7% methylcellulose and an oil-in-water emulsion cream consisting

of 16% Emulsifying Wax, 4% paraffin. For the aqueous gels, a tetracaine free base

concentration of 4% applied for 30 min produced adequate anesthesia after 40 min.

The emulsion cream required 8% to 12% tetracaine free base to be effective, but the

onset time was the same as for the aqueous gels. A higher concentration did not

decrease the onset time, but did increase the duration of anesthesia. The onset of

anesthesia after removing the formulation implied that the stratum corneum was the

limiting resistance to diffusion. Our results for onset time and duration of anesthesia

with tetracaine in a different solvent are similar and support this hypothesis.

Small et al.80 used one of the aqueous gels developed by Woolfson et al.95

before cutting skin grafts. The clinical procedure was modified from previous

experiments by increasing the area (as needed), dose (1 mm layer), gel application

time (> 1 hr), and the period of time between the removal of the gel and the start

of the procedure (60 to 300 min). Skin graft removal was pain-free in 64 of 80 cases.

In in vivo trials, McCafferty et al.54 compared the clinically available EMLA

eutecticc mixture of local anesthetics) cream to their 0.35 mmol/g tetracaine cream.

The tetracaine cream produced longer and more rapid anesthesia than the EMLAe

cream.

Woolfson et al.94 conducted an expanded clinical assessment of their aqueous

tetracaine gel in a pediatric environment to evaluate the level of anesthesia and

reactions in 1241 patients. The level of success (defined as no sensation during









29

venepuncture or minimal sensation with no discomfort) was 88.7% (1101/1241).

About 7% of the patients had mild reactions (local redness, swelling, and itching).

McGowan et al.59 used laser doppler velocimetry to measure changes in blood

perfusion during vasodilation caused by the percutaneous absorption of tetracaine

from the gel described on page 28. They confirmed the clinically obtained minimum

onset time of 30 min, but could not measure the duration of anesthesia.


Specific Objectives


Topical Local Anesthetic


The objective, of course, is the development of a topical local anesthetic

formulation suitable for clinical use by hospital patients. Ideally this preparation

should be effective, fast acting, and long lasting without irritation or other discomfort.

Its effectiveness should be measured by its ability to alleviate the discomfort

associated with the insertion of an intravenous needle no more than one hour after

application and for a period of at least 5 hours.

Pediatric applications

Children experience greater stress in a hospital environment than adults.

Preventing the discomfort of inserting intravenous needles would benefit the patients

as well as physicians and staff. Local anesthesia would make intravenous access

easier because the patient would be less likely to flinch during the procedure.










Outpatient applications

Patients could be given anesthetic patches and instructed to apply them a

specified time before their outpatient procedures. Self-application of the anesthetic

patch would require advanced preparation of the device. Since the anesthetic base

may deteriorate at room temperature, the patient would need to store the patch in

his/her refrigerator if the procedure was to take place more than three or four days

later. This should not be a problem since patients are occasionally given sera that

must be refrigerated to remain effective.

Pain management

Continued relief of the discomfort of iv's could also make hospital stays more

pleasant for patients. A non-invasive local anesthetic formulation makes systemic

analgesics unnecessary. The anesthetic patch can be designed to last longer than

twelve hours.


Theoretical Modelling


The objectives of theoretical modelling go beyond developing equations that

mimic experimental data. Developing totally empirical correlations does not increase

the understanding of the processes of transdermal diffusion. The main, theoretical

goal of this work is to apply diffusion theory to transdermal diffusion in vitro and

develop a model that has applicability beyond topical local anesthesia.










Novel techniques

The quasi-steady state assumption is far from novel. It is simply the

assumption that the boundary concentrations do not change appreciably during the

period of interest. Cussler describes the technique very early in his book on mass

transfer.20 Use of this assumption for transdermal diffusion is novel. Furthermore,

experimentally measured skin swelling data is added to give the model greater

accuracy and predictive ability.

Improved understanding of mechanism

In modelling the diffusion of drugs generally and tetracaine specifically, as few

assumptions as possible were made while trying to obtain an analytical solution. It

was hoped an analytical solution of Fick's second law for in vitro diffusion would

illuminate the mechanism of transdermal diffusion. The insight gained could guide

research and development toward a better understanding of transdermal diffusion

and could lead to better patient care.

Importance of swelling in vitro

No theoretical model for transdermal diffusion has ever included skin swelling

before. Others have measured this phenomenon, but have never presented the data

in enough detail for inclusion in a theoretical model. A simple moving boundary

conceptualization is, admittedly, naive; but it is also a first step toward accounting for

the change of environment during in vitro transdermal diffusion. Obviously, more

than the dimensions of the skin change; the chemical nature must also play a role in

the diffusion rate as the stratum corneum becomes hydrophilic. However, our data









32

suggest that the effect of the chemical changes in the stratum corneum are

overshadowed by the change in its physical dimensions.














CHAPTER 2
MATERIALS AND METHODS


Materials


This section describes the properties of the materials used in this project.

Two general classes of materials are used, drugs and solvents. First the solvents are

described, then the properties of the drugs are described. The properties referred

to are solubility, surface tension, specific conductivity, ultraviolet light absorption, and

liquid phase chromatography behavior.


Solvents


The solvents used in the diffusion through skin experiments (excluding those

used for separation in the HPLC) were: (1) distilled water or 0.9% saline (NaC1)

solution (made from distilled water and biological grade NaC1), and, (2) USP grade

propylene glycol(1,2-propanediol) purchased from Fisher Scientific. Numerous

solutions of these two liquids were used as vehicles for the delivery of drugs through

the skin. These solvents are completely miscible and their ratio was varied primarily

to control the solubility of the drugs (drug solubility is discussed in the following

section).









34

Propylene glycol is widely considered to be a penetration enhancer for the

percutaneous absorption of various drugs.32'50'69'87 The effect of propylene glycol on

the diffusion of the drugs in this study, however, is complex.

All solvents used in the HPLC (high pressure liquid chromatograph) were

prepared from HPLC grade solvents from Fisher Scientific. Methanol (CH3OH) and

acetonitrile (CH3CN) were used as received and phosphoric-acid buffer was prepared

in the laboratory from HPLC grade water and HPLC grade phosphoric acid (H3PO4).

The solution was buffered to pH 3 using ACS grade KOH from Fisher Scientific.

The HPLC solvent mix used to analyze the local anesthetics was essentially that

recommended in the Supelco chromatography catalog for lidocaine, but altered to

decrease the retention time of the drugs. Resolution of components was not a

concern in this analysis since the drugs were the only components which eluted from

the HPLC.


Local Anesthetics


Four drugs were used in this project. The majority of the diffusion through

skin experiments used tetracaine (a local anesthetic). Hydrocortisone, scopolamine,

and lidocaine were used for calibration or preliminary experiments and to test the

experimental procedure for measuring diffusion through skin. Figure 2 contains

schematic representations of these drugs. The diffusion of hydrocortisone through

synthetic membranes has been studied previously.49 Diffusion of hydrocortisone

(from Sigma and used as received) through synthetic membranes was used to














Hydrocortisone


/CH,


NH-C

-CH


II
- C- CHCH2OH







/CH
-CH-N(
C2H,


Scopolamine







Lidocaine


0
1, II / H
HC- (CH2)- NH C-O-(CH2)- Tetracaine
CH3


Figure 2:
tetracaine


Molecular structure of hydrocortisone, scopolamine, lidocaine, and









36
evaluate the experimental apparatus. The first experiments using mouse skin in this

project used scopolamine as the diffusing drug because previous work on transdermal

scopolamine17 provided a method for evaluating the performance of the in vitro

transdermal experimental procedure. Scopolamine HC1 (Sigma) was converted to

scopolamine free base by ether-extraction from a caustic solution. Transdermal

scopolamine is available commercially for motion sickness (Transderm-Scop from

Ciba).

Lidocaine was the first choice for a local anesthetic to be administered

transdermally because it is chemically stable during storage, resistant to solvent

attack, unlikely to cause allergic reaction, and widely used clinically as an injected

solution. Lidocaine HC1 (Sigma) was used without further purification. Lidocaine

was abandoned in favor of tetracaine which has better partitioning characteristics and

is approximately ten times more effective as a local anesthetic.

Two forms of tetracaine were used in experiments, tetracaine free base (a

hydrophobic ester) and tetracaine HC1 (a hydrophilic salt of the free base). Both

forms of tetracaine (Sigma) were used as received. Tetracaine base penetrates the

neuron more effectively21, but has very low aqueous solubility. Tetracaine salt,

however, is quite soluble in aqueous solutions (>200 g/l). Tetracaine salt is also

much more stable than the free base which must be kept refrigerated and dry.21

Since tetracaine HCI is thermally more stable, it can be sterilized and still remain

effective. For transdermal diffusion however, sterility is not so great a concern and

tetracaine base becomes more attractive.









37

To compromise between the favorable diffusion characteristics of the base

form and the high aqueous solubility of the salt form, a mixture of the base and salt

forms was used. Such a mixture takes advantage of the tetracaine salt:tetracaine free

base equilibrium. Mixing a drug and its HC1 salt in solution is equivalent to adding

HC1 acid to a preparation containing only free base (or adding NaOH to a

preparation containing only the salt form).21

The properties measured were solubility in the solvents, surface tension as a

function of concentration, conductivity as a function of concentration, ultra violet

absorbance spectra, and HPLC behavior.


Methods


This section presents the procedures common to a number of experiments

beginning with those most likely to be familiar to the reader. Descriptions of the

instruments and techniques used to measure solubility, surface tension, specific

conductivity, and UV spectra are followed by more detailed descriptions of high

pressure liquid chromatography (HPLC), in vitro diffusion of drugs through mounted

mouse skin, and in vivo diffusion of drugs (rat tail flick test and clinical trials with

human volunteers).











Solubility


Solubility was determined by rotating a solution in contact with excess drug

at 4 rpm for at least 18 hours at room temperature. A sample was then withdrawn,

filtered, and analyzed by HPLC to get the total drug concentration in solution.


Titration


The acid-base behavior of tetracaine-containing formulations was explored by

simple titration. The apparent pH of the tetracaine formulation was monitored while

measured quantities of either NaOH or HC1 were added. Such measurements

yielded the pK, of tetracaine in various solvent mixtures as well as the pH vs.

tetracaine acid salt-free base ratio.


Thermal Breakdown of Tetracaine


To determine the shelf-life of tetracaine formulations, the concentration of

tetracaine in solution was measured as a function of time at room temperature and

skin temperature (24C and 320C, respectively).


Drug Partitioning


To simulate the environment encountered by the drug when placed in contact

with the skin, the anesthetic preparation was placed in contact with a hydrophobic

organic phase. No account was made for hydrophobic phase solubility in the vehicle









39

or vehicle solubility in the hydrophobic phase. The partition coefficients for

vehicle'-organic systems were found by means similar to those described for

solubility. Vehicle formulations in contact with an equal volume of the hydrophobic

organic phase were rotated at about 4 rpm for at least 18 hours. Total drug

concentration in the hydrophobic phase relative to that in the vehicle was found by

HPLC.


Surface Tension


All surface tension measurements used in this work were made on a Rosano

Surface Tensiometer Model LG with a Wilhelmy plate. This apparatus has a

platinum plate approximately 1 cm x 3 cm x 0.5 mm attached to one arm of a

milligram balance. The balance is adjusted by adding mass to the other arm equal

to the mass of the platinum plate. With the scale reading zero and the arms of the

balance level, the platinum plate is brought into contact with the surface of a liquid

and is consequently pulled into the bulk of the liquid phase. Mass is added to the

free arm of the balance until the arms of the balance are again level. The mass

required to bring the arms to level is proportional to the surface tension of the

liquid. This instrument was calibrated using water with a known surface tension of

72.4 mN/m. The uncertainty of these measurements is approximately 0.2 mN/m.






'The term vehicle is used here and elsewhere to indicate the mixture of
propylene glycol and water (saline) in which the drug is dissolved.











Skin Swelling


Since skin in contact with liquid tends to swell, the extent of swelling was

determined to learn its possible effect on drug diffusion. A skin sample of known

cross-sectional area was weighed as a function of time immersed in water. Any

increase in mass was attributed to uptake of water and a corresponding increase in

volume (using density of water = 1.0 g/ml). The change in area of the upper and

lower faces of the skin sample was assumed to be negligible compared to the

increase in skin thickness. The initial volume of the skin was calculated based on a

density of 1.0 g/ml and its thickness was calculated by considering the skin sample

to be a disk of known radius. The change in skin thickness caused by the absorption

of water was correlated for later use in the theoretical model (Chapter 6, page 131).


Conductivity


Conductivity measurements were made using a YSI conductivity bridge Model

31 with a YSI 3043 Electrode (cell constant = 1/cm). This instrument uses a

scintillation screen to indicate conductance or resistance of the solution in which the

electrode is immersed. The screen's two lighted bars diverge as the calibrated dial

indicating conductance approaches the solution's conductivity. The solution's conduc-

tivity is the dial reading at which the screen's bars reach their maximum separation.

The instrument can measure conductivities from about 0.5 umhos to 2 mhos









41

(resistance from 0.5 f to 2 Mn). Conductivities from this instrument have an

uncertainty of approximately 0.2 tmho.


Ultraviolet Spectrometry


Ultraviolet spectra were measured using a Perkin Elmer scanning spectropho-

tometer Model 576. This model has two lamps (a deuterium lamp as an ultraviolet

source and a tungsten lamp as a visible source) extending its operational range over

any single-source instrument (90 nm to 800 nm). Ultraviolet and visible spectra were

measured against a reference solution and the difference in absorption between the

two solutions was plotted. This instrument was used to screen compounds for

possible detection in the HPLC (the HPLC detector uses ultraviolet or visible light

absorption). A spectrum of a solution containing the compound of interest was

measured over a wide range of wavelengths to determine the wavelengths of

maximum absorption for use with the HPLC. Although this instrument can be used

for quantitative measurements of absorbance (proportional to concentration), it was

only used in this manner for early diffusion experiments before the HPLC had been

installed. Calibration of this instrument showed a constant error of approximately

+ 0.33 nm which is within the manufacturer's tolerance.


High Pressure Liquid Chromatography (HPLC)


By far the most complex instrument, the HPLC is invaluable for this type of

diffusion study (Figure 3). Fully computerized (640 kB Epson Equity I+ running












Autosampler/
/< Injector


Figure 3: Schematic of high pressure liquid chromatograph

DoubleDos and Spectra Physics software LNET2 and SPMENU), this system can

analyze over 80 samples without operator assistance. Once programmed, the system

can inject a sample from a diffusion experiment, identify the components in the

sample, determine the concentration of each component (integrate the signal), store

all information (including the raw data), generate a file for a spreadsheet, and print

a final report. Although the system has several components, the principles of

operation are relatively simple. The HPLC uses the relative affinity of a compound

between a polar and a nonpolar phase to achieve separation. A polar solvent is

pumped through a separation column containing a nonpolar hydrocarbon chemically

bonded to silica. The retention (residence) time in the column depends on the

compound's affinities for the two phases. Consequently, two compounds in the same









43

sample separate as they pass through the column depending on their polarity and

functionality. This type of chromatography is called "reverse-phase".

After the components of the sample are separated by the column, they flow

through an absorbance detector (Spectra Physics Model SP8450) which generates an

electrical signal proportional to the light absorbed by the liquid passing through the

detector. Peaks in plots of this signal correspond to components eluting from the

column. Because retention time depends on the functionality and polarity of the

compounds, the likelihood that two different chemicals will have the same retention

time is remote.

The other instruments in the HPLC system are the pump, autosampler, and

integrator. The pump (Spectra Physics Model SP8800) simply maintains the flow of

carrier solvent through the system at a steady rate. The pump can also mix up to

three miscible solvents in any ratio.

The autosampler (Spectra Physics Model SP8880) contains the sample vials

in four trays mounted on a turntable. Each tray holds twenty vials and the turntable

contains an additional priority-vial position. The autosampler moves each vial to the

sampling position and, when the system is ready, injects a predetermined volume of

the contents into the solvent stream while signalling the other instruments to begin

analysis.

The integrator (Spectra Physics Model SP4290) plots the raw signal from the

detector (optical absorbance of the solvent stream) and determines the presence of

peaks. The integrator calculates the area of peaks and determines if they correspond









44

to programmed compounds. If a peak is identified as a programmed compound,

previously entered calibration data are used to determine the amount of the

compound detected.


Quasi-elastic Light Scattering


Dynamic or quasi-elastic light scattering (QELS) was used to determine the

size of tetracaine micelles in saline, propylene glycol, and mixtures of these solvents.

QELS uses the time-varying scattering intensity and broadening of incident laser light

caused by the Brownian (thermal) motion of micelles. This information is used to

generate the Fourier transform of the power spectrum (an exponential function).

The time constant of this exponential function is directly related to the diffusion

coefficient of the micelles in solution. The apparent micelle diameter can then be

calculated by the Stokes-Einstein equation (assuming the particles are spherical).47


S kT 3
3 7r q DT

d = micelle diameter

k = Boltzmann constant

T = absolute temperature

7 = solvent viscosity

DT = translational diffusion coefficient











In Vitro Diffusion Through Mounted Mouse Skin


The following describes the procedures related to diffusion studies. The

process begins with preparing the skin from hairless mice, mounting the skin to the

diffusion cell, and sampling the drug concentration in the receptor phase.

Preparation of skin

The first step in measuring the diffusion of any compound through mounted

skin was procuring the skin from the mice. Laboratory hairless-mice were used.

Females were used because they are less aggressive and territorial than males and

less likely, therefore, to fight and damage their skin. The average mass of the mice

at sacrifice was about 30 grams.

The mice were sacrificed by cervical dislocation (Figure 4) and weighed.

After being sacrificed, a mouse was placed on its back and all four legs were taped

down (Figure 5). Using surgical scissors, an incision was made across the lower

abdomen just above the lower legs. Connecting incisions up the center and across

the upper abdomen just below the forelegs were then made. At this point the

incision resembled an "I" (Figure 6). The skin was teased away from the underlying

tissue and connective tissue was severed where necessary.

At this point, the rear legs were released, the mouse folded over onto its back,

and the upper and lower incisions continued around the abdomen (Figure 7). The

skin was carefully removed by severing any remaining tissue. The removed skin was

essentially rectangular.








46


Figure 4: Sacrifice of hairless mouse

Diffusion apparatus

In vitro transdermal diffusion was measured using flow-through type Franz

diffusion cells (Figure 9). The diffusion cells have four parts: body, cap, O-ring, and

clamp. The cell body was modified to include a magnetic stirring tee which greatly

increased mixing efficiency and reduced the tendency to form a stagnant boundary

layer adjacent to the skin surface. The cell body, surrounded by a water jacket to

maintain constant temperature, contained the lower (receptor) compartment into

which the drug diffused (= 15 ml). The receptor compartment initially contained









47


Figure 5: Securing hairless mouse

0.9% w/w saline. The cell cap contained the upper (donor) phase (source of diffusing

drug) and held the skin in place. A rubber O-ring sat between the cell body and the

inside surface of the skin. A clamp held the entire assembly together.

The skin sample was placed over the inverted cell cap and the O-ring placed

over the skin (Figure 8). The cell body, with the magnetic stirring assembly inside,

was then fitted on top of the O-ring and the entire inverted assembly secured by the

spring clamp. Once the clamp had been tightened, the cell could be handled as a

single unit.








48


Figure 6: First incision

Donor solution (2 ml) was applied to the external surface of the skin, and the

donor compartment sealed to prevent evaporation. To assure constant sampling

intervals for multiple diffusion cells (generally three), experiments were staggered 5

minutes.

At regular intervals (1 or 2 hrs.), a 0.2 ml to 0.3 ml sample was withdrawn

from the center of the receptor volume through the upper sample port using a long,

thin needle and a 1 ml syringe. This sample was sealed in an autosampler vial for

later analysis by HPLC. The sample volume extracted was replaced by fresh,








49


Figure 7: Second incision

buffered saline injected by a syringe through the upper sample port. (To insure that

no air was drawn into the receptor compartment, the sample volume extracted was

less than the volume in the upper sample port arm.)

The concentrations obtained from HPLC were used to calculate the total mass

transferred through the skin. The following mass balance accounts for the sampling

process.








50


Figure 8: Mounting skin to cell cap

n-1
M(tn) =C(tn) V+Vs,( C(tx))
x=O

M(tn) Total mass transferred at time t,

C(t.) Measured concentration at time t,

V Volume of receptor compartment (. 15 ml)

V, Sampled Volume (=;200 A1)

x Summation index













Cell Cap > Sample Ports
Skin '/ ,

Cell Body -- ,




"% I



Water Jacket
Stirrer

Figure 9: Franz diffusion cell

The total mass obtained from this equation can then be converted to a corrected

concentration by dividing by the receptor compartment volume (V) or to a flux by

dividing by the mass transfer area (diameter = 25 mm) and sampling interval.


In Vivo Diffusion


Two different in vivo procedures were used in this study: rat tail-flick testing

and clinical testing on human volunteers. Both procedures are described below as

well as their relative advantages and disadvantages.

Rat tail-flick test

Cursory screening of prototype anesthetic preparations was carried out by

anesthesiology department personnel associated with this project using the rat tail-
































Figure 10: Schematic of rat tail Flick-o-meter

flick test. The procedure is as follows: A gauze patch moistened with an anesthetic

solution was secured to the tail of a live rat for a given period of time (usually two

hours). After removal of the patch, the rats were placed in a device which focuses

a strong light (pain stimulus) on the tail and measures the time between activation

of the light and movement of the tail out of the light beam. The level of effective-

ness of the anesthetic preparations was measured by the time delay caused by the

application of the patch over the baseline delay for untreated animals. Figure 10 is

a schematic of this device.

Although this method is attractive for screening large numbers of preparations

in a relatively time, rat tails are relatively insensitive. In some cases, the results of








53

the rat tail testing are contrary to clinical testing in human volunteers. Once this fact

surfaced, large scale testing using rats was suspended.

Clinical studies on humans

A much more accurate, but less time efficient method for testing the

anesthetic preparations in vivo is large scale clinical testing with human volunteers.

This method is more accurate because it measures effectiveness of these preparations

in terms of the final goal; local anesthesia in humans. Unfortunately, the subjective

response of a volunteer yields data prone to wide scatter.

The procedure for these human trials was as follows: A measured volume

(usually 0.5 ml) of the anesthetic preparation, either at room temperature or warmed

to 370C, was placed on a transdermal patch (2 cm diam.) from Hill Top Research

Inc. (Figure 11). The patch was then applied to the inner forearm of the subject and

the time of application noted (Figure 12). Ten to twenty subjects were tested for

each series and up to six patches could be applied to each subject to increase the

efficiency of the procedure.

After a specified time (15 to 90 minutes), the patch was removed and any

residual liquid wiped away. Pain stimulus was provided by a hypodermic needle

(Figure 13). The subject was asked to give a rating commensurate to the effective-

ness of the anesthetic. The scale used is called the Visual Analog Scale and allows

the subject to assign a value between 1 and 10 to convey no effect (1) to complete

analgesia (10).








54


Figure 11: Application of drug formulation to skin patch








55


Skin patch on arm of volunteer


Figure 12:

















/


I


f
/
/


Testing response of volunteer to pain stimulus


56


Figure 13:


,!Pk














CHAPTER 3
PHYSICAL PROPERTIES OF DRUG FORMULATIONS


This chapter discusses the physical properties of the tetracaine acid salt, free

base, saline, propylene glycol system as measured by the experimental methods

described in the previous chapter (pages 37-44). The solubility, lipid-phase

partitioning of tetracaine were studied to estimate the transdermal diffusion of

tetracaine formulations. The surface tension, conductivity, acid-base behavior, and

quasi-elastic light scattering of tetracaine were studied to determine to microscopic

structure of the formulations. Ultraviolet absorbance and liquid chromatography

were used to quantitatively determine drug concentrations and the thermal

breakdown characteristics were studied to estimate shelf life of the anesthetic

formulations.


Tetracaine Solubility in Propylene Glycol-water Solvents


Figure 14 shows measured solubilities of tetracaine salt, tetracaine base, and

a 40% acid salt, 60% free base mixture (w/w) in propylene glycol-water solvents.*

The solubility of tetracaine base in aqueous solution is negligible. Adding propylene


'This particular mixture was chosen because at this bulk ratio (mixing tetracaine
free base and acid salt powders) the solution is near the published pKa (8.5).2 The
significance of a solution at its pK, is that there are equal amounts of ionized and
unionized solute.









58

glycol greatly increases the solubility of the base which peaks at about 2.65 M then

falls to 2.17 M in pure propylene glycol. The solubility of tetracaine salt decreases

slightly as the propylene glycol fraction increases, but does not change much overall

(0.5 M _: C 0.8 M). The solubility of a 40% acid salt, 60% free base mixture

peaks at 3.00 M in 50% propylene glycol. The solubility of the mixture is far greater

than the sum of the salt and base solubilities in 50% propylene glycol. This

non-additivity near 50% propylene glycol shows that HC1 acid can enhance solubility

above what would be expected from the pure component solubility curves (pure salt

in solution corresponds to a bulk mixture of equal parts of tetracaine base and HC1









4



-3 h .j --- Acid Salt

--/" -- Free Base
2

-*-- 40% Salt
60% Base



0 10 20 30 40 50 60 70 80 90 100

% Propylene Glycol (v/v)

Figure 14: Tetracaine solubility in propylene glycol and saline









59
acid).21 The increased solubility in 40% free base, 60% acid salt (w/w) mixtures

cannot arise only from the protonation of the tetracaine molecule since an even

larger fraction of molecules is protonated in tetracaine acid salt. Some interaction

between the acid salt and free base forms, each stabilizing the other, appears to

occur. Since the acid salt and the free base are in equilibrium, it is not strictly

correct to consider them two different species. They are more likely assuming some

intermediate structure when they associate (partial charge). These intermediates

must be more soluble in propylene glycol/saline solutions than either the acid salt

or the free base.


Partition Coefficient of Tetracaine from Propylene Glycol-Water Solvents


Drug partitioning between the stratum corneum and the vehicle influences

transdermal diffusion.26'52'76'78'92 Partitioning of substances into the skin can be

roughly simulated by lipid-phase partitioning between a vehicle and a hydrophobic

solvent. The ratio of drug concentrations in the vehicle and the non-polar solvent

at equilibrium is taken as the partition coefficient for the formulation (i.e.,

Csolvent/Cvehicle). In this study, no attempt was made to account for the solubility of

the vehicle in the non-polar solvent or that of the non-polar solvent in the vehicle.

Two solvents were used: 1-octanol and n-octane. Octanol was preferred for

estimating stratum corneum partitioning, but the octanol/propylene glycol/water

system is single-phase above 60% propylene glycol. Therefore, partition coefficients









60

for systems containing more than 60% propylene glycol could not be evaluated using

octanol.

Partitioning into 1-octanol

The partitioning of a 60% tetracaine free base, 40% tetracaine acid salt

mixture between propylene glycol-water solutions and 1-octanol (CH3-(CH2)7-OH)


Table 1: Tetracaine (60% free base, 40% acid salt w/w) equilibrium concentra-
tions and partitioning into 1-octanol

% Propylene CVehicle Coctanol Kp
Glycol (M) (M)

0 3.59 x 10-3 2.29 x 10-2 6.37
20 3.99 x 10-3 2.22 x 10-2 5.55
40 3.87 x 10-3 2.05 x 10-2 5.30
50 3.99 x 10-3 1.99 x 10-2 4.99
60 3.57 x 10-3 1.70 x 10-2 4.75



declines linearly as the organic content of the vehicle increases (Table 1, Figure 15).

At approximately 70% propylene glycol the system of 1-octanol/saline/propylene

glycol no longer develops an interface. Therefore, at high propylene glycol

concentrations, partitioning behavior cannot be assessed. To simulate the

partitioning behavior of tetracaine into a lipid phase at higher propylene glycol

concentrations, a more hydrophobic oil phase is required.














10

8


0 6 Single
U Phase
4 Region

2


0 10 20 30 40 50 60 70 80 90 100:

% Propylene Glycol (v/v)

Figure 15: Tetracaine (60% free base, 40% acid salt w/w) partitioning into
1-octanol

Partitioning into N-octane

The partitioning of tetracaine between propylene glycol-water solutions and

n-octane (H3C-(CH2)6-CH3) is constant at about 0.004 up to 30% propylene glycol.

The partition coefficient then declines steadily with increasing propylene glycol

content up to 70% propylene glycol (Table 2, Figure 16). Above 80%, however,

partitioning into the oil phase seems to increase. It is inferred from these data that

a minimum partition coefficient ( 0.0022) may exist between 70% and 80%

propylene glycol.

Drug solubility in the formulation indicates how much drug can be loaded into

the vehicle and, therefore; how much drug can be delivered to the skin surface. The








62
Table 2: Tetracaine (60% free base, 40% acid salt w/w) equilibrium concentra-
tions and partitioning into n-octane


partition coefficient indicates the fraction of the drug that moves from the vehicle

into a hydrophobic phase. Assuming the partition coefficient holds at saturation, the

product of the partition coefficient and the saturation concentration is an estimate

of the drug concentration at the vehicle-skin interface just inside the skin. The more

drug delivered to the skin-vehicle interface, the more drug available to diffuse across

the skin. The optimal system corresponds to a maximum in the combined solubility-

partitioning parameter. If the 1-octanol partitioning data are used (Table 3,

Figure 17), the optimum system is 50% propylene glycol. If the n-octane partitioning

data are used (Table 4, Figure 18), the optimum system is also 50% propylene glycol.
















0.010


0.008


0.006
UC


0.002



0.000
0 10 20 30 40 50 60 70 80 90 100

% Propylene Glycol (v/v)

Figure 16: Tetracaine (60% free base, 40% acid salt w/w) partitioning into
n-octane

Thus, different solvents with different partitioning behavior can be used to obtain the

same result. The optimum vehicle for tetracaine diffusion through skin as

determined by the combined solubility-partitioning parameter is 50% propylene

glycol and 50% saline regardless of which lipid is used to characterize partitioning.


Surface Tension of Tetracaine Formulations


A surface tension versus concentration plot for tetracaine HC1 in water is

presented in Figure 19. The surface tension decreases rapidly with increasing drug

concentration initially, but eventually flattens out as more drug is added. Such a

strong effect of concentration on surface tension indicates that tetracaine HC1 is










Table 3: Tetracaine (60% free base, 40% acid salt w/w) solubility in propylene
glycol-saline and partitioning between propylene glycol-saline and 1-octanol


% Propylene
Glycol


Csat
(M)


KMCsat
(M)


0 1.527 6.374 9.366
20 1.591 5.547 7.815
40 1.958 5.302 11.05
50 2.979 4.992 14.38


2.806


4.750


13.74


0 10 20 30 40


50 60


70 80 90 100


% Propylene Glycol (v/v)


Product of 1-octanol partitioning and solubility data


strongly surface active and the flattening of the curve at higher concentrations

indicates the presence of micelles at a critical micelle concentration (CMC) of


Single
Phase
Region


Figure 17:








65
Table 4: Tetracaine (60% free base, 40% acid salt w/w) solubility in propylene
glycol-saline and partitioning between propylene glycol-saline and n-octane

% Propylene Csat Kp KCsat
Glycol (M) (M)
0 1.527 3.77 x 10- 5.75 x 10-3
10 1.587 4.03 x 10-3 6.39 x 10-3
20 1.591 4.13 x 10- 6.57 x 10-3
30 1.632 3.97 x 10-3 6.48 x 10-
40 1.958 3.17 x 10-3 6.21 x 10-
50 2.979 3.03 x 10-3 9.01 x 10-3
70 2.757 2.23 x 10-3 6.15 x 10-
80 2.433 2.21 x 10-3 5.37 x 10-
90 1.926 3.08 x 10-3 5.92 x 10-3
100 1.817 2.85 x 10- 5.17 x 10-3



strongly surface active and the flattening of the curve at higher concentrations

indicates the presence of micelles at a critical micelle concentration (CMC) of

approximately 0.1 M. This agrees almost identically with the previously published

value of 0.13 M.3

Similar measurements were made for tetracaine base in water (Figure 20).

The surface tension of the tetracaine base solution decreases more rapidly than for

tetracaine HC1, indicating that it is more surface active. The surface tension drops

to about 40 mN/m before the aqueous solubility of tetracaine base is exceeded.

Tetracaine base shows higher surface activity than the HCI salt, which also appears

to be linked to its lower solubility. The surface tension data indicate that tetracaine















0.0100


0.0075


S0.0050


0.0025


0.0000 '
0 10 20 30 40 50 60 70 80 90 100

% Propylene Glycol (v/v)

Figure 18: Product of n-octane partitioning and solubility data

base does not form micelles like the HCI salt, but precipitates out of solution as solid

crystals.

Similar measurements were also performed in various solvents consisting of

propylene glycol and saline with a 40% tetracaine acid salt, 60% free base (w/w)

solute. The normal surface tension of the solvent ranges from 72.4 mN/m for water

to about 30 mN/m for pure propylene glycol. In order to more clearly illustrate the

effect of added solute, the surface tension (7') has been converted to surface pressure

(re); where wc = Yo -' (yo refers to C = 0 or no solute). Figure 21 shows the

surface pressure of tetracaine in propylene glycol-saline solvents. Surface pressure

rises from 0 in the pure solvent to some maximum value which depends on the

solute-solvent interaction. To determine a CMC, the location of the change in slope














80
T = 23C
70 oo% CMC = 0.1M

g 60


50
0
40 .. .. .
10-3 10-2 10-1 100

C (M)

Figure 19: Surface tension of aqueous tetracaine acid salt

must be identified. Table 5 summarizes the CMC from surface pressure versus

concentration measurements. As the fraction of propylene glycol increases, the CMC

of tetracaine increases. The 20% saline, 80% propylene glycol and 100% propylene

glycol systems do not show micelle formation. The increase in CMC may be caused

by an increase in molecular drug solubility. As the molecular solubility increases, the

tendency to form micelles decreases. Micelles will cease to form as molecular

solubility continues to increase. The decrease in overall solubility of the tetracaine

mixture (60% free base, 40% acid salt w/w) from 80% to 100% propylene glycol

(v/v) may be due to the lack of micelles.








68





80


70 -


60 I

50 T =23C \ d

40
10-5 10-4 10-3 10-2

C (M)

Figure 20: Surface tension of aqueous tetracaine free base


Conductivity


The conductivity of tetracaine salt and base versus concentration has also been

measured. The results of these measurements are in Figure 22 and Figure 23. The

conductivity of these aqueous solutions rises with drug concentration for both forms

(acid salt and free base). By analysis similar to that for surface tension versus

concentration, the critical micelle concentration can be obtained by locating a change

in slope between two linear portions.83 Through this method, the CMC of aqueous

tetracaine salt is found to be 0.03 M which is in general agreement with that from

surface tension measurements (Figure 19).














Topical Formulation D 100% PG
Concentration 5.8spHs8.7
30
S80% PG
6.55pH7.6

0 60% PG
S20 7.0pH<8.2

S* 50% PG
^ 6.2!pHs8.4

SA 40% PG
.....---. 6.3spHs8.3
------ J,-
A 20% PG
S6.3spHs8.5

0 v Saline
0.0 0.5 1.0 6.95pHs8.4

C (M)

Figure 21: Surface pressure of tetracaine (60% free base, 40% acid salt w/w) in
propylene glycol and saline

The graph of conductivity versus concentration for tetracaine base (Figure 23)

indicates that micelles are forming at very low concentration (3 x 10-5 M). This

behavior, quite unlike that suggested by the surface tension versus concentration

graph (Figure 20), further elucidates the uncertainty of CMC values measured by

different means as well as the definition of CMC.

The conductivity vs. concentration behavior for mixtures of tetracaine acid salt

(40% w/w) and tetracaine free base (60% w/w) was also measured in propylene

glycol-saline solvents (see Figure 24 and Table 6). Comparing CMC values from

surface tension (Table 5) and conductivity (Table 6) shows that the values are in

general agreement (33%).









70
Table 5: Critical micelle concentrations of tetracaine (60% free base, 40% acid
salt w/w) in propylene glycol and saline as measured by surface pressure


% Propylene
Glycol


CMC (M)


pH Range
(Apparent)


0 (no CMC) 6.85-8.37
20 0.02 6.30-8.51
40 0.04 6.26-8.29
50 0.07 6.17-8.43
60 0.15 7.03-8.41

80 (no CMC) 6.46-7.55


100






20000


10000


(no CMC)


5.80-8.65


0.1 0.2 0.3

C (M)


Conductivity of aqueous tetracaine acid salt


Figure 22:









71





8

7 cmc 0.00003M *
6

0 5-

4 -

3

2

1 -


0 1 2 3 4

C (M) x 104

Figure 23: Conductivity of aqueous tetracaine free base

The conductivity of propylene glycol-saline mixtures decreases as propylene

glycol content increases. This is a result of fewer ions in solution as water is replaced

by propylene glycol. Propylene glycol does not dissociate appreciably in solution so

it is less capable of solvating ions or conducting electricity.


Ultraviolet Spectroscopy


The ultraviolet absorption spectra of the drugs were most important for

maximizing the sensitivity of the HPLC detector. Spectra were obtained over the

range of the HPLC detector and the wavelengths of maximum absorption determined

for the compounds of interest. The absorbance spectra of hydrocortisone,

















20000


10000


0 0.2 0.4 0.6 0.8 1.0


+ Saline
6.95pHs8.4

A 20% PG
6.35pH<8.5

O 40% PG
6.3!pH8.3

+ 50% PG
6.2spH<8.4

A 60% PG
7.0spHs8.4

* 80% PG
6.5spHs7.5

V 100% PG
5.8spHs8.7


C (M)


Figure 24: Conductivity of tetracaine (60% free base, 40% acid salt w/w) in
propylene glycol and saline

scopolamine, lidocaine, and tetracaine are shown in Figure 25-Figure 28 and the

wavelengths of maximum absorbance are in Table 7.

For hydrocortisone, the uv spectrophotometer was used at a single wavelength.

The primary absorbance maximum for hydrocortisone is 247 nm. The absorbance

at that wavelength was related to the concentration of hydrocortisone in the solution

by Beer's law. This method of determining the concentration of hydrocortisone was

used because, at the time of the diffusion experiments with hydrocortisone, the

HPLC had not yet been installed.


A
I-




#- A^


I









73
Table 6: Critical micelle concentration of tetracaine (60% free base, 40% acid
salt w/w) in propylene glycol and saline as measured by conductivity


% Propylene
Glycol


CMC (M)


pH Range
(Apparent)


0 (no CMC) 6.85-8.37
20 0.03 6.30-8.51
40 0.04 6.26-8.29
50 0.06 6.17-8.43
60 0.18 7.03-8.41

80 (no CMC) 6.46-7.55


100


(no CMC)


5.80-8.65


200 300


X (nm)


Ultraviolet absorbance spectrum of hydrocortisone


Figure 25:
















3



5D
2



0


-1

0
100


200 300


X (nm)


Ultraviolet absorbance spectrum of scopolamine


Ultraviolet absorbance maxima of drugs


Drug


Primary
(nm)


Secondary
(nm)


Hydrocortisone 200 247

Scopolamine 190

Lidocaine 213

Tetracaine 311 196


Chromatography


All drugs were analyzed by the same HPLC solvent mixture. The detector

wavelength was varied to correspond to the absorbance maximum (as in Table 7).


Figure 26:


Table 7:















3



2



0
r 1


0


100 200 300 400

X (nm)

Figure 27: Ultraviolet absorbance spectrum of lidocaine

This HPLC method was originally obtained from a Supelco chromatography catalog

as a method for detecting lidocaine, but it also worked well for scopolamine and

tetracaine. The solvents in the original method were acetonitrile (90%) and aqueous

0.02 M, buffered phosphoric acid (10%) at a flowrate of 1.00 ml/min with a C8

column (a C8 carbon chain covalently bonded to a silica matrix). This method

evolved in subsequent analyses to become 72% acetonitrile, 18% 0.02 M buffered

phosphoric acid, and 10% methanol. This solvent mix minimized the retention time

of the drugs while providing adequate resolution. The identities of the peaks were

established by calibration with pure sample and noting which peak varied with the

concentration of the drug in the sample. The retention times of the drugs varied

with the batch of the phosphoric acid buffer, although Figure 29-Figure 31 show















2






g 1

0




0
100 200 300 400

A (nm)

Figure 28: Ultraviolet absorbance spectrum of tetracaine

typical chromatograms and Table 8 shows representative drug retention times

(scopolamine,* lidocaine, and tetracaine).


Equilibrium Phenomena


As already mentioned, there is an acid-base equilibrium between the acid salt

and free base of tetracaine in solution. In water, tetracaine HC1 partially dissociates

to give a tetracaine cation and a Cl- counter-ion. Alternatively, some tetracaine free

base will accept a proton from water to form the cation (the counter-ion being OH-).

Since tetracaine acid salt in solution is equivalent to an equimolar solution of



'The large, early peak in the scopolamine chromatogram is chloroform which was
used in the preparation of the sample.
















2000


1600


1200


800


400


1 2 3 4

Elapsed Time (min)


HPLC chromatogram of scopolamine


Table 8: Approximate HPLC retention times of drugs


Drugs


Retention Time
(min)


Scopolamine 2.50

Lidocaine 2.60


Tetracaine


3.00


tetracaine free base and HC1 (acid), varying the ratio between tetracaine salt and

tetracaine free base in solution can be studied by a standard acid-base titration.


Figure 29:















2000

1600 Lidocaine
1600

S1200

C 800

J, 400


0
0 1 2 3 4

Elapsed Time (min)

Figure 30: HPLC chromatogram of lidocaine

When NaOH is added to a solution of tetracaine salt, some tetracaine cations

are converted to tetracaine base and NaC1 is formed. Stoichiometry allows the exact

ratio of tetracaine base and salt in the resulting solution to be calculated.

Figure 32, a standard acid-base titration plot of aqueous tetracaine, establishes

the pKa of tetracaine in aqueous solution at 8.7.* This agrees well with the value

quoted by de Jong21 (8.5). This value corresponds to protonation of the tertiary

amine group, although there is one other ionizable group in the tetracaine molecule

(c.f. Figure 2 on page 34). The secondary amine should ionize under more acidic

conditions (pH = 1).



*The scatter is a result of a low concentration of the drug. This low concentra-
tion is necessary because tetracaine base is only marginally soluble in saline.










79





500

C 400 Tetracaine

S 300

0 200
U

100
0

0

-100
0 1 2 3 4

Elapsed Time (min)

Figure 31: HPLC chromatogram of tetracaine

The addition of propylene glycol affects the acid/base equilibrium of the

system. Figure 33 shows the apparent pH versus percent tetracaine base* in

mixtures of propylene glycol and saline. The apparent pKl rises as the amount of

propylene glycol in the solvent increases." Also, tetracaine is unable to buffer the

solution effectively as the propylene glycol fraction increases (the curves' slopes

increase in the buffered region). The inability to buffer the solution may be due to






'This value corresponds to the bulk ratio of tetracaine free base and tetracaine
acid salt that would be required to reconstitute the solution (i.e., a dry mixture).

"The apparent pH of propylene glycol-saline solvents (no drug present) also
increases with increasing propylene glycol content and is probably caused by the
electrode's response to propylene glycol.














10 *

9/
79 ._-gg_7pKeA. = 8.7

8

7 1.19 mmol
Tetracaine HCI
6
0 1 2

NaOH (mmol)

Figure 32: NaOH titration of aqueous tetracaine

the lack of free ions needed to maintain equilibrium which may arise from the lack

of water in the system.

Measuring the apparent pH as a function of concentration can also be used

to determine the CMC. The pH versus concentration behavior for tetracaine (40%

acid salt, 60% free base w/w) in solvents of propylene glycol and saline is illustrated

in the following sequence of graphs (Figure 34-Figure 39). As drug is added to

solution the pH rises monotonically for all systems. At some point, the apparent pH

reaches a maximum and begins to fall. This change in slope indicates a change in

the structure of the solution. This change in structure can be viewed as the onset of

micellization; the concentration at which it occurs can be viewed as the CMC. Based

















14
----- Saline

12 -
S---- 20% PG


10 --- 40% PG

SFl.... .. 50% PG

S--B- 60% PG

-*-- 80% PG

4

% Tetracaine Base (mol/mol)20 40 60 80 100
% Tetracaine Base (mol/mol)


Figure 33: NaOH titration of tetracaine in propylene glycol and saline




9 9
8 8
7 7
6 6

5 NoCMC 5 NoCMC
4 4
0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00

C (M) C (M)

Figure 34: pH of tetracaine in pro- Figure 35: pH of tetracaine in 80%
pylene glycol. propylene glycol and 20% saline (v/v).

on these assumptions, Table 9 lists the CMC of these solutions as measured by

apparent pH versus concentration. With the exception of 20% propylene glycol,









82
Table 9: Critical micelle concentration of tetracaine (60% free base, 40% acid
salt w/w) in propylene glycol and saline as measured by pH


% Propylene CMC (M) pH Range
Glycol (Apparent)

0 0.003 6.85-8.37

20 0.004 6.30-8.51

40 0.025 6.26-8.29

60 0.072 7.03-8.41

80 (no CMC) 6.46-7.55

100 (no CMC) 5.80-8.65







9 9
CMC CMC
8 8
7/ 1 7 *
7 7
6 I 6
5 i 5
4 4
0.00 0.10 0.20 0.30 0.40 0.50 0.00 0.05 0.10 0.15 0.20

C (M) C (M)

Figure 36: pH of tetracaine in 60% Figure 37: pH of tetracaine in 40%
propylene glycol and 40% saline (v/v) propylene glycol and 60% saline (v/v)

these values agree almost as well with those of Table 5 and Table 6 as the latter do

with each other (this method is the most conservative).


Quasi-elastic Light Scattering


Many features of micellar behavior can be deduced through surface pressure,

conductivity, and even pH vs. concentration measurements. One feature, however;




Full Text
Figure 64: Time response for in vivo analgesia by tetracaine (60% free
base, 40% acid salt w/w) in 40% propylene glycol and 60% saline
(v/v) (0.036 M 1.004 M) 120
Figure 65: Schematic of idealized system 123
Figure 66: Predicted donor- and receptor-phase concentrations
(V*2 = 7) 129
Figure 67: Predicted concentration profile within skin 130
Figure 68: Model fits for saline (old mice) 134
Figure 69: Model fits for 5% propylene glycol (old mice) 134
Figure 70: Model fits for 10% propylene glycol (young mice) 134
Figure 71: Model fits for 20% propylene glycol (young mice) 134
Figure 72: Model fits for 20% propylene glycol (old mice) 135
Figure 73: Model fits for 30% propylene glycol (old mice) 135
Figure 74: Model fits for 40% propylene glycol (young mice) 135
Figure 75: Model fits for 40% propylene glycol (old mice) 135
Figure 76: Model fits for 50% propylene glycol (young mice) 135
Figure 77: Model fits for 50% propylene glycol (old mice) 135
Figure 78: Model fits for 60% propylene glycol (young mice #1) 136
Figure 79: Model fits for 60% propylene glycol (young mice #2) 136
Figure 80: Model fits for 70% propylene glycol (young mice #1) 136
Figure 81: Model fits for 70% propylene glycol (young mice #2) 136
Figure 82: Model variance for saline (old mice) 137
Figure 83: Model variance for 5% propylene glycol (old mice) 137
i
Figure 84: Model variance for 10% propylene glycol (old mice) 137
xv


157
The system of tetracaine, propylene glycol, and water shows much interesting
phase behavior. The construction of the ternary phase diagram is a project in its own
right, but would be valuable for future work in this system.
Diffusion Experiments
Franz diffusion cells are used to obtain physical information about the
diffusion of the anesthetic formulations. The use of hairless-mouse skin as a model
for human skin has been questioned9,10,11 and it is generally believed that there are
better in vitro animal models (e.g., pigskin4). In addition, human cadaver skin can
also be used for in vitro studies. Consequently, one possibility for future research is
the study of in vitro transdermal diffusion of these local anesthetic formulations
through pigskin and human cadaver skin to confirm the trends found with hairless-
mouse skin.
The content of the receptor phase may have inhibited the diffusion of the
hydrophobic anesthetic through unfavorable partitioning. Whether the use of saline
as a receptor phase reduced the diffusion of tetracaine in vitro should be determined
by using a more lipophilic receptor phase. The likelihood that this would influence
the results was considered remote because the concentrations in the receptor phase
were very small and the duration of the experiments was usually very short.


Copyright 1991
by
Kenneth James Miller II


69
Topical Formulation
Concentration

O
A

V
100% PG
5.8spHs8.7
80% PG
6.5ipHi7.6
60% PG
7.0pH8.2
50% PG
6.2spHs8.4
40% PG
6.3spHs8.3
20% PG
6.3spHs8.5
Saline
6.9spHs8.4
C (M)
Figure 21: Surface pressure of tetracaine (60% free base, 40% acid salt w/w) in
propylene glycol and saline
The graph of conductivity versus concentration for tetracaine base (Figure 23)
indicates that micelles are forming at very low concentration (3 x 10'5 M). This
behavior, quite unlike that suggested by the surface tension versus concentration
graph (Figure 20), further elucidates the uncertainty of CMC values measured by
different means as well as the definition of CMC.
The conductivity vs. concentration behavior for mixtures of tetracaine acid salt
(40% w/w) and tetracaine free base (60% w/w) was also measured in propylene
glycol-saline solvents (see Figure 24 and Table 6). Comparing CMC values from
surface tension (Table 5) and conductivity (Table 6) shows that the values are in
general agreement (33%).


CHAPTER 8
RECOMMENDATIONS FOR FUTURE WORK
Research into the formulation of topical, local anesthetics and the theoretical
modelling of transdermal diffusion is far from complete and there is a great need for
further study. The work presented in this dissertation has answered many questions
about the physical behavior of topical local anesthetic formulations and the ability
to theoretically model transdermal diffusion, but it has also raised many additional
questions. The following sections contain recommendations for future research into
these subjects. The general areas are physical properties, diffusion experiments,
theoretical modelling, and clinical studies.
Physical Properties
Partition coefficients were measured in only n-octane and 1-octanol as model
lipids for skin. It is possible to measure partition coefficients in isolated stratum
corneum or some other model lipid (tetradecane, isopropyl myristate, linoleic acid,
or dipalmitoyl phosphatidylcholine).43,44
Quasi-elastic light scattering was used to determine the micelle size of
tetracaine in propylene glycol and water as a function of the fraction of propylene
glycol. Additional scattering work could be done to determine how the micelle size
changes as a function of pH.
156


99
Aqueous
--- 50% PG
Time (hr)
Figure 50: Effect of propylene glycol on the diffusion of lidocaine salt through
untreated hairless-mouse skin
figure indicates that the drug diffusion rate is not significantly affected by the
presence of 50% propylene glycol. The testing of lidocaine containing preparations
was suspended when the decision was made to use tetracaine, a more potent drug
with better partitioning characteristics.21
Diffusion of Tetracaine
Tetracaine was chosen as a more attractive drug than lidocaine for trans-
dermal applications because it is more effective as an anesthetic (by weight).21
Tetracaine also partitions more favorably into nerve tissue.21


108
Figure 56: Effect of formaldehyde location on the diffusion of tetracaine (60%
free base, 40% acid salt w/w, 0.36M tetracaine overall) in 40% propylene glycol and
60% saline (v/v) through old hairless-mouse skin
Effect of concentration
Figure 57 shows how donor phase drug concentration affects the flux of a 40%
tetracaine acid salt, 60% free base (w/w) mixture (0.36M tetracaine overall) through
hairless-mouse skin. If the mechanism of diffusion is strictly Fickian, then the flux
should be proportional to the donor phase concentration and the graphs should be
straight lines. The nearly constant transdermal flux, despite doubling the donor
phase concentration, indicates that the driving force for diffusion stays about
constant. A constant driving force suggests that the topical formulation is not a
simple molecular solution and that it probably contains micellar aggregates of


185
L(l) = .069029
END IF
LI = .069029 + .049499 (TIME / 3600 + TIMEO) .0044692 (TIME / 3600
+ TIMEO) A 2
L2 = .18821 (TIME / 3600 + TIMEO) A .050642
IF (TIME / 3600 + TIMEO) < 4.8270328# THEN L(2) = LI ELSE L(2) = L2
RETURN
END SKIN THICKNESS SUBROUTINE
1000
Begin Information Subroutine
INPUT "File name for results"; FILES
INPUT "Time to end integration (hr)"; ENDCALC
INPUT "Convergence Tolerance"; CONV
INPUT "Step size for integration (sec)"; G
ENDCALC = ENDCALC + G / 3600 Last Profile at Endcalc
INPUT "Printing Interval (# of steps)"; COUNTER%
INPUT "Initial Boundary Condition at X=0 (ug/ml)"; Cl
CONCHIGH = 350 2 / 3 / Cl
INPUT "Top Concentration Constant (0/1)"; CONSTTOP


154
most effective in clinical trials is the same formulation that maximized the flux of
tetracaine through hairless-mouse skin in vitro.
Theory
Ouasi-steadv State Model (pages 124 131)
The quasi-steady state assumption in transdermal diffusion states that the drug
reservoir concentrations change slowly compared to the skin concentration. A
theoretical model for in vitro transdermal drug delivery based on this assumption can
analyze diffusion data and determine the effective diffusivity (~ 10"2 x molecular
values in water). This model can also recognize and account for the effects of skin
swelling in vitro and micellization.
Full Numerical Routine (Appendix A, pages 161 168)
The quasi-steady state assumption is not valid under all circumstances.
Numerical integration of the fundamental diffusion equation under the true boundary
and initial conditions of in vitro transdermal drug diffusion is a more rigorous
modelling method. This full numerical routine has all the properties of the quasi
steady state model except speed. The full numerical routine takes more time to
calculate because, unlike the quasi-steady state model, a complete concentration
profile must be calculated at each time step. The full numerical routine yields
effective diffusivities 5% below those of the quasi-steady state model and decreases
the variance (sum of the squared difference) between the model and the experimen-


130
Skin Coordinate (0 = External Surface)
Figure 67: Predicted concentration profile within skin
Inclusion of Skin Swelling In Vitro
Since the time constant is proportional to the square of the skin thickness,
skin swelling can significantly affect the diffusion of drugs through the skin during in
vitro diffusion. To assess the degree of swelling in vitro, the thickness of hairless-
mouse skin was measured versus time immersed in water (details of this procedure
are in Chapter 2, page 40, results are in Chapter 3, page 92). These measured
thicknesses were then correlated as L(t) for use in the diffusion model. To fit this
swelling, two equations were used: a parabolic equation for the early, rapid swelling
of the first 4 to 5 hours and an exponential equation for the later, slower swelling.


ACKNOWLEDGEMENTS
There are so many people and organizations without whom much of this work
would not exist that it is difficult to acknowledge them without creating a second
dissertation. Chief among these is, of course, Professor Shah. Professor Shah and
I have now worked together some three and a half years and I am convinced that no
one has a better "feel" for the subject of surface science. Professor Westermann-
Clark has also been invaluable in this work, and I will always remember him as the
ingenious, "chewing gum and bailing wire" influence. Professor Goodwin has been
instrumental in helping me understand much of the medical jargon permeating this
field and will always remain for me, a selfless individual who manages to wear more
hats than I can count. Professor Sloan has taught me much more than the procedure
of in vitro diffusion and is another tireless researcher whom I can never hope to
mimic. When Professor Park and I were introduced, I was amazed that he knew so
much about my work at West Virginia and impressed that he took such an interest
in me so early in my graduate career. Thank you all.
I am also immensely grateful to the members of my family (whom I have not
seen in a long time). To my mother, I can finally say "now" for all the times she has
asked, "When will you be graduating?". To my father, I can say, "Thank you for your
IV


TABLE OF CONTENTS
ACKNOWLEDGEMENTS iv
LIST OF TABLES x
LIST OF FIGURES xi
ABSTRACT xvii
CHAPTERS
1 INTRODUCTION 1
Literature Review 1
Theoretical Development 1
Diffusion Through Synthetic Barriers 7
Transport Through Biological Membranes 10
Differences between in vitro and in vivo systems 22
Specific Objectives 29
Topical Local Anesthetic 29
Theoretical Modelling 30
2 MATERIALS AND METHODS 33
Materials 33
Solvents 33
Local Anesthetics 34
Methods 37
Solubility 38
Titration 38
Thermal Breakdown of Tetracaine 38
Drug Partitioning 38
Surface Tension 39
Skin Swelling 40
Conductivity 40
Ultraviolet Spectrometry 41
vi


100
Tetracaine salt (50% propylene glycol versus saline)
Experiments using tetracaine HC1 exclusively as the anesthetic examined the
effect of propylene glycol on diffusion. These experiments attempted to parallel
experiments with lidocaine HC1 and lead to comparisons of the effect of propylene
glycol on the diffusion of tetracaine HC1 through hairless-mouse skin.
Figure 51 shows the cumulative flux into the receptor phase as a function of
time for the diffusion of tetracaine HC1 from saline and 50% propylene glycol, 50%
Aqueous
pH4.8
50% PG
pH5.1
Time (hrs)
Figure 51: Effect of propylene glycol on the diffusion of tetracaine HC1 through
hairless-mouse skin
saline solutions. The 50% propylene glycol solution inhibited the diffusion of the
drug across the skin. There are several possible reasons for this: The increased
viscosity of the 50% propylene glycol solution may result in a formidable boundary


137
Conditions
Figure 82: Model variance for saline
(old mice)
80000
70000
60000
I 50000
S 40000
> 30000
20000
10000
0
abed
Conditions
Figure 84: Model variance for 10%
propylene glycol (old mice)
Conditions
Figure 86: Model variance for 20%
propylene glycol (old mice)
Conditions
Figure 83: Model variance for 5%
propylene glycol (old mice)
Conditio ns
Figure 85: Model variance for 20%
propylene glycol (young mice)
Conditions
Figure 87: Model variance for 30%
propylene glycol (old mice)


REFERENCES
1. J. Adriani and H. Dalili, Penetration of local anesthetics through epithelial
barriers, Anesth. and Analg., 56(5), 834-41, (1971).
2. B.D. Anderson, W.I. Higuchi, and P.V. Raykar, Heterogeneity effects on
permeability-partition coefficient relationships in human stratum corneum,
Pharm. Res., 5, 566-73, (1988).
3. D. Attwood and A.T. Florence, Surfactant Systems: Their Chemistry.
Pharmacy, and Biology. Chapman and Hall, London, (1983).
4. B.W. Barry, Dermatological Formulations. Marcel Dekker, New York,
(1983).
5. B.W. Barry, Some problems in predicting human percutaneous absorption
via in vitro animal models, in Prediction of Percutaneous Penetration
Proceedings. April 1989, R.C. Scott, R.H. Guy, and J. Hadgraft (eds), IBC
Technical Services, London, 204-12 (1990).
6. C.R. Behl, N.H. Bellantone, and G.L. Flynn, Influence of age on
percutaneous absorption of drug substances, in Percutaneous Absorption:
Mechanisms. Methodology. Drug Delivery. R. Bronaugh and H. Maibach
(eds), Marcel Dekker, New York, 183-212 (1985).
7. R.B. Bird, W.E. Stewart, and E.N. Lightfoot, Transport Phenomena. Wiley,
New York, (1960).
8. I.H. Blank, The effect of hydration on the permeability of the skin, in
Percutaneous Absorption: Mechanisms, methodology, drug delivery. R.
Bronaugh and H. Maibach (eds), Marcel Dekker, New York, 97-105
(1985).
9. J.R. Bond and B.W. Barry, Damaging effect of acetone on the permeability
barrier of hairless mouse skin compared with that of human skin, Int. J.
Pharm., 41, 91-3, (1988).
202


187
CONCENTR(SKINNUM%, 1) = CONCENTR(SKINNUM%, 2)
300 LASTC1 = CONCENTR(0, 2)
LASTC2 = CONCENTR(SKINNUM%, 2)
Evaluate Series
IF TIME = G THEN BOTSER = -Cl / 2: TOPSER = -Cl: GOTO 425
TOPSER = 0
BOTSER = 0
LASTTOP = 0
LASTBOT = 0
N% = 0
400 N% = N% + 1
LASTTOP = TOPSER: LASTBOT = BOTSER
EXPONENT = EXP(-N% A 2 TIME D PI# A 2 / L(2) A 2)
TOPSER = TOPSER + ((-1) A N% LASTC2 LASTC1) EXPONENT
BOTSER = BOTSER + ((-1) A N% LASTC1 LASTC2) EXPONENT
IF N% = 1 THEN 400
IF (ABS((TOPSER LASTTOP) / LASTTOP) > CONV OR ABS((BOTSER -
LASTBOT) / LASTBOT) > CONV OR N% < MINI%) AND N% <
MAXI% THEN 400
425 CONCENTR(0, 2) = CONCENTR(0, 1) + G D A / L(2) / VI *
(LASTC2 LASTC1 + 2 TOPSER)
IF CONSTTOP = 1 THEN CONCENTR(0, 1) = Cl


109
1000
800
600
400
200
0
0.36 0.72
Donor Concentration (M)
Figure 57: Effect of drug concentration on the diffusion of tetracaine (60% free
base, 40% acid salt w/w) in 40% propylene glycol and 60% saline (v/v) through
hairless-mouse skin
tetracaine. This result agrees with the conclusion that there are indeed micelles in
the tetracaine formulations (page 66).
Effect of mixture ratio (pH effect!
To determine the effect of pH, three solutions were used that were identical
except for their pH. One solution contained tetracaine free base, another, tetracaine
acid salt which, in solution, corresponds in bulk to equal parts of tetracaine base and
HC1 acid; and the third, a 40% acid salt-60% free base (w/w) mixture. This
experiment was further complicated in that a suitable propylene glycokwater ratio
had to be found for which the three systems were single phase. Tetracaine base is
not sufficiently soluble in the optimal 40% propylene glycol solution (solubility had


DATE:
, as copyright holder for the
aforementioned dissertation, hereby grant specific and limited archive and distribution rights to
the Board of Trustees of the University of Florida and its agents. I authorize the University of
Florida to digitize and distribute the dissertation described above for nonprofit, educational
purposes via the Internet or successive technologies.
This is a non-exclusive grant of permissions for specific off-line and on-line uses for an
indefinite term. Off-line uses shall be limited to those specifically allowed by "Fair Use" as
prescribed by the terms of United States copyright legislation (cf, Title 17, U.S. Code) as well as
to the maintenance and preservation of a digital archive copy. Digitization allows the University
of Florida to generate image- and text-based versions as appropriate and to provide and enhance
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This grant of permissions prohibits use of the digitized versions for commercial use or profit.
Signature of Copyright Holder
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Personal information blurred
Date of Signature
Please print, sign and return to:
Cathleen Martyniak
UF Dissertation Project
Preservation Department
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P.O. Box 117007
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40
OLD
YES
NO
l.oo x i -4552
430
-3337
40
OLD
YES
YES
2.64x10'7
-29.94
11.47
1352
40
OLD
NO
NO
3.13 x 10'*
-4.25
11.97
-10.43
40
OLD
NO
YES
1.05 x 107
-0.85
5.61
3.81
50
YOUNG
YFS
NO
1 56x lo-7
-40.07
225.10
-154
50
YOUNG
YES
YES
3.91 X 10-7
-24.15
215.25
-133
50
YOUNG
NO
NO
6.46 V 10'*
19.76
235.31
-2.42
50
YOUNG
NO
YFS
3.69 x 10'7
123.26
225.15
-1.78
50
OLD
YES
NO
1.25 x 10'7
-43.10
4.27
41.79
50
OLD
YFS
YFS
254 x 10'7
-31.61
18.04
15.83
50
OLD
NO
NO
4.10 x 10'*
-3.85
15.74
-8.62
50
OI.D
NO
YES
1.02 x 10'7
-0.97
4.29
18.45
60f#n
YOUNG
YES
NO
9.53 x 10'*
-45.39
1.08
-81.94
or#n
YOUNG
YES
YES
1.28x 10'7
-40.80
2.03
-33.71
60 r#n
YOUNG
NO
NO
2.96 x 10'*
4.06
11.14
-8.86
6or#n
YOUNG
NO
YES
4.24 X 10'*
-1.78
7.28
-10.96
60f#21
YOUNG
YES
NO
1.09 x 10'7
-4456
453
-55.60
60 (#21
YOUNG
YES
YES
1.49v 1 O'7
-38.66
3.46
-5232
60 f#21
YOUNG
NO
NO
3.47v 10'*
-3.67
17.81
-6.60
60 (#2\
YOUNG
NO
YES
5.12 x 10'*
-1.67
1134
-9.80
70 f#n
YOUNG
YES
NO
8.96 x 10'*
-46.54
1.85
-69.43
70 r#n
YOUNG
YES
YES
1.19 x 10'7
-39.49
0.84
-88.28
70 r#n
YOUNG
NO
NO
2.73v 10'*
4.21
2.83
-74.77
70 r#n
YOUNG
NO
YES
3.85 v 10'*
2.013
1.41
-84.27
70 f#21
YOUNG
YES
NO
1.16 x 10'7
43.82
2.72
-68.64
70 (#21
YOUNG
YES
YES
1.61 x 10'7
-37.51
3.51
-3734
70 f#21
YOIING
NO
NO
3.76 x 10'*
-3.84
752
-63.23
70 if 21
young
YES
-1.55
-65.63
Average 4.08 30.32 -16.54
O
GO


105
Effect of age. These same tetracaine formulations were tested on the skin of
older mice (6 to 8 months) to determine how age affects the transdermal diffusion
Apparent pH
% Propylene Glycol (v/v)
Figure 54: Cumulative flux of tetracaine (60% free base, 40% acid salt w/w) in
propylene glycol and saline through hairless-mouse skin (old mice)
of these formulations. The general trend of the data in Figure 54 is unchanged from
that of Figure 53. Although age did not influence the trend, the older mice have
much less permeable skin than the younger mice. The cumulative flux of tetracaine
through the skin of the older mice over eight hours averaged only 20% that through
younger skin for all formulations tested.
Effect of formaldehyde
It has already been established that the process of preservation and hydration
of the skin affects the diffusion of scopolamine (page 95). The data gathered was not


31
Novel techniques
The quasi-steady state assumption is far from novel. It is simply the
assumption that the boundary concentrations do not change appreciably during the
period of interest. Cussler describes the technique very early in his book on mass
transfer.20 Use of this assumption for transdermal diffusion is novel. Furthermore,
experimentally measured skin swelling data is added to give the model greater
accuracy and predictive ability.
Improved understanding of mechanism
In modelling the diffusion of drugs generally and tetracaine specifically, as few
assumptions as possible were made while trying to obtain an analytical solution. It
was hoped an analytical solution of Ficks second law for in vitro diffusion would
illuminate the mechanism of transdermal diffusion. The insight gained could guide
research and development toward a better understanding of transdermal diffusion
and could lead to better patient care.
Importance of swelling in vitro
No theoretical model for transdermal diffusion has ever included skin swelling
before. Others have measured this phenomenon, but have never presented the data
in enough detail for inclusion in a theoretical model. A simple moving boundary
conceptualization is, admittedly, naive; but it is also a first step toward accounting for
the change of environment during in vitro transdermal diffusion. Obviously, more
than the dimensions of the skin change; the chemical nature must also play a role in
the diffusion rate as the stratum corneum becomes hydrophilic. However, our data


88
Stagnant
Stirring Bar
Stirring Tee
Figure 42: Effect of stirring device on the diffusion of aqueous hydrocortisone
through synthetic membranes
Rate effects
A separate experiment illustrates the effect of stirring rate on the efficiency
of the stirring tees to eliminate the boundary layer beneath the skin. The inverse of
the stirring rate is plotted against the flux of hydrocortisone through the same
synthetic membrane (nominal pore diameter of 0.45 un) in Figure 43. Conceptually,
flux should increase monotonically as the stirring rate increases, but the best line
through the scattered data is flat. There are two regions in which the flux is
independent of the stirring rate: the stagnant limit and the completely mixed limit.
In order to determine which regime the plotted data represented, data were collected
at stagnant conditions (0 rpm). The flux was found to be significantly lower than any


95
effect could not be determined (i.e., the results could be due to hydration, the
presence of formaldehyde, or both).
Figure 48 shows the steady state flux of scopolamine through hairless-mouse
skin as determined by Chandrasekaran et al.17 (fully hydrated and preserved) as well
Fresh
Hydrated
Donor Concentration (g/1)
Figure 48: Comparison of experimental scopolamine diffusion data to data of
Chandrasekaran et al.
as the values obtained in this first experiment. The measured flux and the value
reported by Chandrasekaran et al.17 agree for the fully hydrated and chemically
preserved skin. The steady state flux for the untreated skin is an order of magnitude
below that of the hydrated preserved skin, although the scatter makes this difference
insignificant. This difference in the diffusion of scopolamine caused by the treatment
of the skin is the reason for deciding to use fresh untreated skin in subsequent


Figure 8: Mounting skin to cell cap
M(0C(OV+V,(EC(tx))
x=0
M(tn) Total mass transferred at time tn
C(tn) Measured concentration at time tn
V Volume of receptor compartment (15 ml)
Vs Sampled Volume (200 ¡A)
x Summation index


74
Figure 26: Ultraviolet absorbance spectrum of scopolamine
Table 7: Ultraviolet absorbance maxima of drugs
Drug
Primary
(nm)
Secondary
(nm)
Hydrocortisone
200
247
Scopolamine
190
-
Lidocaine
213
-
Tetracaine
311
196
Chromatography
All drugs were analyzed by the same HPLC solvent mixture. The detector
wavelength was varied to correspond to the absorbance maximum (as in Table 7).


45
In Vitro Diffusion Through Mounted Mouse Skin
The following describes the procedures related to diffusion studies. The
process begins with preparing the skin from hairless mice, mounting the skin to the
diffusion cell, and sampling the drug concentration in the receptor phase.
Preparation of skin
The first step in measuring the diffusion of any compound through mounted
skin was procuring the skin from the mice. Laboratory hairless-mice were used.
Females were used because they are less aggressive and territorial than males and
less likely, therefore, to fight and damage their skin. The average mass of the mice
at sacrifice was about 30 grams.
The mice were sacrificed by cervical dislocation (Figure 4) and weighed.
After being sacrificed, a mouse was placed on its back and all four legs were taped
down (Figure 5). Using surgical scissors, an incision was made across the lower
abdomen just above the lower legs. Connecting incisions up the center and across
the upper abdomen just below the forelegs were then made. At this point the
incision resembled an "I" (Figure 6). The skin was teased away from the underlying
tissue and connective tissue was severed where necessary.
At this point, the rear legs were released, the mouse folded over onto its back,
i
|
and the upper and lower incisions continued around the abdomen (Figure 7). The
skin was carefully removed by severing any remaining tissue. The removed skin was
essentially rectangular.


7
Diffusion Through Synthetic Barriers
The study of diffusion through skin is complicated by the complex structure
of the skin. Inter- and intra-species variability in skin leads to differing diffusive
barrier properties. Because of this variability, many researchers substitute synthetic
membranes for biological membranes to more accurately determine differences
between transdermal formulations and avoid complex statistical analyses.
The advantages of synthetic barriers to diffusion are their consistency and well
characterized properties. The use of synthetic barriers requires several assumptions
about transdermal diffusion. It must be assumed that the skin does not metabolize
the drug significantly, which may or may not be true depending upon the drug
involved.81 Secondly, diffusion is assumed to be passive and the drug is assumed to
have an equivalent (or at least similar) affinity for the synthetic medium as for
biologically viable skin. These assumptions are violated to some extent simply
because the skin is an active medium and the chemical content of the synthetic
medium differs from that of skin. Provided one is prepared to make such
assumptions, synthetic media can be used to evaluate transdermal formulations
qualitatively.
Two main systems are used to simulate the barrier properties of skin:
unsupported barriers (usually two immiscible liquids in contact) and supported
barriers (usually two phases separated by a solid, but permeable barrier).
|
Unsupported barriers can be used to measure partition coefficients (equilibrium) or


73
Table 6: Critical micelle concentration of tetracaine (60% free base, 40% acid
salt w/w) in propylene glycol and saline as measured by conductivity
% Propylene
Glycol
CMC (M)
pH Range
(Apparent)
0
(no CMC)
6.85-8.37
20
0.03
6.30-8.51
40
0.04
6.26-8.29
50
0.06
6.17-8.43
60
0.18
7.03-8.41
80
(no CMC)
6.46-7.55
100
(no CMC)
5.80-8.65
Figure 25: Ultraviolet absorbance spectrum of hydrocortisone


92
Since concentration was measured no earlier than one hour, the effect of this warm
up period on diffusion was neglected.
Skin Swelling
The time dependent thickness of the skin after exposure to the solvents was
monitored (as per the procedure in Chapter 2, page 40) in an attempt to determine
the effects such swelling have on transdermal diffusion. The initial thickness of the
Figure 46: Dynamic swelling of excised hairless-mouse skin immersed in water
skin was estimated by assuming a density of 1 g/ml for a skin sample of known mass
and cross-sectional area. This initial thickness was found to be 0.68 mm. The skin


24
Receptor phase Buffered saline or as necessary to keep drug
thermodynamic activity below 10% that in the
donor phase
Miscellaneous Emulate in vivo or clinical system
Topical local anesthesia
The transdermal diffusion of local anesthetics has been more often studied in
vivo than in vitro. Many drugs have been tested, although the results have always
fallen short of expectations because of poor diffusion through the skin.
McCafferty et al.55,96 formulated local anesthetic bases in oil/water creams and
monitored their diffusion through silicone-rubber membranes. Based on their
observations, lignocaine (lidocaine) and amethocaine (tetracaine) were the best
candidates for clinical study.
Adriani and Dalili1 tested the bases and salts of dibucaine, tetracaine,
mepivacaine, prilocaine, lidocaine, procaine, benzocaine, and butesin for anesthetic
effect on more than 150 volunteers. The bases were dissolved in a solvent of 50%
water, 40% ethanol, and 10% glycerol. The salts were applied as aqueous solutions.
After the anesthetic preparations were on the skin for 30 minutes, their effectiveness
was measured by their ability to block itching and burning sensations induced by
electrical current. The time of 30 minutes was established after observations that
effective preparations established a block within 15 minutes. No other investigator
has claimed to produce an anesthetic effect so quickly. Other investigators, however;
have used much more stringent tests for efficacy than the relief of electrically


14
animals is assumed to damage the stratum corneum and increase the diffusion rate.4
In general, it was determined that the permeability of the skin could be increased by
damaging the stratum corneum barrier.
Anatomical Region. Barry describes experiments in which human skin is
evaluated as a barrier to diffusion of hydrocortisone from various anatomical sites.4
Permeability was ranked as follows: scrotum > forehead > scalp > back >
forearms > palms > plantar surface of the foot arch. Wester et al.93 also determined
that the permeability of the skin of the scrotum is greater than that of the abdomen
for both adult and newborn skin.
Rougier et al.72 ranked human stratum corneum permeability as: forehead >
abdomen > thigh > chest > arm > back. Subsequent experiments73 established that
relative absorption depended not only on anatomical region, but also the chemical
nature of the penetrant. The authors did, however, reassess the general permeability
of human stratum corneum as: forehead > postauricular > abdomen > arm. The
forehead was found to be more than two times more permeable than the arm or
abdomen regardless of the substance tested.
Race. Differences in the permeability of skin were also measured between
different races of humans4 Black skin was found to be less permeable than
Caucasian skin, people of Celtic ancestry were more often irritated by toxic chemicals
than people of Mediterranean ancestry, and fair skinned people were found to be
more susceptible to contact dermatitis.
i


APPENDIX A
DERIVATION OF THE FULL NUMERICAL ROUTINE
The full numerical routine is simply the numerical integration of the diffusion
equation (Equation 5). The method for discretizing the diffusion equation is outlined
in the Chemical Engineers Handbook by Perry and Chilton.65
The development of the model begins with the diffusion equation (reproduced
from Chapter 6, page 124).
= D^~ (Al)
dt dx2
To discretize the differential equation, the differential operator d is approximated by
a finite difference A and the second-order differential operator d2C is approximated
by the finite difference operator a(aC).
AC = D A(AC)
At (ax)2
(A2)
At this point, the subscripts i (position index) and j (time index) are introduced and
the differences evaluated.
C C a C a C
,;+i = d i+1 ]
At
Ax
The term ACi+1 j aC¡ j can be further expanded.
(A3)
161


C(ii, 0) = C(ii, 1)
NEXT ii
201
LOCATE 23, 1
PRINT" D Time C2 Variance"
PRINT USING "##.##AAAA ##.## ##.##AAAA
TIMEH; C(M%, 1); VARIANCE;
IF TIMEH = DATAPNTS (F%, 0) THEN
VARIANCE = VARIANCE + (C(M%, 1) -
DATAPNTS(F%, 1)) A 2
COMPVAL(F%) = C(M%, 1)
F% = F% + 1
END IF
TIME = TIME + h
IF CONSTSKN = 0 THEN
GOSUB 300
END IF
NEXT j
RETURN
##.##"AA""; D;
New Skin Thickness
End Numerical Integration Subroutine


46
Figure 4: Sacrifice of hairless mouse
Diffusion apparatus
In vitro transdermal diffusion was measured using flow-through type Franz
diffusion cells (Figure 9). The diffusion cells have four parts: body, cap, O-ring, and
clamp. The cell body was modified to include a magnetic stirring tee which greatly
increased mixing efficiency and reduced the tendency to form a stagnant boundary
layer adjacent to the skin surface. The cell body, surrounded by a water jacket to
maintain constant temperature, contained the lower (receptor) compartment into
which the drug diffused (15 ml). The receptor compartment initially contained


8
diffusion coefficients. However, unsupported barriers usually assume that the
controlling resistance to diffusion is the hydrophobic stratum corneum (represented
by the lipid or hydrophobic, liquid phase). Supported barriers provide a mechanical
barrier that allows the testing of miscible solutions since the liquids are prevented
from mixing by a physical barrier. Supported barriers also allow the addition of a
hydrophilic barrier (the membrane or another liquid phase) to more closely resemble
the layered structure of skin.4
Unsupported barriers
Unsupported barriers are usually prepared by putting two immiscible liquids
in some sort of vessel. The barrier to diffusion in such a system in the phase
boundary between the two liquids. Unsupported barriers can be used to study the
release of a drug from a formulation as a function of time. They can also be used
to estimate the skin-vehicle partitioning behavior of substances.4 The partitioning of
alkyl homologs between water and an immiscible lipid phase was studied to develop
a correlation between partitioning and alkyl chain-length.26 The relationship is linear
when plotted on semi-log axes (i.e., logfpartition coefficient] chain length).
Poulsen and Flynn66 reviewed a study on the release of steroids from water-
propylene glycol gels and creams into a receptor phase of stirred isopropyl myristate.
It was determined that, for all systems, the fraction of propylene glycol that produced
a saturated solution maximized the release rate.
The use of unsupported barriers provides some benefits for the study of
transdermal diffusion. However, the difficulties associated with the technique often


48
Figure 6: First incision
Donor solution (2 ml) was applied to the external surface of the skin, and the
donor compartment sealed to prevent evaporation. To assure constant sampling
intervals for multiple diffusion cells (generally three), experiments were staggered 5
minutes.
At regular intervals (1 or 2 hrs.), a 0.2 ml to 0.3 ml sample was withdrawn
from the center of the receptor volume through the upper sample port using a long,
thin needle and a 1 ml syringe. This sample was sealed in an autosampler vial for
later analysis by HPLC. The sample volume extracted was replaced by fresh,


10
mechanically supports and confines the lipid phase in a well defined region.
Hadgraft and Ridout43 used a cellulose nitrate membrane saturated with isopropyl
myristate as the barrier to diffusion for a wide range of drugs. Isopropyl myristate
showed diffusive properties similar to those of the stratum corneum. The correlation
was very good, but the magnitude of the barriers differed by three orders of
magnitude (true skin being the more effective barrier). They later expanded their
experiments to include dipalmitoyl phosphatidylcholine, linoleic acid, and tetradecane
as model barriers.44 Tetradecane imitated the stratum corneum barrier properties
best. Hadgraft et al45 also used this barrier to study the effect of azone (1-dodecyl-
azacycloheptan-2-one, a penetration enhancer) on the diffusion of salicylate and
determined that azone may form ion pairs with salicylate. Although synthetic
membranes can greatly reduce the difficulties associated with biological variability,
they can only estimate relative effects in transdermal diffusion. Experimental data
on transdermal diffusion must ultimately be obtained using real skin. It is more
difficult to discern trends because of scatter, but it is more likely that these trends
are relevant to a clinical setting.
Transport Through Biological Membranes
Recent developments in transdermal diffusion are organized into the following
groups: system effects, vehicle effects, solute effects, penetration enhancement,
differences between in vitro and in vivo systems, and topical local anesthesia. The


78
Figure 30: HPLC chromatogram of lidocaine
When NaOH is added to a solution of tetracaine salt, some tetracaine cations
are converted to tetracaine base and NaCl is formed. Stoichiometry allows the exact
ratio of tetracaine base and salt in the resulting solution to be calculated.
Figure 32, a standard acid-base titration plot of aqueous tetracaine, establishes
the pKa of tetracaine in aqueous solution at 8.7.* This agrees well with the value
quoted by de Jong21 (8.5). This value corresponds to protonation of the tertiary
amine group, although there is one other ionizable group in the tetracaine molecule
(c.f. Figure 2 on page 34). The secondary amine should ionize under more acidic
conditions (pH 1).
*The scatter is a result of a low concentration of the drug. This low concentra
tion is necessary because tetracaine base is only marginally soluble in saline.


67
Figure 19: Surface tension of aqueous tetracaine acid salt
must be identified. Table 5 summarizes the CMC from surface pressure versus
concentration measurements. As the fraction of propylene glycol increases, the CMC
of tetracaine increases. The 20% saline, 80% propylene glycol and 100% propylene
glycol systems do not show micelle formation. The increase in CMC may be caused
by an increase in molecular drug solubility. As the molecular solubility increases, the
tendency to form micelles decreases. Micelles will cease to form as molecular
solubility continues to increase. The decrease in overall solubility of the tetracaine
mixture (60% free base, 40% acid salt w/w) from 80% to 100% propylene glycol
(v/v) may be due to the lack of micelles.


Figure 11:
Application of drug formulation to skin patch


174
INPUT "Top Concentration Constant (0/1)"; CONSTTOP
INPUT "Minimum Number of Series Terms (over rides convergence criterion)";
MINI%
INPUT "Maximum Number of Series Terms (over rides convergence criterion)";
MAXI%
INPUT "Initial Diffusivity Search Range"; DMAX
INPUT "Skin Thickness Constant (0/1)"; CONSTSKN
INPUT "Dose Volume (ml)"; VI
INPUT "Receptor Volume (ml)"; V2
INPUT "Start Time (Hours after skin in contact with water)"; TIMEO
INPUT "Number of data points [Include time 0}"; DATPOINT96
IF MAXI% = 0 THEN MAXI% = 200
RETURN
END INFORMATION SUBROUTINE
200
BEGIN INTEGRATION AND VARIANCE SUBROUTINE
F% = 1
C2 = DATAPNTS(0, 1)
VARIANCE = 0


Figure 85:
Model
Figure 86:
Model
Figure 87:
Model
Figure 88:
Model
Figure 89:
Model
Figure 90:
Model
Figure 91:
Model
Figure 92:
Model
Figure 93:
Model
Figure 94:
Model
Figure 95:
Model
Figure 96:
Model
Figure 97:
Model
Figure 98:
Model
Figure 99:
Model
Figure 100:
Model
Figure 101:
Model
variance for 20% propylene glycol (young mice)
variance for 20% propylene glycol (old mice)
variance for 30% propylene glycol (old mice)
variance for 40% propylene glycol (young mice)
variance for 40% propylene glycol (old mice)
variance for 50% propylene glycol (young mice)
variance for 50% propylene glycol (old mice)
variance for 60% propylene glycol (young mice #1)
variance for 60% propylene glycol (young mice #2) . .
variance for 70% propylene glycol (young mice #1)
variance for 70% propylene glycol (young mice #2) . .
fits for hydrocortisone in a stagnant cell
fits for hydrocortisone in a poorly stirred cell
fits for hydrocortisone in a well-stirred cell
variance for hydrocortisone in a stagnant cell
variance for hydrocortisone in a poorly-stirred cell
variance for hydrocortisone in a well-stirred cell
137
137
137
138
138
138
138
138
138
139
139
141
141
142
142
142
142
xvi


52
Figure 10: Schematic of rat tail Flick-o-meter
flick test. The procedure is as follows: A gauze patch moistened with an anesthetic
solution was secured to the tail of a live rat for a given period of time (usually two
hours). After removal of the patch, the rats were placed in a device which focuses
a strong light (pain stimulus) on the tail and measures the time between activation
of the light and movement of the tail out of the light beam. The level of effective
ness of the anesthetic preparations was measured by the time delay caused by the
application of the patch over the baseline delay for untreated animals. Figure 10 is
a schematic of this device.
Although this method is attractive for screening large numbers of preparations
in a relatively time, rat tails are relatively insensitive. In some cases, the results of
I


131
The variable skin thickness was incorporated into the quasi-steady state model by
allowing L to change during integration.
Using L(t) in the quasi-steady state model precludes the use of a dimension
less model since the model now contains an additional time dependent function
(L(t)) with a different time scale. Therefore, one must return to Equations 15 and
16 and include an appropriate equation for L(t). The model for drug diffusion
through skin in vitro with skin swelling consists of the following system of four
equations (two for the thickness).
C[+At~ C1t+ffiy.(C2t-C1t+2 (C¡(-l)n-C-t)e
Ei-L =1
C2,+a' C2*+^5^(C1,-C2'+2 (Ci(-l)n-C2)e
=i
L{t) =0.069029 +0.049499i-0.0044692t2 (l < 5 hours)
L(i)=0.18821i0050642 (l > 5 hours)
Results
The following section compares the experimental data for diffusion in vitro
with the theoretical quasi-steady state model. The model is evaluated by comparing
the goodness-of-fit under different circumstances. The model can be used to
simulate transdermal diffusion in vitro with or without skin swelling and can also
hold the donor-phase concentration constant (as in a micellar solution).


138
Conditions
Figure 88: Model variance for 40%
propylene glycol (young mice)
Conditions
Figure 89: Model variance for 40%
propylene glycol (old mice)
Conditions
Figure 90: Model variance for 50%
propylene glycol (young mice)
Conditions
Figure 91: Model variance for 50%
propylene glycol (old mice)
Conditions Conditions
Figure 92: Model variance for 60% Figure 93: Model variance for 60%
propylene glycol (young mice #1) propylene glycol (young mice #2)


186
INPUT "Initial Boundary Condition at X=1 (ug/ml)"; C2
INPUT "Minimum Number of Series Terms"; MINI%
INPUT "Maximum Number of Series Terms"; MAXI%
IF MAXI% = 0 THEN MAXI% = 10000
INPUT "Diffusion Coefficient (cnC2/s)"; D
INPUT "Skin Thickness Constant (0/1)"; CONSTSKN
INPUT "Dose Volume (ml)"; VI
INPUT "Receptor Volume (ml)"; V2
INPUT "Start Time (Hours after skin in contact with water)"; TIME0
INPUT "Resolution of skin profile (number of steps)"; SKINNUM%
CONCWIDE = 700 / (SKINNUM% + 1)
SCREEN 3
RETURN
End Information Subroutine
2000
Begin Boundary Condition Subroutine
CONCENTR(0, 0) = CONCENTR(0, 1)
CONCENTR(SKINNUM%, 0) = CONCENTR(SKINNUM%, 1)
CONCENTR(0, 1) = CONCENTR(0, 2)


87
were readily available in the laboratory. The first experiments used the spectropho
tometer to find the concentration of hydrocortisone in both the donor and receptor
phases as a function of time. Since hydrocortisone diffused quickly through the
synthetic membrane relative to the diffusion of the anesthetics through skin, data
from all stages of the diffusion process were obtained (initial behavior through the
approach to equilibrium). This would have taken weeks or months with real skin or
a less permeable drug. In addition, the rapid diffusion of hydrocortisone helped
amplify the effect of stirring on diffusion since the boundary layer effects are most
pronounced for rapidly diffusing compounds.
Device effects
The effect of different types of stirring apparatus is shown in Figure 42. The
three curves represent the diffusion of hydrocortisone through a synthetic micro-
porous membrane when a) no stirring apparatus was used, b) a small stirring magnet
which only stirred the lower portion of the receptor compartment was used, and, c)
a wire tee which stirred the entire receptor compartment was used. The upper
(donor) phase of the diffusion cell was stagnant in all experiments. In b) and c) the
stirring rate (rpm) was the same. The graph shows that the stirring bar was
ineffective. The use of the wire tee efficiently decreased the effect of the stagnant
boundary layer in the receptor compartment.
Based on the results of these experiments stirring tees were constructed of
nylon for use in all subsequent diffusion experiments. Each tee had a small magnet
in its base driven by a magnetic stirrer.


72
+
Saline
6.9pH8.4
20% PG
6.3spHs8.5
40% PG
6.3pH8.3
50% PG
6.2spHs8.4
60% PG
7.0spH8.4
80% PG
6.5spHs7.5
100% PG
5.8spHs8.7
Figure 24: Conductivity of tetracaine (60% free base, 40% acid salt w/w) in
propylene glycol and saline
scopolamine, lidocaine, and tetracaine are shown in Figure 25-Figure 28 and the
wavelengths of maximum absorbance are in Table 7.
For hydrocortisone, the uv spectrophotometer was used at a single wavelength.
The primary absorbance maximum for hydrocortisone is 247 nm. The absorbance
at that wavelength was related to the concentration of hydrocortisone in the solution
by Beers law. This method of determining the concentration of hydrocortisone was
used because, at the time of the diffusion experiments with hydrocortisone, the
HPLC had not yet been installed.


110
100% 40% Acid Salt 100%
Acid Salt 60% Free Base Free Base
PH
Figure 58: Effect of pH on the diffusion of tetracaine (60% free base, 40% acid
salt w/w, 0.36M tetracaine overall) in 40% propylene glycol and 60% saline (v/v)
through young hairless-mouse skin
to be at least 0.36 M for all three systems to reproduce conditions already studied).
Consequently, a higher propylene glycol content of 70% was used. Figure 58 shows
the results of tetracaine diffusion in 70% propylene glycol experiments at pH = 4.71,
8.5, and 12.2 with an overall drug concentration of 0.36 M through young hairless-
mouse skin. The figure shows that the flux of drug is significant in the range
8.5 < pH < 12.2 and negligible for pH < 4.71. Below some minimum value of pH,
therefore, the flux of tetracaine through skin falls to zero. This is probably caused
by the decreasing amount of tetracaine free base available in solution. Tetracaine
free base has been found to penetrate the skin much better than the acid salt.61


159
An in vivo model could also be developed by altering the in vitro model to
include expressions for metabolism and removal of drug by the circulatory system.
Such a model would require data similar to in vitro receptor-phase concentration
versus time or additional relationships to determine these concentrations as a
function of excretion rate or blood concentration.
Clinical Studies
The subjective nature of in vivo trials with human volunteers makes
interpretation of data difficult, i.e., responses vary from person to person. There is
always the possibility of preconceived notions, e.g., "my skin is thick.," "nothing works
on me," "I have a high pain threshold," etc. These kinds of uncertainties make it
difficult to interpret limited data sets. Large scale clinical trials (n > 200) are
needed to draw statistically relevant conclusions. Consequently, the conclusions in
Chapter 5 are qualitative and are used as supporting evidence for the in vitro
conclusions.
The effects of varying propylene glycol content were only investigated in detail
through hairless-mouse skin in vitro. A more comprehensive study of the effects of
propylene glycol on the diffusion of tetracaine through human skin in vivo should
also be carried out.
Clinical studies can also be used to determine the concentration profile in the
skin by tape-stripping to verify the theoretical concentration profile in the skin.
Successive strippings (removal of the outer layers of the skin by adhesive tape) could


35
O
Hydrocortisone
O.
/CH3
N.
O
O
c chch2oh
Scopolamine
ch3
\ ? /C2h5
"-nh-c- ch,-n;
x C2H5
CH,
Lidocaine
O
/
CH,
h,c-(CH,)r nh^ Vc-o-(ciyr ^ tetrac aine
CH,
I
I
Figure 2: Molecular structure of hydrocortisone, scopolamine, lidocaine, and
tetracaine


165
conditions. Consequently, the difference between the effective diffusivities calculated
by the full numerical routine and the quasi-steady state model does not affect either
models ability to describe transdermal diffusion.
A models ability to describe transdermal diffusion is determined by how well
the model follows experimental data. The difference between the standard deviation
(s, where s2 = E(Cmodel(t) Cexp(t))2/(n -1)) associated with the two models averages
-1.33 mg/1 or -16.54% (i.e., the full numerical model is an average 1.33 mg/1 closer
to the experimental data or reduces the error by an average of 16.54% relative to the
quasi-steady state model).
The full numerical routine does follow the experimental diffusion data better
than the quasi-steady state model, but the difference in calculation time is significant.
The additional variable in the full numerical model (position) causes it to run much
more slowly than the quasi-steady state model. A complete concentration profile
must be calculated at each time step in order to evaluate the reservoir concentra
tions. Furthermore, the full numerical model requires a smaller time step (10% that
of the quasi-steady state model) to assure convergence. The combination of the
additional variable and a smaller time step slow the full numerical routine to such
an extent that the quasi-steady state model may be preferable.
There can be no doubt that the full numerical routine more closely
approximates a true, analytical solution to this idealized system. Furthermore, the
full numerical routine can be used under any circumstances since it is immune to the
assumptions of the quasi-steady state model. The degree of accuracy required to


106
sufficient to determine the individual effects of formaldehyde and hydration on
transdermal diffusion. Hydration has long been known to increase the permeation
of many substances. The effect of formaldehyde on diffusion was not so well
established. An additional experiment examined the effect of formaldehyde on
tetracaine diffusion through fresh, untreated skin.
The effect of low concentrations (0.1% w/w) of the preservative formaldehyde
on tetracaine diffusion through the skin is illustrated in Figure 55. The figure shows
Figure 55: Effect of 0.1 % (w/w) formaldehyde on the diffusion of tetracaine
(60% free base, 40% acid salt w/w, 0.36M tetracaine overall) in 40% propylene
glycol and 60% saline (v/v) through old hairless-mouse skin
the flux of 40% tetracaine acid salt, 60% free base (w/w) (0.36M tetracaine overall)
in 40% propylene glycol through mounted mouse skin into buffered saline or


171
LOCATE 1, 52
PRINT "Raw Data from file INFILES
LOCATE 3, 55
PRINT "Time C2"
LOCATE 5, 1
FOR K% = 0 TO DATPOINT% 1
INPUT #2, DATAPNTS(K%, 0), DATAPNTS(K%, 1)
LOW(l) = LOW(l) + DATAPNTS(K%, 1) A 2
PRINT USING ##.##
#####.###"; DATAPNTS(K%, 0); DATAPNTS(K%, 1)
NEXT
ENDCALC = DATAPNTS(DATPOINT% 1, 0)
LOCATE 14, 1
PRINT "STATUS: INITIALIZING"
D = (DMIN + DMAX) / 2
GOSUB 200 INTEGRATION AND VARIANCE
MID(0) = D
MID(l) = VARIANCE
D = DMAX
GOSUB 200 INTEGRATION AND VARIANCE
HIGH(0) = D
HIGH(l) = VARIANCE


89
0.040
'
w 0.030
m
+-
g
6 0.020
v->
es
Jj 0.010
E
0.000
0.000 0.001 0.002 0.003 0.004
(Stirring Rate (rpm))1
Figure 43: Effect of stirring rate on the diffusion of aqueous hydrocortisone
through synthetic membranes
of the stirred systems. Therefore, the collected data represented the completely
mixed limit and nothing would be gained by increasing the stirring rate beyond 300
rpm.
Temperature Behavior of Diffusion Apparatus
Every attempt was made to simulate in vivo conditions in the diffusion cells.
The temperature behavior of the diffusion cells before and after application of the
transdermal formulation was evaluated to anticipate possible transient effects of
temperature on diffusion. Such effects, if detected, would have to accounted for
when interpreting the data.


188
CONCENTR(SKINNUM%, 2) = CONCENTR(SKINNUM%, 1) + G D A /
L(2) / V2 (LASTC1 LASTC2 + 2 BOTSER)
IF CONCENTR(0, 2) < 0 THEN CONCENTR(0, 2) = 0
IF CONCENTR(SKINNUM%, 2) < 0 THEN CONCENTR(SKINNUM%, 2) =
0
IF ABS((CONCENTR(0, 2) LASTC1) / LASTC1) > CONV OR
ABS((CONCENTR(SKINNUM%, 2) LASTC2) / LASTC2) > CONV
THEN 300
RETURN
End Boundary Condition Subroutine
3000
Begin Skin Concentration Profile Subroutine
IF TIME < 3 G THEN 575
DELTATOP = (CONCENTR(0, 2) CONCENTR(0, 0)) / 2
DELTABOT = (CONCENTR(SKINNUM%, 2) CONCENTR(SKINNUM%,
0))/2
DELTAL = L(2) L(0)
Evaluate Skin Series for Each Location
FOR SKINCOUN% = 1 TO SKINNUM% 1


179
60 IF ITER% = 1 THEN DEST = (MID(O) + HIGH(O)) / 2: GOTO 50
REP% = 1
LOW(O) = MID(O)
MID(O) = HIGH(O)
HIGH(O) = TEMP(O)
LOW(l) = MID(l)
MID(l) = HIGH(l)
HIGH(l) = TEMP(l)
GOTO 500
END PARABOLIC MINIMIZATION SUBROUTINE
5000 RESUME NEXT ERROR HANDLER
ENDVALUS.BAS
This program will generate the boundary concentrations for various times in the
Franz diffusion cell.
ON ERROR GOTO 450
30 CLS
40 DEFDBL A-Z
50 PI# = 4 ATN(l)
A = 2.5 ^ 2 PI# / 4


150
Skin Longevity
The barrier properties of hairless-mouse skin with respect to aqueous
lidocaine acid salt were studied for 72 hours. During this time period, no significant
change in the diffusion behavior was observed (page 98). Based on this experiment,
subsequent diffusion studies (usually 8 hours) were conducted without chemical
preservation of the skin.
Effect of Propylene Glycol
Synthetic membranes (pages 101 102)
The highest flux of a tetracaine mixture (60% free base, 40% acid salt w/w)
through a synthetic polycarbonate membrane occurs in an aqueous solution. This
may be a wetting phenomenon since the membrane is hydrophilic. There is also a
local maximum in the drug flux at 40% propylene glycol and the flux decreases with
increasing propylene glycol fraction. The combined solubility-partitioning parameters
for 1-octanol and n-octane suggest a similar vehicle for transdermal delivery of
tetracaine (50% propylene glycol for either solvent). There is no reason to believe
that these two phenomena should be related because the solubility-partitioning
parameter represents partitioning into a hydrophobic membrane. Therefore, there
must be some other property unique to this 40% propylene glycol vehicle that cannot
be measured by solubility or partitioning.


190
NEXT SKINCOUN%
575 RETURN
End Skin Concentration Profile Subroutine
4000
Begin Print Subroutine
LPRINT USING "##.### (TIME G) / 3600;
PRINT #1, USING "##.### (TIME G) / 3600;
CLS
FOR SKINCOUN% = 0 TO SKINNUM%
LPRINT USING "#####.### "; CONCENTR(SKINCOUN%, 1);
PRINT #1, USING "#####.### "; CONCENTR(SKINCOUN%, 1);
LINE (10 + SKINCOUN% CONCWIDE, 340)-(10 + (SKINCOUN% + 1) *
CONCWIDE, 340 CONCHIGH CONCENTR(SKINCOUN%, 1)), BF
NEXT SKINCOUN%
PRINT #1,
LPRINT
RETURN
End Time Check Subroutine


144
The absolute circumstances under which the quasi-steady state assumption is
valid are the subject of some debate. Indeed, there has been direct criticism to its
application in this context. A more rigorous method for modelling this system is
numerical integration of the diffusion equation (Equation 5). The major drawback
to this method is that the concentration profile within the skin must be evaluated
after each time step. The quasi-steady state model has only one independent
variable (time), while the full numerical routine has two (time and position). This
additional degree of freedom makes the full numerical routine slower to converge
and less stable to changes in the parameters (D, Vj, V2, L(t), etc.).
The derivation of the full numerical routine has been delegated to the
appendix along with comparisons to the quasi-steady state results. Over the body of
the modelled data for tetracaine diffusing through hairless-mouse skin (Figure 68-
Figure 81) the models differ in their estimates of the effective diffusion coefficient
by approximately 5%. There is an improvement in the ability of the full numerical
routine to model the experimental data as compared to the quasi-steady state model.
This improvement, however; averages only 16.5%.


76
A (nm)
Figure 28: Ultraviolet absorbance spectrum of tetracaine
typical chromatograms and Table 8 shows representative drug retention times
(scopolamine,* lidocaine, and tetracaine).
Equilibrium Phenomena
As already mentioned, there is an acid-base equilibrium between the acid salt
and free base of tetracaine in solution. In water, tetracaine HC1 partially dissociates
to give a tetracaine cation and a Cl" counter-ion. Alternatively, some tetracaine free
base will accept a proton from water to form the cation (the counter-ion being OH').
Since tetracaine acid salt in solution is equivalent to an equimolar solution of
*The large, early peak in the scopolamine chromatogram is chloroform which was
used in the preparation of the sample.


53
the rat tail testing are contrary to clinical testing in human volunteers. Once this fact
surfaced, large scale testing using rats was suspended.
Clinical studies on humans
A much more accurate, but less time efficient method for testing the
anesthetic preparations in vivo is large scale clinical testing with human volunteers.
This method is more accurate because it measures effectiveness of these preparations
in terms of the final goal; local anesthesia in humans. Unfortunately, the subjective
response of a volunteer yields data prone to wide scatter.
The procedure for these human trials was as follows: A measured volume
(usually 0.5 ml) of the anesthetic preparation, either at room temperature or warmed
to 37C, was placed on a transdermal patch (2 cm diam.) from Hill Top Research
Inc. (Figure 11). The patch was then applied to the inner forearm of the subject and
the time of application noted (Figure 12). Ten to twenty subjects were tested for
each series and up to six patches could be applied to each subject to increase the
efficiency of the procedure.
After a specified time (15 to 90 minutes), the patch was removed and any
residual liquid wiped away. Pain stimulus was provided by a hypodermic needle
(Figure 13). The subject was asked to give a rating commensurate to the effective
ness of the anesthetic. The scale used is called the Visual Analog Scale and allows
the subject to assign a value between 1 and 10 to convey no effect (1) to complete
analgesia (10).


32
suggest that the effect of the chemical changes in the stratum corneum are
overshadowed by the change in its physical dimensions.


28
carbomer wax or 7% methylcellulose and an oil-in-water emulsion cream consisting
of 16% Emulsifying Wax, 4% paraffin. For the aqueous gels, a tetracaine free base
concentration of 4% applied for 30 min produced adequate anesthesia after 40 min.
The emulsion cream required 8% to 12% tetracaine free base to be effective, but the
onset time was the same as for the aqueous gels. A higher concentration did not
decrease the onset time, but did increase the duration of anesthesia. The onset of
anesthesia after removing the formulation implied that the stratum corneum was the
limiting resistance to diffusion. Our results for onset time and duration of anesthesia
with tetracaine in a different solvent are similar and support this hypothesis.
Small et al.80 used one of the aqueous gels developed by Woolfson et al.95
before cutting skin grafts. The clinical procedure was modified from previous
experiments by increasing the area (as needed), dose (1 mm layer), gel application
time (s: 1 hr), and the period of time between the removal of the gel and the start
of the procedure (60 to 300 min). Skin graft removal was pain-free in 64 of 80 cases.
In in vivo trials, McCafferty et al.54 compared the clinically available EMLA
(eutectic mixture of local anesthetics) cream to their 0.35 mmol/g tetracaine cream.
The tetracaine cream produced longer and more rapid anesthesia than the EMLA
cream.
Woolfson et al.94 conducted an expanded clinical assessment of their aqueous
tetracaine gel in a pediatric environment to evaluate the level of anesthesia and
reactions in 1241 patients. The level of success (defined as no sensation during


125
o)-A fw |0
K1 Jo

qo-c^o)-^. [(-£>9^) |0)rfx
V\ JQ dx
t
c1(t)=c1(o)+^ [(*^1 L,)dx
V1 {, dX
C2(t)=C2(0)+^r ¡N U dx =
V2 J0
t
C2(t)=C2(0)* (-Z)l^) I^Jdx.
V2 Jo dX
t
C2()=C2(0)-^ lw>fc
2 O
N is the drug flux in the +x direction
Vl is the volume of the drug dose
V2 is the volume of the receptor phase
The mass balances (Equations 7 and 8) contain derivatives of the
concentration profile with respect to position (x). To evaluate these derivatives, the
analytical solution for the concentration profile (Equation 6) is differentiated with
respect to position.
?££.£ =(C2-CX- +
dx v 2 VL
2j, C2{ 1Y Cl^niCy^n7CXy -DnVt/L^
Lt Z/
7rn=i
(Ci-Cjl+l-Y, (C^-ir-CJcosi^e
L L,n^ i L
n
00
9


12
t
00
.Siratiiin Corn mini (15 uni)
Viable Epidermis (150 pm)
Dermis (2000 pm)
Figure 1: General schematic of skin structure
corneum thickness, number of sweat glands, number of hair follicles, and blood
supply will affect the routes and overall resistance of skin to diffusion.4,74,75,88 Some
of these parameters have been systematically studied and the results are reviewed
below.
Age. The effect of subject age on transdermal diffusion has been studied in
detail under a variety of conditions. In 1962, Marzulli53 identified a trend of
decreasing permeability with age of human skin in vitro. Since that time, other
researchers have confirmed this trend.4,6,34,89 There is some evidence that the general
permeability increases in elderly subjects4 or is dependent on the substance
investigated.6,34 The general trend of decreasing permeability with age is attributed
to the progressive decrease in moisture content in the skin of the elderly.34


123
Modelled System
x=0 External Surface
x=L Internal Surface
Boundary and Initial Conditions
x=0; C(x,t)=Ci(t) x=L; C(x,t)=C2(t)
t=0; C(x,t)=0 (0 Assumptions
* Diffusion in one direction only
* Homogeneous barrier to diffusion
* No counter- or co-diffusion
* Boundary layers neglected
Figure 65: Schematic of idealized system
diffuse in one direction (perpendicular to the surface of the skin). Temperature is
held constant and, therefore; is not considered as a parameter.
The cross sectional area for diffusion is A, the effective diffusivity is D, the
time since application of the drug is t, the drug concentration in the donor phase is
C1(t), and the drug concentration in the receptor phase is C2(t). The region of
interest lies between x = 0 (donor phase boundary) and x=L (receptor phase
boundary) and the effects of boundary layers are neglected (concentrations at the
skin surfaces equal bulk concentrations).


20
at elevated temperatures. Durrheim et al.23 also measured the diffusion of n-alkanols
through skin as a function of temperature (Arrhenius plot) and got a similar value
of approximately 19 kcal/mol.
Scheuplein76 measured the diffusion of water and ethanol through human
stratum corneum as a function of temperature and found that the results depended
on whether the temperature was increasing or decreasing (hysteresis effect). This
effect was attributed to the fluidization and partial dissolution of the lipids in the
membrane (permanent damage to the barrier at elevated temperatures).
Raising the temperature can also affect the barrier properties of the stratum
corneum. Poulsen and Flynn66 found that the barrier properties of human and
hairless-mouse stratum corneum remain relatively constant up to approximately 80C.
Above this temperature there is a rapid, dramatic, and permanent loss of barrier
function.
In summary, the literature indicates that there are two effects of temperature:
a conventional thermal motion effect and a stratum corneum dissolution effect.
Penetration enhancers
Rnepp et al.50 summarize the ideal features of a penetration enhancer as:
1: No pharmacological response
2: Specific in its action
3: Acts immediately and reversibly with predictable duration
4: Chemically and physically stable and compatible in formulation


162
(A4)
The resulting equation is rearranged into an explicit equation for the concentration
at position = i and time = j + 1 as a function of concentrations at time = j.
(A5)
DAt
(A6)
r
Equation A5 is only valid for i = 1, M 1 where M is the resolution of the skin
concentration-profile. Boundary conditions must be established for i = 0 and i = M.
The boundary conditions are mass balances which depend on the volumes and
initial concentrations of the reservoirs. The equations for the concentration in the
reservoirs have already been derived (Equation 7 on page 125 and Equation 8 on
page 125) and are reproduced below.
(A8)
Taking the derivative of Equations A7 and A8 with respect to time eliminates the
integral (these equations will be numerically integrated with respect to time with
Equation A5).


199
RETURN
60 IF ITER% = 1 THEN DEST = (MID(O) + HIGH(O)) / 2: GOTO 50
REP% = 1
LOW(O) = MID(O)
MID(O) = HIGH(O)
HIGH(O) = TEMP(O)
LOW(l) = MID(l)
MID(l) = HIGH(l)
HIGH(l) = TEMP(l)
GOTO 500
END PARABOLIC MINIMIZATION SUBROUTINE
5000 RESUME NEXT ERROR HANDLER
200
Begin Numerical Integration Subroutine
F% = 1
C2 = DATAPNTS(0, 1)
VARIANCE = 0
TIME = 0
GOSUB 300 CALCULATE INITIAL SKIN THICKNESS


53.
F.N. Marzulli, Barriers to skin penetration, J. Inv. Derm., 39, 387-93
(1962).
207
54. D.F. McCafferty, A.D. Woolfson, and V. Boston, In vivo assessment of
percutaneous local anaesthetic preparations, Br. J. Anaesth., 62(1), 17-21
(1989).
55. D.F. McCafferty, A.D. Woolfson, K.H. McClelland, and V. Boston,
Comparative in vivo and in vitro assessment of the percutaneous
absorption of local anesthetics, Br. J. Anaesth., 60(1), 64-9 (1988).
56. J.N. McDougal, H.J. Clewell III, M.E. Andersen, and G.W. Jepson,
Physiologically-based pharmacokinetic modelling of skin penetration, in
Prediction of Percutaneous Penetration Proceedings. April 1989, R.C. Scott,
R.H. Guy, and J. Hadgraft (eds), IBC Technical Services, London, 263-272
(1990).
57. J.N. McDougal, G.W. Jepson, H.J. Clewell III, M.G. MacNaughton, and
Melvin E. Andersen, A physiological pharmacokinetic model for dermal
absorption of vapors in the rat, Toxicol. Appl. Pharmacol., 85, 286-94,
(1986).
58. J.C. McElnay, M.P. Matthews, R. Harland, and D.F. McCafferty, The effect
of ultrasound on the percutaneous absorption of lignocaine, Br. J. Clin.
Pharmacol., 20(4), 421-4 (1985).
59. K.E. McGowan, A.D. Woolfson, and D.F. McCafferty, Laser Doppler
Velocimetry: Prediction of the optimum application time for a
percutaneous local anesthetic formulation, in Prediction of Percutaneous
Penetration Proceedings. April 1989, R.C. Scott, R.H. Guy, and J. Hadgraft
(eds), IBC Technical Services, London, 376-82 (1990).
60. A.S. Michaels, S.K. Chandrasekaran, J.E. Shaw, Drug Permeation Through
Human Skin: Theory and in vitro experimental measurement, AIChE J,
21(5), 985-996 (1975).
61. S. Monash, Topical anesthesia of the unbroken skin, A.M.A. Arch. Derm.,
76, 752-6, (1957).
62. R. Neubert, W. Wohlrab, and C. Bendas, A new multilayer membrane
system for studying absorption from topical formulations, in Prediction of
Percutaneous Penetration Proceedings. April 1989, R.C. Scott, R.H. Guy,
and J. Hadgraft (eds), IBC Technical Services, London, 431-6 (1990).


I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Dinesh 0. Shah, Chair
Professor of Chemical
Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Gerald B. Westermann-Clark
Associate Professor of
Chemical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Chanc/'W-Park
Assistant Professor of
Chemical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Salvatore R. Goodwin
Associate Professor of
Anesthesiology
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
B. Sloan
Associate Professor of
Medicinal Chemistry


120
oo
<
>
Placebo
0.036 M
(1.0% w/v)
0.125 M
(3.5% w/v)
0.251 M
(7.0% w/v)
0.502 M
(14.0% w/v)
1.004 M
(28.0% w/v)
Time (hr)
Figure 64: Time response for in vivo analgesia by tetracaine (60% free base, 40%
acid salt w/w) in 40% propylene glycol and 60% saline (v/v) (0.036 M 1.004 M)
parameters for 1-octanol and n-octane also predict the optimum formulation in this
vicinity (Figure 17, Table 3 and Figure 18, Table 4). Therefore, the system of 60%
tetracaine free base, 40% tetracaine acid salt (w/w) in a solvent of 40% propylene
glycol and 60% saline (v/v) is confirmed as the optimum combination by in vitro
diffusion and in vivo diffusion. The existence of an optimum vehicle is also
supported by the combined solubility-partitioning parameters for 1-octanol
(Figure 17, Table 3) and n-octane (Figure 18, Table 4). The similarity between the
in vitro and in vivo results also indicates that in vitro fluxes and human subject
responses are related.


197
END NEW SKIN THICKNESS SUBROUTINE
500
BEGIN PARABOLIC MINIMIZATION SUBROUTINE
bnum = LOW(O) A 2 MID(l) + MID(O) A 2 HIGH(l) + HIGH(O) A 2 *
LOW(l) LOW(O) A 2 HIGH(l) MID(O) A 2 LOW(l) HIGH(O) A 2
* MID(l)
bden = LOW(O) A 2 MID(O) + MID(O) A 2 HIGH(O) + LOW(O) HIGH(O)
A 2 LOW(O) MID(O) A 2 LOW(O) A 2 HIGH(O) MID(O) *
HIGH(O) A 2
Y = bnum / bden
Z = (MID(l) LOW(l) + Y (LOW(O) MID(O))) / (MID(O) A 2 LOW(O) A
2)
X = LOW(l) Y LOW(O) Z LOW(O) A 2
LOCATE 14, 1
IF Z < 0 OR increase > 1 THEN
IF REP% > 0 THEN
CLS


126
The mass balance equations require the above derivative to be evaluated at the
boundaries (x=0 and x=L).
dC(x,t) i +
dx *=0 ^ 2 1 L
1 (C^-iy-CJcos^
-^=1
(Ct-Cjl+lf; (C2(-ir-Ct)e
L ->n=1
10
dC(x,t)
dX
tY. i.C2(-Vr-C2)cos(n*)e
11
(C2-C2)l*l (C2-C2(-ir)e -D"V/L>
J-> 1-' n=l
Equations 10 and 11 can now be put into Equations 7 and 8; the time dependent
boundary conditions.
t
cx(t),c2(0)+£. [((CyxJ-Cyx))!*
v\ Jo ^
(C2(x)(-1)"-C1(x))e =
L>n=l
t
C'(0)+W f (C2 V\L Jo
2 (C^X-iy-C^e -D"'AlL)d\
n=\
12


151
Hairless-mouse skin (pages 102 103)
The highest flux of a tetracaine mixture (60% free base, 40% acid salt w/w)
through hairless-mouse skin occurs at 40% propylene glycol. This value is near the
value suggested by the combined solubility-partitioning parameters for 1-octanol and
n-octane (50% propylene glycol for either solvent). The combined solubility
partitioning parameter can be used as a method for estimating the optimum vehicle
composition, but it should not be relied on for estimating relative flux.
Effect of Age
The flux of tetracaine mixtures (60% free base, 40% acid salt) through
hairless-mouse skin generally decreases with age. For mice aged 6 to 8 months,
transdermal flux decreased an average of 20% relative to the flux through the skin
of mice aged 6 to 8 weeks (page 105). The relative effect of propylene glycol on the
flux of tetracaine mixtures through hairless-mouse skin seems to be unaffected by
age.
Effect of Formaldehyde (pages 105 107)
Formaldehyde seems to decrease the flux of tetracaine through hairless-mouse
skin by decreasing the permeability of the skin. Other experiments with scopolamine
also indicated that formaldehyde at a concentration of 0.1% (w/w) decreases flux,
however; the difference was not significant in either case.


155
tal data an average of 20%. Should there be great doubt concerning the validity of
the quasi-steady state assumption, the full numerical routine can be used with
confidence.


22.
D. Dupuis, A. Rougier, R. Roguet, C. Lotte, and G. Kalopissis, In vivo
relationship between horny layer reservoir effect and percutaneous
absorption in human and rat, J. Inv. Derm., 82(4), 353-6 (1984).
204
23. H. Durrheim, G.L. Flynn, W.I. Higuchi, and C.R. Behl, Permeation of
Hairless Mouse Skin: I. Experimental methods and comparison with human
epidermal permeation by alkanols, J. Pharm. Sci., 69(7), 781-6, (1980).
24. P.E. Elias, The importance of epidermal lipids for the stratum corneum
barrier, in Topical Drug Delivery Formulations. D.W. Osborne and A.H.
Amann (eds), Marcel Dekker, New York, 13-28 (1989).
25. R. Fleming, R.H. Guy, and J. Hadgraft, Kinetics and thermodynamics of
interfacial transfer, J. Pharm. Sci., 72(2), 142-5 (1983).
26. G.L. Flynn, Mechanism of percutaneous absorption from physicochemical
evidence, in Percutaneous Absorption: Mechanisms. Methodology. Drug
Delivery. R. Bronaugh and H. Maibach (eds), Marcel Dekker, New York,
17-42 (1985).
27. E.J. French, C.W. Pouton, and G. Steele, Fluidization of Lipid Bilayers by
Non-ionic Surfactants: Structure activity studies using a fluorescent probe,
in Prediction of Percutaneous Penetration Proceedings. April 1989, R.C.
Scott, R.H. Guy, and J. Hadgraft (eds), IBC Technical Services, London,
308-15 (1990).
28. S.E. Friberg, I.H. Kayali, M. Margosiak, D.W. Obsorne, and AJ.I.Ward,
Stratum corneum structure and transport properties, in Topical Drug
Delivery Formulations. D.W. Osborne and A.H. Amann (eds), Marcel
Dekker, New York, 29-45 (1989).
29. C.L. Gay, J. Hadgraft, I.W. Kellaway, J.C. Evans, and C.C. Rowlands, The
Effect of Skin Penetration Enhancers on Human Stratum Corneum Lipids:
An electron spin resonance study, in Prediction of Percutaneous
Penetration Proceedings. April 1989, R.C. Scott, R.H. Guy, and J. Hadgraft
(eds), IBC Technical Services, London, 322-32 (1990).
30. A. Gesztes and M. Mezei, Topical anesthesia of the skin by liposome-
encapsulated tetracaine, Anesth. Analg., 67, 1079-81, (1988).
C.L. Gummer, The in vitro evaluation of transdermal delivery, in
Transdermal Drug Delivery: Developmental Issues and Research
Initiatives. J. Hadgraft and R.H. Guy (eds), Marcel Dekker, New York,
177-96 (1989).
31.


149
Donor phase
The properties of the formulations introduced into the donor reservoir vary
widely both in composition and temperature. A worst-case scenario was adopted to
determine whether the time required for the donor phase to reach thermal
equilibrium would affect the diffusion results. As a model of all formulations,
propylene glycol at ambient temperature (2 ml) was introduced into a Franz diffusion
cell. The diffusion cell was already at thermal equilibrium with 37C water
circulating through the cell jacket. The donor phase reached thermal equilibrium
within three minutes of its introduction into the diffusion cell. This result indicated
that the donor phase reaches thermal equilibrium quickly relative to the rate of
diffusion since the first concentration measurement was taken after one hour (page
91).
Skin Swelling
The swelling of hairless-mouse skin immersed in water was measured as a
function of time (page 92) and incorporated into theoretical models of transdermal
drug diffusion through correlations (page 130). Hairless-mouse skin was found to
swell to four times its original thickness (0.6 mm) when immersed in water for 2 days.
The swelling also seemed to occur in two stages; a rapid, early stage that suggested
tissue swelling and a slower, later stage that suggested tissue dissolution.


58
glycol greatly increases the solubility of the base which peaks at about 2.65 M then
falls to 2.17 M in pure propylene glycol. The solubility of tetracaine salt decreases
slightly as the propylene glycol fraction increases, but does not change much overall
(0.5 M < C 0.8 M). The solubility of a 40% acid salt, 60% free base mixture
peaks at 3.00 M in 50% propylene glycol. The solubility of the mixture is far greater
than the sum of the salt and base solubilities in 50% propylene glycol. This
non-additivity near 50% propylene glycol shows that HC1 acid can enhance solubility
above what would be expected from the pure component solubility curves (pure salt
in solution corresponds to a bulk mixture of equal parts of tetracaine base and HC1
% Propylene Glycol (v/v)
Acid Salt
Free Base
40% Salt
60% Base
Figure 14: Tetracaine solubility in propylene glycol and saline


Drug Diffusion In Vivo
Rat Tail-flick Test (page 111)
The rat tail-flick response to a painful light beam was used to evaluate the
ability of anesthetic formulations to produce analgesia in rat tails. This test was
originally adopted because it facilitated rapid, large-scale screening of prospective
anesthetic formulations. Unfortunately, this test lacked the necessary sensitivity and
did not correspond to data for humans. In addition, test results had no correlation
with concentration and their wide variation ruled out the influence of micellization.
Rat tail-flick testing was abandoned in favor of clinical testing with volunteers.
Clinical Trials (pages 113 119)
Attempts at formulating an effective, lidocaine-containing topical, anesthetic
were unsuccessful. Tetracaine was found to be more effective than lidocaine as a
topical anesthetic. Two effective topical, tetracaine formulations were developed.
Both of these contained mixtures of tetracaine free base and tetracaine acid salt in
vehicles composed of propylene glycol and saline. One of these formulations (60%
free base, 40% acid salt in 40% propylene glycol and 60% saline) was capable of
producing profound local anesthesia after 45 minutes and at much lower concentra
tions than the other. A lower concentration of tetracaine reduces the likelihood of
skin irritation as well as the cost of the formulation. The formulation found to be


70
Table 5: Critical micelle concentrations of tetracaine (60% free base, 40% acid
salt w/w) in propylene glycol and saline as measured by surface pressure
% Propylene
Glycol
CMC (M)
pH Range
(Apparent)
0
(no CMC)
6.85-8.37
20
0.02
6.30-8.51
40
0.04
6.26-8.29
50
0.07
6.17-8.43
60
0.15
7.03-8.41
80
(no CMC)
6.46-7.55
100
(no CMC)
5.80-8.65
Figure 22: Conductivity of aqueous tetracaine acid salt


148
Drug Diffusion In Vitro
Stirring
The efficiency of stirring in Franz diffusion-cells was evaluated two ways:
device and stirring rate. Identical diffusion studies under stagnant conditions, with
a small stirring bar, or with a larger stirring tee determined that the small stirring
bars available were inadequate for mixing the receptor phase of a Franz cell (page
87). Stirring tees were constructed for all diffusion cells and were used in all
subsequent diffusion experiments.
The rate at which the stirring tees should be rotated was determined by
plotting the cumulative flux of hydrocortisone through a synthetic membrane versus
the inverse of the stirring rate (200 400 rpm). The best line through these points
is flat and significantly greater than the stagnant flux indicating that the reservoir is
fully mixed and further increase of the mixing rate would not increase the flux (page
88).
Temperature Behavior of Franz Diffusion Cells
Receptor phase
The temperature behavior of the larger reservoir (15 ml) of the Franz cell was
monitored by a thermocouple. The receptor phase reaches thermal equilibrium
(32C) within 15 minutes when 37C water is circulated through the cell jacket (page
90).


164
C
i, O
O
v i O M
C,
o, o
(dose)
(usu. = 0)
calculating the concentration profile, and marching ahead in time.
(All)
(A5)
(A12)
The full numerical routine was used to calculate the effective diffusivity of the
same in vitro transdermal-diffusion data as the quasi-steady state model (Figure 68 -
Figure 81, pages 134 136). A summary of the modelling data appears at the end
of this section.
The average variation of the effective diffusivity calculated from the full
numerical model relative to the quasi-steady state model is 4.08% (i.e., the full
numerical routine yields effective diffusivities that are 4.08% greater than those from
the quasi-steady state model). As already stated, the numerical value of the effective
diffusivity has limited physical meaning due to the nature of the system. The true
path length of diffusion, the actual area of diffusion, and the relative contributions
of skin strata are all subject to some speculation. Without a fundamental under
standing of these parameters, the effective diffusivity is a lumped parameter with a
value that is only relevant to other effective diffusivities calculated under the same


170
The third program (PROFILE) generates the theoretical concentration profile
through the skin. The program is actually a variation of the ENDVALUS program
and much of the code is the same. An additional subroutine was added to calculate
the concentration profile using the previously calculated boundary concentrations.
The last program (FNR) uses a full numerical routine rather than the quasi
steady state model developed in Chapter 6. This program was written last and, with
the exception of the numerical routine, the initial search values, and the use of a
batch data file, combines the functions of the previous programs. Consequently, this
single program is all that is required to determine the effective diffusivity and
generate time-dependent concentrations within the skin and in the reservoirs.
VARFIT.BAS
This program will generate the boundary concentrations for various times in the
Franz diffusion cell.
ON ERROR GOTO 5000
CLS
DEFDBL A-Z
PI# = 4 ATN(l)
GOSUB 100 INFORMATION SUBROUTINE
DIM DATAPNTS(DATPOINT% 1, 4), TOP(l), BOT(l), LOW(l), MID(l),
HIGH(l), TEMP(l)
CLS


113
formulations, there is a correlation between the tail-flick delay and the diffusion of
tetracaine in vitro.
Clinical Trials
Although both lidocaine and tetracaine preparations were tested on human
volunteers, the vast majority of the tests involved tetracaine (88 versus 6 for
lidocaine). Lidocaine was phased out in favor of tetracaine and rat tail-flick testing
was phased out in favor of clinical testing. The procedure for clinical trials is
discussed in Chapter 2 (page 53).
Lidocaine
The lidocaine preparations tested on volunteers and their performance in
clinical testing are summarized in Table 11. The visual analog scale (VAS) uses
values of 1 (to indicate no effect) to 10 (complete anesthesia). The inability to
produce significant analgesia by lidocaine in clinical trials (VAS > 7), led to the
decision to abandon lidocaine as the anesthetic agent for transdermal formulations.
Tetracaine
Clinical testing of anesthetic formulations containing tetracaine succeeded the
lidocaine trials. Several parameters related to the in vivo transdermal diffusion
procedure were investigated. Site preparation, time, and dose response data helped
to optimize and characterize the topical formulation.


64
Table 3: Tetracaine (60% free base, 40% acid salt w/w) solubility in propylene
glycol-saline and partitioning between propylene glycol-saline and 1-octanol
% Propylene
Q>at
Kp
KpCsat
Glycol
(M)
(M)
0
1.527
6.374
9.366
20
1.591
5.547
7.815
40
1.958
5.302
11.05
50
2.979
4.992
14.38
60
2.806
4.750
13.74
Figure 17:
strongly surface active and the flattening of the curve at higher concentrations
indicates the presence of micelles at a critical micelle concentration (CMC) of


2
material. The second section is a more detailed account of theoretical transdermal
diffusion.
Diffusion through membranes
Membrane diffusion is controlled by three basic effects: osmotic pressure,
solute diffusion, and fluid flow.20 In transdermal diffusion there are no osmotic
pressure effects because all species can diffuse through the membrane. Equilibrium
is approached through solute diffusion and solvent flow through the membrane
(solvent diffusion). Consequently, there is diffusion in both directions as the system
approaches equilibrium, with all components moving from higher concentration to
lower concentration.
This process can be described mathematically by Ficks laws of diffusion.
Ficks first law of diffusion states that flux is proportional to the concentration
gradient and the constant of proportionality is defined as the diffusivity.7
JA = ~DAB VCA 1
JA = Molar flux of component A
Dab = Molar diffusivity of component A in B
CA = Molar concentration of component A
A special case of this law occurs when the gradient is constant. In such circumstanc
es, the flux is constant (steady state). In a closed system, this occurs after long times,
but does not imply equilibrium.


112
Table 10: Best rat tail-flick test results
Test solution
Mean delay (s)
Standard
deviation (s)
1.33 M aqueous
tetracaine salt
2.08
1.77
1.65 M tetracaine base
in 73% propylene glycol
and 27% saline
1.89
1.29
2.87 M tetracaine
(62.5% free base, 37.5%
acid salt) in 50% propyl
ene glycol and 50%
saline
1.75
1.52
0.83 M tetracaine salt in
50% propylene glycol
and 50% saline
1.58
0.94
0.31 M lidocaine
salt micro
emulsion
1.53
1.58
0.33 M lidocaine salt
macro-emulsion
1.30
1.12
0.83 M aqueous tetra
caine salt
1.23
0.63
1.39 M lidocaine salt
micro
emulsion
1.18
1.87
0.92 M lidocaine salt
micro-emulsion
1.14
0.88
1.33 M aqueous tetra
caine salt
1.10
2.07
tetracaine free base and 37.5% acid salt) ranked #3 by the rat tail-flick test.
Therefore, although the rat tail-flick test cannot be relied upon for ranking anesthetic


Figure 38: pH of tetracaine in 20% propylene glycol and 80% saline
(v/v) 83
Figure 39: pH of tetracaine in saline 83
Figure 40: Micelle diameter of tetracaine (60% free base, 40% acid salt,
0.36 M) in propylene glycol and saline by QELS 83
Figure 41: Thermal breakdown of tetracaine (60% free base, 40% acid salt
w/w) in 40% propylene glycol, 60% saline (v/v) 85
Figure 42: Effect of stirring device on the diffusion of aqueous
hydrocortisone through synthetic membranes 88
Figure 43: Effect of stirring rate on the diffusion of aqueous hydrocortisone
through synthetic membranes 89
Figure 44: Dynamic receptor phase temperature in Franz cell 90
Figure 45: Dynamic donor-phase temperature in Franz cell (VD = 2 ml) 91
Figure 46: Dynamic swelling of excised hairless-mouse skin immersed in
water 92
Figure 47: Diffusion of aqueous scopolamine through fresh and chemically
preserved hairless-mouse skin 94
Figure 48: Comparison of experimental scopolamine diffusion data to data
of Chandrasekaran et al 95
Figure 49: Long-term diffusion of aqueous lidocaine salt through untreated
hairless-mouse skin 98
Figure 50: Effect of propylene glycol on the diffusion of lidocaine salt
through untreated hairless-mouse skin 99
Figure 51: Effect of propylene glycol on the diffusion of tetracaine HC1
through hairless-mouse skin 100
Figure 52: Effect of propylene glycol on the diffusion of tetracaine (60%
free base, 40% acid salt w/w) through synthetic polycarbonate
membranes 102
Xlll


-AL
128
Volume ratio
v2
L2
T
Time constant
D-k2
At
8=
Step size
T
}
Index
17
7T 77 = 1
-K 771
18
The only dimensional quantities in the final expressions for the boundary concentra
tions are the boundary concentrations themselves. The model is developed in this
way so that raw diffusion data (C2(t) vs. t) can be used to find the time constant and,
in turn, the effective diffusivity. Figure 66 shows the model results; the insert shows
the response of the receptor phase just after applying the drug. To determine the
concentration profile inside the skin, boundary values from Equations 17 and 18 are
cycled back into the analytical solution for the concentration profile (Equation 6).
Figure 67 shows the concentration within the skin calculated by Equations 6,
17, and 18 as a function of position (x=0 is the external surface) for different
dimensionless times (experimental time/time constant). Such calculations assume
the drug diffusion coefficient is the same everywhere in the skin, i.e., that the skin
can be considered a homogeneous medium for diffusion. If one views the skin as


191
End Program Text
FNR.BAS
This program controls the fnr program and inputs the files to be analyzed
sequentially
ON ERROR GOTO 5000
CLS
DEFDBL A-Z
DEFDBL I-J, N
pi# = 4 ATN(l)
A = 2.5 ^ 2 pi / 4
FILES "*.bch"
INPUT "File containing batch data"; batfileS
INPUT "File to output data"; outfileS
OPEN "O", #1, outfileS + ".out"
OPEN T, #3, batfileS + ".bch"
1 INPUT #3, INFILES
IF EOF(3) THEN END
increase = 0
GOSUB 5 solve for optimum diffusivity
CLOSE #2


122
concentration profile is achieved quickly, then assuming steady state is valid. During
steady state, determining concentration is relatively easy; prior to steady state,
calculations are more difficult. The quasi-steady state model can often be used for
cases where the steady state assumption is not valid. Its sole assumption is that the
concentrations on either side of the skin change much more slowly than the
concentration within the skin.
The model developed here is a numerically integrated, quasi-steady state, one
dimensional Fickian diffusion model with appropriate boundary conditions. The
model uses an effective diffusion coefficient for the drug and describes the diffusion
of drug from a finite donor phase, through the skin, into a receptor phase.
For in vitro diffusion in a Franz cell, the receptor phase is a finite sink, but
for in vivo diffusion the receptor phase concentration would be determined by skin
metabolism and circulatory removal of drug.
Idealized System
The in vitro model of transdermal diffusion is designed to simulate the
diffusion of substances through mounted hairless-mouse skin in a Franz diffusion cell.
Every attempt has been made to accurately represent the system used to gather the
in vitro data (Chapter 4: In Vitro Diffusion of Drugs).
The idealized system that forms the basis for the model is illustrated in
Figure 65. The drug is assumed to be the only species diffusing and assumed to


193
ENDCALC = DATAPNTS(DATPOINT% 1, 0)
N = ENDCALC 3600 / h
LOCATE 14, 1
PRINT "STATUS: INITIALIZING"
D = DMIN
GOSUB 200 INTEGRATION AND VARIANCE
LOW(O) = D
LOW(l) = VARIANCE
D = DEST
GOSUB 200 INTEGRATION AND VARIANCE
MID(0) = D
MID(l) = VARIANCE
D = DMAX
GOSUB 200 INTEGRATION AND VARIANCE
HIGH(0) = D
HIGH(l) = VARIANCE
ITER% = 1
10 IF ABS(LSTD D) / D < DIFCONV THEN 99
LSTD = D
GOSUB 500 ESTIMATE DIFFUSION COEFFICIENT
D = DEST
LSTVAR = VARIANCE


98
Longevity of skin
The diffusion of aqueous lidocaine HC1 through fresh, untreated hairless-
mouse skin was observed over 72 hours. During this experiment, no dramatic change
Time (hrs)
Figure 49: Long-term diffusion of aqueous lidocaine salt through untreated
hairless-mouse skin
in the diffusion rate occurred (note the nearly constant slope in Figure 49). It was
decided, therefore, that fresh, untreated skin would be adequate as the barrier to
drug diffusion for periods not to exceed 10 hours.
Effect of 50% propylene glvcol versus saline
Figure 50 shows the cumulative flux versus time behavior for the diffusion of
lidocaine HC1 through hairless-mouse skin from saline and a 50% propylene glycol,
50% saline solution (v/v) at a drug concentration of approximately 1.86 M. The


22
Differences between in vitro and in vivo systems
Studying transdermal diffusion on living, intact organisms is more difficult than
studying diffusion in vitro. The difficulties of sample collection, sample analysis,
consistent dosing, variations between individuals, and effects of metabolism
complicate in vivo studies. Despite the experimental difficulties, topical formulations
must pass through a clinical in vivo testing phase before being approved for
widespread use. For some variables the effects are the same for in vitro and in vivo
studies; for others, such as metabolism, circulation, and radial diffusion, there are no
in vitro parallels.
Metabolism. Barry4 states that drug metabolism has been neglected in past
studies. Both inactive and active metabolites may form in the skin and can affect the
results of a transdermal diffusion experiment if not accounted for properly. Tauber81
details the effects of in vivo metabolism in detail.
One potential benefit of in vivo drug metabolism is the ability to specifically
engineer drug precursors (prodrugs) to improve their percutaneous absorption.
Prodrugs have little or no therapeutic activity, but are metabolized after absorption
I
into an active drug.36,37
Circulation. Blood flow in vivo creates an open system while an in vitro
system is usually closed. Blood flow carries drug from the skin and distributes it
throughout the body preventing equilibrium. In a closed, in vitro system,
the drug
builds up in the receptor phase and the concentration difference across the
membrane decreases with time.


85
Time (days)
Figure 41: Thermal breakdown of tetracaine (60% free base, 40% acid salt w/w)
in 40% propylene glycol, 60% saline (v/v)
is two to three days. This limitation means that the formulation must either be
prepared no more than three days before use or kept at 5C. All formulations in
this study were prepared one day in advance so that the thermal breakdown of
tetracaine base in solution is not an issue.


152
Effect of Concentration
Increasing tetracaine concentration (60% free base, 40% acid salt) does not
increase the transdermal flux of tetracaine from a 40% propylene glycol, 60% saline
vehicle (page 108). This observation is consistent with the observation that this is a
micellar solution and increasing drug concentration only increases the number of
micelles in the formulation. If the micelles do not diffuse through the skin, then the
concentration of dispersed drug molecules determines the rate of diffusion by Ficks
law. In a micellar solution, the concentration of dispersed solute remains relatively
constant. Therefore, increasing the solute concentration of a micellar solution will
not increase the driving force for diffusion (assuming the micelles do not diffuse).
Effect of pH
Tetracaine is a weak base and the relative proportions of ionized and
unionized drug in solution is determined by the pH of the solution. The diffusion
of a tetracaine mixture (60% free base, 40% acid salt) from a vehicle of 70%
propylene glycol and 30% saline is strongly pH dependent (page 110). Tetracaine
flux is equal at pH = 12.2 and pH = 8.5, but negligible at pH = 4.7. This behavior
suggests that tetracaine free base diffuses preferentially to the acid salt.


18
use of a microemulsion or a lyotropic liquid crystalline system can increase the
thermodynamic stability of the drug in the formulation and its penetration into the
skin. There are exceptions which point up the fact that more information on the
effects of these systems is needed.
Uster82 discusses the use of liposome vehicles for topical delivery of drugs.
Liposomes differ from micelles in that the vesicles are defined by bilayers of lipids
(much like cell membranes) and separate the bulk aqueous phase from an entrapped
aqueous phase. Their advantage seems to be their ability to increase the concentra
tion of drug in the skin without increasing the amount of drug entering the receptor
phase or the circulatory system. This effect could be caused by liposomes binding
to the skin surface and releasing their contents there. For small, water soluble
molecules, diffusion through lipid bilayers constitutes the rate-limiting step and the
additional bilayers formed by liposomes significantly inhibit their diffusion.
pH. Diffusion through skin can be affected by pH if the solute is a weak
electrolyte. Changes in pH shift the fractions of acid and base in solution. Since
these two forms of the solute have different properties, they will differ in their ability
to cross the skin barrier.60 Flynn26 hypothesizes that in lipoidal membranes (e.g.,
skin) ionic species will be less favorable in the membrane as compared to the
unionized species. Flynn later confirms this hypothesis experimentally. Therefore,
manipulation of the pH of the vehicle can have a profound effect on the transdermal
diffusion of ionizable substances. ;
i
I
i
i


60 INPUT "File name for results"; FILES
70 INPUT "Time to end integration (hr)"; ENDCALC
71 INPUT "Convergence Tolerance"; CONV
80 INPUT "Step size for integration (sec)"; G
90 INPUT "Printing Interval (# of steps)"; COUNTER%
100 INPUT "Initial Boundary Condition at X=0 (ug/ml)"; Cl
INPUT "Top Concentration Constant (0/1)"; CONSTTOP
110 INPUT "Initial Boundary Condition at X=1 (ug/ml)"; C2
120 INPUT "Minimun Number of Series Terms (over rides convergence
criterion)"; MINI%
130 INPUT "Maximum Number of Series Terms (over rides convergence
criterion)"; MAXI%
INPUT "Diffusion Coefficient (cmA2/s)"; D
INPUT "Skin Thickness Constant (0/1)"; CONSTSKN
INPUT "Dose Volume (ml)"; VI
INPUT "Receptor Volume (ml)"; V2
INPUT "Start Time (Hours after skin in contact with water)"; TIME0
160 DIM TOP(l), BOT(l)
170 TOP(l) = Cl: BOT(l) = C2
180 OPEN "O", #1, FILES + ".prn"
190 IF MAXI% = 0 THEN MAXI% = 200


140
experimental error. The next best model assumes swelling skin and varying donor-
phase concentration (d) and the variance for this case is significantly lower than the
remaining two systems (a and c). This second choice is more in keeping with the
neighboring formulations.
For solutions containing 50% propylene glycol or more, the model shows that
the system is best described by skin swelling and a constant donor-phase concentra
tion. This is consistent with the measured CMCs for these formulations in Chapter
3 (pages 66, 69, and 80). For 40% propylene glycol, the best model is no skin
swelling and constant donor-phase concentration. Closer inspection of the theoretical
curves, however; reveals that they are decreasing in slope (approaching equilibrium)
unlike the continued upward trend of the experimental data. Consequently, the
modelled system most resembling the experimental data at 40% propylene glycol
does not have the lowest variance, it is the same model as for higher propylene glycol
fractions.
In summary, the model suggests that systems of 60% tetracaine free base, 40%
tetracaine acid salt (w/w), in solutions of propylene glycol and saline form micelles
when the propylene glycol fraction is 40% (v/v) or greater. The model also suggests
that skin swelling plays an important role in transdermal diffusion in vitro and may
be accounted for theoretically. To determine whether the skin swelling calculations
in the quasi-steady state model really account for in vitro swelling, the model is
compared to data from a non-swelling system. The effective diffusivities found by
the model are all of order 10'8 to 107 cm2/s. This is approximately two orders of


4
concentration. These simplifications yielded a model in which the flux was
proportional to the donor phase concentration.
Another model that assumed a steady state profile was that of Fleming et
al.25,42 They treated transdermal diffusion in a closed system as a first-order kinetic
process (J = kAC where J = flux, k = overall rate constant or mass transfer
coefficient, and AC = concentration difference across the membrane). The overall
rate constant (k) was assumed to be the result of diffusion through a series of
resistances (stagnant boundary layer/membrane/stagnant boundary layer). This
model predicted an exponential decay of concentration scaled by the ratio of the
compartment volumes.
McDougal et al. used a similar approach to model the absorption of vapors
in the lungs57 and in the skin56 of rats in vivo. Permeability (mass transfer)
coefficients, partition coefficients, and blood flows from experimental data were used
in the model. The use of experimentally measured partition and permeability
coefficients required no theoretical understanding of phase equilibrium or diffusion.
Consequently, the model was able to emulate experimental data, but provided little
insight into the mechanics of percutaneous absorption.
Zatz97 also developed a model that assumed a steady state concentration
profile, but increased its complexity by using multiple resistances in series to
represent the membrane. These additional resistances allowed the model j to more
closely fit experimental data, but did little to increase the fundamental understanding
of transdermal diffusion.


103
Apparent pH
% Propylene Glycol (v/v)
Figure 53: Cumulative flux of tetracaine (60% free base, 40% acid salt w/w) in
propylene glycol and saline through hairless-mouse skin (young mice)
flux in this system corresponds to a vehicle of 40% propylene glycol and 60% saline
(v/v).
In Chapter 3 (page 62), the product of solubility and partition coefficient
(combined solubility-partitioning parameter or KpCsat) is used to predict the relative
flux of tetracaine from vehicles of propylene glycol and saline. Although 1-octanol
and n-octane are vastly different in terms of their affinity for tetracaine, they both
predict the maximum flux at 50% propylene glycol. The accuracy of these earlier
predictions can be assessed by comparing these data with the experimental fluxes
(synthetic membrane and hairless-mouse skin).


71
Figure 23: Conductivity of aqueous tetracaine free base
The conductivity of propylene glycol-saline mixtures decreases as propylene
glycol content increases. This is a result of fewer ions in solution as water is replaced
by propylene glycol. Propylene glycol does not dissociate appreciably in solution so
it is less capable of solvating ions or conducting electricity.
Ultraviolet Spectroscopy
The ultraviolet absorption spectra of the drugs were most important for
maximizing the sensitivity of the HPLC detector. Spectra were obtained over the
range of the HPLC detector and the wavelengths of maximum absorption determined
for the compounds of interest. The absorbance spectra of hydrocortisone,


97
The result of these assumptions is that the driving force for diffusion is now
determined solely by the bulk concentration and partitioning between the solution
and the skin.
Vehicle/stratum corneum partition coefficients are difficult to measure
experimentally so an organic solvent is usually substituted for the skin. This requires
assuming that drug partitioning into the organic solvent is similar to partitioning into
the stratum corneum.
The structure of the skin affects transdermal diffusion. The location, size,
number, and geometry of structures in the skin affect the overall resistance to
diffusion in the skin. The sheer complexity of the skin makes any theoretical
accounting for these structures effects on diffusion almost impossible. Consequently,
the skin is assumed to be homogeneous, devoid of all internal structure, and
characterized by a lumped parameter. Once homogeneity is assumed, the parameters
describing the resistance to diffusion are the thickness of the skin and the overall
diffusivity of the drug within the skin.
Lidocaine Salt
As already mentioned, lidocaine was the first drug used for both in vitro and
in vivo transdermal diffusion experiments. The in vitro experiments involving
lidocaine helped to establish the maximum length of experiments, but lidocaine was
later abandoned in favor of tetracaine for transdermal diffusion.


166
model transdermal diffusion in vitro is determined by the experimental data. Both
models are able to describe the experimental data at a level far below the variation
between individuals. Under most circumstances, meaningful results are achieved
using the quasi-steady state model in less time than the full numerical routine.
%


91
and as soon as the constant temperature circulator reached equilibrium the cells were
assumed to be at equilibrium.
Donor phase
The temperature behavior of all donor phases was estimated using a worst-
case scenario of the most viscous donor phase (pure propylene glycol with 0.36 M
tetracaine) at room temperature. The temperature of the donor phase was
monitored with time using an iron-constantan thermocouple as 37C water circulated
through the cell jacket. The results of the experiment (Figure 45) show that the
temperature of the donor phase reached equilibrium in approximately 3 minutes.
0 5 10 15
Time (min)
Figure 45: Dynamic donor-phase temperature in Franz cell (VD = 2 ml)


136
Time (hr)
Figure 78: Model fits for 60% propyl- Figure 79: Model fits for 60% propyl
ene glycol (young mice #1) ene glycol (young mice #2)
Figure 80: Model fits for 70% propyl- Figure 81: Model fits for 70% propyl
ene glycol (young mice #1) ene glycol (young mice #2)
can shed light on the physical system by answering questions as to whether the skin
is swelling or if the concentration in a micellar solution is constant.
For solutions of saline, 5%, 20%, and 30% propylene glycol (v/v), the best
model assumes skin swelling and varying donor-phase concentration (d). In only one
case was a CMC detected in these systems and its value was very small (0.03 M or


209
73. A. Rougier, C. Lotte, and H.I. Maibach, In Vivo Percutaneous Penetration
of Some Organic Compounds Related to Anatomical Site in Humans:
Predictive assessment by the stripping method, J. Pharm. Sci., 76(6), 451-4
(1987).
74. H. Schaefer, F. Watts, J. Brod, and B. Illel, Follicular penetration, in
Prediction of Percutaneous Penetration Proceedings. April 1989, R.C. Scott,
R.H. Guy, and J. Hadgraft (eds), IBC Technical Services, London, 163-73
(1990).
75. W. Schalla and H. Schaefer, Localization of compounds in different skin
layers and its use as an indicator of percutaneous absorption, in
Percutaneous Absorption: Mechanisms. Methodology. Drug Delivery. R.
Bronaugh and H. Maibach (eds), Marcel Dekker, New York, 281-304
(1985).
76. R.J. Scheuplein, Mechanism of Percutaneous Adsorption: I. Routes of
penetration and the influence of solubility, J. Inv. Derm., 45(5), 334-46,
(1965).
77. R.J. Scheuplein and I.H. Blank, Permeability of the skin, Physiological
Rev., 51(4), 702-47, (1971).
78. K.B. Sloan, The use of solubility parameters of drug and vehicle to
describe skin transport, in Topical Drug Delivery Formulations. D.W.
Osborne and A.H. Amann (eds), Marcel Dekker, New York, 245-70 (1990).
79. K.B. Sloan, S.A.M. Koch, K.G. Siver, and F.P. Flowers, Use of solubility
parameters of drug and vehicle to predict flux through skin, J. Inv. Derm.,
87(2), 244-52 (1986).
80. J. Small, R.G. Wallace, R. Millar, A.D. Woolfson, and D.F. McCafferty,
Pain-free cutting of split skin grafts by application of a percutaneous local
anesthetic cream, Br. J. Plast. Surg., 41(5), 539-43 (1988).
81. U. Tauber, Drug Metabolism in the Skin: Advantages and disadvantages,
in Transdermal Drug Delivery Developmental Issues and Research
Initiatives. J. Hadgraft and R.H. Guy (eds), Marcel Dekker, New York,
(1989).
82. P.S. Uster, Liposome-based vehicles for topical delivery, in Topical Drug
Delivery Formulations. D.W. Osborne and A.H. Amann (eds), Marcel
Dekker, New York, 327-48 (1990).


39
or vehicle solubility in the hydrophobic phase. The partition coefficients for
vehicle*-organic systems were found by means similar to those described for
solubility. Vehicle formulations in contact with an equal volume of the hydrophobic
organic phase were rotated at about 4 rpm for at least 18 hours. Total drug
concentration in the hydrophobic phase relative to that in the vehicle was found by
HPLC.
Surface Tension
All surface tension measurements used in this work were made on a Rosano
Surface Tensiometer Model LG with a Wilhelmy plate. This apparatus has a
platinum plate approximately 1 cm x 3 cm x 0.5 mm attached to one arm of a
milligram balance. The balance is adjusted by adding mass to the other arm equal
to the mass of the platinum plate. With the scale reading zero and the arms of the
balance level, the platinum plate is brought into contact with the surface of a liquid
and is consequently pulled into the bulk of the liquid phase. Mass is added to the
free arm of the balance until the arms of the balance are again level. The mass
required to bring the arms to level is proportional to the surface tension of the
liquid. This instrument was calibrated using water with a known surface tension of
72.4 mN/m. The uncertainty of these measurements is approximately 0.2 mN/m.
*The term vehicle is used here and elsewhere to indicate the mixture of
propylene glycol and water (saline) in which the drug is dissolved.


10.
J.R Bond and B.W. Barry, Hairless mouse skin is limited as a model for
assessing the effects of penetration enhancers in human skin, J. Inv.
Dermatol., 90, 810-3, (1988).
203
11. J.R. Bond and B.W. Barry, Limitations of Hairless Mouse Skin as a Model
for In Vitro Permeation Studies Through Human Skin: Hydration damage,
J. Inv. Dermatol., 90, 486-9, (1988).
12. R.L. Bronaugh and R.F. Stewart, Methods for In Vitro Percutaneous
Absorption Studies III: Hydrophobic compounds, J. Pharm. Sci., 73(9),
1255-8 (1984).
13. R.L. Bronaugh and T.J. Franz, Vehicle Effects on Percutaneous
Absorption: In vivo and in vitro comparisons with human skin, Br. J.
Derm., 115, 1-11, (1986).
14. L. Brown and R. Langer, Transdermal delivery of drugs, Ann. Rev. Med.,
39, 221-9 (1988).
15. D. Campbell and J. Adriani, Absorption of local anesthetics, JAMA,
168(7), 873-7 (1958).
16. H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids. Oxford,
London, (1950).
17. S.K. Chandrasekaran, A.S. Michaels, P.S. Campbell, and J.E. Shaw,
Scopolamine permeation through human skin in vitro, AIChE J., 22(5),
828-32 (1976).
18. Y.W. Chien, Developmental concepts and practice in transdermal
therapeutic systems, in Transdermal Controlled Systemic Medications
Drugs and the Pharmaceutical Series vol. 31, Y.W. Chien (ed), Marcel
Dekker, New York, 25-81 (1987).
19. E.R. Cooper, Vehicle effects on skin penetration, in Percutaneous
Absorption: Mechanisms. Methodology. Drug Delivery. R. Bronaugh and
H. Maibach (eds), Marcel Dekker, New York, 525-30 (1985).
20. E.L. Cussler, Diffusion: Mass Transfer in Fluid Systems. Cambridge,
Cambridge, UK, (1984).
21.
R.H. de Jong, Physiology and Pharmacology of Local Anesthesia. Charles
C. Thomas, Springfield, (1970).


79
Figure 31: HPLC chromatogram of tetracaine
The addition of propylene glycol affects the acid/base equilibrium of the
system. Figure 33 shows the apparent pH versus percent tetracaine base* in
mixtures of propylene glycol and saline. The apparent pKa rises as the amount of
propylene glycol in the solvent increases.* Also, tetracaine is unable to buffer the
solution effectively as the propylene glycol fraction increases (the curves slopes
increase in the buffered region). The inability to buffer the solution may be due to
This value corresponds to the bulk ratio of tetracaine free base and tetracaine
acid salt that would be required to reconstitute the solution (i.e., a dry mixture).
"The apparent pH of propylene glycol-saline solvents (no drug present) also
increases with increasing propylene glycol content and is probably caused by the
electrodes response to propylene glycol.


160
be analyzed for drug content to get a rough estimate of the concentration profile
similar to the method of Dupuis et al.22,71,72


116
% (w/v)
O 20 40 60 80
Figure 60: Dose response for tetracaine free base in 75% propylene glycol and
25% saline (v/v) through human skin in vivo
seems to increase until the concentration reaches approximately 0.3 M. Above
0.3 M, the subjects responses seem to level off, indicating that the maximum rate of
transfer has been achieved. The scatter in the clinical response data makes it
difficult to interpret because the trend is not statistically significant. Furthermore,
the level of analgesia is unsatisfactory (VAS < 5).
The dose response data for a system consisting of 50% tetracaine free base
and 50% acid salt (w/w) in 40% propylene glycol and 60% saline after one hour are
in Figure 61. This preparation gives higher scores than the system containing only
tetracaine free base and the scores increase beyond a tetracaine concentration of
4 M. This preparation achieves a mean VAS of 8.6 at 4.2 M and could be used


Table 12: Full numerical routine summary and comparison to quasi-steady state model,
OS
<1
% PG (v/v)
Mice Group
Swell
CMC
D (cm2/s)
AD%
s (mg/1)
As%
0
OTD
YFS
NO
1.21 xl 07
-41-16
4.00
-4543
n
OTD
YKS
YFS
1.20 x 10'7
-4i 67
4.26
-85.26
n
OTT)
NO
NO
105x10-*
.3 7*
20 44
-6.51
n
OTD
NO
YFS
1.88x10*
-7 14
20.77
16.22
5
OTD
YFS
NO
1.10 x10-7
44 SR
1.59
45.09
5
OTD
YFS
YFS
1.07 x 10"7
.On 40
20.66
6R2
5
OTD
NO
NO
1-51 x 10*
1370 ns
16.69
-676
5
OTD
NO
YFS
5.01 x 10"7
-0.16
12-05
7 61
in
YOUNG
YFS
NO
1.68 x 10'7
-30 R6
45 37
4R4
in
YO! NG
YFS
YFS
1.24x10*
-3R 13
136 52
41.51
in
YOUNG
NO
NO
6.02x10*
-4 35
12.68
1£]
m
0
2
3
0
>-
NO
YFS
9.57 x 10'7
-0.34
73 OR
1.76
70
YOUNG
YFS
NO
1 12 v lo-7
44 46
3R4
-75.12
70
YOl ING
YFS
YFS
5.06 x 10'7
-17.61
73 12
1034
70
YOUNG
NO
NO
1.59x10*
-4 7 A
11.68
-10.49
70
YOI ING
NO
YFS
2.25x10'7
.0 53
11.92
334
70
OTD
YFS
NO
1.02 x 10"7
-45.34
6.79
57 07
70
OT D
YFS
YFS
4.04 x 10'7
*22-32
20.57
8.87.
70
OT D
NO
NO
1.20 x 10*
-4 02
.5.09
-77.59
70
OT D
NO
YFS
1.76 x 10'7
-0.6R
14.04
2.51
7,0
OTD
YFS
NO
8.51x10*
-46 OR
2-80
14 R5
30
OTD
YFS
YFS
7.10x10*
.32 2R
0 76
11.68
3n
OTD
NO
NO
7.58x10*
-4 5R
4 61
-16.47
3n
OTD
NO
YFS
8.90x10*
-0.08
4 01
5.78
4n
YOUNG
YFS
NO
1 81 v 10-7
-3700
74 43
4.00
40
YOT ING
YFS
YFS
8.28x1 O7
-9.21
47 04
10.810
40
YOUNG
NO
NO
1.11x10*
.53 03
.57.71
.3 77
40
YOUNG
NO
YES
1.05 x 10'7
-71.65
21.69
1.25


65
Table 4: Tetracaine (60% free base, 40% acid salt w/w) solubility in propylene
glycol-saline and partitioning between propylene glycol-saline and n-octane
% Propylene
CSat
Kr
KpCsat
Glycol
(M)
(M)
0
1.527
3.77 x 10'3
5.75 x 10-3
10
1.587
4.03 x 10-3
6.39 x 10'3
20
1.591
4.13 x 103
6.57 x lO'3
30
1.632
3.97 x 103
6.48 x 103
40
1.958
3.17 x 103
6.21 x 10'3
50
2.979
3.03 x 10-3
9.01 x 10'3
70
2.757
2.23 x 10-3
6.15 x lO'3
80
2.433
2.21 x 10'3
5.37 x 10'3
90
1.926
3.08 x 10'3
5.92 x 10'3
100
1.817
2.85 x 10'3
5.17 x lO3
strongly surface active and the flattening of the curve at higher concentrations
indicates the presence of micelles at a critical micelle concentration (CMC) of
approximately 0.1 M. This agrees almost identically with the previously published
value of 0.13 M.3
Similar measurements were made for tetracaine base in water (Figure 20).
The surface tension of the tetracaine base solution decreases more rapidly than for
tetracaine HC1, indicating that it is more surface active. The surface tension drops
to about 40 mN/m before the aqueous solubility of tetracaine base is exceeded.
Tetracaine base shows higher surface activity than the HC1 salt, which also appears
to be linked to its lower solubility. The surface tension data indicate that tetracaine


81
Saline
60% PG
% Tetracaine Base (mol/mol)
Figure 33: NaOH titration of tetracaine in propylene glycol and saline
K
o.
C (M)
Figure 34: pH of tetracaine in pro
pylene glycol.
0.00 0.25 0.50 0.75 1.00
C (M)
Figure 35: pH of tetracaine in 80%
propylene glycol and 20% saline (v/v).
on these assumptions, Table 9 lists the CMC of these solutions as measured by
apparent pH versus concentration. With the exception of 20% propylene glycol,


133
path to reach the receptor-phase. If the diffusion is very fast, the drug reaches the
receptor-phase before the skin swells appreciably. In this case, the time lag is
unaffected by skin swelling and the effect of constant donor-phase concentration is
as before.
Tetracaine Diffusion Through Hairless-mouse Skin
The quasi-steady state model is compared to in vitro tetracaine diffusion data
from propylene glycol-saline solutions. The figures on the following pages
(Figure 68-Figure 81) show the experimental data and the best match by the model
assuming:
a: no skin swelling and fixed donor-phase concentration,
b: no skin swelling and variable donor-phase concentration,
c: skin swelling and fixed donor-phase concentration, and
d: skin swelling and variable donor-phase concentration.
When the concentration is held constant, the average CMC as determined in Chapter
3 is used.
To aid interpretation of the data, the total variance* between the model
predictions and experimental data is plotted under the conditions described above
(Figure 82-Figure 95). This format makes it easier to compare the modelling
schemes. Usually, the best modelling scheme is the one that minimizes the variance
*The total variance here is defined as the sum of the squared error and is
equivalent to the experimental variance when divided by the degrees of freedom
(n 1).


37
To compromise between the favorable diffusion characteristics of the base
form and the high aqueous solubility of the salt form, a mixture of the base and salt
forms was used. Such a mixture takes advantage of the tetracaine salt:tetracaine free
base equilibrium. Mixing a drug and its HC1 salt in solution is equivalent to adding
HC1 acid to a preparation containing only free base (or adding NaOH to a
preparation containing only the salt form).21
The properties measured were solubility in the solvents, surface tension as a
function of concentration, conductivity as a function of concentration, ultra violet
absorbance spectra, and HPLC behavior.
Methods
This section presents the procedures common to a number of experiments
beginning with those most likely to be familiar to the reader. Descriptions of the
instruments and techniques used to measure solubility, surface tension, specific
conductivity, and UV spectra are followed by more detailed descriptions of high
pressure liquid chromatography (HPLC), in vitro diffusion of drugs through mounted
mouse skin, and in vivo diffusion of drugs (rat tail flick test and clinical trials with
human volunteers).
I
I


36
evaluate the experimental apparatus. The first experiments using mouse skin in this
project used scopolamine as the diffusing drug because previous work on transdermal
scopolamine17 provided a method for evaluating the performance of the in vitro
transdermal experimental procedure. Scopolamine HC1 (Sigma) was converted to
scopolamine free base by ether-extraction from a caustic solution. Transdermal
scopolamine is available commercially for motion sickness (Transderm-Scop from
Ciba).
Lidocaine was the first choice for a local anesthetic to be administered
transdermally because it is chemically stable during storage, resistant to solvent
attack, unlikely to cause allergic reaction, and widely used clinically as an injected
solution. Lidocaine HC1 (Sigma) was used without further purification. Lidocaine
was abandoned in favor of tetracaine which has better partitioning characteristics and
is approximately ten times more effective as a local anesthetic.
Two forms of tetracaine were used in experiments, tetracaine free base (a
hydrophobic ester) and tetracaine HC1 (a hydrophilic salt of the free base). Both
forms of tetracaine (Sigma) were used as received. Tetracaine base penetrates the
neuron more effectively21, but has very low aqueous solubility. Tetracaine salt,
however, is quite soluble in aqueous solutions (>200 g/1). Tetracaine salt is also
much more stable than the free base which must be kept refrigerated and dry.21
Since tetracaine HC1 is thermally more stable, it can be sterilized and still remain
effective. For transdermal diffusion however, sterility is not so great a concern and
tetracaine base becomes more attractive.


182
300 IF TIME% / COUNTER% = CINT(TIME% / COUNTER%) THEN
LPRINT USING "###.### ######.### #####.####
##.###"; TIME / 3600; TOP(l); BOT(l); L
PRINT #1, USING "###.### ######.### #####.####
##.###"; TIME / 3600; TOP(l); BOT(l); L
IF CONSTSKN = 0 THEN GOSUB 1000CALCULATE SKIN THICKNESS
301 IF TIME / 3600 < ENDCALC THEN TIME = TIME + G: GOTO 241
LPRINT : LPRINT : LPRINT
340 END
350 Evaluate Series
351 IF TIME = G THEN BOTSER = -Cl / 2: TOPSER = -Cl: RETURN
360 TOPSER = 0: BOTSER = 0: LASTTOP = 0: LASTBOT = 0: N% = 0
370 N% = N% + 1
380 LASTTOP = TOPSER: LASTBOT = BOTSER
390 EXPONENT = EXP(-N% A 2 (TIME G) D PI# A 2 / L A 2)
400 TOPSER = TOPSER + ((-1) A N% BOT(O) TOP(O)) EXPONENT
410 BOTSER = BOTSER + ((-1) A N% TOP(O) BOT(O)) EXPONENT
420 IF N% = 1 THEN 370
430 IF (ABS((TOPSER LASTTOP) / LASTTOP) > CONV OR
ABS((BOTSER LASTBOT) / LASTBOT) > CONV OR N% < MINI%)
AND N% < MAXI% THEN 370
440 RETURN


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
INTERFACIAL, DIFFUSIONAL, THEORETICAL,
AND CLINICAL ASPECTS OF TOPICAL,
LOCAL ANESTHETIC FORMULATIONS
By
Kenneth James Miller II
December 1991
Chairperson: Dinesh O. Shah
Major Department: Department of Chemical Engineering
In general, local anesthetics do not penetrate the skin. There is considerable
need for a formulation that can allow the transdermal delivery of local anesthetics.
Using a combination of the salt and base forms of tetracaine as well as mixed
solvents of saline and propylene glycol, several compositions were developed that are
effective in the transdermal delivery of local anesthetics. Solubilization behavior and
diffusion through excised hairless-mouse skin of the salt and base forms of tetracaine
were studied in detail. The permeability behavior of the drug through the skin as a
function of several variables such as time, stirring rate, drug concentration, and
propylene glycol concentration were investigated. The results show that the mixed
solvents intricately influence the solubilization of the base form of the drug as well
as its partitioning into the skin.
XVII


CHAPTER 1
INTRODUCTION
This chapter has two sections: literature review and specific objectives. The
literature review discusses current transdermal research. The latter section of this
chapter is a list of specific objectives for this project.
Literature Review
The literature review for this project covers theoretical background, diffusion
through synthetic barriers, and diffusion through biological membranes. The
theoretical background discusses diffusion through membranes in general, and then
transdermal diffusion specifically. Diffusion through synthetic barriers discusses both
unsupported and supported barriers as analogues of skins resistance to diffusion.
Diffusion through biological membranes discusses the use of skin to study
transdermal diffusion.
Theoretical Development
The review of past theoretical work pertaining to transdermal diffusion is
divided into two parts. The first section reviews the theory surrounding diffusion
through membranes. Readers familiar with Ficks laws of diffusion may skip this
1


CHAPTER 3
PHYSICAL PROPERTIES OF DRUG FORMULATIONS
This chapter discusses the physical properties of the tetracaine acid salt, free
base, saline, propylene glycol system as measured by the experimental methods
described in the previous chapter (pages 37-44). The solubility, lipid-phase
partitioning of tetracaine were studied to estimate the transdermal diffusion of
tetracaine formulations. The surface tension, conductivity, acid-base behavior, and
quasi-elastic light scattering of tetracaine were studied to determine to microscopic
structure of the formulations. Ultraviolet absorbance and liquid chromatography
were used to quantitatively determine drug concentrations and the thermal
breakdown characteristics were studied to estimate shelf life of the anesthetic
formulations.
Tetracaine Solubility in Propylene Glycol-water Solvents
Figure 14 shows measured solubilities of tetracaine salt, tetracaine base, and
a 40% acid salt, 60% free base mixture (w/w) in propylene glycol-water solvents.*
The solubility of tetracaine base in aqueous solution is negligible. Adding propylene
*This particular mixture was chosen because at this bulk ratio (mixing tetracaine
free base and acid salt powders) the solution is near the published pK* (8.5).21 The
significance of a solution at its pKa is that there are equal amounts of ionized and
unionized solute.
57


60
for systems containing more than 60% propylene glycol could not be evaluated using
octanol.
Partitioning into 1-octanol
The partitioning of a 60% tetracaine free base, 40% tetracaine acid salt
mixture between propylene glycol-water solutions and 1-octanol (CH3-(CH2)7-OH)
Table 1: Tetracaine (60% free base, 40% acid salt w/w) equilibrium concentra
tions and partitioning into 1-octanol
% Propylene
^-"Vehicle
c
'-'Octanol
Kr
Glycol
(M)
(M)
0
3.59 x 10-3
2.29 x 10'2
6.37
20
3.99 x 10-3
2.22 x 10'2
5.55
40
3.87 x 10-3
2.05 x 102
5.30
50
3.99 x 10'3
1.99 x 10-2
4.99
60
3.57 x 10-3
1.70 x IQ'2
4.75
declines linearly as the organic content of the vehicle increases (Table 1, Figure 15).
At approximately 70% propylene glycol the system of 1-octanol/saline/propylene
glycol no longer develops an interface. Therefore, at high propylene glycol
concentrations, partitioning behavior cannot be assessed. To simulate the
partitioning behavior of tetracaine into a lipid phase at higher propylene glycol
i
concentrations, a more hydrophobic oil phase is required.


CHAPTER 4
DRUG DIFFUSION IN VITRO
Calibration
The diffusion of solubilized drugs through skin was measured with procedures
already outlined (page 45). The results of these experiments are presented in two
parts: calibration experiments and the diffusion of local anesthetics through mounted
mouse skin.
The calibration experiments served many purposes such as locating difficulties
in the experimental procedure and the relative effects of different parameters on the
flux of drugs through skin and porous membranes. The factors studied through these
calibration experiments were stirring rate, the behavior of skin relative to a synthetic
membrane, the temperature behavior of the system, and the effect of hydration and
swelling of the skin.
Stirring Effects Using Synthetic Membranes
The first diffusion experiments involved the diffusion of aqueous hydrocorti
sone through a synthetic, microporous, polycarbonate membrane (nominal pore
diameter of 0.22 /im). This system was chosen because both the drug and the
membrane had been well characterized by previous investigators49 and the materials
86


34
Propylene glycol is widely considered to be a penetration enhancer for the
percutaneous absorption of various drugs.32,50,69,87 The effect of propylene glycol on
the diffusion of the drugs in this study, however, is complex.
All solvents used in the HPLC (high pressure liquid chromatograph) were
prepared from HPLC grade solvents from Fisher Scientific. Methanol (CH3OH) and
acetonitrile (CH3CN) were used as received and phosphoric-acid buffer was prepared
in the laboratory from HPLC grade water and HPLC grade phosphoric acid (H3P04).
The solution was buffered to pH 3 using ACS grade KOH from Fisher Scientific.
The HPLC solvent mix used to analyze the local anesthetics was essentially that
recommended in the Supelco chromatography catalog for lidocaine, but altered to
decrease the retention time of the drugs. Resolution of components was not a
concern in this analysis since the drugs were the only components which eluted from
the HPLC.
Local Anesthetics
Four drugs were used in this project. The majority of the diffusion through
skin experiments used tetracaine (a local anesthetic). Hydrocortisone, scopolamine,
and lidocaine were used for calibration or preliminary experiments and to test the
experimental procedure for measuring diffusion through skin. Figure 2 contains
schematic representations of these drugs. The diffusion of hydrocortisone through
synthetic membranes has been studied previously.49 Diffusion of hydrocortisone
i
j
(from Sigma and used as received) through synthetic membranes was used to


For everyone whos wondered what Ive been doing lately.


90
Receptor phase and constant temperature circulator
The warm-up behavior of the temperature controller and the receptor phase
of the diffusion cells was investigated to determine whether the time required for the
Uncapped
Capped
Time (min)
Figure 44: Dynamic receptor phase temperature in Franz cell
diffusion apparatus to come to thermal equilibrium (ready for drug application)
would be restrictive. The temperature of the lower (receptor) phase was monitored
as a function of time for both capped and uncapped cells as the circulator was turned
on (Figure 44). These data show that the receptor phase reached thermal
equilibrium in 10 to 15 minutes with a temperature difference of approximately 3.5C
(capped). In practice, the circulator would be at room temperature as well, so the
shorter time required for the cells to reach equilibrium was not considered a factor


Figure 53: Cumulative flux of tetracaine (60% free base, 40% acid salt
w/w) in propylene glycol and saline through hairless-mouse skin
(young mice) 103
Figure 54: Cumulative flux of tetracaine (60% free base, 40% acid salt
w/w) in propylene glycol and saline through hairless-mouse skin (old
mice) 105
Figure 55: Effect of 0.1 % (w/w) formaldehyde on the diffusion of
tetracaine (60% free base, 40% acid salt w/w, 0.36M tetracaine
overall) in 40% propylene glycol and 60% saline (v/v) through old
hairless-mouse skin 106
Figure 56: Effect of formaldehyde location on the diffusion of tetracaine
(60% free base, 40% acid salt w/w, 0.36M tetracaine overall) in 40%
propylene glycol and 60% saline (v/v) through old hairless-mouse
skin 108
Figure 57: Effect of drug concentration on the diffusion of tetracaine (60%
free base, 40% acid salt w/w) in 40% propylene glycol and 60% saline
(v/v) through hairless-mouse skin 109
Figure 58: Effect of pH on the diffusion of tetracaine (60% free base, 40%
acid salt w/w, 0.36M tetracaine overall) in 40% propylene glycol and
60% saline (v/v) through young hairless-mouse skin 110
Figure 59: Effect of alcohol cleansing on the diffusion of tetracaine (60%
free base, 40% acid salt w/w) in 40% propylene glycol and 60% saline
(v/v) through human skin in vivo 115
Figure 60: Dose response for tetracaine free base in 75% propylene glycol
and 25% saline (v/v) through human skin in vivo 116
Figure 61: Dose response for 50% tetracaine free base and 50% acid salt
(w/w) in 40% propylene glycol and 60% saline (v/v) through human
skin in vivo J . 117
Figure 62: Dose response for 60% tetracaine free base 40% acid salt
(w/w) in 40% propylene glycol and 60% saline (v/v) through human
skin in vivo 118
Figure 63: Time response for in vivo analgesia by tetracaine (60% free
base, 40% acid salt w/w in 40% propylene glycol and 60% saline (v/v)
(1.1 M, 1.8 M) 119
xiv


11
literature is organized in this way to present general findings first and then focus
more closely on aspects directly related to this study.
In vitro cell geometry
The design of an in vitro transdermal diffusion cell affects not only its ability
to mimic in vivo conditions, but also the ease of using the device. Almost all in vitro
transdermal diffusion experiments are done with either vertical or horizontal
transdermal diffusion cells31 (orientation refers to the direction of diffusion).
Gummer31 states that horizontal cells are easier to stir than vertical cells. The upper
phase in a vertical cell is open to the atmosphere and the skin forms its base so a
stirring magnet in the upper phase would rest on the skin. The donor-phase volume
in a vertical cell can be varied from bare coverage of the skin to the capacity of the
upper compartment. The use of the horizontal cell, however, requires the skin to be
fully immersed in a liquid phase and thus fixes the volumes of both receptor and
donor phases. The fact that the donor phase in a vertical cell is not usually jacketed
also complicates any attempt at temperature control.
Membrane effects
Variation in the experimental system such as the source of the membrane and
degree of hydration can profoundly affect transdermal diffusion. Figure 1 is a very
general schematic of skin structure for reference to the following material. The
permeability of human skin can vary as much from person to person as from place
to place on a given individual.4 The structure and physical properties of the stratum
corneum have been studied and described in detail.2428,6377,84 Variation in stratum


129
Donor
Receptor
Dimensionless Time
Figure 66: Predicted donor- and receptor-phase concentrations (4\/4>2 = 7)
stratified, then the model may easily be modified to include a series of layers in
which the drug has different diffusivities. Each layer is then described by the same
equations (Equations 6, 17, and 18) and shares boundary conditions with adjacent
layers. Another possible view of skin structure is as mortar and bricks. In this case,
diffusion occurs through different media simultaneously and some diffusion
resistances are in parallel while others are in series. This case, although not
impossible to model, presents significant difficulties. Since drug diffusivities are
unavailable for various regions within the skin, the approach here is to adopt an
effective or apparent diffusivity resulting from diffusion in several layers.


172
ITER% = 1
10 GOSUB 500 ESTIMATE DIFFUSION COEFFICIENT
IF ABS(DEST D) / D < DIFCONV THEN 99
LSTD = D
D = DEST
LSTVAR = VARIANCE
GOSUB 200 INTEGRATION AND VARIANCE
ITER% = ITER% + 1
IF DEST > MID(0) THEN
TEMP(0) = LOW(O)
TEMP(l) = LOW(l)
LOW(O) = MID(0)
LOW(l) = MID(l)
MID(0) = DEST
MID(l) = VARIANCE
ELSE TEMP(0) = HIGH(0)
TEMP(l) = HIGH(l)
HIGH(0) = MID(0)
HIGH(l) = MID(l)
MID(0) = DEST
MID(l) = VARIANCE


CHAPTER 5
DRUG DIFFUSION IN VIVO
Rat Tail-flick Test
Many compounds were tested using the rat tail-flick test, however only a few
are significant to this project. Formulations of lidocaine and tetracaine showed, as
a whole, little ability to cause analgesia in the rat tails. Specifically, most compounds
tested could not produce a significant delay of the tail-flick response (the rat tail-flick
test is described in Chapter 2, page 51).
Twenty-eight different rat tail-flick tests were conducted. The best ten
compounds, those that caused the longest delay of the rat tail-flick response, are
listed in Table 10. For some general anesthetic applications, an infinite delay of the
tail flick response may be observed (complete loss of sensation). Some solutions
referred to in Table 10 did not give consistent results. Furthermore, neither the
aqueous tetracaine HC1 solutions nor the lidocaine HC1 microemulsions rank
themselves by their concentrations. The discrepancy may result from anatomical
differences like density of nerve cells, blood flow, fat content, and temperature.
However, the rat tail-flick test does generally rank tetracaine formulations above
lidocaine formulations. Furthermore, a solution similar to the formulation found to
be optimal in in vitro studies (50% propylene glycol, 50% saline with 62.5%
111


LIST OF TABLES
Table 1: Tetracaine (60% free base, 40% acid salt w/w) equilibrium
concentrations and partitioning into 1-octanol 60
Table 2: Tetracaine (60% free base, 40% acid salt w/w) equilibrium
concentrations and partitioning into n-octane 62
Table 3: Tetracaine (60% free base, 40% acid salt w/w) solubility in
propylene glycol-saline and partitioning between propylene glycol-
saline and 1-octanol 64
Table 4: Tetracaine (60% free base, 40% acid salt w/w) solubility in
propylene glycol-saline and partitioning between propylene glycol-
saline and n-octane 65
Table 5: Critical micelle concentrations of tetracaine (60% free base,
40% acid salt w/w) in propylene glycol and saline as measured by
surface pressure 70
Table 6: Critical micelle concentration of tetracaine (60% free base, 40%
acid salt w/w) in propylene glycol and saline as measured by
conductivity 73
Table 7: Ultraviolet absorbance maxima of drugs 74
Table 8: Approximate HPLC retention times of drugs 77
Table 9: Critical micelle concentration of tetracaine (60% free base, 40%
acid salt w/w) in propylene glycol and saline as measured by pH .... 82
Table 10: Best rat tail-flick test results 112
Table 11: Clinical trials of lidocaine preparations J. 114
Table 12: Full numerical routine summary and comparison to quasi-steady
state model 167
x


support." (monetary and otherwise). To my sister, I can say, "Lets go for a ride."
And, to my niece, I can finally say, "Hello, Im Uncle Ken."
This is the second time I have tried to thank Donna for her help in the
acknowledgements of a thesis. Even now, I sit at her computer typing what will be
the last few words of my dissertation. Words, however, cannot acknowledge the help
she has given me or my gratitude to her, but now its my turn to help her.
v


BIOGRAPHICAL SKETCH
Kenneth Miller II received his B.S. in chemical engineering from Carnegie
Mellon University in 1986 with special emphasis on colloid, polymer, and surface
sciences. During the summers of 1982-1985, Mr. Miller worked at the Pittsburgh
Energy Technology Center (Department of Energy) on characterization of
regional coals, zeolite reduction catalysis, and process design. He received his
M.S. in chemical engineering from West Virginia University in 1988. While at
West Virginia University, Mr. Miller worked at the Fluidized Bed Research
Center on small-particle force measurement and correlation in glass bead/air
systems.
Kenneth Miller received his Ph.D. in chemical engineering from the
University of Florida (departments of chemical engineering and anesthesiology)
under Professor D.O. Shah in 1991.
212


INTERFACIAL, DIFFUSIONAL, THEORETICAL,
AND CLINICAL ASPECTS OF TOPICAL,
LOCAL ANESTHETIC FORMULATIONS
By
KENNETH JAMES MILLER II
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1991

Copyright 1991
by
Kenneth James Miller II

For everyone whos wondered what Ive been doing lately.

ACKNOWLEDGEMENTS
There are so many people and organizations without whom much of this work
would not exist that it is difficult to acknowledge them without creating a second
dissertation. Chief among these is, of course, Professor Shah. Professor Shah and
I have now worked together some three and a half years and I am convinced that no
one has a better "feel" for the subject of surface science. Professor Westermann-
Clark has also been invaluable in this work, and I will always remember him as the
ingenious, "chewing gum and bailing wire" influence. Professor Goodwin has been
instrumental in helping me understand much of the medical jargon permeating this
field and will always remain for me, a selfless individual who manages to wear more
hats than I can count. Professor Sloan has taught me much more than the procedure
of in vitro diffusion and is another tireless researcher whom I can never hope to
mimic. When Professor Park and I were introduced, I was amazed that he knew so
much about my work at West Virginia and impressed that he took such an interest
in me so early in my graduate career. Thank you all.
I am also immensely grateful to the members of my family (whom I have not
seen in a long time). To my mother, I can finally say "now" for all the times she has
asked, "When will you be graduating?". To my father, I can say, "Thank you for your
IV

support." (monetary and otherwise). To my sister, I can say, "Lets go for a ride."
And, to my niece, I can finally say, "Hello, Im Uncle Ken."
This is the second time I have tried to thank Donna for her help in the
acknowledgements of a thesis. Even now, I sit at her computer typing what will be
the last few words of my dissertation. Words, however, cannot acknowledge the help
she has given me or my gratitude to her, but now its my turn to help her.
v

TABLE OF CONTENTS
ACKNOWLEDGEMENTS iv
LIST OF TABLES x
LIST OF FIGURES xi
ABSTRACT xvii
CHAPTERS
1 INTRODUCTION 1
Literature Review 1
Theoretical Development 1
Diffusion Through Synthetic Barriers 7
Transport Through Biological Membranes 10
Differences between in vitro and in vivo systems 22
Specific Objectives 29
Topical Local Anesthetic 29
Theoretical Modelling 30
2 MATERIALS AND METHODS 33
Materials 33
Solvents 33
Local Anesthetics 34
Methods 37
Solubility 38
Titration 38
Thermal Breakdown of Tetracaine 38
Drug Partitioning 38
Surface Tension 39
Skin Swelling 40
Conductivity 40
Ultraviolet Spectrometry 41
vi

High Pressure Liquid Chromatography (HPLC) 41
Quasi-elastic Light Scattering 44
In Vitro Diffusion Through Mounted Mouse Skin 45
In Vivo Diffusion 51
3 PHYSICAL PROPERTIES OF DRUG FORMULATIONS 57
Tetracaine Solubility in Propylene Glycol-water Solvents 57
Partition Coefficient of Tetracaine from Propylene Glycol-Water
Solvents 59
Partitioning into 1-octanol 60
Partitioning into N-octane 61
Surface Tension of Tetracaine Formulations 63
Conductivity 68
Ultraviolet Spectroscopy 71
Chromatography 74
Equilibrium Phenomena 76
Quasi-elastic Light Scattering 82
Thermal Breakdown of Tetracaine 84
4 DRUG DIFFUSION IN VITRO 86
Calibration 86
Stirring Effects Using Synthetic Membranes 86
Temperature Behavior of Diffusion Apparatus 89
Skin Swelling 92
Scopolamine Diffusion 93
Transdermal Diffusion of Local Anesthetics 96
Theoretical Considerations 96
Lidocaine Salt 97
Diffusion of Tetracaine 99
5 DRUG DIFFUSION IN VIVO Ill
Rat Tail-flick Test Ill
Clinical Trials 113
Lidocaine 113
Tetracaine 113
6 THEORY 121
Idealized System 122
Model Derivation 124
Inclusion of Skin Swelling In Vitro 130
vii

Results 131
General Behavior of Model 132
Tetracaine Diffusion Through Hairless-mouse Skin 133
Diffusion of Hydrocortisone Through Synthetic Membranes . 141
Concentration Profile Within the Skin 143
7 CONCLUSIONS 145
Physical Properties of Drug Formulations 145
Solubility 145
Partitioning and Solubility 145
Surface Activity 146
Micelle Size 147
Thermal Breakdown 147
Drug Diffusion In Vitro 148
Stirring 148
Temperature Behavior of Franz Diffusion Cells 148
Skin Swelling 149
Skin Longevity 150
Effect of Propylene Glycol 150
Effect of Age 151
Effect of Formaldehyde 151
Effect of Concentration 152
Effect of pH 152
Drug Diffusion In Vivo 153
Rat Tail-flick Test 153
Clinical Trials 153
Theory 154
Quasi-steady State Model 154
Full Numerical Routine 154
8 RECOMMENDATIONS FOR FUTURE WORK 156
Physical Properties 156
Diffusion Experiments 157
Theoretical Modelling 158
Clinical Studies 159
APPENDICES
A DERIVATION OF THE FULL NUMERICAL ROUTINE 161
B COMPUTER PROGRAMS 169
Vlll

VARFIT.BAS 170
ENDVALUS.BAS 179
PROFILE.BAS 183
FNR.BAS 191
REFERENCES 202
BIOGRAPHICAL SKETCH 212
ix

LIST OF TABLES
Table 1: Tetracaine (60% free base, 40% acid salt w/w) equilibrium
concentrations and partitioning into 1-octanol 60
Table 2: Tetracaine (60% free base, 40% acid salt w/w) equilibrium
concentrations and partitioning into n-octane 62
Table 3: Tetracaine (60% free base, 40% acid salt w/w) solubility in
propylene glycol-saline and partitioning between propylene glycol-
saline and 1-octanol 64
Table 4: Tetracaine (60% free base, 40% acid salt w/w) solubility in
propylene glycol-saline and partitioning between propylene glycol-
saline and n-octane 65
Table 5: Critical micelle concentrations of tetracaine (60% free base,
40% acid salt w/w) in propylene glycol and saline as measured by
surface pressure 70
Table 6: Critical micelle concentration of tetracaine (60% free base, 40%
acid salt w/w) in propylene glycol and saline as measured by
conductivity 73
Table 7: Ultraviolet absorbance maxima of drugs 74
Table 8: Approximate HPLC retention times of drugs 77
Table 9: Critical micelle concentration of tetracaine (60% free base, 40%
acid salt w/w) in propylene glycol and saline as measured by pH .... 82
Table 10: Best rat tail-flick test results 112
Table 11: Clinical trials of lidocaine preparations J. 114
Table 12: Full numerical routine summary and comparison to quasi-steady
state model 167
x

LIST OF FIGURES
Figure 1: General schematic of skin structure 12
Figure 2: Molecular structure of hydrocortisone, scopolamine, lidocaine,
and tetracaine 35
Figure 3: Schematic of high pressure liquid chromatograph 42
Figure 4: Sacrifice of hairless mouse 46
Figure 5: Securing hairless mouse 47
Figure 6: First incision 48
Figure 7: Second incision 49
Figure 8: Mounting skin to cell cap 50
Figure 9: Franz diffusion cell 51
Figure 10: Schematic of rat tail Flick-o-meter 52
Figure 11: Application of drug formulation to skin patch 54
Figure 12: Skin patch on arm of volunteer 55
Figure 13: Testing response of volunteer to pain stimulus 56
Figure 14: Tetracaine solubility in propylene glycol and saline 58
Figure 15: Tetracaine (60% free base, 40% acid salt w/w) partitioning into
1-octanol 61
Figure 16: Tetracaine (60% free base, 40% acid salt w/w) partitioning into
n-octane 63
Figure 17: Product of 1-octanol partitioning and solubility data 64
xi

Figure 18: Product of n-octane partitioning and solubility data 66
Figure 19: Surface tension of aqueous tetracaine acid salt 67
Figure 20: Surface tension of aqueous tetracaine free base 68
Figure 21: Surface pressure of tetracaine (60% free base, 40% acid salt
w/w) in propylene glycol and saline 69
Figure 22: Conductivity of aqueous tetracaine acid salt 70
Figure 23: Conductivity of aqueous tetracaine free base 71
Figure 24: Conductivity of tetracaine (60% free base, 40% acid salt w/w)
in propylene glycol and saline 72
Figure 25: Ultraviolet absorbance spectrum of hydrocortisone 73
Figure 26: Ultraviolet absorbance spectrum of scopolamine 74
Figure 27: Ultraviolet absorbance spectrum of lidocaine 75
Figure 28: Ultraviolet absorbance spectrum of tetracaine 76
Figure 29: HPLC chromatogram of scopolamine 77
Figure 30: HPLC chromatogram of lidocaine 78
Figure 31: HPLC chromatogram of tetracaine 79
Figure 32: NaOH titration of aqueous tetracaine 80
Figure 33: NaOH titration of tetracaine in propylene glycol and saline ... 81
Figure 34: pH of tetracaine in propylene glycol 81
Figure 35: pH of tetracaine in 80% propylene glycol and 20% saline
(v/v) 81
Figure 36: pH of tetracaine in 60% propylene glycol and 40% saline
(v/v) 82
Figure 37: pH of tetracaine in 40% propylene glycol and 60% saline
(v/v) 82
xii

Figure 38: pH of tetracaine in 20% propylene glycol and 80% saline
(v/v) 83
Figure 39: pH of tetracaine in saline 83
Figure 40: Micelle diameter of tetracaine (60% free base, 40% acid salt,
0.36 M) in propylene glycol and saline by QELS 83
Figure 41: Thermal breakdown of tetracaine (60% free base, 40% acid salt
w/w) in 40% propylene glycol, 60% saline (v/v) 85
Figure 42: Effect of stirring device on the diffusion of aqueous
hydrocortisone through synthetic membranes 88
Figure 43: Effect of stirring rate on the diffusion of aqueous hydrocortisone
through synthetic membranes 89
Figure 44: Dynamic receptor phase temperature in Franz cell 90
Figure 45: Dynamic donor-phase temperature in Franz cell (VD = 2 ml) 91
Figure 46: Dynamic swelling of excised hairless-mouse skin immersed in
water 92
Figure 47: Diffusion of aqueous scopolamine through fresh and chemically
preserved hairless-mouse skin 94
Figure 48: Comparison of experimental scopolamine diffusion data to data
of Chandrasekaran et al 95
Figure 49: Long-term diffusion of aqueous lidocaine salt through untreated
hairless-mouse skin 98
Figure 50: Effect of propylene glycol on the diffusion of lidocaine salt
through untreated hairless-mouse skin 99
Figure 51: Effect of propylene glycol on the diffusion of tetracaine HC1
through hairless-mouse skin 100
Figure 52: Effect of propylene glycol on the diffusion of tetracaine (60%
free base, 40% acid salt w/w) through synthetic polycarbonate
membranes 102
Xlll

Figure 53: Cumulative flux of tetracaine (60% free base, 40% acid salt
w/w) in propylene glycol and saline through hairless-mouse skin
(young mice) 103
Figure 54: Cumulative flux of tetracaine (60% free base, 40% acid salt
w/w) in propylene glycol and saline through hairless-mouse skin (old
mice) 105
Figure 55: Effect of 0.1 % (w/w) formaldehyde on the diffusion of
tetracaine (60% free base, 40% acid salt w/w, 0.36M tetracaine
overall) in 40% propylene glycol and 60% saline (v/v) through old
hairless-mouse skin 106
Figure 56: Effect of formaldehyde location on the diffusion of tetracaine
(60% free base, 40% acid salt w/w, 0.36M tetracaine overall) in 40%
propylene glycol and 60% saline (v/v) through old hairless-mouse
skin 108
Figure 57: Effect of drug concentration on the diffusion of tetracaine (60%
free base, 40% acid salt w/w) in 40% propylene glycol and 60% saline
(v/v) through hairless-mouse skin 109
Figure 58: Effect of pH on the diffusion of tetracaine (60% free base, 40%
acid salt w/w, 0.36M tetracaine overall) in 40% propylene glycol and
60% saline (v/v) through young hairless-mouse skin 110
Figure 59: Effect of alcohol cleansing on the diffusion of tetracaine (60%
free base, 40% acid salt w/w) in 40% propylene glycol and 60% saline
(v/v) through human skin in vivo 115
Figure 60: Dose response for tetracaine free base in 75% propylene glycol
and 25% saline (v/v) through human skin in vivo 116
Figure 61: Dose response for 50% tetracaine free base and 50% acid salt
(w/w) in 40% propylene glycol and 60% saline (v/v) through human
skin in vivo J . 117
Figure 62: Dose response for 60% tetracaine free base 40% acid salt
(w/w) in 40% propylene glycol and 60% saline (v/v) through human
skin in vivo 118
Figure 63: Time response for in vivo analgesia by tetracaine (60% free
base, 40% acid salt w/w in 40% propylene glycol and 60% saline (v/v)
(1.1 M, 1.8 M) 119
xiv

Figure 64: Time response for in vivo analgesia by tetracaine (60% free
base, 40% acid salt w/w) in 40% propylene glycol and 60% saline
(v/v) (0.036 M 1.004 M) 120
Figure 65: Schematic of idealized system 123
Figure 66: Predicted donor- and receptor-phase concentrations
(V*2 = 7) 129
Figure 67: Predicted concentration profile within skin 130
Figure 68: Model fits for saline (old mice) 134
Figure 69: Model fits for 5% propylene glycol (old mice) 134
Figure 70: Model fits for 10% propylene glycol (young mice) 134
Figure 71: Model fits for 20% propylene glycol (young mice) 134
Figure 72: Model fits for 20% propylene glycol (old mice) 135
Figure 73: Model fits for 30% propylene glycol (old mice) 135
Figure 74: Model fits for 40% propylene glycol (young mice) 135
Figure 75: Model fits for 40% propylene glycol (old mice) 135
Figure 76: Model fits for 50% propylene glycol (young mice) 135
Figure 77: Model fits for 50% propylene glycol (old mice) 135
Figure 78: Model fits for 60% propylene glycol (young mice #1) 136
Figure 79: Model fits for 60% propylene glycol (young mice #2) 136
Figure 80: Model fits for 70% propylene glycol (young mice #1) 136
Figure 81: Model fits for 70% propylene glycol (young mice #2) 136
Figure 82: Model variance for saline (old mice) 137
Figure 83: Model variance for 5% propylene glycol (old mice) 137
i
Figure 84: Model variance for 10% propylene glycol (old mice) 137
xv

Figure 85:
Model
Figure 86:
Model
Figure 87:
Model
Figure 88:
Model
Figure 89:
Model
Figure 90:
Model
Figure 91:
Model
Figure 92:
Model
Figure 93:
Model
Figure 94:
Model
Figure 95:
Model
Figure 96:
Model
Figure 97:
Model
Figure 98:
Model
Figure 99:
Model
Figure 100:
Model
Figure 101:
Model
variance for 20% propylene glycol (young mice)
variance for 20% propylene glycol (old mice)
variance for 30% propylene glycol (old mice)
variance for 40% propylene glycol (young mice)
variance for 40% propylene glycol (old mice)
variance for 50% propylene glycol (young mice)
variance for 50% propylene glycol (old mice)
variance for 60% propylene glycol (young mice #1)
variance for 60% propylene glycol (young mice #2) . .
variance for 70% propylene glycol (young mice #1)
variance for 70% propylene glycol (young mice #2) . .
fits for hydrocortisone in a stagnant cell
fits for hydrocortisone in a poorly stirred cell
fits for hydrocortisone in a well-stirred cell
variance for hydrocortisone in a stagnant cell
variance for hydrocortisone in a poorly-stirred cell
variance for hydrocortisone in a well-stirred cell
137
137
137
138
138
138
138
138
138
139
139
141
141
142
142
142
142
xvi

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
INTERFACIAL, DIFFUSIONAL, THEORETICAL,
AND CLINICAL ASPECTS OF TOPICAL,
LOCAL ANESTHETIC FORMULATIONS
By
Kenneth James Miller II
December 1991
Chairperson: Dinesh O. Shah
Major Department: Department of Chemical Engineering
In general, local anesthetics do not penetrate the skin. There is considerable
need for a formulation that can allow the transdermal delivery of local anesthetics.
Using a combination of the salt and base forms of tetracaine as well as mixed
solvents of saline and propylene glycol, several compositions were developed that are
effective in the transdermal delivery of local anesthetics. Solubilization behavior and
diffusion through excised hairless-mouse skin of the salt and base forms of tetracaine
were studied in detail. The permeability behavior of the drug through the skin as a
function of several variables such as time, stirring rate, drug concentration, and
propylene glycol concentration were investigated. The results show that the mixed
solvents intricately influence the solubilization of the base form of the drug as well
as its partitioning into the skin.
XVII

There have been many models proposed which attempt to predict the
diffusion of substances through the skin. The major assumption made in most of
these models is a steady state or linear concentration profile within the skin. A new
model was developed which avoids the limiting assumptions of previous work and
allows the prediction of concentration within the skin as well as flux through the skin
at any time. This model has been successfully used for the prediction of tetracaine
diffusion from topical preparations through mounted hairless-mouse skin. In
addition, this model can account for the swelling of the excised skin as a function of
time immersed in saline. This model could also be easily adapted, through minor
modifications, to predict diffusion through skin in vivo.
xvm

CHAPTER 1
INTRODUCTION
This chapter has two sections: literature review and specific objectives. The
literature review discusses current transdermal research. The latter section of this
chapter is a list of specific objectives for this project.
Literature Review
The literature review for this project covers theoretical background, diffusion
through synthetic barriers, and diffusion through biological membranes. The
theoretical background discusses diffusion through membranes in general, and then
transdermal diffusion specifically. Diffusion through synthetic barriers discusses both
unsupported and supported barriers as analogues of skins resistance to diffusion.
Diffusion through biological membranes discusses the use of skin to study
transdermal diffusion.
Theoretical Development
The review of past theoretical work pertaining to transdermal diffusion is
divided into two parts. The first section reviews the theory surrounding diffusion
through membranes. Readers familiar with Ficks laws of diffusion may skip this
1

2
material. The second section is a more detailed account of theoretical transdermal
diffusion.
Diffusion through membranes
Membrane diffusion is controlled by three basic effects: osmotic pressure,
solute diffusion, and fluid flow.20 In transdermal diffusion there are no osmotic
pressure effects because all species can diffuse through the membrane. Equilibrium
is approached through solute diffusion and solvent flow through the membrane
(solvent diffusion). Consequently, there is diffusion in both directions as the system
approaches equilibrium, with all components moving from higher concentration to
lower concentration.
This process can be described mathematically by Ficks laws of diffusion.
Ficks first law of diffusion states that flux is proportional to the concentration
gradient and the constant of proportionality is defined as the diffusivity.7
JA = ~DAB VCA 1
JA = Molar flux of component A
Dab = Molar diffusivity of component A in B
CA = Molar concentration of component A
A special case of this law occurs when the gradient is constant. In such circumstanc
es, the flux is constant (steady state). In a closed system, this occurs after long times,
but does not imply equilibrium.

3
Ficks second law of diffusion incorporates the time rate-of-change of
concentration to the flux with a mass balance.7
dC^
dt
-VJA =Dab
v2C
2
Difficulty in analyzing diffusion data is usually encountered when the second
or combined law of diffusion (Equation 2) is integrated. The boundary and initial
conditions imposed by the system geometry and experimental apparatus often
complicate integration despite simplifying assumptions.
Transdermal diffusion theory*
Transdermal diffusion consists of many phases; including, release of the solute
from the solvent, diffusion of the solute through the solvent to the membrane,
partitioning of the solute into the membrane (establish equilibrium across the phase
boundary), diffusion through the membrane, partitioning out of the membrane,
reaction, and removal by the circulatory system.
For drug diffusion through the skin, some models assumed that the
concentration gradient and, consequently, the flux were constant. One of the earliest
theoretical models for transdermal diffusion was developed by Michaels et al.60
Their model described diffusion through a homogeneous barrier with a steady state
(linear) concentration profile within the skin and negligible receptor-phase drug
*An excellent and much more complete description of the mechanics of diffusion
as they relate to transdermal diffusion can be found in B.W. Barrys Dermatological
Formulations. Percutaneous Absorption Chapter 2.4

4
concentration. These simplifications yielded a model in which the flux was
proportional to the donor phase concentration.
Another model that assumed a steady state profile was that of Fleming et
al.25,42 They treated transdermal diffusion in a closed system as a first-order kinetic
process (J = kAC where J = flux, k = overall rate constant or mass transfer
coefficient, and AC = concentration difference across the membrane). The overall
rate constant (k) was assumed to be the result of diffusion through a series of
resistances (stagnant boundary layer/membrane/stagnant boundary layer). This
model predicted an exponential decay of concentration scaled by the ratio of the
compartment volumes.
McDougal et al. used a similar approach to model the absorption of vapors
in the lungs57 and in the skin56 of rats in vivo. Permeability (mass transfer)
coefficients, partition coefficients, and blood flows from experimental data were used
in the model. The use of experimentally measured partition and permeability
coefficients required no theoretical understanding of phase equilibrium or diffusion.
Consequently, the model was able to emulate experimental data, but provided little
insight into the mechanics of percutaneous absorption.
Zatz97 also developed a model that assumed a steady state concentration
profile, but increased its complexity by using multiple resistances in series to
represent the membrane. These additional resistances allowed the model j to more
closely fit experimental data, but did little to increase the fundamental understanding
of transdermal diffusion.

Sloan et al.78,79 expanded on the model of Fleming et al.25,42 by describing the
phenomenon of partitioning across a membrane. Using the Gibbs-Duhem equation
(equivalent activities between phases in equilibrium), they related the drug
permeability to the theoretically determined partition coefficient and were able to
estimate permeability from theoretical solubility parameters.
Others have attempted to solve both Ficks first and second laws without
assuming a steady state profile. In 1979, Hadgraft41 attempted to derive rigorous
expressions for diffusion through the stratum corneum (hydrophobic outer layer of
keratinized cells), the epidermis, and the capillary bed. His derivation began with
Ficks second law and a solution was sought through Laplace transformation. To
simplify the mathematics, only solutions at long times were considered. Assumptions
about the relative values of the parameters and simplification by single term
expansions of transcendental functions permitted the Laplace solution to be inverted.
The effects of diffusion routes (transcellular versus intercellular), partition
coefficients, and skin binding were simulated by the model. Our quasi-steady state
model does not require these types of assumptions or simplifications and is valid for
all stages of diffusion in vitro.
In 1983, Guy and Hadgraft35 expanded their non-steady state model to include
transport from the vehicle to the membrane and from the membrane to the
capillaries. Transport between phases of the model was assumed to follow first-order
kinetics. They give few details of the mathematics, but the relative magnitudes of

6
their dimensionless groups and limiting cases were used to get expressions for the
amount of drug removed from the skin.
In 1983, Guy et al.39 examined the release of drug from liposomes in a topical
formulation. This theoretical treatment was based on Fickian diffusion in a spherical
geometry. To get an analytical solution, infinite sink conditions were adopted at the
boundary. Short and long times were used as limiting cases. The result was
expanded to account for multilamellar vesicles by assuming that a first-order rate
constant accounts for diffusion through the interface.
In 1985, Guy and Hadgraft34 derived equations for diffusion through skin
modelled as a bilaminate structure with layers of different dimensions, diffiisivities,
and partition coefficients. The path through the stratum corneum was assumed to
be intercellular and tortuous. They also presented an expression for the concentra
tion profile within the stratum corneum,33 but they gave no details of the derivation
or the boundary conditions the equation represented. Results were plotted to
illustrate the ability of the model to simulate experimentally observed phenomena.
Most recently, Hadgraft42 built upon previous work25 by adding the resistances of a
drug reservoir and an adhesive layer to diffusion. These additional resistances are
supposed to represent those of a commercial transdermal therapeutic system (ITS).
The equation presented by Guy and Hadgraft represents the concentration
within a finite slab as a function of time and position with constant boundary
conditions and no drug present initially. The model presented in this work (Chapter
6: Theory page 131) also made use of this solution to Ficks second law. For our
model, however, additional modifications were used to account for the changing
concentrations at the boundaries and the swelling of the skin.

7
Diffusion Through Synthetic Barriers
The study of diffusion through skin is complicated by the complex structure
of the skin. Inter- and intra-species variability in skin leads to differing diffusive
barrier properties. Because of this variability, many researchers substitute synthetic
membranes for biological membranes to more accurately determine differences
between transdermal formulations and avoid complex statistical analyses.
The advantages of synthetic barriers to diffusion are their consistency and well
characterized properties. The use of synthetic barriers requires several assumptions
about transdermal diffusion. It must be assumed that the skin does not metabolize
the drug significantly, which may or may not be true depending upon the drug
involved.81 Secondly, diffusion is assumed to be passive and the drug is assumed to
have an equivalent (or at least similar) affinity for the synthetic medium as for
biologically viable skin. These assumptions are violated to some extent simply
because the skin is an active medium and the chemical content of the synthetic
medium differs from that of skin. Provided one is prepared to make such
assumptions, synthetic media can be used to evaluate transdermal formulations
qualitatively.
Two main systems are used to simulate the barrier properties of skin:
unsupported barriers (usually two immiscible liquids in contact) and supported
barriers (usually two phases separated by a solid, but permeable barrier).
|
Unsupported barriers can be used to measure partition coefficients (equilibrium) or

8
diffusion coefficients. However, unsupported barriers usually assume that the
controlling resistance to diffusion is the hydrophobic stratum corneum (represented
by the lipid or hydrophobic, liquid phase). Supported barriers provide a mechanical
barrier that allows the testing of miscible solutions since the liquids are prevented
from mixing by a physical barrier. Supported barriers also allow the addition of a
hydrophilic barrier (the membrane or another liquid phase) to more closely resemble
the layered structure of skin.4
Unsupported barriers
Unsupported barriers are usually prepared by putting two immiscible liquids
in some sort of vessel. The barrier to diffusion in such a system in the phase
boundary between the two liquids. Unsupported barriers can be used to study the
release of a drug from a formulation as a function of time. They can also be used
to estimate the skin-vehicle partitioning behavior of substances.4 The partitioning of
alkyl homologs between water and an immiscible lipid phase was studied to develop
a correlation between partitioning and alkyl chain-length.26 The relationship is linear
when plotted on semi-log axes (i.e., logfpartition coefficient] chain length).
Poulsen and Flynn66 reviewed a study on the release of steroids from water-
propylene glycol gels and creams into a receptor phase of stirred isopropyl myristate.
It was determined that, for all systems, the fraction of propylene glycol that produced
a saturated solution maximized the release rate.
The use of unsupported barriers provides some benefits for the study of
transdermal diffusion. However, the difficulties associated with the technique often

9
make supported membranes more attractive. Unsupported barriers do not accurately
represent the properties of skin because they can only be used when they are
immiscible with the formulation and they are subject to convection currents. For
these reasons, synthetic polymer membranes are often used with or without
hydrophobic liquids.
Supported barriers
Micro-porous membranes have been used to study many systems. Semi
permeable membranes are routinely used to measure diffusion coefficients, osmotic
pressures, and streaming potentials in aqueous systems. Semi-permeable membranes
are also used for separations (ultra-filtration, reverse osmosis, dialysis, etc.). Johnson
studied the diffusion of steroids through microporous membranes in aqueous
systems.49 His experiments determined the diffusion coefficients for steroids diffusing
in porous polycarbonate membranes and provided the basis for the stirring-rate
studies in Chapter 4: Drug Diffusion In Vitro.
Silicone-rubber membranes have been used as diffusion barriers for a variety
of penetrants.4,26,4648,5568 These rubber membranes are very hydrophobic and a
comparison to studies using skin helped to establish that the primary diffusive barrier
of skin is lipophilic.26 Neubert modified an in vitro system using a silicone rubber
membrane by utilizing a non-polar receptor phase to study the diffusion of
hydrophobic drugs.62 j
¡
A synthetic membrane and a hydrophobic liquid phase can be combined to
simulate the behavior of skin as a barrier to diffusion. The synthetic membrane

10
mechanically supports and confines the lipid phase in a well defined region.
Hadgraft and Ridout43 used a cellulose nitrate membrane saturated with isopropyl
myristate as the barrier to diffusion for a wide range of drugs. Isopropyl myristate
showed diffusive properties similar to those of the stratum corneum. The correlation
was very good, but the magnitude of the barriers differed by three orders of
magnitude (true skin being the more effective barrier). They later expanded their
experiments to include dipalmitoyl phosphatidylcholine, linoleic acid, and tetradecane
as model barriers.44 Tetradecane imitated the stratum corneum barrier properties
best. Hadgraft et al45 also used this barrier to study the effect of azone (1-dodecyl-
azacycloheptan-2-one, a penetration enhancer) on the diffusion of salicylate and
determined that azone may form ion pairs with salicylate. Although synthetic
membranes can greatly reduce the difficulties associated with biological variability,
they can only estimate relative effects in transdermal diffusion. Experimental data
on transdermal diffusion must ultimately be obtained using real skin. It is more
difficult to discern trends because of scatter, but it is more likely that these trends
are relevant to a clinical setting.
Transport Through Biological Membranes
Recent developments in transdermal diffusion are organized into the following
groups: system effects, vehicle effects, solute effects, penetration enhancement,
differences between in vitro and in vivo systems, and topical local anesthesia. The

11
literature is organized in this way to present general findings first and then focus
more closely on aspects directly related to this study.
In vitro cell geometry
The design of an in vitro transdermal diffusion cell affects not only its ability
to mimic in vivo conditions, but also the ease of using the device. Almost all in vitro
transdermal diffusion experiments are done with either vertical or horizontal
transdermal diffusion cells31 (orientation refers to the direction of diffusion).
Gummer31 states that horizontal cells are easier to stir than vertical cells. The upper
phase in a vertical cell is open to the atmosphere and the skin forms its base so a
stirring magnet in the upper phase would rest on the skin. The donor-phase volume
in a vertical cell can be varied from bare coverage of the skin to the capacity of the
upper compartment. The use of the horizontal cell, however, requires the skin to be
fully immersed in a liquid phase and thus fixes the volumes of both receptor and
donor phases. The fact that the donor phase in a vertical cell is not usually jacketed
also complicates any attempt at temperature control.
Membrane effects
Variation in the experimental system such as the source of the membrane and
degree of hydration can profoundly affect transdermal diffusion. Figure 1 is a very
general schematic of skin structure for reference to the following material. The
permeability of human skin can vary as much from person to person as from place
to place on a given individual.4 The structure and physical properties of the stratum
corneum have been studied and described in detail.2428,6377,84 Variation in stratum

12
t
00
.Siratiiin Corn mini (15 uni)
Viable Epidermis (150 pm)
Dermis (2000 pm)
Figure 1: General schematic of skin structure
corneum thickness, number of sweat glands, number of hair follicles, and blood
supply will affect the routes and overall resistance of skin to diffusion.4,74,75,88 Some
of these parameters have been systematically studied and the results are reviewed
below.
Age. The effect of subject age on transdermal diffusion has been studied in
detail under a variety of conditions. In 1962, Marzulli53 identified a trend of
decreasing permeability with age of human skin in vitro. Since that time, other
researchers have confirmed this trend.4,6,34,89 There is some evidence that the general
permeability increases in elderly subjects4 or is dependent on the substance
investigated.6,34 The general trend of decreasing permeability with age is attributed
to the progressive decrease in moisture content in the skin of the elderly.34

13
Skin components. Marzulli53 separated human skin into its components to
measure their barrier properties individually. Statistical significance was only
detected between full thickness skin and the dermis, however, the sectioned skins
were generally more permeable than intact skin. Scheuplein76 found that the water
permeability of the outer layer of human skin was approximately one order of
magnitude lower than that of deeper tissue. Much later, Anderson et al.2 compared
the barrier properties of full thickness human skin to isolated stratum corneum.
They found that the isolated stratum corneum resembled the behavior of the full
thickness skin for both partitioning and diffusion. Findings such as these were
instrumental in identifying the stratum corneum as the primary resistance to
transdermal diffusion.
Damage and disease. Barry4 describes experiments investigating transdermal
diffusion as a function of skin condition. Permeability of mouse skin to hydrocorti
sone was found to increase when the mice were deficient in essential fatty acids,
exposed to UV light, exposed to vitamin A acid, exposed to 10% acetic acid in
acetone, or exposed to solvents that fluidized or extracted the stratum corneum lipids.
Abraded skin was found to be equally permeable to steroids as unabraded skin in
rats, but more permeable in monkeys.4 Tape stripping* increased the rate of water
loss to approximately that of a free water surface and also increased the permeability
of the skin to most substances. Shaving of hair from both humans and laboratory
Tape stripping refers to the removal of outer skin cells by applying and removing
adhesive tape.

14
animals is assumed to damage the stratum corneum and increase the diffusion rate.4
In general, it was determined that the permeability of the skin could be increased by
damaging the stratum corneum barrier.
Anatomical Region. Barry describes experiments in which human skin is
evaluated as a barrier to diffusion of hydrocortisone from various anatomical sites.4
Permeability was ranked as follows: scrotum > forehead > scalp > back >
forearms > palms > plantar surface of the foot arch. Wester et al.93 also determined
that the permeability of the skin of the scrotum is greater than that of the abdomen
for both adult and newborn skin.
Rougier et al.72 ranked human stratum corneum permeability as: forehead >
abdomen > thigh > chest > arm > back. Subsequent experiments73 established that
relative absorption depended not only on anatomical region, but also the chemical
nature of the penetrant. The authors did, however, reassess the general permeability
of human stratum corneum as: forehead > postauricular > abdomen > arm. The
forehead was found to be more than two times more permeable than the arm or
abdomen regardless of the substance tested.
Race. Differences in the permeability of skin were also measured between
different races of humans4 Black skin was found to be less permeable than
Caucasian skin, people of Celtic ancestry were more often irritated by toxic chemicals
than people of Mediterranean ancestry, and fair skinned people were found to be
more susceptible to contact dermatitis.
i

15
Animal models. In 1980, Durrheim et al.23 concluded that hairless-mouse skin
was a reasonable model for human skin through comparison of their data on the
diffusion of n-alkanols through hairless-mouse skin in vitro and previously published
data using human skin in vitro. The measured permeability of hairless-mouse skin
differed significantly from human skin for many substances,22,67 but the trends were
similar.
Hairless-mouse skin has been criticized as a model for human skin based upon
its reaction to long-term hydration,9 acetone attack,10 and penetration enhancers.11
Under such conditions, hairless-mouse skin cannot confidently mimic the trends of
human skin.
Barry5 has suggested the use of shed snake skin (Indian python or American
black rat snake) as a model for the permeability of human skin. Shed snake skin is
plentiful, can be collected without harm to the snake, and can be stored at room
temperature. Snake skin was found to be less susceptible to hydration and acetone
damage than mouse skin and performed more like human skin under these
circumstances. The effects of penetration enhancers were less dramatic for snake
skin than for mouse skin, but did not model human skin any better. The damage
caused by a number of pesticides was also investigated. The results indicated that
I
snake skin and human skin do not react similarly to the attack of the pesticides.
Overall the author suggested that snake skin is no better as a model for human skin
than other biological membranes like collagen, egg shell membranes, etc.

16
Many animal models have been investigated. The general trend of
permeability can be summarized: rabbit > rat > monkey swine man.4,37
Pigskin has been suggested as an in vitro model for human skin4 and the rhesus
monkey has been suggested as an in vivo model for human skin.34
Hydration. Excessive absorption of water increases the skins thickness and
changes its relative chemical composition. These effects result in changes in the
skins ability to act as a barrier to diffusion. Barry4 reviews much of the literature
concerning skin hydration and concludes that hydration increases the permeability
of the skin to all substances except small, polar molecules.
Blank8 treats hydration and skin permeability as the subject for an entire
chapter. He and co-workers measured the diffusion of water through stratum
corneum as a function of time and degree of hydration. They use this information
to calculate the thickness of the skin and the flux of water through the skin as a
function of the surface concentration of water (or relative humidity).
Vehicle effects
The subject of vehicles has received more attention than receptor phases in
transdermal diffusion. The receptor phase can only be altered in in vitro experiments
while the donor phase can be altered either in vitro or in vivo. The donor phase can
be altered to affect either the drug itself or the skin.* There are many reasons for
varying the donor phase composition to affect the drug (particularly its
Vehicles that affect the permeability of the skin are known as penetration
enhancers. These effects are reviewed in another section (page 20).

17
thermodynamic activity) in solution. The effects of drug solubility, drug partitioning
(the ratio of equilibrium concentrations in the skin and vehicle respectively),
emulsification, and pH control are summarized below.
Solubility and partitioning.* Roberts et al.70 correlated the permeability of
phenolic compounds, aromatic alcohols, and aliphatic alcohols with their partitioning
behavior in octanol. The log-log plot is linear up to a partition coefficient of about
100, but decreases in slope at higher partition coefficients.
Bronaugh and Franz13 determined that partitioning into the stratum corneum
was the determining factor for skin permeability in the absence of overriding
solubility constraints in the system. Other researchers have also demonstrated
this.11,23,26 Gummer32 concluded that, for a given concentration, the rate of diffusion
is inversely proportional to the saturation concentration (saturation implies maximum
thermodynamic activity in the vehicle) and proportional to the partition coefficient
of the drug (large partition coefficient implies low activity in skin).
Ward86 discusses the use of surfactants as a means of increasing the solubility
of the penetrant. A comprehensive algorithm is presented to optimize the vehicle
based on structure, interfacial properties, and phase behavior. In general, it was
found that increasing partitioning into the skin and approaching the solubility limit
aid transdermal diffusion.
Emulsions, liquid crystals, and liposomes. Emulsification of the drug in the
vehicle can be of benefit for a poorly soluble drug. Osborne et al.64 state that the
Solubility and partitioning are, of course, properties of both solvent and solute.

18
use of a microemulsion or a lyotropic liquid crystalline system can increase the
thermodynamic stability of the drug in the formulation and its penetration into the
skin. There are exceptions which point up the fact that more information on the
effects of these systems is needed.
Uster82 discusses the use of liposome vehicles for topical delivery of drugs.
Liposomes differ from micelles in that the vesicles are defined by bilayers of lipids
(much like cell membranes) and separate the bulk aqueous phase from an entrapped
aqueous phase. Their advantage seems to be their ability to increase the concentra
tion of drug in the skin without increasing the amount of drug entering the receptor
phase or the circulatory system. This effect could be caused by liposomes binding
to the skin surface and releasing their contents there. For small, water soluble
molecules, diffusion through lipid bilayers constitutes the rate-limiting step and the
additional bilayers formed by liposomes significantly inhibit their diffusion.
pH. Diffusion through skin can be affected by pH if the solute is a weak
electrolyte. Changes in pH shift the fractions of acid and base in solution. Since
these two forms of the solute have different properties, they will differ in their ability
to cross the skin barrier.60 Flynn26 hypothesizes that in lipoidal membranes (e.g.,
skin) ionic species will be less favorable in the membrane as compared to the
unionized species. Flynn later confirms this hypothesis experimentally. Therefore,
manipulation of the pH of the vehicle can have a profound effect on the transdermal
diffusion of ionizable substances. ;
i
I
i
i

19
Solute concentration
Concentration refers to molecularly dispersed substances; literature on the
effects of emulsification (i.e., systems in which the solute is not molecularly
dispersed) is reviewed on page 17. The theoretical response to increased concentra
tion is a proportional increase in flux (according to Ficks first law). Chandrasekaran
et al.17 found that the diffusion of scopolamine through human epidermis followed
such a trend. There are also accounts of deviation from this expected response (both
positive and negative).13,32,70'91 Many of these effects appear to be due to confusion
between the overall concentration and the concentration of drug molecularly
dispersed in the medium.
Effect of temperature
The thermal motion of molecules is the driving force for diffusion. Increasing
the amplitude of thermal motion (temperature) should increase the rate of diffusion
of drugs through the skin just as it increases the rate of diffusion of other solutes in
other systems. The difference in the barrier properties of skin at different
anatomical sites may at least be partially due to differences in temperature.4 Barry
also states that the effect of temperature on transdermal diffusion is usually studied
by an Arrhenius plot (log of drug permeability versus the inverse of temperature).
Such analysis has determined that the activation energies of n-alkanols (ethanol to
pentanol) are constant ( ~ 16.5 kcal/mol) between ambient and body temperature.
Heavier n-alkanols do not yield constant activation energies. It is suggested that this
may be caused by the melting or extraction of some lipids in the stratum corneum

20
at elevated temperatures. Durrheim et al.23 also measured the diffusion of n-alkanols
through skin as a function of temperature (Arrhenius plot) and got a similar value
of approximately 19 kcal/mol.
Scheuplein76 measured the diffusion of water and ethanol through human
stratum corneum as a function of temperature and found that the results depended
on whether the temperature was increasing or decreasing (hysteresis effect). This
effect was attributed to the fluidization and partial dissolution of the lipids in the
membrane (permanent damage to the barrier at elevated temperatures).
Raising the temperature can also affect the barrier properties of the stratum
corneum. Poulsen and Flynn66 found that the barrier properties of human and
hairless-mouse stratum corneum remain relatively constant up to approximately 80C.
Above this temperature there is a rapid, dramatic, and permanent loss of barrier
function.
In summary, the literature indicates that there are two effects of temperature:
a conventional thermal motion effect and a stratum corneum dissolution effect.
Penetration enhancers
Rnepp et al.50 summarize the ideal features of a penetration enhancer as:
1: No pharmacological response
2: Specific in its action
3: Acts immediately and reversibly with predictable duration
4: Chemically and physically stable and compatible in formulation

21
5: Odorless, colorless, tasteless
6: Nontoxic, nonallergenic, nonirritant
Brown and Langer14 describe penetration enhancers as "vehicles that reduce the
barrier properties of the stratum corneum in such a way as to increase the
penetration of the drug of interest." Many substances have been investigated as
potential penetration enhancers. Chien18 lists the following as representative classes
of penetration enhancers: alkyl methyl sulfoxides, surfactants, and azones
(1-alkyl azacycloheptan-2-ones).
One mechanism for penetration enhancement seems to be disruption of the
stratum corneum lipids and proteins.19,85 Fluidization and extraction of stratum
corneum lipids by some proven penetration enhancers has been shown experiment-
ally.27,29,40 These same authors have also noted that some established penetration
enhancers (N-methyl-2-pyrrolidone, n-alkanols) do not affect the stratum corneum
and must act through some other mechanism.
Another process by which some penetration enhancers (cationic amines) may
increase drug flux is by forming ion pairs with the drug. Briefly, the mechanism of
facilitated transport by ion pairs at the skin surface is:85 long chain cationic amines
ionize and may pair with ionized permeant; the uncharged pair diffuses through the
i
stratum corneum; within the skin the pH rises, causing the amine to deprotonate and
freeing it to diffuse back through the skin.

22
Differences between in vitro and in vivo systems
Studying transdermal diffusion on living, intact organisms is more difficult than
studying diffusion in vitro. The difficulties of sample collection, sample analysis,
consistent dosing, variations between individuals, and effects of metabolism
complicate in vivo studies. Despite the experimental difficulties, topical formulations
must pass through a clinical in vivo testing phase before being approved for
widespread use. For some variables the effects are the same for in vitro and in vivo
studies; for others, such as metabolism, circulation, and radial diffusion, there are no
in vitro parallels.
Metabolism. Barry4 states that drug metabolism has been neglected in past
studies. Both inactive and active metabolites may form in the skin and can affect the
results of a transdermal diffusion experiment if not accounted for properly. Tauber81
details the effects of in vivo metabolism in detail.
One potential benefit of in vivo drug metabolism is the ability to specifically
engineer drug precursors (prodrugs) to improve their percutaneous absorption.
Prodrugs have little or no therapeutic activity, but are metabolized after absorption
I
into an active drug.36,37
Circulation. Blood flow in vivo creates an open system while an in vitro
system is usually closed. Blood flow carries drug from the skin and distributes it
throughout the body preventing equilibrium. In a closed, in vitro system,
the drug
builds up in the receptor phase and the concentration difference across the
membrane decreases with time.

23
Radial diffusion. For a topically applied formulation in vivo, diffusion is not
limited to one direction. Radial diffusion can be a significant factor.38 In an in vitro
diffusion cell, radial transport is impossible since the drug cannot diffuse through the
walls of the diffusion cell or laterally through the skin.
Receptor phase. The choice of receptor phase can affect the ability of the
diffusing substance to partition from the skin into the receptor compartment. In
addition, the solubility of the diffusing substance in the receptor fluid can affect
interpretation of results if an infinite sink is assumed. Bronaugh and Stewart12 varied
the receptor fluid for the diffusion of two lipophilic fragrance chemicals. They found
that increasing the lipophilicity of receptor phase increased the flux of the fragrances
through the skin.
Recommendations. Wester and Maibach90 suggested ways to help match in
vivo conditions of humans using an in vitro diffusion cell.
Membranes Human skin should be used if possible
Cell design A large receptor volume minimizes the effects of
low solubility in the receptor phase
Temperature Circulating temperature should be 37C (results
in a skin temperature of 32C, average for skin in
vivo)

24
Receptor phase Buffered saline or as necessary to keep drug
thermodynamic activity below 10% that in the
donor phase
Miscellaneous Emulate in vivo or clinical system
Topical local anesthesia
The transdermal diffusion of local anesthetics has been more often studied in
vivo than in vitro. Many drugs have been tested, although the results have always
fallen short of expectations because of poor diffusion through the skin.
McCafferty et al.55,96 formulated local anesthetic bases in oil/water creams and
monitored their diffusion through silicone-rubber membranes. Based on their
observations, lignocaine (lidocaine) and amethocaine (tetracaine) were the best
candidates for clinical study.
Adriani and Dalili1 tested the bases and salts of dibucaine, tetracaine,
mepivacaine, prilocaine, lidocaine, procaine, benzocaine, and butesin for anesthetic
effect on more than 150 volunteers. The bases were dissolved in a solvent of 50%
water, 40% ethanol, and 10% glycerol. The salts were applied as aqueous solutions.
After the anesthetic preparations were on the skin for 30 minutes, their effectiveness
was measured by their ability to block itching and burning sensations induced by
electrical current. The time of 30 minutes was established after observations that
effective preparations established a block within 15 minutes. No other investigator
has claimed to produce an anesthetic effect so quickly. Other investigators, however;
have used much more stringent tests for efficacy than the relief of electrically

25
induced itching. Saturated solutions of the bases were found effective in most cases
and the order of decreasing efficacy was: tetracaine, mepivacaine, lidocaine,
benzocaine, and procaine. None of the anesthetic salts were effective. Adriani and
Dalili also tested 30 commercially available topical anesthetic preparations and found
that none could relieve the experimentally induced itching and burning except
Americaine (containing 20% benzocaine base). Adriani and Dalili stated that the
anesthetic effect of all topically applied formulations dissipated only 10 to 60 seconds
after being removed from the skin. Again, this result contradicts all other reports on
topical application of anesthetics. The rapid onset and subsidence of anesthetic
effect as measured by Adriani and Dalili could be a result of the electrical
conductivity of the anesthetics themselves or some other surface effect. The inability
of other investigators to even approach these results indicates that the anesthetics,
in fact, never reach the nerve endings.
Campbell and Adriani15 studied the systemic levels of local anesthetics
administered by three routes (infusion, infiltration, and topical application) in both
human volunteers and dogs. The drugs tested were tetracaine, cocaine, procaine, and
benzocaine. Intravenous injection was used as the control. Absorption of the
anesthetics from the mucous membranes of the pharynx and trachea was comparable
to the absorption when administered intravenously. Transdermal diffusion was
j
detectable only when the skin was abraded or suffered third degree burns prior to
application. The authors concern was avoiding toxic systemic levels of the drugs and
there was no assessment of analgesia.

26
Gesztes and Mezei30 studied the release of 0.5% tetracaine base from
multilamellar phospholipid vesicles. The anesthetic preparation was evaluated in
adult volunteers using the pinprick method.* The preparation was applied for one
hour and reportedly provided at least four hours of topical anesthesia. Pontocaine
cream, used as a control, was found to be ineffective. Despite clear details about the
anesthetic preparation and its administration, our attempts to reproduce the
published results were unsuccessful. The performance of their liposomal formulation
was also compared to the tetracaine preparation developed in our laboratory and
found to be less effective clinically. Their preparation was less concentrated,
however; and their comments about the benefits of low concentration for self
administration by outpatients are important.
Kushla and Zatz,51 using an approach similar to that of Campbell and Adriani
for evaluating local anesthesia, induced pain electrically. Their anesthetic
formulation was lidocaine base (5%) in vehicles of either an aqueous gel containing
40% propylene glycol or an oil-in-water emulsion cream (77.5% water). Placebos of
the vehicles were used as controls. Tests of the topical formulations revealed that
the gel was not effective, but the cream was. Maximum effect was observed two to
three hours after application and lasted up to six hours.
Monash61 studied the diffusion of anesthetic salts and bases through both
mucous membranes and skin in vivo in human volunteers. The anesthetic bases were
dissolved in a solvent of 45% alcohol (probably ethanol), 45% water and 10%
j
The subjects are asked to rate the pain level produced by a pin prick.

27
glycerine. The salts were dissolved either in the same solvent as the base or in water.
The bases of tripelennamine, lidocaine, tetracaine, phenacaine, and benoxinate
produced anesthesia after 45 to 60 min contact under occlusion at concentrations of
2%. The salts required at least two hours to produce anesthesia.
The use of ethanol and water as solvents for tetracaine was investigated in our
laboratory. These solvents were not compatible with tetracaine because the drug
broke down into a variety of aromatic aldehydes. Neither water nor ethanol alone
caused tetracaine to decompose. Therefore, even though the results of Monash were
equal to the current state-of-the-art in transdermal local anesthesia; we found his
system to be unstable.
McElnay et al.58 investigated the use of ultrasound to promote the in vivo
transdermal diffusion of lidocaine from a cream base. No statistical difference was
detected using volunteers, although the trend of the data suggested that ultrasound
decreased the onset time of anesthesia.
McCafferty et al.55 compared in vitro and in vivo percutaneous absorption of
several anesthetic bases in an oil-in-water emulsion cream (77.5% water). The
anesthetic concentration was 0.35 mmol/g. Drug diffusion was evaluated ¡either in
vitro through a silicone rubber membrane or in vivo by the pinprick method. Of the
drugs tested, tetracaine (amethocaine) was the most effective both in vitro and in
vivo.
i
|
Woolfson et al.95 characterized the concentration response of three tetracaine
free base formulations: water, and two aqueous systems gelled with either 1.5%

28
carbomer wax or 7% methylcellulose and an oil-in-water emulsion cream consisting
of 16% Emulsifying Wax, 4% paraffin. For the aqueous gels, a tetracaine free base
concentration of 4% applied for 30 min produced adequate anesthesia after 40 min.
The emulsion cream required 8% to 12% tetracaine free base to be effective, but the
onset time was the same as for the aqueous gels. A higher concentration did not
decrease the onset time, but did increase the duration of anesthesia. The onset of
anesthesia after removing the formulation implied that the stratum corneum was the
limiting resistance to diffusion. Our results for onset time and duration of anesthesia
with tetracaine in a different solvent are similar and support this hypothesis.
Small et al.80 used one of the aqueous gels developed by Woolfson et al.95
before cutting skin grafts. The clinical procedure was modified from previous
experiments by increasing the area (as needed), dose (1 mm layer), gel application
time (s: 1 hr), and the period of time between the removal of the gel and the start
of the procedure (60 to 300 min). Skin graft removal was pain-free in 64 of 80 cases.
In in vivo trials, McCafferty et al.54 compared the clinically available EMLA
(eutectic mixture of local anesthetics) cream to their 0.35 mmol/g tetracaine cream.
The tetracaine cream produced longer and more rapid anesthesia than the EMLA
cream.
Woolfson et al.94 conducted an expanded clinical assessment of their aqueous
tetracaine gel in a pediatric environment to evaluate the level of anesthesia and
reactions in 1241 patients. The level of success (defined as no sensation during

29
venepuncture or minimal sensation with no discomfort) was 88.7% (1101/1241).
About 7% of the patients had mild reactions (local redness, swelling, and itching).
McGowan et al.59 used laser doppler velocimetry to measure changes in blood
perfusion during vasodilation caused by the percutaneous absorption of tetracaine
from the gel described on page 28. They confirmed the clinically obtained minimum
onset time of 30 min, but could not measure the duration of anesthesia. ;
Specific Objectives
Topical Local Anesthetic
The objective, of course, is the development of a topical local anesthetic
formulation suitable for clinical use by hospital patients. Ideally this preparation
should be effective, fast acting, and long lasting without irritation or other discomfort.
Its effectiveness should be measured by its ability to alleviate the discomfort
associated with the insertion of an intravenous needle no more than one hour after
application and for a period of at least 5 hours.
Pediatric applications
i
Children experience greater stress in a hospital environment than adults.
Preventing the discomfort of inserting intravenous needles would benefit the patients
as well as physicians and staff. Local anesthesia would make intravenous access
easier because the patient would be less likely to flinch during the procedure.

30
Outpatient applications
Patients could be given anesthetic patches and instructed to apply them a
specified time before their outpatient procedures. Self-application of the anesthetic
patch would require advanced preparation of the device. Since the anesthetic base
may deteriorate at room temperature, the patient would need to store the patch in
his/her refrigerator if the procedure was to take place more than three or four days
later. This should not be a problem since patients are occasionally given sera that
must be refrigerated to remain effective.
Pain management
Continued relief of the discomfort of ivs could also make hospital stays more
pleasant for patients. A non-invasive local anesthetic formulation makes systemic
analgesics unnecessary. The anesthetic patch can be designed to last longer than
twelve hours.
Theoretical Modelling
The objectives of theoretical modelling go beyond developing equations that
mimic experimental data. Developing totally empirical correlations does not increase
the understanding of the processes of transdermal diffusion. The main, theoretical
goal of this work is to apply diffusion theory to transdermal diffusion in vitro and
develop a model that has applicability beyond topical local anesthesia.

31
Novel techniques
The quasi-steady state assumption is far from novel. It is simply the
assumption that the boundary concentrations do not change appreciably during the
period of interest. Cussler describes the technique very early in his book on mass
transfer.20 Use of this assumption for transdermal diffusion is novel. Furthermore,
experimentally measured skin swelling data is added to give the model greater
accuracy and predictive ability.
Improved understanding of mechanism
In modelling the diffusion of drugs generally and tetracaine specifically, as few
assumptions as possible were made while trying to obtain an analytical solution. It
was hoped an analytical solution of Ficks second law for in vitro diffusion would
illuminate the mechanism of transdermal diffusion. The insight gained could guide
research and development toward a better understanding of transdermal diffusion
and could lead to better patient care.
Importance of swelling in vitro
No theoretical model for transdermal diffusion has ever included skin swelling
before. Others have measured this phenomenon, but have never presented the data
in enough detail for inclusion in a theoretical model. A simple moving boundary
conceptualization is, admittedly, naive; but it is also a first step toward accounting for
the change of environment during in vitro transdermal diffusion. Obviously, more
than the dimensions of the skin change; the chemical nature must also play a role in
the diffusion rate as the stratum corneum becomes hydrophilic. However, our data

32
suggest that the effect of the chemical changes in the stratum corneum are
overshadowed by the change in its physical dimensions.

CHAPTER 2
MATERIALS AND METHODS
Materials
This section describes the properties of the materials used in this project.
Two general classes of materials are used, drugs and solvents. First the solvents are
described, then the properties of the drugs are described. The properties referred
to are solubility, surface tension, specific conductivity, ultraviolet light absorption, and
liquid phase chromatography behavior.
Solvents
The solvents used in the diffusion through skin experiments (excluding those
used for separation in the HPLC) were: (1) distilled water or 0.9% saline (NaCl)
solution (made from distilled water and biological grade NaCl), and, (2) USP grade
propylene glycol( 1,2-propanediol) purchased from Fisher Scientific. Numerous
solutions of these two liquids were used as vehicles for the delivery of drugs through
the skin. These solvents are completely miscible and their ratio was varied primarily
to control the solubility of the drugs (drug solubility is discussed in the following
section).
33

34
Propylene glycol is widely considered to be a penetration enhancer for the
percutaneous absorption of various drugs.32,50,69,87 The effect of propylene glycol on
the diffusion of the drugs in this study, however, is complex.
All solvents used in the HPLC (high pressure liquid chromatograph) were
prepared from HPLC grade solvents from Fisher Scientific. Methanol (CH3OH) and
acetonitrile (CH3CN) were used as received and phosphoric-acid buffer was prepared
in the laboratory from HPLC grade water and HPLC grade phosphoric acid (H3P04).
The solution was buffered to pH 3 using ACS grade KOH from Fisher Scientific.
The HPLC solvent mix used to analyze the local anesthetics was essentially that
recommended in the Supelco chromatography catalog for lidocaine, but altered to
decrease the retention time of the drugs. Resolution of components was not a
concern in this analysis since the drugs were the only components which eluted from
the HPLC.
Local Anesthetics
Four drugs were used in this project. The majority of the diffusion through
skin experiments used tetracaine (a local anesthetic). Hydrocortisone, scopolamine,
and lidocaine were used for calibration or preliminary experiments and to test the
experimental procedure for measuring diffusion through skin. Figure 2 contains
schematic representations of these drugs. The diffusion of hydrocortisone through
synthetic membranes has been studied previously.49 Diffusion of hydrocortisone
i
j
(from Sigma and used as received) through synthetic membranes was used to

35
O
Hydrocortisone
O.
/CH3
N.
O
O
c chch2oh
Scopolamine
ch3
\ ? /C2h5
"-nh-c- ch,-n;
x C2H5
CH,
Lidocaine
O
/
CH,
h,c-(CH,)r nh^ Vc-o-(ciyr ^ tetrac aine
CH,
I
I
Figure 2: Molecular structure of hydrocortisone, scopolamine, lidocaine, and
tetracaine

36
evaluate the experimental apparatus. The first experiments using mouse skin in this
project used scopolamine as the diffusing drug because previous work on transdermal
scopolamine17 provided a method for evaluating the performance of the in vitro
transdermal experimental procedure. Scopolamine HC1 (Sigma) was converted to
scopolamine free base by ether-extraction from a caustic solution. Transdermal
scopolamine is available commercially for motion sickness (Transderm-Scop from
Ciba).
Lidocaine was the first choice for a local anesthetic to be administered
transdermally because it is chemically stable during storage, resistant to solvent
attack, unlikely to cause allergic reaction, and widely used clinically as an injected
solution. Lidocaine HC1 (Sigma) was used without further purification. Lidocaine
was abandoned in favor of tetracaine which has better partitioning characteristics and
is approximately ten times more effective as a local anesthetic.
Two forms of tetracaine were used in experiments, tetracaine free base (a
hydrophobic ester) and tetracaine HC1 (a hydrophilic salt of the free base). Both
forms of tetracaine (Sigma) were used as received. Tetracaine base penetrates the
neuron more effectively21, but has very low aqueous solubility. Tetracaine salt,
however, is quite soluble in aqueous solutions (>200 g/1). Tetracaine salt is also
much more stable than the free base which must be kept refrigerated and dry.21
Since tetracaine HC1 is thermally more stable, it can be sterilized and still remain
effective. For transdermal diffusion however, sterility is not so great a concern and
tetracaine base becomes more attractive.

37
To compromise between the favorable diffusion characteristics of the base
form and the high aqueous solubility of the salt form, a mixture of the base and salt
forms was used. Such a mixture takes advantage of the tetracaine salt:tetracaine free
base equilibrium. Mixing a drug and its HC1 salt in solution is equivalent to adding
HC1 acid to a preparation containing only free base (or adding NaOH to a
preparation containing only the salt form).21
The properties measured were solubility in the solvents, surface tension as a
function of concentration, conductivity as a function of concentration, ultra violet
absorbance spectra, and HPLC behavior.
Methods
This section presents the procedures common to a number of experiments
beginning with those most likely to be familiar to the reader. Descriptions of the
instruments and techniques used to measure solubility, surface tension, specific
conductivity, and UV spectra are followed by more detailed descriptions of high
pressure liquid chromatography (HPLC), in vitro diffusion of drugs through mounted
mouse skin, and in vivo diffusion of drugs (rat tail flick test and clinical trials with
human volunteers).
I
I

38
Solubility
Solubility was determined by rotating a solution in contact with excess drug
at 4 rpm for at least 18 hours at room temperature. A sample was then withdrawn,
filtered, and analyzed by HPLC to get the total drug concentration in solution.
Titration
The acid-base behavior of tetracaine-containing formulations was explored by
simple titration. The apparent pH of the tetracaine formulation was monitored while
measured quantities of either NaOH or HC1 were added. Such measurements
yielded the pKa of tetracaine in various solvent mixtures as well as the pH vs.
tetracaine acid salt-free base ratio.
Thermal Breakdown of Tetracaine
To determine the shelf-life of tetracaine formulations, the concentration of
tetracaine in solution was measured as a function of time at room temperature and
¡
skin temperature (24C and 32C, respectively).
Drug Partitioning
To simulate the environment encountered by the drug when placed in contact
with the skin, the anesthetic preparation was placed in contact with a hydrophobic
organic phase. No account was made for hydrophobic phase solubility in the vehicle

39
or vehicle solubility in the hydrophobic phase. The partition coefficients for
vehicle*-organic systems were found by means similar to those described for
solubility. Vehicle formulations in contact with an equal volume of the hydrophobic
organic phase were rotated at about 4 rpm for at least 18 hours. Total drug
concentration in the hydrophobic phase relative to that in the vehicle was found by
HPLC.
Surface Tension
All surface tension measurements used in this work were made on a Rosano
Surface Tensiometer Model LG with a Wilhelmy plate. This apparatus has a
platinum plate approximately 1 cm x 3 cm x 0.5 mm attached to one arm of a
milligram balance. The balance is adjusted by adding mass to the other arm equal
to the mass of the platinum plate. With the scale reading zero and the arms of the
balance level, the platinum plate is brought into contact with the surface of a liquid
and is consequently pulled into the bulk of the liquid phase. Mass is added to the
free arm of the balance until the arms of the balance are again level. The mass
required to bring the arms to level is proportional to the surface tension of the
liquid. This instrument was calibrated using water with a known surface tension of
72.4 mN/m. The uncertainty of these measurements is approximately 0.2 mN/m.
*The term vehicle is used here and elsewhere to indicate the mixture of
propylene glycol and water (saline) in which the drug is dissolved.

40
Skin Swelling
Since skin in contact with liquid tends to swell, the extent of swelling was
determined to learn its possible effect on drug diffusion. A skin sample of known
cross-sectional area was weighed as a function of time immersed in water. Any
increase in mass was attributed to uptake of water and a corresponding increase in
volume (using density of water = 1.0 g/ml). The change in area of the upper and
lower faces of the skin sample was assumed to be negligible compared to the
increase in skin thickness. The initial volume of the skin was calculated based on a
density of 1.0 g/ml and its thickness was calculated by considering the skin sample
to be a disk of known radius. The change in skin thickness caused by the absorption
of water was correlated for later use in the theoretical model (Chapter 6, page 131).
Conductivity
Conductivity measurements were made using a YSI conductivity bridge Model
31 with a YSI 3043 Electrode (cell constant = 1/cm). This instrument uses a
scintillation screen to indicate conductance or resistance of the solution in which the
electrode is immersed. The screens two lighted bars diverge as the calibrated dial
indicating conductance approaches the solutions conductivity. The solutions'conduc-
i
tivity is the dial reading at which the screens bars reach their maximum separation.
The instrument can measure conductivities from about 0.5 tmhos to 2 mhos

41
(resistance from 0.5 0 to 2 Mil). Conductivities from this instrument have an
uncertainty of approximately 0.2 /unho.
Ultraviolet Spectrometry
Ultraviolet spectra were measured using a Perkin Elmer scanning spectropho
tometer Model 576. This model has two lamps (a deuterium lamp as an ultraviolet
source and a tungsten lamp as a visible source) extending its operational range over
any single-source instrument (90 nm to 800 nm). Ultraviolet and visible spectra were
measured against a reference solution and the difference in absorption between the
two solutions was plotted. This instrument was used to screen compounds for
possible detection in the HPLC (the HPLC detector uses ultraviolet or visible light
absorption). A spectrum of a solution containing the compound of interest was
measured over a wide range of wavelengths to determine the wavelengths of
maximum absorption for use with the HPLC. Although this instrument can be used
for quantitative measurements of absorbance (proportional to concentration), it was
only used in this manner for early diffusion experiments before the HPLC had been
installed. Calibration of this instrument showed a constant error of approximately
+ 0.33 nm which is within the manufacturers tolerance.
High Pressure Liquid Chromatography (HPLC)
By far the most complex instrument, the HPLC is invaluable for this type of
diffusion study (Figure 3). Fully computerized (640 kB Epson Equity 1+
running

42
DoubleDos and Spectra Physics software LNET2 and SPMENU), this system can
analyze over 80 samples without operator assistance. Once programmed, the system
can inject a sample from a diffusion experiment, identify the components in the
sample, determine the concentration of each component (integrate the signal), store
all information (including the raw data), generate a file for a spreadsheet, and print
a final report. Although the system has several components, the principles of
operation are relatively simple. The HPLC uses the relative affinity of a compound
between a polar and a nonpolar phase to achieve separation. A polar solvent is
pumped through a separation column containing a nonpolar hydrocarbon chemically
bonded to silica. The retention (residence) time in the column depends on the
compounds affinities for the two phases. Consequently, two compounds in the same

43
sample separate as they pass through the column depending on their polarity and
functionality. This type of chromatography is called "reverse-phase".
After the components of the sample are separated by the column, they flow
through an absorbance detector (Spectra Physics Model SP8450) which generates an
electrical signal proportional to the light absorbed by the liquid passing through the
detector. Peaks in plots of this signal correspond to components eluting from the
column. Because retention time depends on the functionality and polarity of the
compounds, the likelihood that two different chemicals will have the same retention
time is remote.
The other instruments in the HPLC system are the pump, autosampler, and
integrator. The pump (Spectra Physics Model SP8800) simply maintains the flow of
carrier solvent through the system at a steady rate. The pump can also mix up to
three miscible solvents in any ratio.
The autosampler (Spectra Physics Model SP8880) contains the sample vials
in four trays mounted on a turntable. Each tray holds twenty vials and the turntable
contains an additional priority-vial position. The autosampler moves each vial to the
sampling position and, when the system is ready, injects a predetermined volume of
the contents into the solvent stream while signalling the other instruments to begin
analysis.
The integrator (Spectra Physics Model SP4290) plots the raw signal from the
detector (optical absorbance of the solvent stream) and determines the presence of
peaks. The integrator calculates the area of peaks and determines if they correspond

44
to programmed compounds. If a peak is identified as a programmed compound,
previously entered calibration data are used to determine the amount of the
compound detected.
Quasi-elastic Light Scattering
Dynamic or quasi-elastic light scattering (QELS) was used to determine the
size of tetracaine micelles in saline, propylene glycol, and mixtures of these solvents.
QELS uses the time-varying scattering intensity and broadening of incident laser light
caused by the Brownian (thermal) motion of micelles. This information is used to
generate the Fourier transform of the power spectrum (an exponential function).
The time constant of this exponential function is directly related to the diffusion
coefficient of the micelles in solution. The apparent micelle diameter can then be
calculated by the Stokes-Einstein equation (assuming the particles are spherical).47
d = 3
3 7T 7] Dj
d = micelle diameter
k = Boltzmann constant
T = absolute temperature
Tj = solvent viscosity
Dt = translational diffusion coefficient

45
In Vitro Diffusion Through Mounted Mouse Skin
The following describes the procedures related to diffusion studies. The
process begins with preparing the skin from hairless mice, mounting the skin to the
diffusion cell, and sampling the drug concentration in the receptor phase.
Preparation of skin
The first step in measuring the diffusion of any compound through mounted
skin was procuring the skin from the mice. Laboratory hairless-mice were used.
Females were used because they are less aggressive and territorial than males and
less likely, therefore, to fight and damage their skin. The average mass of the mice
at sacrifice was about 30 grams.
The mice were sacrificed by cervical dislocation (Figure 4) and weighed.
After being sacrificed, a mouse was placed on its back and all four legs were taped
down (Figure 5). Using surgical scissors, an incision was made across the lower
abdomen just above the lower legs. Connecting incisions up the center and across
the upper abdomen just below the forelegs were then made. At this point the
incision resembled an "I" (Figure 6). The skin was teased away from the underlying
tissue and connective tissue was severed where necessary.
At this point, the rear legs were released, the mouse folded over onto its back,
i
|
and the upper and lower incisions continued around the abdomen (Figure 7). The
skin was carefully removed by severing any remaining tissue. The removed skin was
essentially rectangular.

46
Figure 4: Sacrifice of hairless mouse
Diffusion apparatus
In vitro transdermal diffusion was measured using flow-through type Franz
diffusion cells (Figure 9). The diffusion cells have four parts: body, cap, O-ring, and
clamp. The cell body was modified to include a magnetic stirring tee which greatly
increased mixing efficiency and reduced the tendency to form a stagnant boundary
layer adjacent to the skin surface. The cell body, surrounded by a water jacket to
maintain constant temperature, contained the lower (receptor) compartment into
which the drug diffused (15 ml). The receptor compartment initially contained

47
I'
Figure 5: Securing hairless mouse
0.9% w/w saline. The cell cap contained the upper (donor) phase (source of diffusing
drug) and held the skin in place. A rubber O-ring sat between the cell body and the
inside surface of the skin. A clamp held the entire assembly together.
The skin sample was placed over the inverted cell cap and the O-ring placed
over the skin (Figure 8). The cell body, with the magnetic stirring assembly inside,
was then fitted on top of the O-ring and the entire inverted assembly secured by the
spring clamp. Once the clamp had been tightened, the cell could be handled as a
single unit.

48
Figure 6: First incision
Donor solution (2 ml) was applied to the external surface of the skin, and the
donor compartment sealed to prevent evaporation. To assure constant sampling
intervals for multiple diffusion cells (generally three), experiments were staggered 5
minutes.
At regular intervals (1 or 2 hrs.), a 0.2 ml to 0.3 ml sample was withdrawn
from the center of the receptor volume through the upper sample port using a long,
thin needle and a 1 ml syringe. This sample was sealed in an autosampler vial for
later analysis by HPLC. The sample volume extracted was replaced by fresh,

Figure 7: Second incision
buffered saline injected by a syringe through the upper sample port. (To insure that
no air was drawn into the receptor compartment, the sample volume extracted was
less than the volume in the upper sample port arm.)
The concentrations obtained from HPLC were used to calculate the total mass
transferred through the skin. The following mass balance accounts for the sampling
process.

Figure 8: Mounting skin to cell cap
M(0C(OV+V,(EC(tx))
x=0
M(tn) Total mass transferred at time tn
C(tn) Measured concentration at time tn
V Volume of receptor compartment (15 ml)
Vs Sampled Volume (200 ¡A)
x Summation index

51
Figure 9: Franz diffusion cell
The total mass obtained from this equation can then be converted to a corrected
concentration by dividing by the receptor compartment volume (V) or to a flux by
dividing by the mass transfer area (diameter = 25 mm) and sampling interval.
In Vivo Diffusion
Two different in vivo procedures were used in this study: rat tail-flick testing
and clinical testing on human volunteers. Both procedures are described below as
well as their relative advantages and disadvantages.
Rat tail-flick test
i
Cursory screening of prototype anesthetic preparations was carried out by
anesthesiology department personnel associated with this project using the rat tail-

52
Figure 10: Schematic of rat tail Flick-o-meter
flick test. The procedure is as follows: A gauze patch moistened with an anesthetic
solution was secured to the tail of a live rat for a given period of time (usually two
hours). After removal of the patch, the rats were placed in a device which focuses
a strong light (pain stimulus) on the tail and measures the time between activation
of the light and movement of the tail out of the light beam. The level of effective
ness of the anesthetic preparations was measured by the time delay caused by the
application of the patch over the baseline delay for untreated animals. Figure 10 is
a schematic of this device.
Although this method is attractive for screening large numbers of preparations
in a relatively time, rat tails are relatively insensitive. In some cases, the results of
I

53
the rat tail testing are contrary to clinical testing in human volunteers. Once this fact
surfaced, large scale testing using rats was suspended.
Clinical studies on humans
A much more accurate, but less time efficient method for testing the
anesthetic preparations in vivo is large scale clinical testing with human volunteers.
This method is more accurate because it measures effectiveness of these preparations
in terms of the final goal; local anesthesia in humans. Unfortunately, the subjective
response of a volunteer yields data prone to wide scatter.
The procedure for these human trials was as follows: A measured volume
(usually 0.5 ml) of the anesthetic preparation, either at room temperature or warmed
to 37C, was placed on a transdermal patch (2 cm diam.) from Hill Top Research
Inc. (Figure 11). The patch was then applied to the inner forearm of the subject and
the time of application noted (Figure 12). Ten to twenty subjects were tested for
each series and up to six patches could be applied to each subject to increase the
efficiency of the procedure.
After a specified time (15 to 90 minutes), the patch was removed and any
residual liquid wiped away. Pain stimulus was provided by a hypodermic needle
(Figure 13). The subject was asked to give a rating commensurate to the effective
ness of the anesthetic. The scale used is called the Visual Analog Scale and allows
the subject to assign a value between 1 and 10 to convey no effect (1) to complete
analgesia (10).

Figure 11:
Application of drug formulation to skin patch

Figure 12:
Skin patch on arm of volunteer

56
Figure 13: Testing response of volunteer to pain stimulus
*

CHAPTER 3
PHYSICAL PROPERTIES OF DRUG FORMULATIONS
This chapter discusses the physical properties of the tetracaine acid salt, free
base, saline, propylene glycol system as measured by the experimental methods
described in the previous chapter (pages 37-44). The solubility, lipid-phase
partitioning of tetracaine were studied to estimate the transdermal diffusion of
tetracaine formulations. The surface tension, conductivity, acid-base behavior, and
quasi-elastic light scattering of tetracaine were studied to determine to microscopic
structure of the formulations. Ultraviolet absorbance and liquid chromatography
were used to quantitatively determine drug concentrations and the thermal
breakdown characteristics were studied to estimate shelf life of the anesthetic
formulations.
Tetracaine Solubility in Propylene Glycol-water Solvents
Figure 14 shows measured solubilities of tetracaine salt, tetracaine base, and
a 40% acid salt, 60% free base mixture (w/w) in propylene glycol-water solvents.*
The solubility of tetracaine base in aqueous solution is negligible. Adding propylene
*This particular mixture was chosen because at this bulk ratio (mixing tetracaine
free base and acid salt powders) the solution is near the published pK* (8.5).21 The
significance of a solution at its pKa is that there are equal amounts of ionized and
unionized solute.
57

58
glycol greatly increases the solubility of the base which peaks at about 2.65 M then
falls to 2.17 M in pure propylene glycol. The solubility of tetracaine salt decreases
slightly as the propylene glycol fraction increases, but does not change much overall
(0.5 M < C 0.8 M). The solubility of a 40% acid salt, 60% free base mixture
peaks at 3.00 M in 50% propylene glycol. The solubility of the mixture is far greater
than the sum of the salt and base solubilities in 50% propylene glycol. This
non-additivity near 50% propylene glycol shows that HC1 acid can enhance solubility
above what would be expected from the pure component solubility curves (pure salt
in solution corresponds to a bulk mixture of equal parts of tetracaine base and HC1
% Propylene Glycol (v/v)
Acid Salt
Free Base
40% Salt
60% Base
Figure 14: Tetracaine solubility in propylene glycol and saline

59
acid).21 The increased solubility in 40% free base, 60% acid salt (w/w) mixtures
cannot arise only from the protonation of the tetracaine molecule since an even
larger fraction of molecules is protonated in tetracaine acid salt. Some interaction
between the acid salt and free base forms, each stabilizing the other, appears to
occur. Since the acid salt and the free base are in equilibrium, it is not strictly
correct to consider them two different species. They are more likely assuming some
intermediate structure when they associate (partial charge). These intermediates
must be more soluble in propylene glycol/saline solutions than either the acid salt
or the free base.
Partition Coefficient of Tetracaine from Propylene Glvcol-Water Solvents
Drug partitioning between the stratum corneum and the vehicle influences
transdermal diffusion.26,52,76,78,92 Partitioning of substances into the skin can be
roughly simulated by lipid-phase partitioning between a vehicle and a hydrophobic
solvent. The ratio of drug concentrations in the vehicle and the non-polar solvent
at equilibrium is taken as the partition coefficient for the formulation (i.e.,
Qoivent/Qehicie)- In this study, no attempt was made to account for the solubility of
the vehicle in the non-polar solvent or that of the non-polar solvent in the vehicle.
Two solvents were used: 1-octanol and n-octane. Octanol was preferred for
estimating stratum corneum partitioning, but the octanol/propylene glycol/water
system is single-phase above 60% propylene glycol. Therefore, partition coefficients

60
for systems containing more than 60% propylene glycol could not be evaluated using
octanol.
Partitioning into 1-octanol
The partitioning of a 60% tetracaine free base, 40% tetracaine acid salt
mixture between propylene glycol-water solutions and 1-octanol (CH3-(CH2)7-OH)
Table 1: Tetracaine (60% free base, 40% acid salt w/w) equilibrium concentra
tions and partitioning into 1-octanol
% Propylene
^-"Vehicle
c
'-'Octanol
Kr
Glycol
(M)
(M)
0
3.59 x 10-3
2.29 x 10'2
6.37
20
3.99 x 10-3
2.22 x 10'2
5.55
40
3.87 x 10-3
2.05 x 102
5.30
50
3.99 x 10'3
1.99 x 10-2
4.99
60
3.57 x 10-3
1.70 x IQ'2
4.75
declines linearly as the organic content of the vehicle increases (Table 1, Figure 15).
At approximately 70% propylene glycol the system of 1-octanol/saline/propylene
glycol no longer develops an interface. Therefore, at high propylene glycol
concentrations, partitioning behavior cannot be assessed. To simulate the
partitioning behavior of tetracaine into a lipid phase at higher propylene glycol
i
concentrations, a more hydrophobic oil phase is required.

61

X
O
oc
u
0 10 20 30 40 50 60 70 80 90 100
% Propylene Glycol (v/v)
Figure 15: Tetracaine (60% free base, 40% acid salt w/w) partitioning into
1-octanol
Partitioning into N-octane
The partitioning of tetracaine between propylene glycol-water solutions and
n-octane (H3C-(CH2)6-CH3) is constant at about 0.004 up to 30% propylene glycol.
The partition coefficient then declines steadily with increasing propylene glycol
content up to 70% propylene glycol (Table 2, Figure 16). Above 80%, however,
partitioning into the oil phase seems to increase. It is inferred from these data that
i
a minimum partition coefficient (~0.0022) may exist between 70% and 80%
propylene glycol.
Drug solubility in the formulation indicates how much drug can be loaded into
the vehicle and, therefore; how much drug can be delivered to the skin surface. The

62
Table 2: Tetracaine (60% free base, 40% acid salt w/w) equilibrium concentra
tions and partitioning into n-octane
% Propylene
^-"Vehicle
c
'-'Octane
Kr
Glycol
(M)
(M)
0
9.38 x 10'3
3.53 x 10-5
3.77 x 10-3
10
1.08 x 10-2
4.37 x 10-5
4.03 x 10-3
20
9.56 x 10-3
3.95 x 10-5
4.13 x 10-3
30
9.73 x 103
3.86 x 10-5
3.97 x 10-3
40
1.05 x 10-2
3.34 x 10-5
3.17 x 10'3
50
1.23 x 102
3.73 x 105
3.03 x 10'3
60
9.07 x 10-3
3.04 x 10'5
3.35 x 10-3
70
1.73 x 10'2
3.86 x 10-5
2.23 x 10'3
80
1.97 x 10'2
4.34 x 105
2.21 x 10'3
90
1.19 x 10'2
3.66 x 105
3.08 x 10-3
100
1.21 x 102
3.43 x 10'5
2.85 x 10'3
partition coefficient indicates the fraction of the drug that moves from the vehicle
into a hydrophobic phase. Assuming the partition coefficient holds at saturation, the
product of the partition coefficient and the saturation concentration is an estimate
of the drug concentration at the vehicle-skin interface just inside the skin. The more
drug delivered to the skin-vehicle interface, the more drug available to diffuse across
the skin. The optimal system corresponds to a maximum in the combined solubility
partitioning parameter. If the 1-octanol partitioning data are used (Table 3,
Figure 17), the optimum system is 50% propylene glycol. If the n-octane partitioning
data are used (Table 4, Figure 18), the optimum system is also 50% propylene glycol.

63
Figure 16: Tetracaine (60% free base, 40% acid salt w/w) partitioning into
n-octane
Thus, different solvents with different partitioning behavior can be used to obtain the
same result. The optimum vehicle for tetracaine diffusion through skin as
determined by the combined solubility-partitioning parameter is 50% propylene
glycol and 50% saline regardless of which lipid is used to characterize partitioning.
Surface Tension of Tetracaine Formulations
A surface tension versus concentration plot for tetracaine HC1 in water is
presented in Figure 19. The surface tension decreases rapidly with increasing drug
concentration initially, but eventually flattens out as more drug is added. Such a
strong effect of concentration on surface tension indicates that tetracaine HC1 is

64
Table 3: Tetracaine (60% free base, 40% acid salt w/w) solubility in propylene
glycol-saline and partitioning between propylene glycol-saline and 1-octanol
% Propylene
Q>at
Kp
KpCsat
Glycol
(M)
(M)
0
1.527
6.374
9.366
20
1.591
5.547
7.815
40
1.958
5.302
11.05
50
2.979
4.992
14.38
60
2.806
4.750
13.74
Figure 17:
strongly surface active and the flattening of the curve at higher concentrations
indicates the presence of micelles at a critical micelle concentration (CMC) of

65
Table 4: Tetracaine (60% free base, 40% acid salt w/w) solubility in propylene
glycol-saline and partitioning between propylene glycol-saline and n-octane
% Propylene
CSat
Kr
KpCsat
Glycol
(M)
(M)
0
1.527
3.77 x 10'3
5.75 x 10-3
10
1.587
4.03 x 10-3
6.39 x 10'3
20
1.591
4.13 x 103
6.57 x lO'3
30
1.632
3.97 x 103
6.48 x 103
40
1.958
3.17 x 103
6.21 x 10'3
50
2.979
3.03 x 10-3
9.01 x 10'3
70
2.757
2.23 x 10-3
6.15 x lO'3
80
2.433
2.21 x 10'3
5.37 x 10'3
90
1.926
3.08 x 10'3
5.92 x 10'3
100
1.817
2.85 x 10'3
5.17 x lO3
strongly surface active and the flattening of the curve at higher concentrations
indicates the presence of micelles at a critical micelle concentration (CMC) of
approximately 0.1 M. This agrees almost identically with the previously published
value of 0.13 M.3
Similar measurements were made for tetracaine base in water (Figure 20).
The surface tension of the tetracaine base solution decreases more rapidly than for
tetracaine HC1, indicating that it is more surface active. The surface tension drops
to about 40 mN/m before the aqueous solubility of tetracaine base is exceeded.
Tetracaine base shows higher surface activity than the HC1 salt, which also appears
to be linked to its lower solubility. The surface tension data indicate that tetracaine

66
Figure 18: Product of n-octane partitioning and solubility data
base does not form micelles like the HC1 salt, but precipitates out of solution as solid
crystals.
Similar measurements were also performed in various solvents consisting of
propylene glycol and saline with a 40% tetracaine acid salt, 60% free base (w/w)
solute. The normal surface tension of the solvent ranges from 72.4 mN/m for water
to about 30 mN/m for pure propylene glycol. In order to more clearly illustrate the
effect of added solute, the surface tension (yc) has been converted to surface pressure
(7rc); where irc = y0- yc (yG refers to C = 0 or no solute). Figure 21 shows the
surface pressure of tetracaine in propylene glycol-saline solvents. Surface pressure
rises from 0 in the pure solvent to some maximum value which depends on the
solute-solvent interaction. To determine a CMC, the location of the change in slope

67
Figure 19: Surface tension of aqueous tetracaine acid salt
must be identified. Table 5 summarizes the CMC from surface pressure versus
concentration measurements. As the fraction of propylene glycol increases, the CMC
of tetracaine increases. The 20% saline, 80% propylene glycol and 100% propylene
glycol systems do not show micelle formation. The increase in CMC may be caused
by an increase in molecular drug solubility. As the molecular solubility increases, the
tendency to form micelles decreases. Micelles will cease to form as molecular
solubility continues to increase. The decrease in overall solubility of the tetracaine
mixture (60% free base, 40% acid salt w/w) from 80% to 100% propylene glycol
(v/v) may be due to the lack of micelles.

68
Figure 20: Surface tension of aqueous tetracaine free base
Conductivity
The conductivity of tetracaine salt and base versus concentration has also been
measured. The results of these measurements are in Figure 22 and Figure 23. The
conductivity of these aqueous solutions rises with drug concentration for both forms
(acid salt and free base). By analysis similar to that for surface tension versus
concentration, the critical micelle concentration can be obtained by locating a change
in slope between two linear portions.83 Through this method, the CMC of aqueous
tetracaine salt is found to be 0.03 M which is in general agreement with that from
surface tension measurements (Figure 19).

69
Topical Formulation
Concentration

O
A

V
100% PG
5.8spHs8.7
80% PG
6.5ipHi7.6
60% PG
7.0pH8.2
50% PG
6.2spHs8.4
40% PG
6.3spHs8.3
20% PG
6.3spHs8.5
Saline
6.9spHs8.4
C (M)
Figure 21: Surface pressure of tetracaine (60% free base, 40% acid salt w/w) in
propylene glycol and saline
The graph of conductivity versus concentration for tetracaine base (Figure 23)
indicates that micelles are forming at very low concentration (3 x 10'5 M). This
behavior, quite unlike that suggested by the surface tension versus concentration
graph (Figure 20), further elucidates the uncertainty of CMC values measured by
different means as well as the definition of CMC.
The conductivity vs. concentration behavior for mixtures of tetracaine acid salt
(40% w/w) and tetracaine free base (60% w/w) was also measured in propylene
glycol-saline solvents (see Figure 24 and Table 6). Comparing CMC values from
surface tension (Table 5) and conductivity (Table 6) shows that the values are in
general agreement (33%).

70
Table 5: Critical micelle concentrations of tetracaine (60% free base, 40% acid
salt w/w) in propylene glycol and saline as measured by surface pressure
% Propylene
Glycol
CMC (M)
pH Range
(Apparent)
0
(no CMC)
6.85-8.37
20
0.02
6.30-8.51
40
0.04
6.26-8.29
50
0.07
6.17-8.43
60
0.15
7.03-8.41
80
(no CMC)
6.46-7.55
100
(no CMC)
5.80-8.65
Figure 22: Conductivity of aqueous tetracaine acid salt

71
Figure 23: Conductivity of aqueous tetracaine free base
The conductivity of propylene glycol-saline mixtures decreases as propylene
glycol content increases. This is a result of fewer ions in solution as water is replaced
by propylene glycol. Propylene glycol does not dissociate appreciably in solution so
it is less capable of solvating ions or conducting electricity.
Ultraviolet Spectroscopy
The ultraviolet absorption spectra of the drugs were most important for
maximizing the sensitivity of the HPLC detector. Spectra were obtained over the
range of the HPLC detector and the wavelengths of maximum absorption determined
for the compounds of interest. The absorbance spectra of hydrocortisone,

72
+
Saline
6.9pH8.4
20% PG
6.3spHs8.5
40% PG
6.3pH8.3
50% PG
6.2spHs8.4
60% PG
7.0spH8.4
80% PG
6.5spHs7.5
100% PG
5.8spHs8.7
Figure 24: Conductivity of tetracaine (60% free base, 40% acid salt w/w) in
propylene glycol and saline
scopolamine, lidocaine, and tetracaine are shown in Figure 25-Figure 28 and the
wavelengths of maximum absorbance are in Table 7.
For hydrocortisone, the uv spectrophotometer was used at a single wavelength.
The primary absorbance maximum for hydrocortisone is 247 nm. The absorbance
at that wavelength was related to the concentration of hydrocortisone in the solution
by Beers law. This method of determining the concentration of hydrocortisone was
used because, at the time of the diffusion experiments with hydrocortisone, the
HPLC had not yet been installed.

73
Table 6: Critical micelle concentration of tetracaine (60% free base, 40% acid
salt w/w) in propylene glycol and saline as measured by conductivity
% Propylene
Glycol
CMC (M)
pH Range
(Apparent)
0
(no CMC)
6.85-8.37
20
0.03
6.30-8.51
40
0.04
6.26-8.29
50
0.06
6.17-8.43
60
0.18
7.03-8.41
80
(no CMC)
6.46-7.55
100
(no CMC)
5.80-8.65
Figure 25: Ultraviolet absorbance spectrum of hydrocortisone

74
Figure 26: Ultraviolet absorbance spectrum of scopolamine
Table 7: Ultraviolet absorbance maxima of drugs
Drug
Primary
(nm)
Secondary
(nm)
Hydrocortisone
200
247
Scopolamine
190
-
Lidocaine
213
-
Tetracaine
311
196
Chromatography
All drugs were analyzed by the same HPLC solvent mixture. The detector
wavelength was varied to correspond to the absorbance maximum (as in Table 7).

75
X (nm)
Figure 27: Ultraviolet absorbance spectrum of lidocaine
This HPLC method was originally obtained from a Supelco chromatography catalog
as a method for detecting lidocaine, but it also worked well for scopolamine and
tetracaine. The solvents in the original method were acetonitrile (90%) and aqueous
0.02 M, buffered phosphoric acid (10%) at a flowrate of 1.00 ml/min with a C8
column (a C8 carbon chain covalently bonded to a silica matrix). This method
evolved in subsequent analyses to become 72% acetonitrile, 18% 0.02 M buffered
phosphoric acid, and 10% methanol. This solvent mix minimized the retention time
of the drugs while providing adequate resolution. The identities of the peaks were
established by calibration with pure sample and noting which peak varied with the
concentration of the drug in the sample. The retention times of the drugs varied
with the batch of the phosphoric acid buffer, although Figure 29-Figure 31 show

76
A (nm)
Figure 28: Ultraviolet absorbance spectrum of tetracaine
typical chromatograms and Table 8 shows representative drug retention times
(scopolamine,* lidocaine, and tetracaine).
Equilibrium Phenomena
As already mentioned, there is an acid-base equilibrium between the acid salt
and free base of tetracaine in solution. In water, tetracaine HC1 partially dissociates
to give a tetracaine cation and a Cl" counter-ion. Alternatively, some tetracaine free
base will accept a proton from water to form the cation (the counter-ion being OH').
Since tetracaine acid salt in solution is equivalent to an equimolar solution of
*The large, early peak in the scopolamine chromatogram is chloroform which was
used in the preparation of the sample.

77
Figure 29: HPLC chromatogram of scopolamine
Table 8: Approximate HPLC retention times of drugs
Drugs
Retention Time
(min)
Scopolamine
2.50
Lido caine
2.60
Tetracaine
3.00
tetracaine free base and HC1 (acid), varying the ratio between tetracaine salt and
tetracaine free base in solution can be studied by a standard acid-base titration.

78
Figure 30: HPLC chromatogram of lidocaine
When NaOH is added to a solution of tetracaine salt, some tetracaine cations
are converted to tetracaine base and NaCl is formed. Stoichiometry allows the exact
ratio of tetracaine base and salt in the resulting solution to be calculated.
Figure 32, a standard acid-base titration plot of aqueous tetracaine, establishes
the pKa of tetracaine in aqueous solution at 8.7.* This agrees well with the value
quoted by de Jong21 (8.5). This value corresponds to protonation of the tertiary
amine group, although there is one other ionizable group in the tetracaine molecule
(c.f. Figure 2 on page 34). The secondary amine should ionize under more acidic
conditions (pH 1).
*The scatter is a result of a low concentration of the drug. This low concentra
tion is necessary because tetracaine base is only marginally soluble in saline.

79
Figure 31: HPLC chromatogram of tetracaine
The addition of propylene glycol affects the acid/base equilibrium of the
system. Figure 33 shows the apparent pH versus percent tetracaine base* in
mixtures of propylene glycol and saline. The apparent pKa rises as the amount of
propylene glycol in the solvent increases.* Also, tetracaine is unable to buffer the
solution effectively as the propylene glycol fraction increases (the curves slopes
increase in the buffered region). The inability to buffer the solution may be due to
This value corresponds to the bulk ratio of tetracaine free base and tetracaine
acid salt that would be required to reconstitute the solution (i.e., a dry mixture).
"The apparent pH of propylene glycol-saline solvents (no drug present) also
increases with increasing propylene glycol content and is probably caused by the
electrodes response to propylene glycol.

80
NaOH (mmol)
Figure 32: NaOH titration of aqueous tetracaine
the lack of free ions needed to maintain equilibrium which may arise from the lack
¡
j
of water in the system.
Measuring the apparent pH as a function of concentration can also be used
to determine the CMC. The pH versus concentration behavior for tetracaine (40%
i
acid salt, 60% free base w/w) in solvents of propylene glycol and saline is illustrated
in the following sequence of graphs (Figure 34-Figure 39). As drug is added to
solution the pH rises monotonically for all systems. At some point, the apparent pH
reaches a maximum and begins to fall. This change in slope indicates a change in
the structure of the solution. This change in structure can be viewed as the onset of
micellization; the concentration at which it occurs can be viewed as the CMC. Based

81
Saline
60% PG
% Tetracaine Base (mol/mol)
Figure 33: NaOH titration of tetracaine in propylene glycol and saline
K
o.
C (M)
Figure 34: pH of tetracaine in pro
pylene glycol.
0.00 0.25 0.50 0.75 1.00
C (M)
Figure 35: pH of tetracaine in 80%
propylene glycol and 20% saline (v/v).
on these assumptions, Table 9 lists the CMC of these solutions as measured by
apparent pH versus concentration. With the exception of 20% propylene glycol,

82
Table 9: Critical micelle concentration of tetracaine (60% free base, 40% acid
salt w/w) in propylene glycol and saline as measured by pH
% Propylene
Glycol
CMC (M)
pH Range
(Apparent)
0
0.003
6.85-8.37
20
0.004
6.30-8.51
40
0.025
6.26-8.29
60
0.072
7.03-8.41
80
(no CMC)
6.46-7.55
100
(no CMC)
5.80-8.65
C (M)
C (M)
Figure 36: pH of tetracaine in 60% Figure 37: pH of tetracaine in 40%
propylene glycol and 40% saline (v/v) propylene glycol and 60% saline (v/v)
these values agree almost as well with those of Table 5 and Table 6 as the latter do
with each other (this method is the most conservative).
Quasi-elastic Light Scattering
Many features of micellar behavior can be deduced through surface pressure,
conductivity, and even pH vs. concentration measurements. One feature, however;

83
Figure 38: pH of tetracaine in 20% Figure 39: pH of tetracaine in saline
propylene glycol and 80% saline (v/v)
% Propylene Glycol (v/v)
Figure 40: Micelle diameter of tetracaine (60% free base, 40% acid salt, 0.36 M)
in propylene glycol and saline by QELS
cannot be determined with these methods: micelle size. Micelle size can be
accurately determined with light scattering techniques. Figure 40 shows the diameter
of micelles made of 40% acid salt (w/w) and 60% free base (w/w) at a concentration

84
of 0.36 M overall in selected solvents of propylene glycol and saline. The largest
micelles are in the purely aqueous system and micelle size decreases rapidly as the
organic fraction increases until at 80% propylene glycol no micelles are detected.
Therefore, as the fraction of propylene glycol increases; the CMC increases and the
micelle diameter decreases. The enormous size of the micelles in the aqueous
solution suggests that the micelles may not be typical spherical micelles.
Thermal Breakdown of Tetracaine
The thermal degradation of tetracaine was measured to determine the
maximum shelf-life of a transdermal formulation containing tetracaine free base.
The concentration of tetracaine (40% acid salt, 60% free base w/w) in a solution of
40% propylene glycol and 60% saline (v/v) was measured over 14 days. The
measured concentration of solutions at 24C and 32C were scaled relative to an
identical solution stored at 5C. The remaining fraction of tetracaine in solution was
termed viability.
The thermal breakdown of tetracaine is more rapid at 32 C than at 24 C,
although there is measurable loss of drug even at room temperature (Figure 41). To
limit thermal breakdown to 10%, the maximum storage life (at room temperature)
To determine the micelle diameter using QELS the viscosity and refractive index
of the solvent were estimated. This was accomplished by linear interpolation based
on the fraction of propylene glycol. The refractive index of propylene glycol was
obtained from The CRC Handbook of Chemistry and Physics. The viscosity of
propylene glycol was calculated using a correlation in The Properties of Gases and
Liquids by Reid, Prausnitz, and Sherwood.

85
Time (days)
Figure 41: Thermal breakdown of tetracaine (60% free base, 40% acid salt w/w)
in 40% propylene glycol, 60% saline (v/v)
is two to three days. This limitation means that the formulation must either be
prepared no more than three days before use or kept at 5C. All formulations in
this study were prepared one day in advance so that the thermal breakdown of
tetracaine base in solution is not an issue.

CHAPTER 4
DRUG DIFFUSION IN VITRO
Calibration
The diffusion of solubilized drugs through skin was measured with procedures
already outlined (page 45). The results of these experiments are presented in two
parts: calibration experiments and the diffusion of local anesthetics through mounted
mouse skin.
The calibration experiments served many purposes such as locating difficulties
in the experimental procedure and the relative effects of different parameters on the
flux of drugs through skin and porous membranes. The factors studied through these
calibration experiments were stirring rate, the behavior of skin relative to a synthetic
membrane, the temperature behavior of the system, and the effect of hydration and
swelling of the skin.
Stirring Effects Using Synthetic Membranes
The first diffusion experiments involved the diffusion of aqueous hydrocorti
sone through a synthetic, microporous, polycarbonate membrane (nominal pore
diameter of 0.22 /im). This system was chosen because both the drug and the
membrane had been well characterized by previous investigators49 and the materials
86

87
were readily available in the laboratory. The first experiments used the spectropho
tometer to find the concentration of hydrocortisone in both the donor and receptor
phases as a function of time. Since hydrocortisone diffused quickly through the
synthetic membrane relative to the diffusion of the anesthetics through skin, data
from all stages of the diffusion process were obtained (initial behavior through the
approach to equilibrium). This would have taken weeks or months with real skin or
a less permeable drug. In addition, the rapid diffusion of hydrocortisone helped
amplify the effect of stirring on diffusion since the boundary layer effects are most
pronounced for rapidly diffusing compounds.
Device effects
The effect of different types of stirring apparatus is shown in Figure 42. The
three curves represent the diffusion of hydrocortisone through a synthetic micro-
porous membrane when a) no stirring apparatus was used, b) a small stirring magnet
which only stirred the lower portion of the receptor compartment was used, and, c)
a wire tee which stirred the entire receptor compartment was used. The upper
(donor) phase of the diffusion cell was stagnant in all experiments. In b) and c) the
stirring rate (rpm) was the same. The graph shows that the stirring bar was
ineffective. The use of the wire tee efficiently decreased the effect of the stagnant
boundary layer in the receptor compartment.
Based on the results of these experiments stirring tees were constructed of
nylon for use in all subsequent diffusion experiments. Each tee had a small magnet
in its base driven by a magnetic stirrer.

88
Stagnant
Stirring Bar
Stirring Tee
Figure 42: Effect of stirring device on the diffusion of aqueous hydrocortisone
through synthetic membranes
Rate effects
A separate experiment illustrates the effect of stirring rate on the efficiency
of the stirring tees to eliminate the boundary layer beneath the skin. The inverse of
the stirring rate is plotted against the flux of hydrocortisone through the same
synthetic membrane (nominal pore diameter of 0.45 un) in Figure 43. Conceptually,
flux should increase monotonically as the stirring rate increases, but the best line
through the scattered data is flat. There are two regions in which the flux is
independent of the stirring rate: the stagnant limit and the completely mixed limit.
In order to determine which regime the plotted data represented, data were collected
at stagnant conditions (0 rpm). The flux was found to be significantly lower than any

89
0.040
'
w 0.030
m
+-
g
6 0.020
v->
es
Jj 0.010
E
0.000
0.000 0.001 0.002 0.003 0.004
(Stirring Rate (rpm))1
Figure 43: Effect of stirring rate on the diffusion of aqueous hydrocortisone
through synthetic membranes
of the stirred systems. Therefore, the collected data represented the completely
mixed limit and nothing would be gained by increasing the stirring rate beyond 300
rpm.
Temperature Behavior of Diffusion Apparatus
Every attempt was made to simulate in vivo conditions in the diffusion cells.
The temperature behavior of the diffusion cells before and after application of the
transdermal formulation was evaluated to anticipate possible transient effects of
temperature on diffusion. Such effects, if detected, would have to accounted for
when interpreting the data.

90
Receptor phase and constant temperature circulator
The warm-up behavior of the temperature controller and the receptor phase
of the diffusion cells was investigated to determine whether the time required for the
Uncapped
Capped
Time (min)
Figure 44: Dynamic receptor phase temperature in Franz cell
diffusion apparatus to come to thermal equilibrium (ready for drug application)
would be restrictive. The temperature of the lower (receptor) phase was monitored
as a function of time for both capped and uncapped cells as the circulator was turned
on (Figure 44). These data show that the receptor phase reached thermal
equilibrium in 10 to 15 minutes with a temperature difference of approximately 3.5C
(capped). In practice, the circulator would be at room temperature as well, so the
shorter time required for the cells to reach equilibrium was not considered a factor

91
and as soon as the constant temperature circulator reached equilibrium the cells were
assumed to be at equilibrium.
Donor phase
The temperature behavior of all donor phases was estimated using a worst-
case scenario of the most viscous donor phase (pure propylene glycol with 0.36 M
tetracaine) at room temperature. The temperature of the donor phase was
monitored with time using an iron-constantan thermocouple as 37C water circulated
through the cell jacket. The results of the experiment (Figure 45) show that the
temperature of the donor phase reached equilibrium in approximately 3 minutes.
0 5 10 15
Time (min)
Figure 45: Dynamic donor-phase temperature in Franz cell (VD = 2 ml)

92
Since concentration was measured no earlier than one hour, the effect of this warm
up period on diffusion was neglected.
Skin Swelling
The time dependent thickness of the skin after exposure to the solvents was
monitored (as per the procedure in Chapter 2, page 40) in an attempt to determine
the effects such swelling have on transdermal diffusion. The initial thickness of the
Figure 46: Dynamic swelling of excised hairless-mouse skin immersed in water
skin was estimated by assuming a density of 1 g/ml for a skin sample of known mass
and cross-sectional area. This initial thickness was found to be 0.68 mm. The skin

93
sample was then immersed in water and its mass monitored periodically. The skin
was found to absorb water rapidly for the first 5 to 6 hours and much more slowly
afterwards. Figure 46 shows the thickness versus time for skin immersed in water for
approximately two days. The data show that full thickness hairless-mouse skin can
absorb about four times its mass in water and swells to a comparable degree. The
increasing scatter of the data with time results from a loss of the skins integrity.
Scopolamine Diffusion
The first full-scale diffusion experiment performed for this project was the
diffusion of aqueous scopolamine base through mounted mouse skin. The purpose
of this experiment was to identify problems in the experimental procedure and
compare the experimental results to those published previously.
Another aim of this experiment was to determine the dynamic role of skin
hydration on diffusion (using scopolamine) since this study focuses on short term
behavior. In previous experiments in transdermal diffusion, interest centered on
systemic drugs. The goal of these experiments was to determine the long term
(steady state) flux of drug through the skin. To accomplish this goal, the skin had
to be chemically preserved to avoid decomposition. For the delivery of local
anesthetics, the experiments were to be of much shorter duration. The swelling of
the skin early in the experiments could be significant as could the presence of a
chemical preservative.

94
Figure 47 shows the cumulative flux of scopolamine through hairless-mouse
skin as a function of time for skin treated two different ways. In one case, the skin
Fresh
Hydrated and
Preserved
Time (hrs)
Figure 47: Diffusion of aqueous scopolamine through fresh and chemically
preserved hairless-mouse skin
is mounted in the diffusion cell and allowed to contact a solution of 0.1% (w/w)
formaldehyde on both sides for 48 hours. In the other case, the skin is fresh and
untreated. For a preliminary experiment, the quality of the data is good and shows
the validity of the technique and the reliability of the HPLC as a method for
determining trace concentrations of scopolamine. The error is due to the differences
between individual mice. Hydration and preservation of the skin have a strange
effect on the diffusion of scopolamine. This single experiment could only establish
that the processes of hydration and preservation increase flux. The source of the

95
effect could not be determined (i.e., the results could be due to hydration, the
presence of formaldehyde, or both).
Figure 48 shows the steady state flux of scopolamine through hairless-mouse
skin as determined by Chandrasekaran et al.17 (fully hydrated and preserved) as well
Fresh
Hydrated
Donor Concentration (g/1)
Figure 48: Comparison of experimental scopolamine diffusion data to data of
Chandrasekaran et al.
as the values obtained in this first experiment. The measured flux and the value
reported by Chandrasekaran et al.17 agree for the fully hydrated and chemically
preserved skin. The steady state flux for the untreated skin is an order of magnitude
below that of the hydrated preserved skin, although the scatter makes this difference
insignificant. This difference in the diffusion of scopolamine caused by the treatment
of the skin is the reason for deciding to use fresh untreated skin in subsequent

96
experiments and more closely simulate the behavior of live skin in vivo. The results
of this experiment suggest that hydration and preservation of the skin significantly
alter diffusion. The deconvolution of hydration and preservation effects is explored
later in this chapter (page 105).
Transdermal Diffusion of Local Anesthetics
Measuring the diffusion of lidocaine and tetracaine through mounted mouse
skin identifies preparations likely to be effective for human use. Parallel experi
ments, using identical local anesthetic preparations for both in vitro (mouse skin) and
in vivo (human volunteers) systems, show a high degree of correlation (cf. Chapter
6). The main advantage of the in vitro method is the ability to achieve more
accurate quantitative results. Other issues studied are the effect of formaldehyde as
a preservative for in vitro transdermal diffusion, skin swelling in vitro, time limits for
experiments, and the effects of propylene glycol, pH, concentration, and mouse age.
Theoretical Considerations
Assuming Fickian diffusion, the parameters which influence diffusion are well
defined. The driving force for diffusion is the concentration at the inner surface of
the skin. This concentration is determined by the concentration in solution, the
characteristics of the boundary layer, and the partition coefficient between the
solution and the skin. If the boundary layer thickness is assumed to be negligible,
then the concentration at the outer surface of the skin equals the bulk concentration.

97
The result of these assumptions is that the driving force for diffusion is now
determined solely by the bulk concentration and partitioning between the solution
and the skin.
Vehicle/stratum corneum partition coefficients are difficult to measure
experimentally so an organic solvent is usually substituted for the skin. This requires
assuming that drug partitioning into the organic solvent is similar to partitioning into
the stratum corneum.
The structure of the skin affects transdermal diffusion. The location, size,
number, and geometry of structures in the skin affect the overall resistance to
diffusion in the skin. The sheer complexity of the skin makes any theoretical
accounting for these structures effects on diffusion almost impossible. Consequently,
the skin is assumed to be homogeneous, devoid of all internal structure, and
characterized by a lumped parameter. Once homogeneity is assumed, the parameters
describing the resistance to diffusion are the thickness of the skin and the overall
diffusivity of the drug within the skin.
Lidocaine Salt
As already mentioned, lidocaine was the first drug used for both in vitro and
in vivo transdermal diffusion experiments. The in vitro experiments involving
lidocaine helped to establish the maximum length of experiments, but lidocaine was
later abandoned in favor of tetracaine for transdermal diffusion.

98
Longevity of skin
The diffusion of aqueous lidocaine HC1 through fresh, untreated hairless-
mouse skin was observed over 72 hours. During this experiment, no dramatic change
Time (hrs)
Figure 49: Long-term diffusion of aqueous lidocaine salt through untreated
hairless-mouse skin
in the diffusion rate occurred (note the nearly constant slope in Figure 49). It was
decided, therefore, that fresh, untreated skin would be adequate as the barrier to
drug diffusion for periods not to exceed 10 hours.
Effect of 50% propylene glvcol versus saline
Figure 50 shows the cumulative flux versus time behavior for the diffusion of
lidocaine HC1 through hairless-mouse skin from saline and a 50% propylene glycol,
50% saline solution (v/v) at a drug concentration of approximately 1.86 M. The

99
Aqueous
--- 50% PG
Time (hr)
Figure 50: Effect of propylene glycol on the diffusion of lidocaine salt through
untreated hairless-mouse skin
figure indicates that the drug diffusion rate is not significantly affected by the
presence of 50% propylene glycol. The testing of lidocaine containing preparations
was suspended when the decision was made to use tetracaine, a more potent drug
with better partitioning characteristics.21
Diffusion of Tetracaine
Tetracaine was chosen as a more attractive drug than lidocaine for trans-
dermal applications because it is more effective as an anesthetic (by weight).21
Tetracaine also partitions more favorably into nerve tissue.21

100
Tetracaine salt (50% propylene glycol versus saline)
Experiments using tetracaine HC1 exclusively as the anesthetic examined the
effect of propylene glycol on diffusion. These experiments attempted to parallel
experiments with lidocaine HC1 and lead to comparisons of the effect of propylene
glycol on the diffusion of tetracaine HC1 through hairless-mouse skin.
Figure 51 shows the cumulative flux into the receptor phase as a function of
time for the diffusion of tetracaine HC1 from saline and 50% propylene glycol, 50%
Aqueous
pH4.8
50% PG
pH5.1
Time (hrs)
Figure 51: Effect of propylene glycol on the diffusion of tetracaine HC1 through
hairless-mouse skin
saline solutions. The 50% propylene glycol solution inhibited the diffusion of the
drug across the skin. There are several possible reasons for this: The increased
viscosity of the 50% propylene glycol solution may result in a formidable boundary

101
layer above the skin.* Propylene glycol may have some effect on the skin which
increases the skins resistance to diffusion or propylene glycol may decrease the
partitioning of tetracaine into the skin as it makes the formulation more lipophilic.
Another possibility is that propylene glycol somehow affects the equilibrium between
tetracaine HC1 and tetracaine base and reduces the amount of free base available
for diffusion.
Tetracaine mixtures
Effect of propylene glycol. The effect of propylene glycol on the diffusion of
tetracaine mixtures is complex. The diffusion of tetracaine mixtures (40% acid salt,
60% free base w/w 0.36 M overall) in solvents of propylene glycol and 0.9% saline
was investigated in two systems. The flux of tetracaine through polycarbonate
synthetic membranes was studied to determine the effect of propylene glycol on a
simple, well characterized membrane. Then identical formulations were allowed to
diffuse through skin from mice approximately 6 to 8 weeks old.
The cumulative flux of these tetracaine formulations through synthetic
polycarbonate membranes (nominal pore diameter of 0.45 /m) after five minutes is
shown in Figure 52. The polycarbonate membrane is hydrophilic and, not
surprisingly, the highest flux through the membrane results from the fully aqueous
formulation since the membrane is easily wetted by the aqueous formulation. It is
also not surprising that the flux of tetracaine decreases at higher propylene glycol
*The viscosity of propylene glycol is about 24.7 cp. The viscosity of water is
about 0.9 cp at room temperature.

102
Apparent pH
% Propylene Glycol (v/v)
Figure 52: Effect of propylene glycol on the diffusion of tetracaine (60% free base,
40% acid salt w/w) through synthetic polycarbonate membranes
concentrations since the viscosity and hydrophobicity both increase. The existence
of a local maximum in flux at 40% propylene glycol, however, is surprising. Although
such a maximum is suggested by the partitioning and solubility data in Chapter 3,
that data represents partitioning into a hydrophobic medium and do not necessarily
apply to this hydrophilic membrane. Nonetheless, it appears that there is something
special about this 40% propylene glycol solvent beyond those properties already
measured.
Figure 53 shows the cumulative flux of tetracaine (60% free base, 40% acid
salt w/w, 0.36M overall) through hairless-mouse skin over 8 hours. The maximum

103
Apparent pH
% Propylene Glycol (v/v)
Figure 53: Cumulative flux of tetracaine (60% free base, 40% acid salt w/w) in
propylene glycol and saline through hairless-mouse skin (young mice)
flux in this system corresponds to a vehicle of 40% propylene glycol and 60% saline
(v/v).
In Chapter 3 (page 62), the product of solubility and partition coefficient
(combined solubility-partitioning parameter or KpCsat) is used to predict the relative
flux of tetracaine from vehicles of propylene glycol and saline. Although 1-octanol
and n-octane are vastly different in terms of their affinity for tetracaine, they both
predict the maximum flux at 50% propylene glycol. The accuracy of these earlier
predictions can be assessed by comparing these data with the experimental fluxes
(synthetic membrane and hairless-mouse skin).

104
The measured fluxes through synthetic membranes and hairless-mouse skin
(Figure 52 and Figure 53) both show a maximum at 40% propylene glycol. The
combined solubility-partitioning parameters for both 1-octanol (Figure 17 and
Table 3) and n-octane (Figure 18 and Table 4) predict a maximum at 50% propylene
glycol. Therefore, this combined solubility-partitioning parameter does roughly
estimate the composition of the optimum vehicle.
The results of these diffusion experiments establish the composition of the
vehicle for the transdermal delivery of tetracaine as 40% propylene glycol and 60%
saline. The existence of this optimum vehicle can be partly explained by the
relatively high solubility of tetracaine and favorable partitioning of the drug into
lipids. Thus, a major goal of this project is realized; the optimization of a topical,
local anesthetic formulation.
The combined solubility-partitioning parameter for 1-octanol (Figure 17 and
Table 3) also predicts the decreasing flux between saline and 20% propylene glycol
for both synthetic membranes and hairless-mouse skin, but fails to predict the rapid
decrease of flux at higher propylene glycol contents (> 60%). Alternately, the
combined solubility-partitioning parameter for n-octane (Figure 18 and Table 4) fails
to predict the high flux at 40% propylene glycol. Consequently, the combined
solubility-partitioning parameter has limitations as a correlation for transdermal flux
and should not be relied on as a definitive method for predicting relative transdermal
flux. A more appropriate and conservative role for this data is as a first estimate of
the optimum vehicle which should be subsequently established by diffusion studies.

105
Effect of age. These same tetracaine formulations were tested on the skin of
older mice (6 to 8 months) to determine how age affects the transdermal diffusion
Apparent pH
% Propylene Glycol (v/v)
Figure 54: Cumulative flux of tetracaine (60% free base, 40% acid salt w/w) in
propylene glycol and saline through hairless-mouse skin (old mice)
of these formulations. The general trend of the data in Figure 54 is unchanged from
that of Figure 53. Although age did not influence the trend, the older mice have
much less permeable skin than the younger mice. The cumulative flux of tetracaine
through the skin of the older mice over eight hours averaged only 20% that through
younger skin for all formulations tested.
Effect of formaldehyde
It has already been established that the process of preservation and hydration
of the skin affects the diffusion of scopolamine (page 95). The data gathered was not

106
sufficient to determine the individual effects of formaldehyde and hydration on
transdermal diffusion. Hydration has long been known to increase the permeation
of many substances. The effect of formaldehyde on diffusion was not so well
established. An additional experiment examined the effect of formaldehyde on
tetracaine diffusion through fresh, untreated skin.
The effect of low concentrations (0.1% w/w) of the preservative formaldehyde
on tetracaine diffusion through the skin is illustrated in Figure 55. The figure shows
Figure 55: Effect of 0.1 % (w/w) formaldehyde on the diffusion of tetracaine
(60% free base, 40% acid salt w/w, 0.36M tetracaine overall) in 40% propylene
glycol and 60% saline (v/v) through old hairless-mouse skin
the flux of 40% tetracaine acid salt, 60% free base (w/w) (0.36M tetracaine overall)
in 40% propylene glycol through mounted mouse skin into buffered saline or

107
buffered saline with 0.1% formaldehyde (w/w). Formaldehyde seems to inhibit
tetracaine diffusion through mouse skin by an average of 8% over an 8 hour period.
This result may be due to either a chemical change in the skin structure brought on
by formaldehyde or a decrease in drug flux caused by the counter diffusion of
formaldehyde through the skin.
To find whether formaldehydes inhibition of tetracaine diffusion is a result
of counter diffusion, an identical system was prepared with formaldehyde in equal
concentration on both sides of the skin. This configuration eliminates the
formaldehyde concentration-differences. If the effect of formaldehyde is solely
through counter-diffusion, this system should behave like the system with no
formaldehyde. If formaldehyde reduces the permeability of the skin, then it should
reduce permeability below even that found with formaldehyde in the downstream
reservoir.
The results show that the total amount of formaldehyde in the system is the
key (Figure 56). The low formaldehyde concentration (0.1% w/w) probably does not
affect the drug solubility or partitioning. Although Figure 56 does not show a great
difference between the three systems, higher formaldehyde content tends to cause
lower fluxes. Formaldehyde, therefore, increases the resistance to diffusion through
some interaction with the skin.

108
Figure 56: Effect of formaldehyde location on the diffusion of tetracaine (60%
free base, 40% acid salt w/w, 0.36M tetracaine overall) in 40% propylene glycol and
60% saline (v/v) through old hairless-mouse skin
Effect of concentration
Figure 57 shows how donor phase drug concentration affects the flux of a 40%
tetracaine acid salt, 60% free base (w/w) mixture (0.36M tetracaine overall) through
hairless-mouse skin. If the mechanism of diffusion is strictly Fickian, then the flux
should be proportional to the donor phase concentration and the graphs should be
straight lines. The nearly constant transdermal flux, despite doubling the donor
phase concentration, indicates that the driving force for diffusion stays about
constant. A constant driving force suggests that the topical formulation is not a
simple molecular solution and that it probably contains micellar aggregates of

109
1000
800
600
400
200
0
0.36 0.72
Donor Concentration (M)
Figure 57: Effect of drug concentration on the diffusion of tetracaine (60% free
base, 40% acid salt w/w) in 40% propylene glycol and 60% saline (v/v) through
hairless-mouse skin
tetracaine. This result agrees with the conclusion that there are indeed micelles in
the tetracaine formulations (page 66).
Effect of mixture ratio (pH effect!
To determine the effect of pH, three solutions were used that were identical
except for their pH. One solution contained tetracaine free base, another, tetracaine
acid salt which, in solution, corresponds in bulk to equal parts of tetracaine base and
HC1 acid; and the third, a 40% acid salt-60% free base (w/w) mixture. This
experiment was further complicated in that a suitable propylene glycokwater ratio
had to be found for which the three systems were single phase. Tetracaine base is
not sufficiently soluble in the optimal 40% propylene glycol solution (solubility had

110
100% 40% Acid Salt 100%
Acid Salt 60% Free Base Free Base
PH
Figure 58: Effect of pH on the diffusion of tetracaine (60% free base, 40% acid
salt w/w, 0.36M tetracaine overall) in 40% propylene glycol and 60% saline (v/v)
through young hairless-mouse skin
to be at least 0.36 M for all three systems to reproduce conditions already studied).
Consequently, a higher propylene glycol content of 70% was used. Figure 58 shows
the results of tetracaine diffusion in 70% propylene glycol experiments at pH = 4.71,
8.5, and 12.2 with an overall drug concentration of 0.36 M through young hairless-
mouse skin. The figure shows that the flux of drug is significant in the range
8.5 < pH < 12.2 and negligible for pH < 4.71. Below some minimum value of pH,
therefore, the flux of tetracaine through skin falls to zero. This is probably caused
by the decreasing amount of tetracaine free base available in solution. Tetracaine
free base has been found to penetrate the skin much better than the acid salt.61

CHAPTER 5
DRUG DIFFUSION IN VIVO
Rat Tail-flick Test
Many compounds were tested using the rat tail-flick test, however only a few
are significant to this project. Formulations of lidocaine and tetracaine showed, as
a whole, little ability to cause analgesia in the rat tails. Specifically, most compounds
tested could not produce a significant delay of the tail-flick response (the rat tail-flick
test is described in Chapter 2, page 51).
Twenty-eight different rat tail-flick tests were conducted. The best ten
compounds, those that caused the longest delay of the rat tail-flick response, are
listed in Table 10. For some general anesthetic applications, an infinite delay of the
tail flick response may be observed (complete loss of sensation). Some solutions
referred to in Table 10 did not give consistent results. Furthermore, neither the
aqueous tetracaine HC1 solutions nor the lidocaine HC1 microemulsions rank
themselves by their concentrations. The discrepancy may result from anatomical
differences like density of nerve cells, blood flow, fat content, and temperature.
However, the rat tail-flick test does generally rank tetracaine formulations above
lidocaine formulations. Furthermore, a solution similar to the formulation found to
be optimal in in vitro studies (50% propylene glycol, 50% saline with 62.5%
111

112
Table 10: Best rat tail-flick test results
Test solution
Mean delay (s)
Standard
deviation (s)
1.33 M aqueous
tetracaine salt
2.08
1.77
1.65 M tetracaine base
in 73% propylene glycol
and 27% saline
1.89
1.29
2.87 M tetracaine
(62.5% free base, 37.5%
acid salt) in 50% propyl
ene glycol and 50%
saline
1.75
1.52
0.83 M tetracaine salt in
50% propylene glycol
and 50% saline
1.58
0.94
0.31 M lidocaine
salt micro
emulsion
1.53
1.58
0.33 M lidocaine salt
macro-emulsion
1.30
1.12
0.83 M aqueous tetra
caine salt
1.23
0.63
1.39 M lidocaine salt
micro
emulsion
1.18
1.87
0.92 M lidocaine salt
micro-emulsion
1.14
0.88
1.33 M aqueous tetra
caine salt
1.10
2.07
tetracaine free base and 37.5% acid salt) ranked #3 by the rat tail-flick test.
Therefore, although the rat tail-flick test cannot be relied upon for ranking anesthetic

113
formulations, there is a correlation between the tail-flick delay and the diffusion of
tetracaine in vitro.
Clinical Trials
Although both lidocaine and tetracaine preparations were tested on human
volunteers, the vast majority of the tests involved tetracaine (88 versus 6 for
lidocaine). Lidocaine was phased out in favor of tetracaine and rat tail-flick testing
was phased out in favor of clinical testing. The procedure for clinical trials is
discussed in Chapter 2 (page 53).
Lidocaine
The lidocaine preparations tested on volunteers and their performance in
clinical testing are summarized in Table 11. The visual analog scale (VAS) uses
values of 1 (to indicate no effect) to 10 (complete anesthesia). The inability to
produce significant analgesia by lidocaine in clinical trials (VAS > 7), led to the
decision to abandon lidocaine as the anesthetic agent for transdermal formulations.
Tetracaine
Clinical testing of anesthetic formulations containing tetracaine succeeded the
lidocaine trials. Several parameters related to the in vivo transdermal diffusion
procedure were investigated. Site preparation, time, and dose response data helped
to optimize and characterize the topical formulation.

114
Table 11: Clinical trials of lidocaine preparations
Test Solution
Mean response
(VAS)
Standard
deviation (VAS)
1.85 M aqueous
lidocaine salt
0.95
1.70
1.85 M lidocaine salt in
50% propylene glycol
1.15
1.50
1.71 M lidocaine base in
70% propylene glycol
2.54
3.20
1.07 M lidocaine base in
50% propylene glycol
4.46
3.70
1.00 M lidocaine (50%
free base, 50% acid salt
w/w) in 65% propylene
glycol
5.07
3.60
1.59 M lidocaine (50%
free base, 50% acid salt
w/w) in 70% propylene
glycol
3.20
3.40
Site preparation
Cleansing the skin with isopropyl alcohol before applying the tetracaine
formulation increases the mean response after one hour by approximately 20%
(Figure 59). Presumably, this cleansing removes excess lipids from the skin and
provides better contact for the anesthetic formulation. Unfortunately, the scatter in
this data makes this difference statistically insignificant.

115
oo
<
>
Figure 59: Effect of alcohol cleansing on the diffusion of tetracaine (60% free
base, 40% acid salt w/w) in 40% propylene glycol and 60% saline (v/v) through
human skin in vivo
Dose response
The minimum concentration of drug required to produce effective analgesia
in one hour was measured by applying patches wetted with the anesthetic formulation
and testing the subjects responses to the pain stimuli after one hour. Three different
systems were evaluated for minimum drug concentration: 1) tetracaine free base in
75% propylene glycol-25% saline (v/v), 2) 50% tetracaine free base-50% tetracaine
acid salt (w/w) in 40% propylene glycol-60% saline (v/v), and 3) 60% tetracaine free
base-40% tetracaine acid salt (w/w) in 40% propylene glycol-60% saline (v/v).
The dose response data for tetracaine free base in 75% propylene glycol and
25% saline (v/v) are in Figure 60. The effectiveness of the anesthetic preparation

116
% (w/v)
O 20 40 60 80
Figure 60: Dose response for tetracaine free base in 75% propylene glycol and
25% saline (v/v) through human skin in vivo
seems to increase until the concentration reaches approximately 0.3 M. Above
0.3 M, the subjects responses seem to level off, indicating that the maximum rate of
transfer has been achieved. The scatter in the clinical response data makes it
difficult to interpret because the trend is not statistically significant. Furthermore,
the level of analgesia is unsatisfactory (VAS < 5).
The dose response data for a system consisting of 50% tetracaine free base
and 50% acid salt (w/w) in 40% propylene glycol and 60% saline after one hour are
in Figure 61. This preparation gives higher scores than the system containing only
tetracaine free base and the scores increase beyond a tetracaine concentration of
4 M. This preparation achieves a mean VAS of 8.6 at 4.2 M and could be used

117
% (w/v)
O 20 40 60 80 100 120 140
Figure 61: Dose response for 50% tetracaine free base and 50% acid salt (w/w)
in 40% propylene glycol and 60% saline (v/v) through human skin in vivo
reliably in a clinical setting. Unfortunately, such high concentrations of tetracaine
cause erythema (local redness) in most human subjects making this formulation
unsuitable.
The last system investigated consists of 60% tetracaine free base, 40% acid
salt (w/w) in 40% propylene glycol and 60% saline (v/v). This system also produces
very high scores, but at much lower concentrations. Figure 62 shows that the
response plateau is achieved at only 0.3 M (8.4% w/v) tetracaine. This concentration
is sufficiently low to make erythema rare.

118
% (w/v)
O 20 40 60 80 100
Figure 62: Dose response for 60% tetracaine free base 40% acid salt (w/w) in
40% propylene glycol and 60% saline (v/v) through human skin in vivo
Time response
The onset of analgesia is measured by testing for topical anesthesia as a
function of time. Several identical patches are applied to a subject and, at a
specified time, one patch is removed and the area tested (as in Chapter 2: Materials
and Methods, page 53). Figure 63 shows the time response curves for high drug
concentrations (1.1 M, 1.8 M); Figure 64 shows the time response curves for low to
medium concentrations (0.036 M 1.004 M). For comparison, these plots also show
the placebo effect. The formulations consist of varying concentrations of tetracaine
(40% acid salt, 60% free base w/w) in a solvent of 40% propylene glycol and 60%
saline. For high concentrations of tetracaine, the anesthetic formulations were

119
piacebo
1.8 M
(50% w/v)
-o- 1.1 M
(30% w/v)
Concentration
0
1
2
Time (hr)
Figure 63: Time response for in vivo analgesia by tetracaine (60% free base, 40%
acid salt w/w in 40% propylene glycol and 60% saline (v/v) (1.1 M, 1.8 M)
distinguishable from the placebo after 45 minutes. For lower concentrations,
however; no statistically significant distinction was achieved because, although the
subject responses are very high, the scatter makes data difficult to interpret.
Comparison to in vitro results
Of all the systems tested on human subjects in vivo, the formulation consisting
of 60% tetracaine free base, 40% acid salt (w/w) in 40% propylene glycol and 60%
saline (v/v) is the most effective. This is precisely the system found to be most
effective in in vitro experiments with hairless-mouse skin (Chapter 4, Figure 53 and
Figure 54, pages 102 and 105). Formulations containing 40% propylene glycol gave
the highest transdermal fluxes in vitro. The combined solubility-partitioning

120
oo
<
>
Placebo
0.036 M
(1.0% w/v)
0.125 M
(3.5% w/v)
0.251 M
(7.0% w/v)
0.502 M
(14.0% w/v)
1.004 M
(28.0% w/v)
Time (hr)
Figure 64: Time response for in vivo analgesia by tetracaine (60% free base, 40%
acid salt w/w) in 40% propylene glycol and 60% saline (v/v) (0.036 M 1.004 M)
parameters for 1-octanol and n-octane also predict the optimum formulation in this
vicinity (Figure 17, Table 3 and Figure 18, Table 4). Therefore, the system of 60%
tetracaine free base, 40% tetracaine acid salt (w/w) in a solvent of 40% propylene
glycol and 60% saline (v/v) is confirmed as the optimum combination by in vitro
diffusion and in vivo diffusion. The existence of an optimum vehicle is also
supported by the combined solubility-partitioning parameters for 1-octanol
(Figure 17, Table 3) and n-octane (Figure 18, Table 4). The similarity between the
in vitro and in vivo results also indicates that in vitro fluxes and human subject
responses are related.

CHAPTER 6
THEORY
Many models predict percutaneous absorption, but most assume the drug
concentration-profile within the skin has reached steady state (i.e., the concentration
profile is linear within the skin).25,42,60,97 Although steady state may be a valid
assumption for drugs that diffuse quickly, steady state models cannot predict the early
stages of drug diffusion which disobey the linear concentration-profile assumption.
When a substance is applied to the skin, the existing steady state changes
suddenly. Where no drug was present, there is now a high concentration at the
external surface. Predictions of the concentration profile within the skin can help
predict the drug flux through the skin. Such predictions are valuable for substances
that have relatively low therapeutic or toxic levels. These substances can have
profound effects long before steady state is reached. In other applications, e.g.,
dermatological, knowledge of drug concentration versus depth within the skin is
essential. Drug diffusing into drug-free skin initially creates an exponential*
concentration profile.26 With time, the concentration profile becomes linear (i.e.,
steady state). If the amount of drug crossing the skin is small and if a linear
Actually, the initial concentration profile is described by an error function
(erf(x)) and such a solution can be found in Transport Phenomena by Bird, Stewart,
and Lightfoot.7
121

122
concentration profile is achieved quickly, then assuming steady state is valid. During
steady state, determining concentration is relatively easy; prior to steady state,
calculations are more difficult. The quasi-steady state model can often be used for
cases where the steady state assumption is not valid. Its sole assumption is that the
concentrations on either side of the skin change much more slowly than the
concentration within the skin.
The model developed here is a numerically integrated, quasi-steady state, one
dimensional Fickian diffusion model with appropriate boundary conditions. The
model uses an effective diffusion coefficient for the drug and describes the diffusion
of drug from a finite donor phase, through the skin, into a receptor phase.
For in vitro diffusion in a Franz cell, the receptor phase is a finite sink, but
for in vivo diffusion the receptor phase concentration would be determined by skin
metabolism and circulatory removal of drug.
Idealized System
The in vitro model of transdermal diffusion is designed to simulate the
diffusion of substances through mounted hairless-mouse skin in a Franz diffusion cell.
Every attempt has been made to accurately represent the system used to gather the
in vitro data (Chapter 4: In Vitro Diffusion of Drugs).
The idealized system that forms the basis for the model is illustrated in
Figure 65. The drug is assumed to be the only species diffusing and assumed to

123
Modelled System
x=0 External Surface
x=L Internal Surface
Boundary and Initial Conditions
x=0; C(x,t)=Ci(t) x=L; C(x,t)=C2(t)
t=0; C(x,t)=0 (0 Assumptions
* Diffusion in one direction only
* Homogeneous barrier to diffusion
* No counter- or co-diffusion
* Boundary layers neglected
Figure 65: Schematic of idealized system
diffuse in one direction (perpendicular to the surface of the skin). Temperature is
held constant and, therefore; is not considered as a parameter.
The cross sectional area for diffusion is A, the effective diffusivity is D, the
time since application of the drug is t, the drug concentration in the donor phase is
C1(t), and the drug concentration in the receptor phase is C2(t). The region of
interest lies between x = 0 (donor phase boundary) and x=L (receptor phase
boundary) and the effects of boundary layers are neglected (concentrations at the
skin surfaces equal bulk concentrations).

124
Model Derivation
The differential equation for one-dimensional diffusion through a stagnant
(solid) medium such as skin is shown in Equation 5.7
=pd2C 5
3t dx2
The initial condition is C(0) = 0. If the boundary conditions are independent of time,
then this equation can be analytically integrated to obtain Equation 6.16
cm-c,-KC2-c1)£+
* 1
C2(:1)''~Clsin(^)e-c"v^i
6
If the boundary concentrations change slowly relative to the concentration
within the skin (quasi-steady state), then the above analytical solution, Equation 6,
can still be used, but the boundary conditions then become weak functions of time.20
These boundary conditions for the concentrations are mass balances. Evaluating
these mass balances requires integration of the concentration equation to find the
cumulative fluxes through the skin. For the donor and receptor phases the mass
balances are Equations 7 and 8, respectively.

125
o)-A fw |0
K1 Jo

qo-c^o)-^. [(-£>9^) |0)rfx
V\ JQ dx
t
c1(t)=c1(o)+^ [(*^1 L,)dx
V1 {, dX
C2(t)=C2(0)+^r ¡N U dx =
V2 J0
t
C2(t)=C2(0)* (-Z)l^) I^Jdx.
V2 Jo dX
t
C2()=C2(0)-^ lw>fc
2 O
N is the drug flux in the +x direction
Vl is the volume of the drug dose
V2 is the volume of the receptor phase
The mass balances (Equations 7 and 8) contain derivatives of the
concentration profile with respect to position (x). To evaluate these derivatives, the
analytical solution for the concentration profile (Equation 6) is differentiated with
respect to position.
?££.£ =(C2-CX- +
dx v 2 VL
2j, C2{ 1Y Cl^niCy^n7CXy -DnVt/L^
Lt Z/
7rn=i
(Ci-Cjl+l-Y, (C^-ir-CJcosi^e
L L,n^ i L
n
00
9

126
The mass balance equations require the above derivative to be evaluated at the
boundaries (x=0 and x=L).
dC(x,t) i +
dx *=0 ^ 2 1 L
1 (C^-iy-CJcos^
-^=1
(Ct-Cjl+lf; (C2(-ir-Ct)e
L ->n=1
10
dC(x,t)
dX
tY. i.C2(-Vr-C2)cos(n*)e
11
(C2-C2)l*l (C2-C2(-ir)e -D"V/L>
J-> 1-' n=l
Equations 10 and 11 can now be put into Equations 7 and 8; the time dependent
boundary conditions.
t
cx(t),c2(0)+£. [((CyxJ-Cyx))!*
v\ Jo ^
(C2(x)(-1)"-C1(x))e =
L>n=l
t
C'(0)+W f (C2 V\L Jo
2 (C^X-iy-C^e -D"'AlL)d\
n=\
12

127
C2(f)-C2(0)-rd£ [((C^-C^T
2 (C2(X)-C,(X)(-l)")e vVi.yx =
^-1 13
t
C2(0)tW (C,(X)-C2(X))*
' j0
2 (C,(x)(-l)"-C2(X))e ~D"Vx/iV*
n=1
Equations 12 and 13 are numerically integrated to get the boundary concentrations
as functions of time. The integration scheme used is quite simple.
Ct+At~Ct+M()t 14
dt
Substituting Equations 12 and 13 into Equation 14 gives explicit, time dependent
expressions for the donor and receptor phase concentrations.
j-, t+At
s-i t 4A /, t *-t t
'-'1 + T, t _^1
KL
2E (c2'(-i)''-Q> ~d"v'//-2
-I
s^t+At t AD At i n i i
^2 ~ ^2 +1 V^l ^2 '
2E (Q'(-i)-qV V/2
n=l
Adopting dimensionless groups gives further simplification.
15
16
4>x-
AL K
Volume ratio (Vs = Skin Volume)

-AL
128
Volume ratio
v2
L2
T
Time constant
D-k2
At
8=
Step size
T
}
Index
17
7T 77 = 1
-K 771
18
The only dimensional quantities in the final expressions for the boundary concentra
tions are the boundary concentrations themselves. The model is developed in this
way so that raw diffusion data (C2(t) vs. t) can be used to find the time constant and,
in turn, the effective diffusivity. Figure 66 shows the model results; the insert shows
the response of the receptor phase just after applying the drug. To determine the
concentration profile inside the skin, boundary values from Equations 17 and 18 are
cycled back into the analytical solution for the concentration profile (Equation 6).
Figure 67 shows the concentration within the skin calculated by Equations 6,
17, and 18 as a function of position (x=0 is the external surface) for different
dimensionless times (experimental time/time constant). Such calculations assume
the drug diffusion coefficient is the same everywhere in the skin, i.e., that the skin
can be considered a homogeneous medium for diffusion. If one views the skin as

129
Donor
Receptor
Dimensionless Time
Figure 66: Predicted donor- and receptor-phase concentrations (4\/4>2 = 7)
stratified, then the model may easily be modified to include a series of layers in
which the drug has different diffusivities. Each layer is then described by the same
equations (Equations 6, 17, and 18) and shares boundary conditions with adjacent
layers. Another possible view of skin structure is as mortar and bricks. In this case,
diffusion occurs through different media simultaneously and some diffusion
resistances are in parallel while others are in series. This case, although not
impossible to model, presents significant difficulties. Since drug diffusivities are
unavailable for various regions within the skin, the approach here is to adopt an
effective or apparent diffusivity resulting from diffusion in several layers.

130
Skin Coordinate (0 = External Surface)
Figure 67: Predicted concentration profile within skin
Inclusion of Skin Swelling In Vitro
Since the time constant is proportional to the square of the skin thickness,
skin swelling can significantly affect the diffusion of drugs through the skin during in
vitro diffusion. To assess the degree of swelling in vitro, the thickness of hairless-
mouse skin was measured versus time immersed in water (details of this procedure
are in Chapter 2, page 40, results are in Chapter 3, page 92). These measured
thicknesses were then correlated as L(t) for use in the diffusion model. To fit this
swelling, two equations were used: a parabolic equation for the early, rapid swelling
of the first 4 to 5 hours and an exponential equation for the later, slower swelling.

131
The variable skin thickness was incorporated into the quasi-steady state model by
allowing L to change during integration.
Using L(t) in the quasi-steady state model precludes the use of a dimension
less model since the model now contains an additional time dependent function
(L(t)) with a different time scale. Therefore, one must return to Equations 15 and
16 and include an appropriate equation for L(t). The model for drug diffusion
through skin in vitro with skin swelling consists of the following system of four
equations (two for the thickness).
C[+At~ C1t+ffiy.(C2t-C1t+2 (C¡(-l)n-C-t)e
Ei-L =1
C2,+a' C2*+^5^(C1,-C2'+2 (Ci(-l)n-C2)e
=i
L{t) =0.069029 +0.049499i-0.0044692t2 (l < 5 hours)
L(i)=0.18821i0050642 (l > 5 hours)
Results
The following section compares the experimental data for diffusion in vitro
with the theoretical quasi-steady state model. The model is evaluated by comparing
the goodness-of-fit under different circumstances. The model can be used to
simulate transdermal diffusion in vitro with or without skin swelling and can also
hold the donor-phase concentration constant (as in a micellar solution).

132
The model is designed to allow the donor-phase concentration to fall as drug
is transported across the skin unless otherwise specified. Drug solubility in the
solvent must be considered when modelling is attempted. If the solution is super
saturated, the concentration of the donor phase will remain constant as drug
continues to dissolve and enter the donor phase solution. For a suspension,
emulsion, or micellar solution; the actual concentration in the donor phase would be
the concentration of molecularly dispersed solute and not the overall concentration.
General Behavior of Model
Certain features distinguish the modelled systems from one another.
Qualitative comparisons of the time lag can be made between the non-swelling,
varying concentration model (Figure 66) and the other permutations of the model.
Allowing the skin to swell increases the time lag by increasing the distance between
the donor-phase and the receptor-phase. Holding the donor-phase concentration
constant (infinite source conditions) decreases the time lag because it increases the
rate of diffusion. The concentration difference across the membrane does not
decrease as rapidly as when donor-phase concentration falls, so the rate of diffusion
is greater.
The net effect of combining skin swelling and constant donor-phase
concentration depends on the rate of diffusion. If the diffusion is very slow, skin
swelling greatly increases the time lag since the drug will scarcely have penetrated
the membrane before the skin is fully swollen. The drug must then traverse a longer

133
path to reach the receptor-phase. If the diffusion is very fast, the drug reaches the
receptor-phase before the skin swells appreciably. In this case, the time lag is
unaffected by skin swelling and the effect of constant donor-phase concentration is
as before.
Tetracaine Diffusion Through Hairless-mouse Skin
The quasi-steady state model is compared to in vitro tetracaine diffusion data
from propylene glycol-saline solutions. The figures on the following pages
(Figure 68-Figure 81) show the experimental data and the best match by the model
assuming:
a: no skin swelling and fixed donor-phase concentration,
b: no skin swelling and variable donor-phase concentration,
c: skin swelling and fixed donor-phase concentration, and
d: skin swelling and variable donor-phase concentration.
When the concentration is held constant, the average CMC as determined in Chapter
3 is used.
To aid interpretation of the data, the total variance* between the model
predictions and experimental data is plotted under the conditions described above
(Figure 82-Figure 95). This format makes it easier to compare the modelling
schemes. Usually, the best modelling scheme is the one that minimizes the variance
*The total variance here is defined as the sum of the squared error and is
equivalent to the experimental variance when divided by the degrees of freedom
(n 1).

134
between the theoretical predictions and the experimental data. This may not always
be the case. The shape of the curve can be used to determine whether the diffusion
Time (hr)
Figure 68: Model fits for saline (old
mice)
Figure 70: Model fits for 10% propyl
ene glycol (young mice)
Figure 69: Model fits for 5% propyl
ene glycol (old mice)
Time (hr)
Figure 71: Model fits for 20% propyl
ene glycol (young mice)
process modelled matches that measured (initial increasing slope, constant slope, or
decreasing slope indicating approach to equilibrium). Comparison of the variance
between the theoretical predictions and the experimental data can be used to suggest
a preferred system, but a final determination should be based upon the features of
the concentration versus time plots. Identification of a preferred theoretical system

135
Time (hr)
Figure 72: Model fits for 20% propyl
ene glycol (old mice)
Figure 74: Model fits for 40% propyl
ene glycol (young mice)
0 2 4 6 8
Time (hr)
Figure 76: Model fits for 50% propyl
ene glycol (young mice)
Time (hr)
Figure 73: Model fits for 30% propyl
ene glycol (old mice)
0 2 4 6 8
Time (hr)
Figure 75: Model fits for 40% propyl
ene glycol (old mice)
Time (hr)
Figure 77: Model fits for 50% propyl
ene glycol (old mice)

136
Time (hr)
Figure 78: Model fits for 60% propyl- Figure 79: Model fits for 60% propyl
ene glycol (young mice #1) ene glycol (young mice #2)
Figure 80: Model fits for 70% propyl- Figure 81: Model fits for 70% propyl
ene glycol (young mice #1) ene glycol (young mice #2)
can shed light on the physical system by answering questions as to whether the skin
is swelling or if the concentration in a micellar solution is constant.
For solutions of saline, 5%, 20%, and 30% propylene glycol (v/v), the best
model assumes skin swelling and varying donor-phase concentration (d). In only one
case was a CMC detected in these systems and its value was very small (0.03 M or

137
Conditions
Figure 82: Model variance for saline
(old mice)
80000
70000
60000
I 50000
S 40000
> 30000
20000
10000
0
abed
Conditions
Figure 84: Model variance for 10%
propylene glycol (old mice)
Conditions
Figure 86: Model variance for 20%
propylene glycol (old mice)
Conditions
Figure 83: Model variance for 5%
propylene glycol (old mice)
Conditio ns
Figure 85: Model variance for 20%
propylene glycol (young mice)
Conditions
Figure 87: Model variance for 30%
propylene glycol (old mice)

138
Conditions
Figure 88: Model variance for 40%
propylene glycol (young mice)
Conditions
Figure 89: Model variance for 40%
propylene glycol (old mice)
Conditions
Figure 90: Model variance for 50%
propylene glycol (young mice)
Conditions
Figure 91: Model variance for 50%
propylene glycol (old mice)
Conditions Conditions
Figure 92: Model variance for 60% Figure 93: Model variance for 60%
propylene glycol (young mice #1) propylene glycol (young mice #2)

139
Conditions
Conditions
Figure 94: Model variance for 70% Figure 95: Model variance for 70%
propylene glycol (young mice #1) propylene glycol (young mice #2)
9 g/1).* If the true concentration in the system is less than or equal to 9 g/1, then
the flux in these systems would be so small as to be negligible (overall concentration
is 0.36 M). Since measurable fluxes were obtained, it seems reasonable to assume
that the concentrations in these solutions were greater than the measured CMC
(assuming micelles do not contribute significantly to the flux). Therefore, the
formation of micelles in these systems is unlikely and the indication by the model
that solutions of saline, 5%, 20%, and 30% propylene glycol do not form micelles
(i.e., donor-phase concentration is not constant) makes sense.
At 10% propylene glycol, the best model assumes skin does not swell and the
concentration does vary (b). This result is unique among all the data on in vitro
diffusion through hairless-mouse skin. Coupled with the fact that the experimental
data themselves are anomalous (cf. Chapter 4, Figure 53, page 102), it is likely that
this system either has unique properties or the data are subject to some systematic
The system of 5% propylene glycol does not show a CMC, 20% propylene glycol
does show a CMC, and 30% propylene glycol was not tested.

140
experimental error. The next best model assumes swelling skin and varying donor-
phase concentration (d) and the variance for this case is significantly lower than the
remaining two systems (a and c). This second choice is more in keeping with the
neighboring formulations.
For solutions containing 50% propylene glycol or more, the model shows that
the system is best described by skin swelling and a constant donor-phase concentra
tion. This is consistent with the measured CMCs for these formulations in Chapter
3 (pages 66, 69, and 80). For 40% propylene glycol, the best model is no skin
swelling and constant donor-phase concentration. Closer inspection of the theoretical
curves, however; reveals that they are decreasing in slope (approaching equilibrium)
unlike the continued upward trend of the experimental data. Consequently, the
modelled system most resembling the experimental data at 40% propylene glycol
does not have the lowest variance, it is the same model as for higher propylene glycol
fractions.
In summary, the model suggests that systems of 60% tetracaine free base, 40%
tetracaine acid salt (w/w), in solutions of propylene glycol and saline form micelles
when the propylene glycol fraction is 40% (v/v) or greater. The model also suggests
that skin swelling plays an important role in transdermal diffusion in vitro and may
be accounted for theoretically. To determine whether the skin swelling calculations
in the quasi-steady state model really account for in vitro swelling, the model is
compared to data from a non-swelling system. The effective diffusivities found by
the model are all of order 10'8 to 107 cm2/s. This is approximately two orders of

141
magnitude below the estimated molecular diffusivity of tetracaine in a liquid.65 This
could be a result of the parameters used in the model which are certainly naive
(pathlength = skin thickness, diffusion area = application area, skin = homogeneous
barrier).
Diffusion of Hydrocortisone Through Synthetic Membranes
The addition of a skin swelling routine to the quasi-steady state model
improves its ability to simulate experimental, in vitro, transdermal diffusion data. It
is possible that this phenomenon has nothing to do with skin swelling and simply
reflects a fundamental flaw in the theoretical model. Comparing model curves and
experimental data obtained from a non-swelling system can help make the distinction.
The diffusion of aqueous hydrocortisone through synthetic, polycarbonate
membranes (nominal pore diameter of 0.22 ^m) was modelled to determine which
modelling conditions best represented the experimental data (Figure 96-Figure 98).
Donor-phase concentrations were not held constant in the model because there was
Figure 96: Model fits for hydrocorti- Figure 97: Model fits for hydrocorti
sone in a stagnant cell sone in a poorly stirred cell

142
no indication of micelle formation in aqueous hydrocortisone (the constant donor-
phase concentration curves were designated a and c in Figure 68-Figure 81). Again,
evaluation of the models is aided by examining the variance between the theoretical
data and the experimental data (Figure 99-Figure 101).
Hydrocortisone in Stagnant Call
7
7
§
HHl
y 7i_
y/yyyyy/y/
L
yyyy//
7/
Figure 98: Model fits for hydrocorti- Figure 99: Model variance for hydro-
sone in a well-stirred cell cortisone in a stagnant cell
Hydrocortisone in Poorly Stirred Call
hydrocortisone in Wti-Slirrd Cell
Figure 100: Model variance for hydro- Figure 101: Model variance for hydro
cortisone in a poorly-stirred cell cortisone in a well-stirred cell
In all three cases, the experimental data are best modelled by the non-swelling
model. The theoretical models under-predict the equilibrium concentration in the
well-stirred cell, but this is probably due to an error in the

143
initial, measured concentration. Therefore, the quasi-steady state model determines
that the skin swells during in vitro, transdermal diffusion and that it has a significant
effect on the diffusion. The theoretical model can also indicate the presence of
micelles by identifying data consistent with a constant donor-phase concentration.
Concentration Profile Within the Skin
Although the concentration profile within the skin can be estimated by this
model, it is not likely to have clear physical meaning. The model is based on the
dimensions of full-thickness skin and the primary resistance to diffusion in skin is
generally regarded to be the stratum corneum which is much thinner than full
thickness skin. There is practical value in the theoretical concentration profile if one
decreases the length scale of the model to coincide with the dimensions of the
stratum corneum. It is likely that the model will produce valuable, though rough,
estimates of drug concentration in the stratum corneum.
Many factors that may influence diffusion have not been considered. These
include the diffusion of propylene glycol and saline through the skin, as well as the
changing propylene glycol-saline concentration within the skin as swelling occurs.
Boundary layers are neglected, but the ability of the model to predict the bulk
reservoir concentrations is well within experimental error. Thus, further development
of the model to include solvent diffusion and boundary layers is viewed as
unproductive.

144
The absolute circumstances under which the quasi-steady state assumption is
valid are the subject of some debate. Indeed, there has been direct criticism to its
application in this context. A more rigorous method for modelling this system is
numerical integration of the diffusion equation (Equation 5). The major drawback
to this method is that the concentration profile within the skin must be evaluated
after each time step. The quasi-steady state model has only one independent
variable (time), while the full numerical routine has two (time and position). This
additional degree of freedom makes the full numerical routine slower to converge
and less stable to changes in the parameters (D, Vj, V2, L(t), etc.).
The derivation of the full numerical routine has been delegated to the
appendix along with comparisons to the quasi-steady state results. Over the body of
the modelled data for tetracaine diffusing through hairless-mouse skin (Figure 68-
Figure 81) the models differ in their estimates of the effective diffusion coefficient
by approximately 5%. There is an improvement in the ability of the full numerical
routine to model the experimental data as compared to the quasi-steady state model.
This improvement, however; averages only 16.5%.

CHAPTER 7
CONCLUSIONS
The major conclusions and achievements of "Interfacial, Diffusional,
Theoretical, and Clinical Aspects of Topical, Local Anesthetic Formulations" are
assembled as an overview. This overview follows, as closely as possible, the logical
sequence of the dissertation. In some instances, related material from different
locations in the text is grouped to form conclusions. In either case, the material is
cross-referenced to the body of the dissertation.
Physical Properties of Drug Formulations
Solubility
A mixture of 60% tetracaine free base and 40% tetracaine acid salt (w/w) is
generally more soluble in solvents of propylene glycol and water (saline) than either
tetracaine free base or tetracaine acid salt alone (Figure 14, page 58). This solution
may have unique properties because its pH is near the pIC, of tetracaine (8.5 8.7).
Partitioning and Solubility
The product of solubility and lipid-phase partitioning is an indication of a
formulations ability to promote transdermal diffusion (page 62). Two organic liquids
145

146
were used to assess partitioning: 1-octanol and n-octane. The combined solubility
partitioning parameters (KpCsat) for both solvents predict that the optimum solvent
for the transdermal delivery of a 60% tetracaine free base, 40% tetracaine acid salt
(w/w) mixture is 50% propylene glycol and 50% saline (v/v).
Surface Activity
Like other local anesthetics, tetracaine is highly surface active. Surface
activity was determined by three independent methods: surface tension, specific
conductivity, and pH. For all three phenomena, a discontinuity in the measured
quantity versus concentration indicates the formation of micelles.
Using surface tension and conductivity, we found that tetracaine acid salt
forms micelles in aqueous solution while tetracaine free base probably does not
(pages 65 and 68). The specific conductivity of aqueous tetracaine free base
indicated the presence of micelles, but at unrealistically low concentrations (page 69).
Tetracaine free base is not soluble enough to accumulate sufficient free molecules
in solution to aggregate.
Three independent methods were used to study the surface activity of 60%
tetracaine free base, 40% tetracaine acid salt mixtures (w/w) in solvents of propylene
glycol and saline. Surface tension and conductivity measurements indicated that
these tetracaine mixtures form micelles in solvents of 20% to 60% propylene glycol
(pages 66 and 69). The critical micelle concentrations (CMC) from these two
methods agree very well (within 33%). Critical micelle concentrations determined

147
by pH versus concentration measurements (page 80) were slightly more conservative
although they were in general agreement with those of surface tension and
conductivity. The differences in the CMC values are attributed to the broad range
over which micellization begins and the way micellization affects the measured
properties.
Micelle Size
The size of tetracaine micelles in solvents of propylene glycol and saline (60%
tetracaine free base, 40% acid salt w/w) was measured by quasi-elastic light
scattering or QELS (page 82). Tetracaine micelles are very large in the absence of
propylene glycol (1300 1450) and may not be typical spherical micelles. At 50%
propylene glycol and 50% saline, the micelles are comparatively small (* 25) and
micelles are not present at 80% or 100% propylene glycol.
Thermal Breakdown
Tetracaine free base deteriorates with time and the breakdown is thermally
activated. Consequently, the rate of deterioration increases with temperature. At
room temperature, (24C) formulations containing tetracaine base can be stored for
2 to 3 days before the loss of viable drug exceeds 10% (page 84). At skin tempera
ture, (32C) the time period is much shorter (1 day).

148
Drug Diffusion In Vitro
Stirring
The efficiency of stirring in Franz diffusion-cells was evaluated two ways:
device and stirring rate. Identical diffusion studies under stagnant conditions, with
a small stirring bar, or with a larger stirring tee determined that the small stirring
bars available were inadequate for mixing the receptor phase of a Franz cell (page
87). Stirring tees were constructed for all diffusion cells and were used in all
subsequent diffusion experiments.
The rate at which the stirring tees should be rotated was determined by
plotting the cumulative flux of hydrocortisone through a synthetic membrane versus
the inverse of the stirring rate (200 400 rpm). The best line through these points
is flat and significantly greater than the stagnant flux indicating that the reservoir is
fully mixed and further increase of the mixing rate would not increase the flux (page
88).
Temperature Behavior of Franz Diffusion Cells
Receptor phase
The temperature behavior of the larger reservoir (15 ml) of the Franz cell was
monitored by a thermocouple. The receptor phase reaches thermal equilibrium
(32C) within 15 minutes when 37C water is circulated through the cell jacket (page
90).

149
Donor phase
The properties of the formulations introduced into the donor reservoir vary
widely both in composition and temperature. A worst-case scenario was adopted to
determine whether the time required for the donor phase to reach thermal
equilibrium would affect the diffusion results. As a model of all formulations,
propylene glycol at ambient temperature (2 ml) was introduced into a Franz diffusion
cell. The diffusion cell was already at thermal equilibrium with 37C water
circulating through the cell jacket. The donor phase reached thermal equilibrium
within three minutes of its introduction into the diffusion cell. This result indicated
that the donor phase reaches thermal equilibrium quickly relative to the rate of
diffusion since the first concentration measurement was taken after one hour (page
91).
Skin Swelling
The swelling of hairless-mouse skin immersed in water was measured as a
function of time (page 92) and incorporated into theoretical models of transdermal
drug diffusion through correlations (page 130). Hairless-mouse skin was found to
swell to four times its original thickness (0.6 mm) when immersed in water for 2 days.
The swelling also seemed to occur in two stages; a rapid, early stage that suggested
tissue swelling and a slower, later stage that suggested tissue dissolution.

150
Skin Longevity
The barrier properties of hairless-mouse skin with respect to aqueous
lidocaine acid salt were studied for 72 hours. During this time period, no significant
change in the diffusion behavior was observed (page 98). Based on this experiment,
subsequent diffusion studies (usually 8 hours) were conducted without chemical
preservation of the skin.
Effect of Propylene Glycol
Synthetic membranes (pages 101 102)
The highest flux of a tetracaine mixture (60% free base, 40% acid salt w/w)
through a synthetic polycarbonate membrane occurs in an aqueous solution. This
may be a wetting phenomenon since the membrane is hydrophilic. There is also a
local maximum in the drug flux at 40% propylene glycol and the flux decreases with
increasing propylene glycol fraction. The combined solubility-partitioning parameters
for 1-octanol and n-octane suggest a similar vehicle for transdermal delivery of
tetracaine (50% propylene glycol for either solvent). There is no reason to believe
that these two phenomena should be related because the solubility-partitioning
parameter represents partitioning into a hydrophobic membrane. Therefore, there
must be some other property unique to this 40% propylene glycol vehicle that cannot
be measured by solubility or partitioning.

151
Hairless-mouse skin (pages 102 103)
The highest flux of a tetracaine mixture (60% free base, 40% acid salt w/w)
through hairless-mouse skin occurs at 40% propylene glycol. This value is near the
value suggested by the combined solubility-partitioning parameters for 1-octanol and
n-octane (50% propylene glycol for either solvent). The combined solubility
partitioning parameter can be used as a method for estimating the optimum vehicle
composition, but it should not be relied on for estimating relative flux.
Effect of Age
The flux of tetracaine mixtures (60% free base, 40% acid salt) through
hairless-mouse skin generally decreases with age. For mice aged 6 to 8 months,
transdermal flux decreased an average of 20% relative to the flux through the skin
of mice aged 6 to 8 weeks (page 105). The relative effect of propylene glycol on the
flux of tetracaine mixtures through hairless-mouse skin seems to be unaffected by
age.
Effect of Formaldehyde (pages 105 107)
Formaldehyde seems to decrease the flux of tetracaine through hairless-mouse
skin by decreasing the permeability of the skin. Other experiments with scopolamine
also indicated that formaldehyde at a concentration of 0.1% (w/w) decreases flux,
however; the difference was not significant in either case.

152
Effect of Concentration
Increasing tetracaine concentration (60% free base, 40% acid salt) does not
increase the transdermal flux of tetracaine from a 40% propylene glycol, 60% saline
vehicle (page 108). This observation is consistent with the observation that this is a
micellar solution and increasing drug concentration only increases the number of
micelles in the formulation. If the micelles do not diffuse through the skin, then the
concentration of dispersed drug molecules determines the rate of diffusion by Ficks
law. In a micellar solution, the concentration of dispersed solute remains relatively
constant. Therefore, increasing the solute concentration of a micellar solution will
not increase the driving force for diffusion (assuming the micelles do not diffuse).
Effect of pH
Tetracaine is a weak base and the relative proportions of ionized and
unionized drug in solution is determined by the pH of the solution. The diffusion
of a tetracaine mixture (60% free base, 40% acid salt) from a vehicle of 70%
propylene glycol and 30% saline is strongly pH dependent (page 110). Tetracaine
flux is equal at pH = 12.2 and pH = 8.5, but negligible at pH = 4.7. This behavior
suggests that tetracaine free base diffuses preferentially to the acid salt.

Drug Diffusion In Vivo
Rat Tail-flick Test (page 111)
The rat tail-flick response to a painful light beam was used to evaluate the
ability of anesthetic formulations to produce analgesia in rat tails. This test was
originally adopted because it facilitated rapid, large-scale screening of prospective
anesthetic formulations. Unfortunately, this test lacked the necessary sensitivity and
did not correspond to data for humans. In addition, test results had no correlation
with concentration and their wide variation ruled out the influence of micellization.
Rat tail-flick testing was abandoned in favor of clinical testing with volunteers.
Clinical Trials (pages 113 119)
Attempts at formulating an effective, lidocaine-containing topical, anesthetic
were unsuccessful. Tetracaine was found to be more effective than lidocaine as a
topical anesthetic. Two effective topical, tetracaine formulations were developed.
Both of these contained mixtures of tetracaine free base and tetracaine acid salt in
vehicles composed of propylene glycol and saline. One of these formulations (60%
free base, 40% acid salt in 40% propylene glycol and 60% saline) was capable of
producing profound local anesthesia after 45 minutes and at much lower concentra
tions than the other. A lower concentration of tetracaine reduces the likelihood of
skin irritation as well as the cost of the formulation. The formulation found to be

154
most effective in clinical trials is the same formulation that maximized the flux of
tetracaine through hairless-mouse skin in vitro.
Theory
Ouasi-steadv State Model (pages 124 131)
The quasi-steady state assumption in transdermal diffusion states that the drug
reservoir concentrations change slowly compared to the skin concentration. A
theoretical model for in vitro transdermal drug delivery based on this assumption can
analyze diffusion data and determine the effective diffusivity (~ 10"2 x molecular
values in water). This model can also recognize and account for the effects of skin
swelling in vitro and micellization.
Full Numerical Routine (Appendix A, pages 161 168)
The quasi-steady state assumption is not valid under all circumstances.
Numerical integration of the fundamental diffusion equation under the true boundary
and initial conditions of in vitro transdermal drug diffusion is a more rigorous
modelling method. This full numerical routine has all the properties of the quasi
steady state model except speed. The full numerical routine takes more time to
calculate because, unlike the quasi-steady state model, a complete concentration
profile must be calculated at each time step. The full numerical routine yields
effective diffusivities 5% below those of the quasi-steady state model and decreases
the variance (sum of the squared difference) between the model and the experimen-

155
tal data an average of 20%. Should there be great doubt concerning the validity of
the quasi-steady state assumption, the full numerical routine can be used with
confidence.

CHAPTER 8
RECOMMENDATIONS FOR FUTURE WORK
Research into the formulation of topical, local anesthetics and the theoretical
modelling of transdermal diffusion is far from complete and there is a great need for
further study. The work presented in this dissertation has answered many questions
about the physical behavior of topical local anesthetic formulations and the ability
to theoretically model transdermal diffusion, but it has also raised many additional
questions. The following sections contain recommendations for future research into
these subjects. The general areas are physical properties, diffusion experiments,
theoretical modelling, and clinical studies.
Physical Properties
Partition coefficients were measured in only n-octane and 1-octanol as model
lipids for skin. It is possible to measure partition coefficients in isolated stratum
corneum or some other model lipid (tetradecane, isopropyl myristate, linoleic acid,
or dipalmitoyl phosphatidylcholine).43,44
Quasi-elastic light scattering was used to determine the micelle size of
tetracaine in propylene glycol and water as a function of the fraction of propylene
glycol. Additional scattering work could be done to determine how the micelle size
changes as a function of pH.
156

157
The system of tetracaine, propylene glycol, and water shows much interesting
phase behavior. The construction of the ternary phase diagram is a project in its own
right, but would be valuable for future work in this system.
Diffusion Experiments
Franz diffusion cells are used to obtain physical information about the
diffusion of the anesthetic formulations. The use of hairless-mouse skin as a model
for human skin has been questioned9,10,11 and it is generally believed that there are
better in vitro animal models (e.g., pigskin4). In addition, human cadaver skin can
also be used for in vitro studies. Consequently, one possibility for future research is
the study of in vitro transdermal diffusion of these local anesthetic formulations
through pigskin and human cadaver skin to confirm the trends found with hairless-
mouse skin.
The content of the receptor phase may have inhibited the diffusion of the
hydrophobic anesthetic through unfavorable partitioning. Whether the use of saline
as a receptor phase reduced the diffusion of tetracaine in vitro should be determined
by using a more lipophilic receptor phase. The likelihood that this would influence
the results was considered remote because the concentrations in the receptor phase
were very small and the duration of the experiments was usually very short.

158
Theoretical Modelling
The theoretical model developed in this work can represent the experimental
receptor-phase concentration of tetracaine as a function of time well. It is not based
on data specific to this system and should be able to model data from other systems
equally well. Its parameters are those of full-thickness, hairless-mouse skin. This is
irrelevant for determining the boundary concentrations, but it is relevant for
determining the concentration profile. The concentration profile represents diffusion
through a homogeneous barrier as thick as full-thickness skin. The model can be
altered to represent only the diffusion through the stratum corneum (still represented
as a homogeneous barrier) and the resulting concentration profile would have
physical meaning.
The area of diffusion could also be altered in the model to represent the
actual area available for diffusion. Conventional wisdom states that the diffusion of
hydrophobic substances occurs through intercellular lipid pathways. If this is true,
the actual area available for diffusion through the skin is a microscopic fraction of
the application area and the diffusion path is longer than the skins thickness.
Evaluation and substitution of the correct area along with the correct path length,
could give more physical meaning to the effective diffusion coefficients generated by
the quasi-steady state model. The modular construction of the quasi-steady state
model allows this type of information to be inserted as it becomes available.

159
An in vivo model could also be developed by altering the in vitro model to
include expressions for metabolism and removal of drug by the circulatory system.
Such a model would require data similar to in vitro receptor-phase concentration
versus time or additional relationships to determine these concentrations as a
function of excretion rate or blood concentration.
Clinical Studies
The subjective nature of in vivo trials with human volunteers makes
interpretation of data difficult, i.e., responses vary from person to person. There is
always the possibility of preconceived notions, e.g., "my skin is thick.," "nothing works
on me," "I have a high pain threshold," etc. These kinds of uncertainties make it
difficult to interpret limited data sets. Large scale clinical trials (n > 200) are
needed to draw statistically relevant conclusions. Consequently, the conclusions in
Chapter 5 are qualitative and are used as supporting evidence for the in vitro
conclusions.
The effects of varying propylene glycol content were only investigated in detail
through hairless-mouse skin in vitro. A more comprehensive study of the effects of
propylene glycol on the diffusion of tetracaine through human skin in vivo should
also be carried out.
Clinical studies can also be used to determine the concentration profile in the
skin by tape-stripping to verify the theoretical concentration profile in the skin.
Successive strippings (removal of the outer layers of the skin by adhesive tape) could

160
be analyzed for drug content to get a rough estimate of the concentration profile
similar to the method of Dupuis et al.22,71,72

APPENDIX A
DERIVATION OF THE FULL NUMERICAL ROUTINE
The full numerical routine is simply the numerical integration of the diffusion
equation (Equation 5). The method for discretizing the diffusion equation is outlined
in the Chemical Engineers Handbook by Perry and Chilton.65
The development of the model begins with the diffusion equation (reproduced
from Chapter 6, page 124).
= D^~ (Al)
dt dx2
To discretize the differential equation, the differential operator d is approximated by
a finite difference A and the second-order differential operator d2C is approximated
by the finite difference operator a(aC).
AC = D A(AC)
At (ax)2
(A2)
At this point, the subscripts i (position index) and j (time index) are introduced and
the differences evaluated.
C C a C a C
,;+i = d i+1 ]
At
Ax
The term ACi+1 j aC¡ j can be further expanded.
(A3)
161

162
(A4)
The resulting equation is rearranged into an explicit equation for the concentration
at position = i and time = j + 1 as a function of concentrations at time = j.
(A5)
DAt
(A6)
r
Equation A5 is only valid for i = 1, M 1 where M is the resolution of the skin
concentration-profile. Boundary conditions must be established for i = 0 and i = M.
The boundary conditions are mass balances which depend on the volumes and
initial concentrations of the reservoirs. The equations for the concentration in the
reservoirs have already been derived (Equation 7 on page 125 and Equation 8 on
page 125) and are reproduced below.
(A8)
Taking the derivative of Equations A7 and A8 with respect to time eliminates the
integral (these equations will be numerically integrated with respect to time with
Equation A5).

163
dC1
~df
dC2
~dT
AD (dC(x,t)^ |
V I jt"0
V1 dx
AD(dC{x,t)v ,
V ~ ) Ix=L
V2 dx
Discretizing as before and recognizing that Q(t) = C0 and C2(t) =
equations for the reservoir concentrations at time = j + 1 as
concentrations at time = j.
^0,7+1 AD
At
V1 Ax
C j+1 C0, j AD Cx j C0i j
(-
At Vx Ax
C(),7+1 C0, J + S1(C1 j C0 J)
a^mj+i _ AD
At ~V^K~^x~)
)
Cm, 7+i CM, j AD ^ CM j CM_X' j ^
At ~V7K Ax }
Cm, 7+1 CA, j s2^m, j CM_1;)
AD At
VXAX
AD At
V2ax
(A9)
(A10)
Cm, j give explicit
functions of the
(All)
(A12)
(A13)
(A14)
The model is solved by applying the initial conditions,

164
C
i, O
O
v i O M
C,
o, o
(dose)
(usu. = 0)
calculating the concentration profile, and marching ahead in time.
(All)
(A5)
(A12)
The full numerical routine was used to calculate the effective diffusivity of the
same in vitro transdermal-diffusion data as the quasi-steady state model (Figure 68 -
Figure 81, pages 134 136). A summary of the modelling data appears at the end
of this section.
The average variation of the effective diffusivity calculated from the full
numerical model relative to the quasi-steady state model is 4.08% (i.e., the full
numerical routine yields effective diffusivities that are 4.08% greater than those from
the quasi-steady state model). As already stated, the numerical value of the effective
diffusivity has limited physical meaning due to the nature of the system. The true
path length of diffusion, the actual area of diffusion, and the relative contributions
of skin strata are all subject to some speculation. Without a fundamental under
standing of these parameters, the effective diffusivity is a lumped parameter with a
value that is only relevant to other effective diffusivities calculated under the same

165
conditions. Consequently, the difference between the effective diffusivities calculated
by the full numerical routine and the quasi-steady state model does not affect either
models ability to describe transdermal diffusion.
A models ability to describe transdermal diffusion is determined by how well
the model follows experimental data. The difference between the standard deviation
(s, where s2 = E(Cmodel(t) Cexp(t))2/(n -1)) associated with the two models averages
-1.33 mg/1 or -16.54% (i.e., the full numerical model is an average 1.33 mg/1 closer
to the experimental data or reduces the error by an average of 16.54% relative to the
quasi-steady state model).
The full numerical routine does follow the experimental diffusion data better
than the quasi-steady state model, but the difference in calculation time is significant.
The additional variable in the full numerical model (position) causes it to run much
more slowly than the quasi-steady state model. A complete concentration profile
must be calculated at each time step in order to evaluate the reservoir concentra
tions. Furthermore, the full numerical model requires a smaller time step (10% that
of the quasi-steady state model) to assure convergence. The combination of the
additional variable and a smaller time step slow the full numerical routine to such
an extent that the quasi-steady state model may be preferable.
There can be no doubt that the full numerical routine more closely
approximates a true, analytical solution to this idealized system. Furthermore, the
full numerical routine can be used under any circumstances since it is immune to the
assumptions of the quasi-steady state model. The degree of accuracy required to

166
model transdermal diffusion in vitro is determined by the experimental data. Both
models are able to describe the experimental data at a level far below the variation
between individuals. Under most circumstances, meaningful results are achieved
using the quasi-steady state model in less time than the full numerical routine.
%

Table 12: Full numerical routine summary and comparison to quasi-steady state model,
OS
<1
% PG (v/v)
Mice Group
Swell
CMC
D (cm2/s)
AD%
s (mg/1)
As%
0
OTD
YFS
NO
1.21 xl 07
-41-16
4.00
-4543
n
OTD
YKS
YFS
1.20 x 10'7
-4i 67
4.26
-85.26
n
OTT)
NO
NO
105x10-*
.3 7*
20 44
-6.51
n
OTD
NO
YFS
1.88x10*
-7 14
20.77
16.22
5
OTD
YFS
NO
1.10 x10-7
44 SR
1.59
45.09
5
OTD
YFS
YFS
1.07 x 10"7
.On 40
20.66
6R2
5
OTD
NO
NO
1-51 x 10*
1370 ns
16.69
-676
5
OTD
NO
YFS
5.01 x 10"7
-0.16
12-05
7 61
in
YOUNG
YFS
NO
1.68 x 10'7
-30 R6
45 37
4R4
in
YO! NG
YFS
YFS
1.24x10*
-3R 13
136 52
41.51
in
YOUNG
NO
NO
6.02x10*
-4 35
12.68
1£]
m
0
2
3
0
>-
NO
YFS
9.57 x 10'7
-0.34
73 OR
1.76
70
YOUNG
YFS
NO
1 12 v lo-7
44 46
3R4
-75.12
70
YOl ING
YFS
YFS
5.06 x 10'7
-17.61
73 12
1034
70
YOUNG
NO
NO
1.59x10*
-4 7 A
11.68
-10.49
70
YOI ING
NO
YFS
2.25x10'7
.0 53
11.92
334
70
OTD
YFS
NO
1.02 x 10"7
-45.34
6.79
57 07
70
OT D
YFS
YFS
4.04 x 10'7
*22-32
20.57
8.87.
70
OT D
NO
NO
1.20 x 10*
-4 02
.5.09
-77.59
70
OT D
NO
YFS
1.76 x 10'7
-0.6R
14.04
2.51
7,0
OTD
YFS
NO
8.51x10*
-46 OR
2-80
14 R5
30
OTD
YFS
YFS
7.10x10*
.32 2R
0 76
11.68
3n
OTD
NO
NO
7.58x10*
-4 5R
4 61
-16.47
3n
OTD
NO
YFS
8.90x10*
-0.08
4 01
5.78
4n
YOUNG
YFS
NO
1 81 v 10-7
-3700
74 43
4.00
40
YOT ING
YFS
YFS
8.28x1 O7
-9.21
47 04
10.810
40
YOUNG
NO
NO
1.11x10*
.53 03
.57.71
.3 77
40
YOUNG
NO
YES
1.05 x 10'7
-71.65
21.69
1.25

40
OLD
YES
NO
l.oo x i -4552
430
-3337
40
OLD
YES
YES
2.64x10'7
-29.94
11.47
1352
40
OLD
NO
NO
3.13 x 10'*
-4.25
11.97
-10.43
40
OLD
NO
YES
1.05 x 107
-0.85
5.61
3.81
50
YOUNG
YFS
NO
1 56x lo-7
-40.07
225.10
-154
50
YOUNG
YES
YES
3.91 X 10-7
-24.15
215.25
-133
50
YOUNG
NO
NO
6.46 V 10'*
19.76
235.31
-2.42
50
YOUNG
NO
YFS
3.69 x 10'7
123.26
225.15
-1.78
50
OLD
YES
NO
1.25 x 10'7
-43.10
4.27
41.79
50
OLD
YFS
YFS
254 x 10'7
-31.61
18.04
15.83
50
OLD
NO
NO
4.10 x 10'*
-3.85
15.74
-8.62
50
OI.D
NO
YES
1.02 x 10'7
-0.97
4.29
18.45
60f#n
YOUNG
YES
NO
9.53 x 10'*
-45.39
1.08
-81.94
or#n
YOUNG
YES
YES
1.28x 10'7
-40.80
2.03
-33.71
60 r#n
YOUNG
NO
NO
2.96 x 10'*
4.06
11.14
-8.86
6or#n
YOUNG
NO
YES
4.24 X 10'*
-1.78
7.28
-10.96
60f#21
YOUNG
YES
NO
1.09 x 10'7
-4456
453
-55.60
60 (#21
YOUNG
YES
YES
1.49v 1 O'7
-38.66
3.46
-5232
60 f#21
YOUNG
NO
NO
3.47v 10'*
-3.67
17.81
-6.60
60 (#2\
YOUNG
NO
YES
5.12 x 10'*
-1.67
1134
-9.80
70 f#n
YOUNG
YES
NO
8.96 x 10'*
-46.54
1.85
-69.43
70 r#n
YOUNG
YES
YES
1.19 x 10'7
-39.49
0.84
-88.28
70 r#n
YOUNG
NO
NO
2.73v 10'*
4.21
2.83
-74.77
70 r#n
YOUNG
NO
YES
3.85 v 10'*
2.013
1.41
-84.27
70 f#21
YOUNG
YES
NO
1.16 x 10'7
43.82
2.72
-68.64
70 (#21
YOUNG
YES
YES
1.61 x 10'7
-37.51
3.51
-3734
70 f#21
YOIING
NO
NO
3.76 x 10'*
-3.84
752
-63.23
70 if 21
young
YES
-1.55
-65.63
Average 4.08 30.32 -16.54
O
GO

APPENDIX B
COMPUTER PROGRAMS
The computer programs that generate the model results are listed below. The
first program (VARFIT) examines the raw concentration versus time data and
establishes an effective diffusion coefficient by minimizing the variance. The
program can be set to simulate skin swelling during diffusion or hold the concentra
tion in the donor phase constant (simulating a micellar solution). The program uses
a parabolic model to search for the minimum variance as a function of the effective
diffusion coefficient. The program prompts the user for a maximum diffusion
coefficient (Dmax) and initializes the search routine using effective diffusion
coefficients of 0, Dmax/2, and Dmax. The program converges when the minimum
variance is bracketed by the diffusion-coefficient interval specified by the user.
The second program (ENDVALUS) generates the donor and receptor
concentrations as functions of time. The parameters are the same as for VARFIT
except for the effective diffusion coefficient which is entered by the user. The
program simultaneously prints the results to the default printer and the default disk
drive (disabling the printer does not affect program execution, so a printer is not
required). The resulting data files were imported into Quattro or SlideWrite for
comparison to the experimental data.
169

170
The third program (PROFILE) generates the theoretical concentration profile
through the skin. The program is actually a variation of the ENDVALUS program
and much of the code is the same. An additional subroutine was added to calculate
the concentration profile using the previously calculated boundary concentrations.
The last program (FNR) uses a full numerical routine rather than the quasi
steady state model developed in Chapter 6. This program was written last and, with
the exception of the numerical routine, the initial search values, and the use of a
batch data file, combines the functions of the previous programs. Consequently, this
single program is all that is required to determine the effective diffusivity and
generate time-dependent concentrations within the skin and in the reservoirs.
VARFIT.BAS
This program will generate the boundary concentrations for various times in the
Franz diffusion cell.
ON ERROR GOTO 5000
CLS
DEFDBL A-Z
PI# = 4 ATN(l)
GOSUB 100 INFORMATION SUBROUTINE
DIM DATAPNTS(DATPOINT% 1, 4), TOP(l), BOT(l), LOW(l), MID(l),
HIGH(l), TEMP(l)
CLS

171
LOCATE 1, 52
PRINT "Raw Data from file INFILES
LOCATE 3, 55
PRINT "Time C2"
LOCATE 5, 1
FOR K% = 0 TO DATPOINT% 1
INPUT #2, DATAPNTS(K%, 0), DATAPNTS(K%, 1)
LOW(l) = LOW(l) + DATAPNTS(K%, 1) A 2
PRINT USING ##.##
#####.###"; DATAPNTS(K%, 0); DATAPNTS(K%, 1)
NEXT
ENDCALC = DATAPNTS(DATPOINT% 1, 0)
LOCATE 14, 1
PRINT "STATUS: INITIALIZING"
D = (DMIN + DMAX) / 2
GOSUB 200 INTEGRATION AND VARIANCE
MID(0) = D
MID(l) = VARIANCE
D = DMAX
GOSUB 200 INTEGRATION AND VARIANCE
HIGH(0) = D
HIGH(l) = VARIANCE

172
ITER% = 1
10 GOSUB 500 ESTIMATE DIFFUSION COEFFICIENT
IF ABS(DEST D) / D < DIFCONV THEN 99
LSTD = D
D = DEST
LSTVAR = VARIANCE
GOSUB 200 INTEGRATION AND VARIANCE
ITER% = ITER% + 1
IF DEST > MID(0) THEN
TEMP(0) = LOW(O)
TEMP(l) = LOW(l)
LOW(O) = MID(0)
LOW(l) = MID(l)
MID(0) = DEST
MID(l) = VARIANCE
ELSE TEMP(0) = HIGH(0)
TEMP(l) = HIGH(l)
HIGH(0) = MID(0)
HIGH(l) = MID(l)
MID(0) = DEST
MID(l) = VARIANCE

173
END IF
GOTO 10
99 CLS
LOCATE 14, 1
PRINT "Solution Reached, Calculating Final Values"
LOCATE 16, 1
PRINT USING "Diffusivity (cmA2/s) = ##.###AAAA #/WVA"; D; ABS(D -
LSTD)
PRINT USING Variance (CTT2) = ##.###"^ #""";
VARIANCE; ABS(VARIANCE LSTVAR)
END PROGRAM END
100
BEGIN INFORMATION SUBROUTINE
A = 2.5 ~ 2 PI# / 4
FILES "*.dat"
INPUT "File name containing data"; INFILE$
OPEN "I", #2, INFILES + ".DAT"
INPUT "Series Convergence Tolerance"; CONV
INPUT "Diffusivity Convergence Tolerance"; DIFCONV
INPUT "Step size for integration (sec)"; G
INPUT "Initial Boundary Condition at X = 0 (ug/ml)"; Cl

174
INPUT "Top Concentration Constant (0/1)"; CONSTTOP
INPUT "Minimum Number of Series Terms (over rides convergence criterion)";
MINI%
INPUT "Maximum Number of Series Terms (over rides convergence criterion)";
MAXI%
INPUT "Initial Diffusivity Search Range"; DMAX
INPUT "Skin Thickness Constant (0/1)"; CONSTSKN
INPUT "Dose Volume (ml)"; VI
INPUT "Receptor Volume (ml)"; V2
INPUT "Start Time (Hours after skin in contact with water)"; TIMEO
INPUT "Number of data points [Include time 0}"; DATPOINT96
IF MAXI% = 0 THEN MAXI% = 200
RETURN
END INFORMATION SUBROUTINE
200
BEGIN INTEGRATION AND VARIANCE SUBROUTINE
F% = 1
C2 = DATAPNTS(0, 1)
VARIANCE = 0

175
TIME = O
GOSUB 300
TOP(l) = Cl: BOT(l) = C2
TIME = G
210 TOP(O) = TOP(l): BOT(O) = BOT(l)
GOSUB 400
TOP(l) = TOP(O) + G*D*A/L/V1* (BOT(O) TOP(O) + 2 TOPSER)
IF CONSTTOP = 1 THEN TOP(l) = Cl
BOT(l) = BOT(O) + G*D*A/L/V2* (TOP(O) BOT(O) + 2 BOTSER)
TTMEH = TIME / 3600
LOCATE 23, 1
PRINT" D Time C2"
PRINT USING "##.##/ ##.## D; TIMEH; BOT(l);
IF TTMEH = DATAPNTS(F%, 0) THEN
F% = F% + 1
VARIANCE = VARIANCE + (BOT(l) DATAPNTS(F% 1, 1)) A 2
END IF
IF CONSTSKN = 0 THEN GOSUB 300 CALCULATE NEW SKIN
THICKNESS
IF TTMEH < ENDCALC THEN TIME = TIME + G: GOTO 210
RETURN

176
END INTEGRATION AND VARIANCE SUBROUTINE
300
BEGIN NEW SKIN THICKNESS SUBROUTINE
LI = .069029 + .049499 (TIME / 3600 + TIMEO) .0044692 (TIME / 3600
+ TIMEO) A 2
L2 = .18821 (TIME / 3600 + TIMEO) A .050642
IF (TIME / 3600 + TIMEO) < 4.8270328# THEN L = LI ELSE L = L2
RETURN
END NEW SKIN THICKNESS SUBROUTINE
400
BEGIN Evaluate Series SUBROUTINE
IF TIME = G THEN BOTSER = -Cl / 2: TOPSER = -Cl: RETURN
TOPSER = 0: BOTSER = 0: LASTTOP = 0: LASTBOT = 0: N% = 0
410 N% = N% + 1
LASTTOP = TOPSER: LASTBOT = BOTSER
EXPONENT = EXP(-N% A 2 (TIME G) D PI# A 2 / L A 2)
TOPSER = TOPSER + ((-1) A N% BOT(O) TOP(O)) EXPONENT

177
BOTSER = BOTSER + ((-1) A N% TOP(O) BOT(O)) EXPONENT
IF N% = 1 THEN 410
IF (ABS((TOPSER LASTTOP) / LASTTOP) > CONV OR ABS((BOTSER -
LASTBOT) / LASTBOT) > CONV OR N% < MINI%) AND N% <
MAXI% THEN 410
RETURN
END EVALUATE SERIES SUBROUTINE
500
BEGIN PARABOLIC MINIMIZATION SUBROUTINE
BNUM = LOW(O) A 2 MID(l) + MID(O) A 2 HIGH(l) + HIGH(O) A 2 *
LOW(l) LOW(O) A 2 HIGH(l) MID(O) A 2 LOW(l) HIGH(O) A 2
* MID(l)
BDEN = LOW(O) A 2 MID(O) + MID(O) A 2 HIGH(O) + LOW(O) *
HIGH(O) A 2 LOW(O) MID(O) A 2 LOW(O) A 2 HIGH(O) MID(O)
* HIGH(O) A 2
Y = BNUM / BDEN
Z = (MID(l) LOW(l) + Y (LOW(O) MID(O))) / (MID(O) A 2 LOW(O) A
2)
X = LOW(l) Y LOW(O) Z LOW(O) A 2

178
LOCATE 14, 1
IF Z < 0 THEN
IF REP% > 0 THEN
CLS
PRINT "CANNOT LOCATE MINIMUM; RESTART
PROGRAM WITH NEW PARAMETERS"
PRINT "
END IF
END IF
PRINT "STATUS: MAXIMUM DETECTED IN PARABOLIC MODEL"
PRINT ADJUSTING PARAMETERS TO LOCK ONTO MINIMUM"
GOTO 60
ELSE PRINT "STATUS: SEEKING A MINIMUM
PRINT"
REP% = 0
END IF
DEST = -Y / 2 / Z
IF DEST < 0 THEN DEST = MID(O) / 2
50 ESTVAR = Z DEST A 2 + Y DEST + X
PRINT USING ITERATION NUMBER: ## ERROR: #####%
ITER%; 100 ABS(ESTVAR VARIANCE) / VARIANCE
RETURN

179
60 IF ITER% = 1 THEN DEST = (MID(O) + HIGH(O)) / 2: GOTO 50
REP% = 1
LOW(O) = MID(O)
MID(O) = HIGH(O)
HIGH(O) = TEMP(O)
LOW(l) = MID(l)
MID(l) = HIGH(l)
HIGH(l) = TEMP(l)
GOTO 500
END PARABOLIC MINIMIZATION SUBROUTINE
5000 RESUME NEXT ERROR HANDLER
ENDVALUS.BAS
This program will generate the boundary concentrations for various times in the
Franz diffusion cell.
ON ERROR GOTO 450
30 CLS
40 DEFDBL A-Z
50 PI# = 4 ATN(l)
A = 2.5 ^ 2 PI# / 4

60 INPUT "File name for results"; FILES
70 INPUT "Time to end integration (hr)"; ENDCALC
71 INPUT "Convergence Tolerance"; CONV
80 INPUT "Step size for integration (sec)"; G
90 INPUT "Printing Interval (# of steps)"; COUNTER%
100 INPUT "Initial Boundary Condition at X=0 (ug/ml)"; Cl
INPUT "Top Concentration Constant (0/1)"; CONSTTOP
110 INPUT "Initial Boundary Condition at X=1 (ug/ml)"; C2
120 INPUT "Minimun Number of Series Terms (over rides convergence
criterion)"; MINI%
130 INPUT "Maximum Number of Series Terms (over rides convergence
criterion)"; MAXI%
INPUT "Diffusion Coefficient (cmA2/s)"; D
INPUT "Skin Thickness Constant (0/1)"; CONSTSKN
INPUT "Dose Volume (ml)"; VI
INPUT "Receptor Volume (ml)"; V2
INPUT "Start Time (Hours after skin in contact with water)"; TIME0
160 DIM TOP(l), BOT(l)
170 TOP(l) = Cl: BOT(l) = C2
180 OPEN "O", #1, FILES + ".prn"
190 IF MAXI% = 0 THEN MAXI% = 200

200 PRINT #1, USING "###.### #####.### #####.###
#.########"; G; Cl; C2; D: LPRINT G, Cl, C2, D210 PRINT #1,
LPRINT
LPRINT "Time (hr) Concentration (ug/ml) Thickness (cm)"
LPRINT" Donor Receptor"
LPRINT
LPRINT
240 GOSUB 1000
LPRINT USING "###.### ######.### #####.####
##.### Z; Cl; C2; L;
PRINT #1, USING "###.### ######.### #####.####
##.###"; Z; Cl; C2; L
LPRINT FILES
TIME = G
241 TOP(O) = TOP(l): BOT(O) = BOT(l)
250 GOSUB 350
260 TOP(l) = TOP(O) + G*D*A/L/V1* (BOT(O) TOP(O) + 2 *
TOPSER)
IF CONSTTOP = 1 THEN TOP(l) = Cl
270 BOT(l) = BOT(O) + G*D*A/L/V2* (TOP(O) BOT(O) + 2 *
BOTSER)
271 TTME% = TIME / G

182
300 IF TIME% / COUNTER% = CINT(TIME% / COUNTER%) THEN
LPRINT USING "###.### ######.### #####.####
##.###"; TIME / 3600; TOP(l); BOT(l); L
PRINT #1, USING "###.### ######.### #####.####
##.###"; TIME / 3600; TOP(l); BOT(l); L
IF CONSTSKN = 0 THEN GOSUB 1000CALCULATE SKIN THICKNESS
301 IF TIME / 3600 < ENDCALC THEN TIME = TIME + G: GOTO 241
LPRINT : LPRINT : LPRINT
340 END
350 Evaluate Series
351 IF TIME = G THEN BOTSER = -Cl / 2: TOPSER = -Cl: RETURN
360 TOPSER = 0: BOTSER = 0: LASTTOP = 0: LASTBOT = 0: N% = 0
370 N% = N% + 1
380 LASTTOP = TOPSER: LASTBOT = BOTSER
390 EXPONENT = EXP(-N% A 2 (TIME G) D PI# A 2 / L A 2)
400 TOPSER = TOPSER + ((-1) A N% BOT(O) TOP(O)) EXPONENT
410 BOTSER = BOTSER + ((-1) A N% TOP(O) BOT(O)) EXPONENT
420 IF N% = 1 THEN 370
430 IF (ABS((TOPSER LASTTOP) / LASTTOP) > CONV OR
ABS((BOTSER LASTBOT) / LASTBOT) > CONV OR N% < MINI%)
AND N% < MAXI% THEN 370
440 RETURN

183
450 RESUME NEXT
1000 CALCULATE NEW SKIN THICKNESS
LI = .069029 + .049499 (TIME / 3600 + TIMEO) .0044692 (TIME / 3600
+ TIMEO) A 2
L2 = .18821 (TIME / 3600 + TIMEO) A .050642
IF (TIME / 3600 + TIMEO) < 4.8270328# THEN L = LI ELSE L =
L2
RETURN
PROFILE.BAS
...This program will generate the concentration profile for various times across
skin mounted in a Franz diffusion cell
ON ERROR GOTO 500
CLS
DEFDBL A-Z
PI# = 4 ATN(l)
A = 2.5 A 2 PI# / 4 Area of Diffusion
GOSUB 1000 Enter Information
DIM CONCENTR(SKINNUM%, 2), L(2)
CONCENTR(0, 2) = Cl: CONCENTR(SKINNUM%, 2) = C2
OPEN "O", #1, FILES + ".prn"
GOSUB 600
Initial Skin Thickness

184
TIME = G
100 GOSUB 2000 Calculate Boundary Conditions
GOSUB 3000 Calculate Skin Concentration Profile
TTME% = (TIME G) / G
IF TIME% / COUNTER % = CINT(TIME% / COUNTER%) AND TIME% >
0THEN
GOSUB 4000 Print Results
END IF
IF CONSTSKN = 0 THEN
GOSUB 600 New Skin Thickness
END IF
IF TIME / 3600 < ENDCALC THEN TIME = TIME + G: GOTO 100
END Program End
500 RESUME NEXT Error Handler
600
BEGIN SKIN THICKNESS SUBROUTINE
SUBMARKR% = SUBMARKR% + 1
L(0) = L(l)
L(l) = L(2)
IF SUBMARKR% = 1 THEN
L(0) = .069029

185
L(l) = .069029
END IF
LI = .069029 + .049499 (TIME / 3600 + TIMEO) .0044692 (TIME / 3600
+ TIMEO) A 2
L2 = .18821 (TIME / 3600 + TIMEO) A .050642
IF (TIME / 3600 + TIMEO) < 4.8270328# THEN L(2) = LI ELSE L(2) = L2
RETURN
END SKIN THICKNESS SUBROUTINE
1000
Begin Information Subroutine
INPUT "File name for results"; FILES
INPUT "Time to end integration (hr)"; ENDCALC
INPUT "Convergence Tolerance"; CONV
INPUT "Step size for integration (sec)"; G
ENDCALC = ENDCALC + G / 3600 Last Profile at Endcalc
INPUT "Printing Interval (# of steps)"; COUNTER%
INPUT "Initial Boundary Condition at X=0 (ug/ml)"; Cl
CONCHIGH = 350 2 / 3 / Cl
INPUT "Top Concentration Constant (0/1)"; CONSTTOP

186
INPUT "Initial Boundary Condition at X=1 (ug/ml)"; C2
INPUT "Minimum Number of Series Terms"; MINI%
INPUT "Maximum Number of Series Terms"; MAXI%
IF MAXI% = 0 THEN MAXI% = 10000
INPUT "Diffusion Coefficient (cnC2/s)"; D
INPUT "Skin Thickness Constant (0/1)"; CONSTSKN
INPUT "Dose Volume (ml)"; VI
INPUT "Receptor Volume (ml)"; V2
INPUT "Start Time (Hours after skin in contact with water)"; TIME0
INPUT "Resolution of skin profile (number of steps)"; SKINNUM%
CONCWIDE = 700 / (SKINNUM% + 1)
SCREEN 3
RETURN
End Information Subroutine
2000
Begin Boundary Condition Subroutine
CONCENTR(0, 0) = CONCENTR(0, 1)
CONCENTR(SKINNUM%, 0) = CONCENTR(SKINNUM%, 1)
CONCENTR(0, 1) = CONCENTR(0, 2)

187
CONCENTR(SKINNUM%, 1) = CONCENTR(SKINNUM%, 2)
300 LASTC1 = CONCENTR(0, 2)
LASTC2 = CONCENTR(SKINNUM%, 2)
Evaluate Series
IF TIME = G THEN BOTSER = -Cl / 2: TOPSER = -Cl: GOTO 425
TOPSER = 0
BOTSER = 0
LASTTOP = 0
LASTBOT = 0
N% = 0
400 N% = N% + 1
LASTTOP = TOPSER: LASTBOT = BOTSER
EXPONENT = EXP(-N% A 2 TIME D PI# A 2 / L(2) A 2)
TOPSER = TOPSER + ((-1) A N% LASTC2 LASTC1) EXPONENT
BOTSER = BOTSER + ((-1) A N% LASTC1 LASTC2) EXPONENT
IF N% = 1 THEN 400
IF (ABS((TOPSER LASTTOP) / LASTTOP) > CONV OR ABS((BOTSER -
LASTBOT) / LASTBOT) > CONV OR N% < MINI%) AND N% <
MAXI% THEN 400
425 CONCENTR(0, 2) = CONCENTR(0, 1) + G D A / L(2) / VI *
(LASTC2 LASTC1 + 2 TOPSER)
IF CONSTTOP = 1 THEN CONCENTR(0, 1) = Cl

188
CONCENTR(SKINNUM%, 2) = CONCENTR(SKINNUM%, 1) + G D A /
L(2) / V2 (LASTC1 LASTC2 + 2 BOTSER)
IF CONCENTR(0, 2) < 0 THEN CONCENTR(0, 2) = 0
IF CONCENTR(SKINNUM%, 2) < 0 THEN CONCENTR(SKINNUM%, 2) =
0
IF ABS((CONCENTR(0, 2) LASTC1) / LASTC1) > CONV OR
ABS((CONCENTR(SKINNUM%, 2) LASTC2) / LASTC2) > CONV
THEN 300
RETURN
End Boundary Condition Subroutine
3000
Begin Skin Concentration Profile Subroutine
IF TIME < 3 G THEN 575
DELTATOP = (CONCENTR(0, 2) CONCENTR(0, 0)) / 2
DELTABOT = (CONCENTR(SKINNUM%, 2) CONCENTR(SKINNUM%,
0))/2
DELTAL = L(2) L(0)
Evaluate Skin Series for Each Location
FOR SKINCOUN% = 1 TO SKINNUM% 1

189
SKINSER = 0: LASTSKIN = 0: N% = 0
550 N% = N% + 1
LASTSKIN = SKINSER
EXPONENT = EXP(-N% A 2 (TIME G) D PI# A 2 / L(l) A 2)
FSTTERM = DELTABOT (-1) A N% DELTATOP
SNDTERM = CONCENTR(SKINNUM%, 1) (-1) A N% CONCENTR(0, 1)
TRDTERM = 2 D N% A 2 PI# A 2 TIME / L(l) A 2 (DELTAL / L(l)
- G / TIME)
FTHTERM = SIN(N% PI# ((SKINCOUN%) / (SKINNUM%))) *
EXPONENT / N%
ADDSER = FTHTERM (FSTERM + SNDTERM TRDTERM)
SKINSER = SKINSER + ADDSER
IF N% = 1 THEN 550
IF (ABS((SKINSER LASTSKIN) / LASTSKIN) > CONV OR N% < MINI%)
AND N% < MAXI% THEN 550
DELTACON = DELTATOP + (DELTABOT DELTATOP) (SKINCOUN%)
/ (SKINNUM%) + 2 / PI# SKINSER
CONCENTR(SKINCOUN%, 1) = CONCENTR(SKINCOUN%, 0) +
DELTACON
IF CONCENTR(SKINCOUN%, 1) < 0 THEN CONCENTR(SKINCOUN%, 1)
= 0
CONCENTR(SKINCOUN%, 0) = CONCENTR(SKINCOUN%, 1)

190
NEXT SKINCOUN%
575 RETURN
End Skin Concentration Profile Subroutine
4000
Begin Print Subroutine
LPRINT USING "##.### (TIME G) / 3600;
PRINT #1, USING "##.### (TIME G) / 3600;
CLS
FOR SKINCOUN% = 0 TO SKINNUM%
LPRINT USING "#####.### "; CONCENTR(SKINCOUN%, 1);
PRINT #1, USING "#####.### "; CONCENTR(SKINCOUN%, 1);
LINE (10 + SKINCOUN% CONCWIDE, 340)-(10 + (SKINCOUN% + 1) *
CONCWIDE, 340 CONCHIGH CONCENTR(SKINCOUN%, 1)), BF
NEXT SKINCOUN%
PRINT #1,
LPRINT
RETURN
End Time Check Subroutine

191
End Program Text
FNR.BAS
This program controls the fnr program and inputs the files to be analyzed
sequentially
ON ERROR GOTO 5000
CLS
DEFDBL A-Z
DEFDBL I-J, N
pi# = 4 ATN(l)
A = 2.5 ^ 2 pi / 4
FILES "*.bch"
INPUT "File containing batch data"; batfileS
INPUT "File to output data"; outfileS
OPEN "O", #1, outfileS + ".out"
OPEN T, #3, batfileS + ".bch"
1 INPUT #3, INFILES
IF EOF(3) THEN END
increase = 0
GOSUB 5 solve for optimum diffusivity
CLOSE #2

192
GOTO 1
5 This subroutine will fit the boundary concentrations for various times in the
Franz diffusion cell to experimental data.
GOSUB 100 INFORMATION SUBROUTINE
DIM DATAPNTS(DATPOINT% 1, 4), C(M%, 1), LOW(l), MID(l), HIGH(l),
TEMP(l), COMPVAL(DATPOINT% 1)
CLS
LOCATE 1, 52
PRINT "Raw Data from file INFILES;
PRINT #1, "Raw Data from file INFILES;
IF CONSTSKN = 1 THEN PRINT #1, ", NO SWELLING";
IF CONSTTOP = 1 THEN PRINT #1, ", CMC ="; Cl; ELSE PRINT #1, ",
INITIAL CONCENTRATION = "; Cl;
PRINT #1,
LOCATE 3, 55
PRINT "Time C2"
LOCATE 5, 1
FOR k% = 0 TO DATPOINT% 1
INPUT #2, DATAPNTS(k%, 0), DATAPNTS(k%, 1)
PRINT USING ##.##
#####.###"; DATAPNTS(k%, 0); DATAPNTS(k%, 1)
NEXT

193
ENDCALC = DATAPNTS(DATPOINT% 1, 0)
N = ENDCALC 3600 / h
LOCATE 14, 1
PRINT "STATUS: INITIALIZING"
D = DMIN
GOSUB 200 INTEGRATION AND VARIANCE
LOW(O) = D
LOW(l) = VARIANCE
D = DEST
GOSUB 200 INTEGRATION AND VARIANCE
MID(0) = D
MID(l) = VARIANCE
D = DMAX
GOSUB 200 INTEGRATION AND VARIANCE
HIGH(0) = D
HIGH(l) = VARIANCE
ITER% = 1
10 IF ABS(LSTD D) / D < DIFCONV THEN 99
LSTD = D
GOSUB 500 ESTIMATE DIFFUSION COEFFICIENT
D = DEST
LSTVAR = VARIANCE

194
GOSUB 200 INTEGRATION AND VARIANCE
ITER% = ITER% + 1
IF DEST > MID(O) THEN
TEMP(O) = LOW(O)
TEMP(l) = LOW(l)
LOW(O) = MID(O)
LOW(l) = MID(l)
MID(O) = DEST
MID(l) = VARIANCE
ELSE TEMP(O) = HIGH(O)
TEMP(l) = HIGH(l)
HIGH(O) = MID(O)
HIGH(l) = MID(l)
MID(O) = DEST
MID(l) = VARIANCE
END IF
GOTO 10
99 CLS
LOCATE 14, 1
PRINT "Solution Reached, Calculating Final Values"
PRINT #1, "Solution Reached, Calculating Final Values"
PRINT #1, "Time C2
C2(MOD)

195
FOR k% = 0 TO DATPOINT% 1
PRINT #1, USING "##.## #####.### #####.###";
DATAPNTS(k%, 0); DATAPNTS(k%, 1); COMPVAL(k%)
NEXT
LOCATE 16, 1
PRINT USING "Diffusivity (cnU2/s) = ##.###/ #"""; D; ABS(D-
LSTD)
PRINT USING" Variance (CTT2) = ##.###/ "";
VARIANCE; ABS (VARIANCE LSTVAR)
PRINT #1, USING "Diffusivity (cnU2/s) = ##.###/ D;
ABS(D LSTD)
PRINT #1, USING Variance (CTT2) = ##.###~^ #~wv";
VARIANCE; ABS(VARIANCE LSTVAR)
PRINT #1,
PRINT #1,
PRINT #1,
ERASE DATAPNTS, C, LOW, MID, HIGH, TEMP, COMPVAL
RETURN MAIN SUBROUTINE END
100
BEGIN INFORMATION SUBROUTINE
OPEN "I", #2, INFILES + ".DAT

196
INPUT #3, Cl, CONSTTOP, DEST, CONSTSKN, DATPOINT%
DMIN = .9 DEST
DMAX = 1.1 DEST
DIFCONV = .0001
h = 30
M% = 8
VI = 2
V2 = 14.5
RETURN
END INFORMATION SUBROUTINE
300
BEGIN NEW SKIN THICKNESS SUBROUTINE
LASTL = L
LI = .069029 + .049499 (TIME / 3600 + TIME0) .0044692 (TIME / 3600
+ TIME0) A 2
L2 = .18821 (TIME / 3600 + TIME0) A .050642
IF (TIME / 3600 + TIME0) < 4.8270328# THEN L = LI ELSE L = L2
k = L/M%
r = D*h/kA2
RETURN

197
END NEW SKIN THICKNESS SUBROUTINE
500
BEGIN PARABOLIC MINIMIZATION SUBROUTINE
bnum = LOW(O) A 2 MID(l) + MID(O) A 2 HIGH(l) + HIGH(O) A 2 *
LOW(l) LOW(O) A 2 HIGH(l) MID(O) A 2 LOW(l) HIGH(O) A 2
* MID(l)
bden = LOW(O) A 2 MID(O) + MID(O) A 2 HIGH(O) + LOW(O) HIGH(O)
A 2 LOW(O) MID(O) A 2 LOW(O) A 2 HIGH(O) MID(O) *
HIGH(O) A 2
Y = bnum / bden
Z = (MID(l) LOW(l) + Y (LOW(O) MID(O))) / (MID(O) A 2 LOW(O) A
2)
X = LOW(l) Y LOW(O) Z LOW(O) A 2
LOCATE 14, 1
IF Z < 0 OR increase > 1 THEN
IF REP% > 0 THEN
CLS

198
PRINT "CANNOT LOCATE MINIMUM; RESTART
PROGRAM WITH NEW PARAMETERS"
PRINT #1, "CANNOT LOCATE MINIMUM; RESTART
PROGRAM WITH NEW PARAMETERS"
PRINT "
RETURN
END IF
PRINT "STATUS: MAXIMUM DETECTED IN PARABOLIC MODEL"
PRINT ADJUSTING PARAMETERS TO LOCK ONTO
MINIMUM"
GOTO 60
ELSE PRINT "STATUS: SEEKING A MINIMUM
PRINT"
REP% = 0
END IF
DEST = -Y / 2 / Z
IF DEST < 0 THEN DEST = MID(O) / 2
IF DEST > DMAX THEN DEST = .75 DMAX: increase =
increase + 1
50 ESTVAR = Z DEST A 2 + Y DEST + X
PRINT USING" ITERATION NUMBER: ## ERROR:
#####% "; ITER%; 100 ABS(ESTVAR VARIANCE) / VARIANCE

199
RETURN
60 IF ITER% = 1 THEN DEST = (MID(O) + HIGH(O)) / 2: GOTO 50
REP% = 1
LOW(O) = MID(O)
MID(O) = HIGH(O)
HIGH(O) = TEMP(O)
LOW(l) = MID(l)
MID(l) = HIGH(l)
HIGH(l) = TEMP(l)
GOTO 500
END PARABOLIC MINIMIZATION SUBROUTINE
5000 RESUME NEXT ERROR HANDLER
200
Begin Numerical Integration Subroutine
F% = 1
C2 = DATAPNTS(0, 1)
VARIANCE = 0
TIME = 0
GOSUB 300 CALCULATE INITIAL SKIN THICKNESS

200
TIME = h
FOR i = 0 TO M%
C(i, 0) = 0 RESET ARRAY
NEXT i
C(0, 0) = Cl INITIAL BOUNDARY CONDITIONS
C(M%, 0) = C2
COMPVAL(O) = C(M%, 0)
FOR j = 1 TO N
IF CONSTSKN = 0 THEN GOSUB 300 CALCULATE SKIN
THICKNESS
IF CONSTTOP = 0 THEN
C(0, 1) = C(0, 0) (1 h A D / VI / k) + C(l, 0) h A D / VI /
k
ELSE C(0, 1) = Cl
END IF
TIMEH = TIME / 3600
FOR i = 1 TO M% 1
C(i, 1) = r C(i 1, 0) + (1 2 r) C(i, 0) + r C(i + 1, 0)
NEXT i
C(M%, 1) = C(M%, 0) (1 h A D / V2 / k) + C(M% 1, 0) h *
A D / V2 / k
FOR ii = 0 TO M%

C(ii, 0) = C(ii, 1)
NEXT ii
201
LOCATE 23, 1
PRINT" D Time C2 Variance"
PRINT USING "##.##AAAA ##.## ##.##AAAA
TIMEH; C(M%, 1); VARIANCE;
IF TIMEH = DATAPNTS (F%, 0) THEN
VARIANCE = VARIANCE + (C(M%, 1) -
DATAPNTS(F%, 1)) A 2
COMPVAL(F%) = C(M%, 1)
F% = F% + 1
END IF
TIME = TIME + h
IF CONSTSKN = 0 THEN
GOSUB 300
END IF
NEXT j
RETURN
##.##"AA""; D;
New Skin Thickness
End Numerical Integration Subroutine

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BIOGRAPHICAL SKETCH
Kenneth Miller II received his B.S. in chemical engineering from Carnegie
Mellon University in 1986 with special emphasis on colloid, polymer, and surface
sciences. During the summers of 1982-1985, Mr. Miller worked at the Pittsburgh
Energy Technology Center (Department of Energy) on characterization of
regional coals, zeolite reduction catalysis, and process design. He received his
M.S. in chemical engineering from West Virginia University in 1988. While at
West Virginia University, Mr. Miller worked at the Fluidized Bed Research
Center on small-particle force measurement and correlation in glass bead/air
systems.
Kenneth Miller received his Ph.D. in chemical engineering from the
University of Florida (departments of chemical engineering and anesthesiology)
under Professor D.O. Shah in 1991.
212

This dissertation was submitted to the Graduate Faculty
of the College of Engineering and to the Graduate School and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
December, 1991
lhjL? (X- &
Jo*Winfred M. Phillips
' Dean, College of Engineering
Madelyn M. Lockhart
Dean, Graduate School

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Dinesh 0. Shah, Chair
Professor of Chemical
Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Gerald B. Westermann-Clark
Associate Professor of
Chemical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Chanc/'W-Park
Assistant Professor of
Chemical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Salvatore R. Goodwin
Associate Professor of
Anesthesiology
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
B. Sloan
Associate Professor of
Medicinal Chemistry

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To ken.miller@mylanlabs.com
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bcc
>
07/02/2008 08:13 AM
Subject UF Libraries:DigitaI Dissertation Project
Dear Dr. Kenneth J. Miller, Jr.,
The George A. Smathers Libraries at the University of Florida has initiated a project to
retrospectively digitize and make available on the Internet any dissertation written by a
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Christy Shorey, Project Technician
The Foundation for The Gator Nation
Internet Distribution Consent Agreement
In reference to the following dissertation:
AUTHOR:
TITLE:
Miller, Kenneth
Interfacial diffusional theoretical and clinical aspects of topical local
anesthetic formulation / (record number: 1717488)
PUBLICATION
1991



43
sample separate as they pass through the column depending on their polarity and
functionality. This type of chromatography is called "reverse-phase".
After the components of the sample are separated by the column, they flow
through an absorbance detector (Spectra Physics Model SP8450) which generates an
electrical signal proportional to the light absorbed by the liquid passing through the
detector. Peaks in plots of this signal correspond to components eluting from the
column. Because retention time depends on the functionality and polarity of the
compounds, the likelihood that two different chemicals will have the same retention
time is remote.
The other instruments in the HPLC system are the pump, autosampler, and
integrator. The pump (Spectra Physics Model SP8800) simply maintains the flow of
carrier solvent through the system at a steady rate. The pump can also mix up to
three miscible solvents in any ratio.
The autosampler (Spectra Physics Model SP8880) contains the sample vials
in four trays mounted on a turntable. Each tray holds twenty vials and the turntable
contains an additional priority-vial position. The autosampler moves each vial to the
sampling position and, when the system is ready, injects a predetermined volume of
the contents into the solvent stream while signalling the other instruments to begin
analysis.
The integrator (Spectra Physics Model SP4290) plots the raw signal from the
detector (optical absorbance of the solvent stream) and determines the presence of
peaks. The integrator calculates the area of peaks and determines if they correspond


INTERFACIAL, DIFFUSIONAL, THEORETICAL,
AND CLINICAL ASPECTS OF TOPICAL,
LOCAL ANESTHETIC FORMULATIONS
By
KENNETH JAMES MILLER II
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1991


80
NaOH (mmol)
Figure 32: NaOH titration of aqueous tetracaine
the lack of free ions needed to maintain equilibrium which may arise from the lack
¡
j
of water in the system.
Measuring the apparent pH as a function of concentration can also be used
to determine the CMC. The pH versus concentration behavior for tetracaine (40%
i
acid salt, 60% free base w/w) in solvents of propylene glycol and saline is illustrated
in the following sequence of graphs (Figure 34-Figure 39). As drug is added to
solution the pH rises monotonically for all systems. At some point, the apparent pH
reaches a maximum and begins to fall. This change in slope indicates a change in
the structure of the solution. This change in structure can be viewed as the onset of
micellization; the concentration at which it occurs can be viewed as the CMC. Based


196
INPUT #3, Cl, CONSTTOP, DEST, CONSTSKN, DATPOINT%
DMIN = .9 DEST
DMAX = 1.1 DEST
DIFCONV = .0001
h = 30
M% = 8
VI = 2
V2 = 14.5
RETURN
END INFORMATION SUBROUTINE
300
BEGIN NEW SKIN THICKNESS SUBROUTINE
LASTL = L
LI = .069029 + .049499 (TIME / 3600 + TIME0) .0044692 (TIME / 3600
+ TIME0) A 2
L2 = .18821 (TIME / 3600 + TIME0) A .050642
IF (TIME / 3600 + TIME0) < 4.8270328# THEN L = LI ELSE L = L2
k = L/M%
r = D*h/kA2
RETURN


42
DoubleDos and Spectra Physics software LNET2 and SPMENU), this system can
analyze over 80 samples without operator assistance. Once programmed, the system
can inject a sample from a diffusion experiment, identify the components in the
sample, determine the concentration of each component (integrate the signal), store
all information (including the raw data), generate a file for a spreadsheet, and print
a final report. Although the system has several components, the principles of
operation are relatively simple. The HPLC uses the relative affinity of a compound
between a polar and a nonpolar phase to achieve separation. A polar solvent is
pumped through a separation column containing a nonpolar hydrocarbon chemically
bonded to silica. The retention (residence) time in the column depends on the
compounds affinities for the two phases. Consequently, two compounds in the same


xml record header identifier oai:www.uflib.ufl.edu.ufdc:UF0009018400001datestamp 2009-02-26setSpec [UFDC_OAI_SET]metadata oai_dc:dc xmlns:oai_dc http:www.openarchives.orgOAI2.0oai_dc xmlns:dc http:purl.orgdcelements1.1 xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.openarchives.orgOAI2.0oai_dc.xsd dc:title Interfacial diffusional theoretical, and clinical aspects of topical local anesthetic formulation dc:creator Miller, Kenneth James.dc:type Bookdc:identifier http://www.uflib.ufl.edu/ufdc/?b=UF00090184&v=00001001717488 (alephbibnum)25622360 (oclc)dc:source University of Florida


61

X
O
oc
u
0 10 20 30 40 50 60 70 80 90 100
% Propylene Glycol (v/v)
Figure 15: Tetracaine (60% free base, 40% acid salt w/w) partitioning into
1-octanol
Partitioning into N-octane
The partitioning of tetracaine between propylene glycol-water solutions and
n-octane (H3C-(CH2)6-CH3) is constant at about 0.004 up to 30% propylene glycol.
The partition coefficient then declines steadily with increasing propylene glycol
content up to 70% propylene glycol (Table 2, Figure 16). Above 80%, however,
partitioning into the oil phase seems to increase. It is inferred from these data that
i
a minimum partition coefficient (~0.0022) may exist between 70% and 80%
propylene glycol.
Drug solubility in the formulation indicates how much drug can be loaded into
the vehicle and, therefore; how much drug can be delivered to the skin surface. The


41
(resistance from 0.5 0 to 2 Mil). Conductivities from this instrument have an
uncertainty of approximately 0.2 /unho.
Ultraviolet Spectrometry
Ultraviolet spectra were measured using a Perkin Elmer scanning spectropho
tometer Model 576. This model has two lamps (a deuterium lamp as an ultraviolet
source and a tungsten lamp as a visible source) extending its operational range over
any single-source instrument (90 nm to 800 nm). Ultraviolet and visible spectra were
measured against a reference solution and the difference in absorption between the
two solutions was plotted. This instrument was used to screen compounds for
possible detection in the HPLC (the HPLC detector uses ultraviolet or visible light
absorption). A spectrum of a solution containing the compound of interest was
measured over a wide range of wavelengths to determine the wavelengths of
maximum absorption for use with the HPLC. Although this instrument can be used
for quantitative measurements of absorbance (proportional to concentration), it was
only used in this manner for early diffusion experiments before the HPLC had been
installed. Calibration of this instrument showed a constant error of approximately
+ 0.33 nm which is within the manufacturers tolerance.
High Pressure Liquid Chromatography (HPLC)
By far the most complex instrument, the HPLC is invaluable for this type of
diffusion study (Figure 3). Fully computerized (640 kB Epson Equity 1+
running


134
between the theoretical predictions and the experimental data. This may not always
be the case. The shape of the curve can be used to determine whether the diffusion
Time (hr)
Figure 68: Model fits for saline (old
mice)
Figure 70: Model fits for 10% propyl
ene glycol (young mice)
Figure 69: Model fits for 5% propyl
ene glycol (old mice)
Time (hr)
Figure 71: Model fits for 20% propyl
ene glycol (young mice)
process modelled matches that measured (initial increasing slope, constant slope, or
decreasing slope indicating approach to equilibrium). Comparison of the variance
between the theoretical predictions and the experimental data can be used to suggest
a preferred system, but a final determination should be based upon the features of
the concentration versus time plots. Identification of a preferred theoretical system


CHAPTER 6
THEORY
Many models predict percutaneous absorption, but most assume the drug
concentration-profile within the skin has reached steady state (i.e., the concentration
profile is linear within the skin).25,42,60,97 Although steady state may be a valid
assumption for drugs that diffuse quickly, steady state models cannot predict the early
stages of drug diffusion which disobey the linear concentration-profile assumption.
When a substance is applied to the skin, the existing steady state changes
suddenly. Where no drug was present, there is now a high concentration at the
external surface. Predictions of the concentration profile within the skin can help
predict the drug flux through the skin. Such predictions are valuable for substances
that have relatively low therapeutic or toxic levels. These substances can have
profound effects long before steady state is reached. In other applications, e.g.,
dermatological, knowledge of drug concentration versus depth within the skin is
essential. Drug diffusing into drug-free skin initially creates an exponential*
concentration profile.26 With time, the concentration profile becomes linear (i.e.,
steady state). If the amount of drug crossing the skin is small and if a linear
Actually, the initial concentration profile is described by an error function
(erf(x)) and such a solution can be found in Transport Phenomena by Bird, Stewart,
and Lightfoot.7
121


178
LOCATE 14, 1
IF Z < 0 THEN
IF REP% > 0 THEN
CLS
PRINT "CANNOT LOCATE MINIMUM; RESTART
PROGRAM WITH NEW PARAMETERS"
PRINT "
END IF
END IF
PRINT "STATUS: MAXIMUM DETECTED IN PARABOLIC MODEL"
PRINT ADJUSTING PARAMETERS TO LOCK ONTO MINIMUM"
GOTO 60
ELSE PRINT "STATUS: SEEKING A MINIMUM
PRINT"
REP% = 0
END IF
DEST = -Y / 2 / Z
IF DEST < 0 THEN DEST = MID(O) / 2
50 ESTVAR = Z DEST A 2 + Y DEST + X
PRINT USING ITERATION NUMBER: ## ERROR: #####%
ITER%; 100 ABS(ESTVAR VARIANCE) / VARIANCE
RETURN


175
TIME = O
GOSUB 300
TOP(l) = Cl: BOT(l) = C2
TIME = G
210 TOP(O) = TOP(l): BOT(O) = BOT(l)
GOSUB 400
TOP(l) = TOP(O) + G*D*A/L/V1* (BOT(O) TOP(O) + 2 TOPSER)
IF CONSTTOP = 1 THEN TOP(l) = Cl
BOT(l) = BOT(O) + G*D*A/L/V2* (TOP(O) BOT(O) + 2 BOTSER)
TTMEH = TIME / 3600
LOCATE 23, 1
PRINT" D Time C2"
PRINT USING "##.##/ ##.## D; TIMEH; BOT(l);
IF TTMEH = DATAPNTS(F%, 0) THEN
F% = F% + 1
VARIANCE = VARIANCE + (BOT(l) DATAPNTS(F% 1, 1)) A 2
END IF
IF CONSTSKN = 0 THEN GOSUB 300 CALCULATE NEW SKIN
THICKNESS
IF TTMEH < ENDCALC THEN TIME = TIME + G: GOTO 210
RETURN


21
5: Odorless, colorless, tasteless
6: Nontoxic, nonallergenic, nonirritant
Brown and Langer14 describe penetration enhancers as "vehicles that reduce the
barrier properties of the stratum corneum in such a way as to increase the
penetration of the drug of interest." Many substances have been investigated as
potential penetration enhancers. Chien18 lists the following as representative classes
of penetration enhancers: alkyl methyl sulfoxides, surfactants, and azones
(1-alkyl azacycloheptan-2-ones).
One mechanism for penetration enhancement seems to be disruption of the
stratum corneum lipids and proteins.19,85 Fluidization and extraction of stratum
corneum lipids by some proven penetration enhancers has been shown experiment-
ally.27,29,40 These same authors have also noted that some established penetration
enhancers (N-methyl-2-pyrrolidone, n-alkanols) do not affect the stratum corneum
and must act through some other mechanism.
Another process by which some penetration enhancers (cationic amines) may
increase drug flux is by forming ion pairs with the drug. Briefly, the mechanism of
facilitated transport by ion pairs at the skin surface is:85 long chain cationic amines
ionize and may pair with ionized permeant; the uncharged pair diffuses through the
i
stratum corneum; within the skin the pH rises, causing the amine to deprotonate and
freeing it to diffuse back through the skin.


26
Gesztes and Mezei30 studied the release of 0.5% tetracaine base from
multilamellar phospholipid vesicles. The anesthetic preparation was evaluated in
adult volunteers using the pinprick method.* The preparation was applied for one
hour and reportedly provided at least four hours of topical anesthesia. Pontocaine
cream, used as a control, was found to be ineffective. Despite clear details about the
anesthetic preparation and its administration, our attempts to reproduce the
published results were unsuccessful. The performance of their liposomal formulation
was also compared to the tetracaine preparation developed in our laboratory and
found to be less effective clinically. Their preparation was less concentrated,
however; and their comments about the benefits of low concentration for self
administration by outpatients are important.
Kushla and Zatz,51 using an approach similar to that of Campbell and Adriani
for evaluating local anesthesia, induced pain electrically. Their anesthetic
formulation was lidocaine base (5%) in vehicles of either an aqueous gel containing
40% propylene glycol or an oil-in-water emulsion cream (77.5% water). Placebos of
the vehicles were used as controls. Tests of the topical formulations revealed that
the gel was not effective, but the cream was. Maximum effect was observed two to
three hours after application and lasted up to six hours.
Monash61 studied the diffusion of anesthetic salts and bases through both
mucous membranes and skin in vivo in human volunteers. The anesthetic bases were
dissolved in a solvent of 45% alcohol (probably ethanol), 45% water and 10%
j
The subjects are asked to rate the pain level produced by a pin prick.


63
Figure 16: Tetracaine (60% free base, 40% acid salt w/w) partitioning into
n-octane
Thus, different solvents with different partitioning behavior can be used to obtain the
same result. The optimum vehicle for tetracaine diffusion through skin as
determined by the combined solubility-partitioning parameter is 50% propylene
glycol and 50% saline regardless of which lipid is used to characterize partitioning.
Surface Tension of Tetracaine Formulations
A surface tension versus concentration plot for tetracaine HC1 in water is
presented in Figure 19. The surface tension decreases rapidly with increasing drug
concentration initially, but eventually flattens out as more drug is added. Such a
strong effect of concentration on surface tension indicates that tetracaine HC1 is


114
Table 11: Clinical trials of lidocaine preparations
Test Solution
Mean response
(VAS)
Standard
deviation (VAS)
1.85 M aqueous
lidocaine salt
0.95
1.70
1.85 M lidocaine salt in
50% propylene glycol
1.15
1.50
1.71 M lidocaine base in
70% propylene glycol
2.54
3.20
1.07 M lidocaine base in
50% propylene glycol
4.46
3.70
1.00 M lidocaine (50%
free base, 50% acid salt
w/w) in 65% propylene
glycol
5.07
3.60
1.59 M lidocaine (50%
free base, 50% acid salt
w/w) in 70% propylene
glycol
3.20
3.40
Site preparation
Cleansing the skin with isopropyl alcohol before applying the tetracaine
formulation increases the mean response after one hour by approximately 20%
(Figure 59). Presumably, this cleansing removes excess lipids from the skin and
provides better contact for the anesthetic formulation. Unfortunately, the scatter in
this data makes this difference statistically insignificant.


173
END IF
GOTO 10
99 CLS
LOCATE 14, 1
PRINT "Solution Reached, Calculating Final Values"
LOCATE 16, 1
PRINT USING "Diffusivity (cmA2/s) = ##.###AAAA #/WVA"; D; ABS(D -
LSTD)
PRINT USING Variance (CTT2) = ##.###"^ #""";
VARIANCE; ABS(VARIANCE LSTVAR)
END PROGRAM END
100
BEGIN INFORMATION SUBROUTINE
A = 2.5 ~ 2 PI# / 4
FILES "*.dat"
INPUT "File name containing data"; INFILE$
OPEN "I", #2, INFILES + ".DAT"
INPUT "Series Convergence Tolerance"; CONV
INPUT "Diffusivity Convergence Tolerance"; DIFCONV
INPUT "Step size for integration (sec)"; G
INPUT "Initial Boundary Condition at X = 0 (ug/ml)"; Cl


Results 131
General Behavior of Model 132
Tetracaine Diffusion Through Hairless-mouse Skin 133
Diffusion of Hydrocortisone Through Synthetic Membranes . 141
Concentration Profile Within the Skin 143
7 CONCLUSIONS 145
Physical Properties of Drug Formulations 145
Solubility 145
Partitioning and Solubility 145
Surface Activity 146
Micelle Size 147
Thermal Breakdown 147
Drug Diffusion In Vitro 148
Stirring 148
Temperature Behavior of Franz Diffusion Cells 148
Skin Swelling 149
Skin Longevity 150
Effect of Propylene Glycol 150
Effect of Age 151
Effect of Formaldehyde 151
Effect of Concentration 152
Effect of pH 152
Drug Diffusion In Vivo 153
Rat Tail-flick Test 153
Clinical Trials 153
Theory 154
Quasi-steady State Model 154
Full Numerical Routine 154
8 RECOMMENDATIONS FOR FUTURE WORK 156
Physical Properties 156
Diffusion Experiments 157
Theoretical Modelling 158
Clinical Studies 159
APPENDICES
A DERIVATION OF THE FULL NUMERICAL ROUTINE 161
B COMPUTER PROGRAMS 169
Vlll


29
venepuncture or minimal sensation with no discomfort) was 88.7% (1101/1241).
About 7% of the patients had mild reactions (local redness, swelling, and itching).
McGowan et al.59 used laser doppler velocimetry to measure changes in blood
perfusion during vasodilation caused by the percutaneous absorption of tetracaine
from the gel described on page 28. They confirmed the clinically obtained minimum
onset time of 30 min, but could not measure the duration of anesthesia. ;
Specific Objectives
Topical Local Anesthetic
The objective, of course, is the development of a topical local anesthetic
formulation suitable for clinical use by hospital patients. Ideally this preparation
should be effective, fast acting, and long lasting without irritation or other discomfort.
Its effectiveness should be measured by its ability to alleviate the discomfort
associated with the insertion of an intravenous needle no more than one hour after
application and for a period of at least 5 hours.
Pediatric applications
i
Children experience greater stress in a hospital environment than adults.
Preventing the discomfort of inserting intravenous needles would benefit the patients
as well as physicians and staff. Local anesthesia would make intravenous access
easier because the patient would be less likely to flinch during the procedure.


25
induced itching. Saturated solutions of the bases were found effective in most cases
and the order of decreasing efficacy was: tetracaine, mepivacaine, lidocaine,
benzocaine, and procaine. None of the anesthetic salts were effective. Adriani and
Dalili also tested 30 commercially available topical anesthetic preparations and found
that none could relieve the experimentally induced itching and burning except
Americaine (containing 20% benzocaine base). Adriani and Dalili stated that the
anesthetic effect of all topically applied formulations dissipated only 10 to 60 seconds
after being removed from the skin. Again, this result contradicts all other reports on
topical application of anesthetics. The rapid onset and subsidence of anesthetic
effect as measured by Adriani and Dalili could be a result of the electrical
conductivity of the anesthetics themselves or some other surface effect. The inability
of other investigators to even approach these results indicates that the anesthetics,
in fact, never reach the nerve endings.
Campbell and Adriani15 studied the systemic levels of local anesthetics
administered by three routes (infusion, infiltration, and topical application) in both
human volunteers and dogs. The drugs tested were tetracaine, cocaine, procaine, and
benzocaine. Intravenous injection was used as the control. Absorption of the
anesthetics from the mucous membranes of the pharynx and trachea was comparable
to the absorption when administered intravenously. Transdermal diffusion was
j
detectable only when the skin was abraded or suffered third degree burns prior to
application. The authors concern was avoiding toxic systemic levels of the drugs and
there was no assessment of analgesia.


38
Solubility
Solubility was determined by rotating a solution in contact with excess drug
at 4 rpm for at least 18 hours at room temperature. A sample was then withdrawn,
filtered, and analyzed by HPLC to get the total drug concentration in solution.
Titration
The acid-base behavior of tetracaine-containing formulations was explored by
simple titration. The apparent pH of the tetracaine formulation was monitored while
measured quantities of either NaOH or HC1 were added. Such measurements
yielded the pKa of tetracaine in various solvent mixtures as well as the pH vs.
tetracaine acid salt-free base ratio.
Thermal Breakdown of Tetracaine
To determine the shelf-life of tetracaine formulations, the concentration of
tetracaine in solution was measured as a function of time at room temperature and
¡
skin temperature (24C and 32C, respectively).
Drug Partitioning
To simulate the environment encountered by the drug when placed in contact
with the skin, the anesthetic preparation was placed in contact with a hydrophobic
organic phase. No account was made for hydrophobic phase solubility in the vehicle


115
oo
<
>
Figure 59: Effect of alcohol cleansing on the diffusion of tetracaine (60% free
base, 40% acid salt w/w) in 40% propylene glycol and 60% saline (v/v) through
human skin in vivo
Dose response
The minimum concentration of drug required to produce effective analgesia
in one hour was measured by applying patches wetted with the anesthetic formulation
and testing the subjects responses to the pain stimuli after one hour. Three different
systems were evaluated for minimum drug concentration: 1) tetracaine free base in
75% propylene glycol-25% saline (v/v), 2) 50% tetracaine free base-50% tetracaine
acid salt (w/w) in 40% propylene glycol-60% saline (v/v), and 3) 60% tetracaine free
base-40% tetracaine acid salt (w/w) in 40% propylene glycol-60% saline (v/v).
The dose response data for tetracaine free base in 75% propylene glycol and
25% saline (v/v) are in Figure 60. The effectiveness of the anesthetic preparation


192
GOTO 1
5 This subroutine will fit the boundary concentrations for various times in the
Franz diffusion cell to experimental data.
GOSUB 100 INFORMATION SUBROUTINE
DIM DATAPNTS(DATPOINT% 1, 4), C(M%, 1), LOW(l), MID(l), HIGH(l),
TEMP(l), COMPVAL(DATPOINT% 1)
CLS
LOCATE 1, 52
PRINT "Raw Data from file INFILES;
PRINT #1, "Raw Data from file INFILES;
IF CONSTSKN = 1 THEN PRINT #1, ", NO SWELLING";
IF CONSTTOP = 1 THEN PRINT #1, ", CMC ="; Cl; ELSE PRINT #1, ",
INITIAL CONCENTRATION = "; Cl;
PRINT #1,
LOCATE 3, 55
PRINT "Time C2"
LOCATE 5, 1
FOR k% = 0 TO DATPOINT% 1
INPUT #2, DATAPNTS(k%, 0), DATAPNTS(k%, 1)
PRINT USING ##.##
#####.###"; DATAPNTS(k%, 0); DATAPNTS(k%, 1)
NEXT


195
FOR k% = 0 TO DATPOINT% 1
PRINT #1, USING "##.## #####.### #####.###";
DATAPNTS(k%, 0); DATAPNTS(k%, 1); COMPVAL(k%)
NEXT
LOCATE 16, 1
PRINT USING "Diffusivity (cnU2/s) = ##.###/ #"""; D; ABS(D-
LSTD)
PRINT USING" Variance (CTT2) = ##.###/ "";
VARIANCE; ABS (VARIANCE LSTVAR)
PRINT #1, USING "Diffusivity (cnU2/s) = ##.###/ D;
ABS(D LSTD)
PRINT #1, USING Variance (CTT2) = ##.###~^ #~wv";
VARIANCE; ABS(VARIANCE LSTVAR)
PRINT #1,
PRINT #1,
PRINT #1,
ERASE DATAPNTS, C, LOW, MID, HIGH, TEMP, COMPVAL
RETURN MAIN SUBROUTINE END
100
BEGIN INFORMATION SUBROUTINE
OPEN "I", #2, INFILES + ".DAT


163
dC1
~df
dC2
~dT
AD (dC(x,t)^ |
V I jt"0
V1 dx
AD(dC{x,t)v ,
V ~ ) Ix=L
V2 dx
Discretizing as before and recognizing that Q(t) = C0 and C2(t) =
equations for the reservoir concentrations at time = j + 1 as
concentrations at time = j.
^0,7+1 AD
At
V1 Ax
C j+1 C0, j AD Cx j C0i j
(-
At Vx Ax
C(),7+1 C0, J + S1(C1 j C0 J)
a^mj+i _ AD
At ~V^K~^x~)
)
Cm, 7+i CM, j AD ^ CM j CM_X' j ^
At ~V7K Ax }
Cm, 7+1 CA, j s2^m, j CM_1;)
AD At
VXAX
AD At
V2ax
(A9)
(A10)
Cm, j give explicit
functions of the
(All)
(A12)
(A13)
(A14)
The model is solved by applying the initial conditions,


27
glycerine. The salts were dissolved either in the same solvent as the base or in water.
The bases of tripelennamine, lidocaine, tetracaine, phenacaine, and benoxinate
produced anesthesia after 45 to 60 min contact under occlusion at concentrations of
2%. The salts required at least two hours to produce anesthesia.
The use of ethanol and water as solvents for tetracaine was investigated in our
laboratory. These solvents were not compatible with tetracaine because the drug
broke down into a variety of aromatic aldehydes. Neither water nor ethanol alone
caused tetracaine to decompose. Therefore, even though the results of Monash were
equal to the current state-of-the-art in transdermal local anesthesia; we found his
system to be unstable.
McElnay et al.58 investigated the use of ultrasound to promote the in vivo
transdermal diffusion of lidocaine from a cream base. No statistical difference was
detected using volunteers, although the trend of the data suggested that ultrasound
decreased the onset time of anesthesia.
McCafferty et al.55 compared in vitro and in vivo percutaneous absorption of
several anesthetic bases in an oil-in-water emulsion cream (77.5% water). The
anesthetic concentration was 0.35 mmol/g. Drug diffusion was evaluated ¡either in
vitro through a silicone rubber membrane or in vivo by the pinprick method. Of the
drugs tested, tetracaine (amethocaine) was the most effective both in vitro and in
vivo.
i
|
Woolfson et al.95 characterized the concentration response of three tetracaine
free base formulations: water, and two aqueous systems gelled with either 1.5%


147
by pH versus concentration measurements (page 80) were slightly more conservative
although they were in general agreement with those of surface tension and
conductivity. The differences in the CMC values are attributed to the broad range
over which micellization begins and the way micellization affects the measured
properties.
Micelle Size
The size of tetracaine micelles in solvents of propylene glycol and saline (60%
tetracaine free base, 40% acid salt w/w) was measured by quasi-elastic light
scattering or QELS (page 82). Tetracaine micelles are very large in the absence of
propylene glycol (1300 1450) and may not be typical spherical micelles. At 50%
propylene glycol and 50% saline, the micelles are comparatively small (* 25) and
micelles are not present at 80% or 100% propylene glycol.
Thermal Breakdown
Tetracaine free base deteriorates with time and the breakdown is thermally
activated. Consequently, the rate of deterioration increases with temperature. At
room temperature, (24C) formulations containing tetracaine base can be stored for
2 to 3 days before the loss of viable drug exceeds 10% (page 84). At skin tempera
ture, (32C) the time period is much shorter (1 day).


158
Theoretical Modelling
The theoretical model developed in this work can represent the experimental
receptor-phase concentration of tetracaine as a function of time well. It is not based
on data specific to this system and should be able to model data from other systems
equally well. Its parameters are those of full-thickness, hairless-mouse skin. This is
irrelevant for determining the boundary concentrations, but it is relevant for
determining the concentration profile. The concentration profile represents diffusion
through a homogeneous barrier as thick as full-thickness skin. The model can be
altered to represent only the diffusion through the stratum corneum (still represented
as a homogeneous barrier) and the resulting concentration profile would have
physical meaning.
The area of diffusion could also be altered in the model to represent the
actual area available for diffusion. Conventional wisdom states that the diffusion of
hydrophobic substances occurs through intercellular lipid pathways. If this is true,
the actual area available for diffusion through the skin is a microscopic fraction of
the application area and the diffusion path is longer than the skins thickness.
Evaluation and substitution of the correct area along with the correct path length,
could give more physical meaning to the effective diffusion coefficients generated by
the quasi-steady state model. The modular construction of the quasi-steady state
model allows this type of information to be inserted as it becomes available.


6
their dimensionless groups and limiting cases were used to get expressions for the
amount of drug removed from the skin.
In 1983, Guy et al.39 examined the release of drug from liposomes in a topical
formulation. This theoretical treatment was based on Fickian diffusion in a spherical
geometry. To get an analytical solution, infinite sink conditions were adopted at the
boundary. Short and long times were used as limiting cases. The result was
expanded to account for multilamellar vesicles by assuming that a first-order rate
constant accounts for diffusion through the interface.
In 1985, Guy and Hadgraft34 derived equations for diffusion through skin
modelled as a bilaminate structure with layers of different dimensions, diffiisivities,
and partition coefficients. The path through the stratum corneum was assumed to
be intercellular and tortuous. They also presented an expression for the concentra
tion profile within the stratum corneum,33 but they gave no details of the derivation
or the boundary conditions the equation represented. Results were plotted to
illustrate the ability of the model to simulate experimentally observed phenomena.
Most recently, Hadgraft42 built upon previous work25 by adding the resistances of a
drug reservoir and an adhesive layer to diffusion. These additional resistances are
supposed to represent those of a commercial transdermal therapeutic system (ITS).
The equation presented by Guy and Hadgraft represents the concentration
within a finite slab as a function of time and position with constant boundary
conditions and no drug present initially. The model presented in this work (Chapter
6: Theory page 131) also made use of this solution to Ficks second law. For our
model, however, additional modifications were used to account for the changing
concentrations at the boundaries and the swelling of the skin.


47
I'
Figure 5: Securing hairless mouse
0.9% w/w saline. The cell cap contained the upper (donor) phase (source of diffusing
drug) and held the skin in place. A rubber O-ring sat between the cell body and the
inside surface of the skin. A clamp held the entire assembly together.
The skin sample was placed over the inverted cell cap and the O-ring placed
over the skin (Figure 8). The cell body, with the magnetic stirring assembly inside,
was then fitted on top of the O-ring and the entire inverted assembly secured by the
spring clamp. Once the clamp had been tightened, the cell could be handled as a
single unit.


124
Model Derivation
The differential equation for one-dimensional diffusion through a stagnant
(solid) medium such as skin is shown in Equation 5.7
=pd2C 5
3t dx2
The initial condition is C(0) = 0. If the boundary conditions are independent of time,
then this equation can be analytically integrated to obtain Equation 6.16
cm-c,-KC2-c1)£+
* 1
C2(:1)''~Clsin(^)e-c"v^i
6
If the boundary concentrations change slowly relative to the concentration
within the skin (quasi-steady state), then the above analytical solution, Equation 6,
can still be used, but the boundary conditions then become weak functions of time.20
These boundary conditions for the concentrations are mass balances. Evaluating
these mass balances requires integration of the concentration equation to find the
cumulative fluxes through the skin. For the donor and receptor phases the mass
balances are Equations 7 and 8, respectively.


211
93. R.C. Wester, H.I. Maibach, J. Surinchak, and D.A.W. Bucks, Predictability
of In Vitro Diffusion Systems: Effect of skin types and ages on
percutaneous absorption of triclocarbon, in Percutaneous Absorption:
Mechanisms. Methodology. Drug Delivery. R. Bronaugh and H. Maibach
(eds), Marcel Dekker, New York, 223-6 (1985).
94. A.D. Woolfson, D.F. McCafferty, and V. Boston, Clinical Experiences with
a Novel Percutaneous Amethocaine Preparation: Prevention of pain due to
venepuncture in children, Br. J. Clin. Pharmacol., 30(2), 273-9 (1990).
95. A.D. Woolfson, D.F. McCafferty, K.H. McClelland, and V. Boston,
Concentration-response analysis of percutaneous local anaesthetic
formulations, Br. J. Anaesth., 61, 589-92, (1988).
96. A.D. Woolfson, D.F. McCafferty, and K.E. McGowan, Percutaneous Local
Anaesthesia: Comparison of in vitro predictions with clinical response, in
Prediction of Percutaneous Penetration Proceedings. April 1989, R.C. Scott,
R.H. Guy, and J. Hadgraft (eds), IBC Technical Services, London, 192-8
(1990).
97. J.L. Zatz, Percutaneous Absorption: Computer simulation using multi-
compartmental membrane models, in Percutaneous Absorption:
Mechanisms. Methodology. Drug Delivery. R. Bronaugh and H. Maibach
(eds), Marcel Dekker, New York, 165-82 (1985).


Figure 12:
Skin patch on arm of volunteer


93
sample was then immersed in water and its mass monitored periodically. The skin
was found to absorb water rapidly for the first 5 to 6 hours and much more slowly
afterwards. Figure 46 shows the thickness versus time for skin immersed in water for
approximately two days. The data show that full thickness hairless-mouse skin can
absorb about four times its mass in water and swells to a comparable degree. The
increasing scatter of the data with time results from a loss of the skins integrity.
Scopolamine Diffusion
The first full-scale diffusion experiment performed for this project was the
diffusion of aqueous scopolamine base through mounted mouse skin. The purpose
of this experiment was to identify problems in the experimental procedure and
compare the experimental results to those published previously.
Another aim of this experiment was to determine the dynamic role of skin
hydration on diffusion (using scopolamine) since this study focuses on short term
behavior. In previous experiments in transdermal diffusion, interest centered on
systemic drugs. The goal of these experiments was to determine the long term
(steady state) flux of drug through the skin. To accomplish this goal, the skin had
to be chemically preserved to avoid decomposition. For the delivery of local
anesthetics, the experiments were to be of much shorter duration. The swelling of
the skin early in the experiments could be significant as could the presence of a
chemical preservative.


CHAPTER 2
MATERIALS AND METHODS
Materials
This section describes the properties of the materials used in this project.
Two general classes of materials are used, drugs and solvents. First the solvents are
described, then the properties of the drugs are described. The properties referred
to are solubility, surface tension, specific conductivity, ultraviolet light absorption, and
liquid phase chromatography behavior.
Solvents
The solvents used in the diffusion through skin experiments (excluding those
used for separation in the HPLC) were: (1) distilled water or 0.9% saline (NaCl)
solution (made from distilled water and biological grade NaCl), and, (2) USP grade
propylene glycol( 1,2-propanediol) purchased from Fisher Scientific. Numerous
solutions of these two liquids were used as vehicles for the delivery of drugs through
the skin. These solvents are completely miscible and their ratio was varied primarily
to control the solubility of the drugs (drug solubility is discussed in the following
section).
33


16
Many animal models have been investigated. The general trend of
permeability can be summarized: rabbit > rat > monkey swine man.4,37
Pigskin has been suggested as an in vitro model for human skin4 and the rhesus
monkey has been suggested as an in vivo model for human skin.34
Hydration. Excessive absorption of water increases the skins thickness and
changes its relative chemical composition. These effects result in changes in the
skins ability to act as a barrier to diffusion. Barry4 reviews much of the literature
concerning skin hydration and concludes that hydration increases the permeability
of the skin to all substances except small, polar molecules.
Blank8 treats hydration and skin permeability as the subject for an entire
chapter. He and co-workers measured the diffusion of water through stratum
corneum as a function of time and degree of hydration. They use this information
to calculate the thickness of the skin and the flux of water through the skin as a
function of the surface concentration of water (or relative humidity).
Vehicle effects
The subject of vehicles has received more attention than receptor phases in
transdermal diffusion. The receptor phase can only be altered in in vitro experiments
while the donor phase can be altered either in vitro or in vivo. The donor phase can
be altered to affect either the drug itself or the skin.* There are many reasons for
varying the donor phase composition to affect the drug (particularly its
Vehicles that affect the permeability of the skin are known as penetration
enhancers. These effects are reviewed in another section (page 20).


177
BOTSER = BOTSER + ((-1) A N% TOP(O) BOT(O)) EXPONENT
IF N% = 1 THEN 410
IF (ABS((TOPSER LASTTOP) / LASTTOP) > CONV OR ABS((BOTSER -
LASTBOT) / LASTBOT) > CONV OR N% < MINI%) AND N% <
MAXI% THEN 410
RETURN
END EVALUATE SERIES SUBROUTINE
500
BEGIN PARABOLIC MINIMIZATION SUBROUTINE
BNUM = LOW(O) A 2 MID(l) + MID(O) A 2 HIGH(l) + HIGH(O) A 2 *
LOW(l) LOW(O) A 2 HIGH(l) MID(O) A 2 LOW(l) HIGH(O) A 2
* MID(l)
BDEN = LOW(O) A 2 MID(O) + MID(O) A 2 HIGH(O) + LOW(O) *
HIGH(O) A 2 LOW(O) MID(O) A 2 LOW(O) A 2 HIGH(O) MID(O)
* HIGH(O) A 2
Y = BNUM / BDEN
Z = (MID(l) LOW(l) + Y (LOW(O) MID(O))) / (MID(O) A 2 LOW(O) A
2)
X = LOW(l) Y LOW(O) Z LOW(O) A 2


96
experiments and more closely simulate the behavior of live skin in vivo. The results
of this experiment suggest that hydration and preservation of the skin significantly
alter diffusion. The deconvolution of hydration and preservation effects is explored
later in this chapter (page 105).
Transdermal Diffusion of Local Anesthetics
Measuring the diffusion of lidocaine and tetracaine through mounted mouse
skin identifies preparations likely to be effective for human use. Parallel experi
ments, using identical local anesthetic preparations for both in vitro (mouse skin) and
in vivo (human volunteers) systems, show a high degree of correlation (cf. Chapter
6). The main advantage of the in vitro method is the ability to achieve more
accurate quantitative results. Other issues studied are the effect of formaldehyde as
a preservative for in vitro transdermal diffusion, skin swelling in vitro, time limits for
experiments, and the effects of propylene glycol, pH, concentration, and mouse age.
Theoretical Considerations
Assuming Fickian diffusion, the parameters which influence diffusion are well
defined. The driving force for diffusion is the concentration at the inner surface of
the skin. This concentration is determined by the concentration in solution, the
characteristics of the boundary layer, and the partition coefficient between the
solution and the skin. If the boundary layer thickness is assumed to be negligible,
then the concentration at the outer surface of the skin equals the bulk concentration.


104
The measured fluxes through synthetic membranes and hairless-mouse skin
(Figure 52 and Figure 53) both show a maximum at 40% propylene glycol. The
combined solubility-partitioning parameters for both 1-octanol (Figure 17 and
Table 3) and n-octane (Figure 18 and Table 4) predict a maximum at 50% propylene
glycol. Therefore, this combined solubility-partitioning parameter does roughly
estimate the composition of the optimum vehicle.
The results of these diffusion experiments establish the composition of the
vehicle for the transdermal delivery of tetracaine as 40% propylene glycol and 60%
saline. The existence of this optimum vehicle can be partly explained by the
relatively high solubility of tetracaine and favorable partitioning of the drug into
lipids. Thus, a major goal of this project is realized; the optimization of a topical,
local anesthetic formulation.
The combined solubility-partitioning parameter for 1-octanol (Figure 17 and
Table 3) also predicts the decreasing flux between saline and 20% propylene glycol
for both synthetic membranes and hairless-mouse skin, but fails to predict the rapid
decrease of flux at higher propylene glycol contents (> 60%). Alternately, the
combined solubility-partitioning parameter for n-octane (Figure 18 and Table 4) fails
to predict the high flux at 40% propylene glycol. Consequently, the combined
solubility-partitioning parameter has limitations as a correlation for transdermal flux
and should not be relied on as a definitive method for predicting relative transdermal
flux. A more appropriate and conservative role for this data is as a first estimate of
the optimum vehicle which should be subsequently established by diffusion studies.


198
PRINT "CANNOT LOCATE MINIMUM; RESTART
PROGRAM WITH NEW PARAMETERS"
PRINT #1, "CANNOT LOCATE MINIMUM; RESTART
PROGRAM WITH NEW PARAMETERS"
PRINT "
RETURN
END IF
PRINT "STATUS: MAXIMUM DETECTED IN PARABOLIC MODEL"
PRINT ADJUSTING PARAMETERS TO LOCK ONTO
MINIMUM"
GOTO 60
ELSE PRINT "STATUS: SEEKING A MINIMUM
PRINT"
REP% = 0
END IF
DEST = -Y / 2 / Z
IF DEST < 0 THEN DEST = MID(O) / 2
IF DEST > DMAX THEN DEST = .75 DMAX: increase =
increase + 1
50 ESTVAR = Z DEST A 2 + Y DEST + X
PRINT USING" ITERATION NUMBER: ## ERROR:
#####% "; ITER%; 100 ABS(ESTVAR VARIANCE) / VARIANCE


VARFIT.BAS 170
ENDVALUS.BAS 179
PROFILE.BAS 183
FNR.BAS 191
REFERENCES 202
BIOGRAPHICAL SKETCH 212
ix


17
thermodynamic activity) in solution. The effects of drug solubility, drug partitioning
(the ratio of equilibrium concentrations in the skin and vehicle respectively),
emulsification, and pH control are summarized below.
Solubility and partitioning.* Roberts et al.70 correlated the permeability of
phenolic compounds, aromatic alcohols, and aliphatic alcohols with their partitioning
behavior in octanol. The log-log plot is linear up to a partition coefficient of about
100, but decreases in slope at higher partition coefficients.
Bronaugh and Franz13 determined that partitioning into the stratum corneum
was the determining factor for skin permeability in the absence of overriding
solubility constraints in the system. Other researchers have also demonstrated
this.11,23,26 Gummer32 concluded that, for a given concentration, the rate of diffusion
is inversely proportional to the saturation concentration (saturation implies maximum
thermodynamic activity in the vehicle) and proportional to the partition coefficient
of the drug (large partition coefficient implies low activity in skin).
Ward86 discusses the use of surfactants as a means of increasing the solubility
of the penetrant. A comprehensive algorithm is presented to optimize the vehicle
based on structure, interfacial properties, and phase behavior. In general, it was
found that increasing partitioning into the skin and approaching the solubility limit
aid transdermal diffusion.
Emulsions, liquid crystals, and liposomes. Emulsification of the drug in the
vehicle can be of benefit for a poorly soluble drug. Osborne et al.64 state that the
Solubility and partitioning are, of course, properties of both solvent and solute.


59
acid).21 The increased solubility in 40% free base, 60% acid salt (w/w) mixtures
cannot arise only from the protonation of the tetracaine molecule since an even
larger fraction of molecules is protonated in tetracaine acid salt. Some interaction
between the acid salt and free base forms, each stabilizing the other, appears to
occur. Since the acid salt and the free base are in equilibrium, it is not strictly
correct to consider them two different species. They are more likely assuming some
intermediate structure when they associate (partial charge). These intermediates
must be more soluble in propylene glycol/saline solutions than either the acid salt
or the free base.
Partition Coefficient of Tetracaine from Propylene Glvcol-Water Solvents
Drug partitioning between the stratum corneum and the vehicle influences
transdermal diffusion.26,52,76,78,92 Partitioning of substances into the skin can be
roughly simulated by lipid-phase partitioning between a vehicle and a hydrophobic
solvent. The ratio of drug concentrations in the vehicle and the non-polar solvent
at equilibrium is taken as the partition coefficient for the formulation (i.e.,
Qoivent/Qehicie)- In this study, no attempt was made to account for the solubility of
the vehicle in the non-polar solvent or that of the non-polar solvent in the vehicle.
Two solvents were used: 1-octanol and n-octane. Octanol was preferred for
estimating stratum corneum partitioning, but the octanol/propylene glycol/water
system is single-phase above 60% propylene glycol. Therefore, partition coefficients


15
Animal models. In 1980, Durrheim et al.23 concluded that hairless-mouse skin
was a reasonable model for human skin through comparison of their data on the
diffusion of n-alkanols through hairless-mouse skin in vitro and previously published
data using human skin in vitro. The measured permeability of hairless-mouse skin
differed significantly from human skin for many substances,22,67 but the trends were
similar.
Hairless-mouse skin has been criticized as a model for human skin based upon
its reaction to long-term hydration,9 acetone attack,10 and penetration enhancers.11
Under such conditions, hairless-mouse skin cannot confidently mimic the trends of
human skin.
Barry5 has suggested the use of shed snake skin (Indian python or American
black rat snake) as a model for the permeability of human skin. Shed snake skin is
plentiful, can be collected without harm to the snake, and can be stored at room
temperature. Snake skin was found to be less susceptible to hydration and acetone
damage than mouse skin and performed more like human skin under these
circumstances. The effects of penetration enhancers were less dramatic for snake
skin than for mouse skin, but did not model human skin any better. The damage
caused by a number of pesticides was also investigated. The results indicated that
I
snake skin and human skin do not react similarly to the attack of the pesticides.
Overall the author suggested that snake skin is no better as a model for human skin
than other biological membranes like collagen, egg shell membranes, etc.


CHAPTER 7
CONCLUSIONS
The major conclusions and achievements of "Interfacial, Diffusional,
Theoretical, and Clinical Aspects of Topical, Local Anesthetic Formulations" are
assembled as an overview. This overview follows, as closely as possible, the logical
sequence of the dissertation. In some instances, related material from different
locations in the text is grouped to form conclusions. In either case, the material is
cross-referenced to the body of the dissertation.
Physical Properties of Drug Formulations
Solubility
A mixture of 60% tetracaine free base and 40% tetracaine acid salt (w/w) is
generally more soluble in solvents of propylene glycol and water (saline) than either
tetracaine free base or tetracaine acid salt alone (Figure 14, page 58). This solution
may have unique properties because its pH is near the pIC, of tetracaine (8.5 8.7).
Partitioning and Solubility
The product of solubility and lipid-phase partitioning is an indication of a
formulations ability to promote transdermal diffusion (page 62). Two organic liquids
145


101
layer above the skin.* Propylene glycol may have some effect on the skin which
increases the skins resistance to diffusion or propylene glycol may decrease the
partitioning of tetracaine into the skin as it makes the formulation more lipophilic.
Another possibility is that propylene glycol somehow affects the equilibrium between
tetracaine HC1 and tetracaine base and reduces the amount of free base available
for diffusion.
Tetracaine mixtures
Effect of propylene glycol. The effect of propylene glycol on the diffusion of
tetracaine mixtures is complex. The diffusion of tetracaine mixtures (40% acid salt,
60% free base w/w 0.36 M overall) in solvents of propylene glycol and 0.9% saline
was investigated in two systems. The flux of tetracaine through polycarbonate
synthetic membranes was studied to determine the effect of propylene glycol on a
simple, well characterized membrane. Then identical formulations were allowed to
diffuse through skin from mice approximately 6 to 8 weeks old.
The cumulative flux of these tetracaine formulations through synthetic
polycarbonate membranes (nominal pore diameter of 0.45 /m) after five minutes is
shown in Figure 52. The polycarbonate membrane is hydrophilic and, not
surprisingly, the highest flux through the membrane results from the fully aqueous
formulation since the membrane is easily wetted by the aqueous formulation. It is
also not surprising that the flux of tetracaine decreases at higher propylene glycol
*The viscosity of propylene glycol is about 24.7 cp. The viscosity of water is
about 0.9 cp at room temperature.


There have been many models proposed which attempt to predict the
diffusion of substances through the skin. The major assumption made in most of
these models is a steady state or linear concentration profile within the skin. A new
model was developed which avoids the limiting assumptions of previous work and
allows the prediction of concentration within the skin as well as flux through the skin
at any time. This model has been successfully used for the prediction of tetracaine
diffusion from topical preparations through mounted hairless-mouse skin. In
addition, this model can account for the swelling of the excised skin as a function of
time immersed in saline. This model could also be easily adapted, through minor
modifications, to predict diffusion through skin in vivo.
xvm


107
buffered saline with 0.1% formaldehyde (w/w). Formaldehyde seems to inhibit
tetracaine diffusion through mouse skin by an average of 8% over an 8 hour period.
This result may be due to either a chemical change in the skin structure brought on
by formaldehyde or a decrease in drug flux caused by the counter diffusion of
formaldehyde through the skin.
To find whether formaldehydes inhibition of tetracaine diffusion is a result
of counter diffusion, an identical system was prepared with formaldehyde in equal
concentration on both sides of the skin. This configuration eliminates the
formaldehyde concentration-differences. If the effect of formaldehyde is solely
through counter-diffusion, this system should behave like the system with no
formaldehyde. If formaldehyde reduces the permeability of the skin, then it should
reduce permeability below even that found with formaldehyde in the downstream
reservoir.
The results show that the total amount of formaldehyde in the system is the
key (Figure 56). The low formaldehyde concentration (0.1% w/w) probably does not
affect the drug solubility or partitioning. Although Figure 56 does not show a great
difference between the three systems, higher formaldehyde content tends to cause
lower fluxes. Formaldehyde, therefore, increases the resistance to diffusion through
some interaction with the skin.


82
Table 9: Critical micelle concentration of tetracaine (60% free base, 40% acid
salt w/w) in propylene glycol and saline as measured by pH
% Propylene
Glycol
CMC (M)
pH Range
(Apparent)
0
0.003
6.85-8.37
20
0.004
6.30-8.51
40
0.025
6.26-8.29
60
0.072
7.03-8.41
80
(no CMC)
6.46-7.55
100
(no CMC)
5.80-8.65
C (M)
C (M)
Figure 36: pH of tetracaine in 60% Figure 37: pH of tetracaine in 40%
propylene glycol and 40% saline (v/v) propylene glycol and 60% saline (v/v)
these values agree almost as well with those of Table 5 and Table 6 as the latter do
with each other (this method is the most conservative).
Quasi-elastic Light Scattering
Many features of micellar behavior can be deduced through surface pressure,
conductivity, and even pH vs. concentration measurements. One feature, however;


44
to programmed compounds. If a peak is identified as a programmed compound,
previously entered calibration data are used to determine the amount of the
compound detected.
Quasi-elastic Light Scattering
Dynamic or quasi-elastic light scattering (QELS) was used to determine the
size of tetracaine micelles in saline, propylene glycol, and mixtures of these solvents.
QELS uses the time-varying scattering intensity and broadening of incident laser light
caused by the Brownian (thermal) motion of micelles. This information is used to
generate the Fourier transform of the power spectrum (an exponential function).
The time constant of this exponential function is directly related to the diffusion
coefficient of the micelles in solution. The apparent micelle diameter can then be
calculated by the Stokes-Einstein equation (assuming the particles are spherical).47
d = 3
3 7T 7] Dj
d = micelle diameter
k = Boltzmann constant
T = absolute temperature
Tj = solvent viscosity
Dt = translational diffusion coefficient


This dissertation was submitted to the Graduate Faculty
of the College of Engineering and to the Graduate School and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
December, 1991
lhjL? (X- &
Jo*Winfred M. Phillips
' Dean, College of Engineering
Madelyn M. Lockhart
Dean, Graduate School


68
Figure 20: Surface tension of aqueous tetracaine free base
Conductivity
The conductivity of tetracaine salt and base versus concentration has also been
measured. The results of these measurements are in Figure 22 and Figure 23. The
conductivity of these aqueous solutions rises with drug concentration for both forms
(acid salt and free base). By analysis similar to that for surface tension versus
concentration, the critical micelle concentration can be obtained by locating a change
in slope between two linear portions.83 Through this method, the CMC of aqueous
tetracaine salt is found to be 0.03 M which is in general agreement with that from
surface tension measurements (Figure 19).


119
piacebo
1.8 M
(50% w/v)
-o- 1.1 M
(30% w/v)
Concentration
0
1
2
Time (hr)
Figure 63: Time response for in vivo analgesia by tetracaine (60% free base, 40%
acid salt w/w in 40% propylene glycol and 60% saline (v/v) (1.1 M, 1.8 M)
distinguishable from the placebo after 45 minutes. For lower concentrations,
however; no statistically significant distinction was achieved because, although the
subject responses are very high, the scatter makes data difficult to interpret.
Comparison to in vitro results
Of all the systems tested on human subjects in vivo, the formulation consisting
of 60% tetracaine free base, 40% acid salt (w/w) in 40% propylene glycol and 60%
saline (v/v) is the most effective. This is precisely the system found to be most
effective in in vitro experiments with hairless-mouse skin (Chapter 4, Figure 53 and
Figure 54, pages 102 and 105). Formulations containing 40% propylene glycol gave
the highest transdermal fluxes in vitro. The combined solubility-partitioning


189
SKINSER = 0: LASTSKIN = 0: N% = 0
550 N% = N% + 1
LASTSKIN = SKINSER
EXPONENT = EXP(-N% A 2 (TIME G) D PI# A 2 / L(l) A 2)
FSTTERM = DELTABOT (-1) A N% DELTATOP
SNDTERM = CONCENTR(SKINNUM%, 1) (-1) A N% CONCENTR(0, 1)
TRDTERM = 2 D N% A 2 PI# A 2 TIME / L(l) A 2 (DELTAL / L(l)
- G / TIME)
FTHTERM = SIN(N% PI# ((SKINCOUN%) / (SKINNUM%))) *
EXPONENT / N%
ADDSER = FTHTERM (FSTERM + SNDTERM TRDTERM)
SKINSER = SKINSER + ADDSER
IF N% = 1 THEN 550
IF (ABS((SKINSER LASTSKIN) / LASTSKIN) > CONV OR N% < MINI%)
AND N% < MAXI% THEN 550
DELTACON = DELTATOP + (DELTABOT DELTATOP) (SKINCOUN%)
/ (SKINNUM%) + 2 / PI# SKINSER
CONCENTR(SKINCOUN%, 1) = CONCENTR(SKINCOUN%, 0) +
DELTACON
IF CONCENTR(SKINCOUN%, 1) < 0 THEN CONCENTR(SKINCOUN%, 1)
= 0
CONCENTR(SKINCOUN%, 0) = CONCENTR(SKINCOUN%, 1)


176
END INTEGRATION AND VARIANCE SUBROUTINE
300
BEGIN NEW SKIN THICKNESS SUBROUTINE
LI = .069029 + .049499 (TIME / 3600 + TIMEO) .0044692 (TIME / 3600
+ TIMEO) A 2
L2 = .18821 (TIME / 3600 + TIMEO) A .050642
IF (TIME / 3600 + TIMEO) < 4.8270328# THEN L = LI ELSE L = L2
RETURN
END NEW SKIN THICKNESS SUBROUTINE
400
BEGIN Evaluate Series SUBROUTINE
IF TIME = G THEN BOTSER = -Cl / 2: TOPSER = -Cl: RETURN
TOPSER = 0: BOTSER = 0: LASTTOP = 0: LASTBOT = 0: N% = 0
410 N% = N% + 1
LASTTOP = TOPSER: LASTBOT = BOTSER
EXPONENT = EXP(-N% A 2 (TIME G) D PI# A 2 / L A 2)
TOPSER = TOPSER + ((-1) A N% BOT(O) TOP(O)) EXPONENT


High Pressure Liquid Chromatography (HPLC) 41
Quasi-elastic Light Scattering 44
In Vitro Diffusion Through Mounted Mouse Skin 45
In Vivo Diffusion 51
3 PHYSICAL PROPERTIES OF DRUG FORMULATIONS 57
Tetracaine Solubility in Propylene Glycol-water Solvents 57
Partition Coefficient of Tetracaine from Propylene Glycol-Water
Solvents 59
Partitioning into 1-octanol 60
Partitioning into N-octane 61
Surface Tension of Tetracaine Formulations 63
Conductivity 68
Ultraviolet Spectroscopy 71
Chromatography 74
Equilibrium Phenomena 76
Quasi-elastic Light Scattering 82
Thermal Breakdown of Tetracaine 84
4 DRUG DIFFUSION IN VITRO 86
Calibration 86
Stirring Effects Using Synthetic Membranes 86
Temperature Behavior of Diffusion Apparatus 89
Skin Swelling 92
Scopolamine Diffusion 93
Transdermal Diffusion of Local Anesthetics 96
Theoretical Considerations 96
Lidocaine Salt 97
Diffusion of Tetracaine 99
5 DRUG DIFFUSION IN VIVO Ill
Rat Tail-flick Test Ill
Clinical Trials 113
Lidocaine 113
Tetracaine 113
6 THEORY 121
Idealized System 122
Model Derivation 124
Inclusion of Skin Swelling In Vitro 130
vii


142
no indication of micelle formation in aqueous hydrocortisone (the constant donor-
phase concentration curves were designated a and c in Figure 68-Figure 81). Again,
evaluation of the models is aided by examining the variance between the theoretical
data and the experimental data (Figure 99-Figure 101).
Hydrocortisone in Stagnant Call
7
7
§
HHl
y 7i_
y/yyyyy/y/
L
yyyy//
7/
Figure 98: Model fits for hydrocorti- Figure 99: Model variance for hydro-
sone in a well-stirred cell cortisone in a stagnant cell
Hydrocortisone in Poorly Stirred Call
hydrocortisone in Wti-Slirrd Cell
Figure 100: Model variance for hydro- Figure 101: Model variance for hydro
cortisone in a poorly-stirred cell cortisone in a well-stirred cell
In all three cases, the experimental data are best modelled by the non-swelling
model. The theoretical models under-predict the equilibrium concentration in the
well-stirred cell, but this is probably due to an error in the


143
initial, measured concentration. Therefore, the quasi-steady state model determines
that the skin swells during in vitro, transdermal diffusion and that it has a significant
effect on the diffusion. The theoretical model can also indicate the presence of
micelles by identifying data consistent with a constant donor-phase concentration.
Concentration Profile Within the Skin
Although the concentration profile within the skin can be estimated by this
model, it is not likely to have clear physical meaning. The model is based on the
dimensions of full-thickness skin and the primary resistance to diffusion in skin is
generally regarded to be the stratum corneum which is much thinner than full
thickness skin. There is practical value in the theoretical concentration profile if one
decreases the length scale of the model to coincide with the dimensions of the
stratum corneum. It is likely that the model will produce valuable, though rough,
estimates of drug concentration in the stratum corneum.
Many factors that may influence diffusion have not been considered. These
include the diffusion of propylene glycol and saline through the skin, as well as the
changing propylene glycol-saline concentration within the skin as swelling occurs.
Boundary layers are neglected, but the ability of the model to predict the bulk
reservoir concentrations is well within experimental error. Thus, further development
of the model to include solvent diffusion and boundary layers is viewed as
unproductive.


30
Outpatient applications
Patients could be given anesthetic patches and instructed to apply them a
specified time before their outpatient procedures. Self-application of the anesthetic
patch would require advanced preparation of the device. Since the anesthetic base
may deteriorate at room temperature, the patient would need to store the patch in
his/her refrigerator if the procedure was to take place more than three or four days
later. This should not be a problem since patients are occasionally given sera that
must be refrigerated to remain effective.
Pain management
Continued relief of the discomfort of ivs could also make hospital stays more
pleasant for patients. A non-invasive local anesthetic formulation makes systemic
analgesics unnecessary. The anesthetic patch can be designed to last longer than
twelve hours.
Theoretical Modelling
The objectives of theoretical modelling go beyond developing equations that
mimic experimental data. Developing totally empirical correlations does not increase
the understanding of the processes of transdermal diffusion. The main, theoretical
goal of this work is to apply diffusion theory to transdermal diffusion in vitro and
develop a model that has applicability beyond topical local anesthesia.


32.
205
C.L. Gummer, Vehicles as penetration enhancers, in Percutaneous
Absorption: Mechanisms. Methodology. Drug Delivery. R. Bronaugh and
H. Maibach (eds), Marcel Dekker, New York, 561-70 (1985).
33. R.H. Guy and J. Hadgraft, Mathematical models of percutaneous
absorption, in Percutaneous Absorption: Mechanisms. Methodology. Drug
Delivery. R. Bronaugh and H. Maibach (eds), Marcel Dekker, New York,
3-16 (1985).
34. R.H. Guy and J. Hadgraft, Physicochemical aspects of percutaneous
penetration and its enhancement, Pharm. Res., 5(12), 753-8 (1988).
35. R.H. Guy and J. Hadgraft, Physicochemical interpretation of the
pharmacokinetics of percutaneous absorption, J. Pharmacokinet.
Biopharm., 11(2), 189-203 (1983).
36. R.H. Guy and J. Hadgraft, Skin Metabolism: Theoretical, in Percutaneous
Absorption: Mechanisms. Methodology. Drug Delivery. R. Bronaugh and
H. Maibach (eds), Marcel Dekker, New York, 57-64 (1985).
37. R.H. Guy, J. Hadgraft, R.S. Hinz, K.V. Roskos, and D.A.W. Bucks, In vivo
evaluations of transdermal drug delivery, in Transdermal Controlled
Systemic Medications Drugs and the Pharmaceutical Series vol. 31, Y.W.
Chien (ed), Marcel Dekker, New York, 179-224 (1987).
38. R.H. Guy, J. Hadgraft, and H.I. Maibach, Radial transport in the dermis,
in Percutaneous Absorption: Mechanisms. Methodology. Drug Delivery. R.
Bronaugh and H. Maibach (eds), Marcel Dekker, New York, 335-46
(1985).
39. R.H. Guy, J. Hadgraft, M.J. Taylor, and I.W. Kellaway, Release of non
electrolytes from liposomes, J. Pharm. Pharmacol., 35(1), 12-14 (1983).
40. R.H. Guy, V.H.W. Mak, T. Kai, D. Bommannan, and R.O. Potts,
Percutaneous Penetration Enhancers: Mode of action, in Prediction of
Percutaneous Penetration Proceedings. April 1989, R.C. Scott, R.H. Guy,
and J. Hadgraft (eds), IBC Technical Services, London, 213-23 (1990).
41. J. Hadgraft, The Epidermal Reservoir: A theoretical approach, Int. J.
Pharm, 2, 265-74, (1979).
42.
J. Hadgraft, Mathematical models of skin absorption, in Prediction of
Percutaneous Penetration Proceedings. April 1989, R.C. Scott, R.H. Guy,
and J. Hadgraft (eds), IBC Technical Services, London, 252-62 (1990).


9
make supported membranes more attractive. Unsupported barriers do not accurately
represent the properties of skin because they can only be used when they are
immiscible with the formulation and they are subject to convection currents. For
these reasons, synthetic polymer membranes are often used with or without
hydrophobic liquids.
Supported barriers
Micro-porous membranes have been used to study many systems. Semi
permeable membranes are routinely used to measure diffusion coefficients, osmotic
pressures, and streaming potentials in aqueous systems. Semi-permeable membranes
are also used for separations (ultra-filtration, reverse osmosis, dialysis, etc.). Johnson
studied the diffusion of steroids through microporous membranes in aqueous
systems.49 His experiments determined the diffusion coefficients for steroids diffusing
in porous polycarbonate membranes and provided the basis for the stirring-rate
studies in Chapter 4: Drug Diffusion In Vitro.
Silicone-rubber membranes have been used as diffusion barriers for a variety
of penetrants.4,26,4648,5568 These rubber membranes are very hydrophobic and a
comparison to studies using skin helped to establish that the primary diffusive barrier
of skin is lipophilic.26 Neubert modified an in vitro system using a silicone rubber
membrane by utilizing a non-polar receptor phase to study the diffusion of
hydrophobic drugs.62 j
¡
A synthetic membrane and a hydrophobic liquid phase can be combined to
simulate the behavior of skin as a barrier to diffusion. The synthetic membrane


102
Apparent pH
% Propylene Glycol (v/v)
Figure 52: Effect of propylene glycol on the diffusion of tetracaine (60% free base,
40% acid salt w/w) through synthetic polycarbonate membranes
concentrations since the viscosity and hydrophobicity both increase. The existence
of a local maximum in flux at 40% propylene glycol, however, is surprising. Although
such a maximum is suggested by the partitioning and solubility data in Chapter 3,
that data represents partitioning into a hydrophobic medium and do not necessarily
apply to this hydrophilic membrane. Nonetheless, it appears that there is something
special about this 40% propylene glycol solvent beyond those properties already
measured.
Figure 53 shows the cumulative flux of tetracaine (60% free base, 40% acid
salt w/w, 0.36M overall) through hairless-mouse skin over 8 hours. The maximum


APPENDIX B
COMPUTER PROGRAMS
The computer programs that generate the model results are listed below. The
first program (VARFIT) examines the raw concentration versus time data and
establishes an effective diffusion coefficient by minimizing the variance. The
program can be set to simulate skin swelling during diffusion or hold the concentra
tion in the donor phase constant (simulating a micellar solution). The program uses
a parabolic model to search for the minimum variance as a function of the effective
diffusion coefficient. The program prompts the user for a maximum diffusion
coefficient (Dmax) and initializes the search routine using effective diffusion
coefficients of 0, Dmax/2, and Dmax. The program converges when the minimum
variance is bracketed by the diffusion-coefficient interval specified by the user.
The second program (ENDVALUS) generates the donor and receptor
concentrations as functions of time. The parameters are the same as for VARFIT
except for the effective diffusion coefficient which is entered by the user. The
program simultaneously prints the results to the default printer and the default disk
drive (disabling the printer does not affect program execution, so a printer is not
required). The resulting data files were imported into Quattro or SlideWrite for
comparison to the experimental data.
169


"UFDissertations"
To ken.miller@mylanlabs.com
cc
bcc
>
07/02/2008 08:13 AM
Subject UF Libraries:DigitaI Dissertation Project
Dear Dr. Kenneth J. Miller, Jr.,
The George A. Smathers Libraries at the University of Florida has initiated a project to
retrospectively digitize and make available on the Internet any dissertation written by a
University of Florida doctoral candidate and accepted by the University of Florida. It is
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We would like to add your dissertation, Interfacial diffusional theoretical and clinical
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Christy Shorey, Project Technician
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Internet Distribution Consent Agreement
In reference to the following dissertation:
AUTHOR:
TITLE:
Miller, Kenneth
Interfacial diffusional theoretical and clinical aspects of topical local
anesthetic formulation / (record number: 1717488)
PUBLICATION
1991


Sloan et al.78,79 expanded on the model of Fleming et al.25,42 by describing the
phenomenon of partitioning across a membrane. Using the Gibbs-Duhem equation
(equivalent activities between phases in equilibrium), they related the drug
permeability to the theoretically determined partition coefficient and were able to
estimate permeability from theoretical solubility parameters.
Others have attempted to solve both Ficks first and second laws without
assuming a steady state profile. In 1979, Hadgraft41 attempted to derive rigorous
expressions for diffusion through the stratum corneum (hydrophobic outer layer of
keratinized cells), the epidermis, and the capillary bed. His derivation began with
Ficks second law and a solution was sought through Laplace transformation. To
simplify the mathematics, only solutions at long times were considered. Assumptions
about the relative values of the parameters and simplification by single term
expansions of transcendental functions permitted the Laplace solution to be inverted.
The effects of diffusion routes (transcellular versus intercellular), partition
coefficients, and skin binding were simulated by the model. Our quasi-steady state
model does not require these types of assumptions or simplifications and is valid for
all stages of diffusion in vitro.
In 1983, Guy and Hadgraft35 expanded their non-steady state model to include
transport from the vehicle to the membrane and from the membrane to the
capillaries. Transport between phases of the model was assumed to follow first-order
kinetics. They give few details of the mathematics, but the relative magnitudes of


62
Table 2: Tetracaine (60% free base, 40% acid salt w/w) equilibrium concentra
tions and partitioning into n-octane
% Propylene
^-"Vehicle
c
'-'Octane
Kr
Glycol
(M)
(M)
0
9.38 x 10'3
3.53 x 10-5
3.77 x 10-3
10
1.08 x 10-2
4.37 x 10-5
4.03 x 10-3
20
9.56 x 10-3
3.95 x 10-5
4.13 x 10-3
30
9.73 x 103
3.86 x 10-5
3.97 x 10-3
40
1.05 x 10-2
3.34 x 10-5
3.17 x 10'3
50
1.23 x 102
3.73 x 105
3.03 x 10'3
60
9.07 x 10-3
3.04 x 10'5
3.35 x 10-3
70
1.73 x 10'2
3.86 x 10-5
2.23 x 10'3
80
1.97 x 10'2
4.34 x 105
2.21 x 10'3
90
1.19 x 10'2
3.66 x 105
3.08 x 10-3
100
1.21 x 102
3.43 x 10'5
2.85 x 10'3
partition coefficient indicates the fraction of the drug that moves from the vehicle
into a hydrophobic phase. Assuming the partition coefficient holds at saturation, the
product of the partition coefficient and the saturation concentration is an estimate
of the drug concentration at the vehicle-skin interface just inside the skin. The more
drug delivered to the skin-vehicle interface, the more drug available to diffuse across
the skin. The optimal system corresponds to a maximum in the combined solubility
partitioning parameter. If the 1-octanol partitioning data are used (Table 3,
Figure 17), the optimum system is 50% propylene glycol. If the n-octane partitioning
data are used (Table 4, Figure 18), the optimum system is also 50% propylene glycol.


184
TIME = G
100 GOSUB 2000 Calculate Boundary Conditions
GOSUB 3000 Calculate Skin Concentration Profile
TTME% = (TIME G) / G
IF TIME% / COUNTER % = CINT(TIME% / COUNTER%) AND TIME% >
0THEN
GOSUB 4000 Print Results
END IF
IF CONSTSKN = 0 THEN
GOSUB 600 New Skin Thickness
END IF
IF TIME / 3600 < ENDCALC THEN TIME = TIME + G: GOTO 100
END Program End
500 RESUME NEXT Error Handler
600
BEGIN SKIN THICKNESS SUBROUTINE
SUBMARKR% = SUBMARKR% + 1
L(0) = L(l)
L(l) = L(2)
IF SUBMARKR% = 1 THEN
L(0) = .069029


146
were used to assess partitioning: 1-octanol and n-octane. The combined solubility
partitioning parameters (KpCsat) for both solvents predict that the optimum solvent
for the transdermal delivery of a 60% tetracaine free base, 40% tetracaine acid salt
(w/w) mixture is 50% propylene glycol and 50% saline (v/v).
Surface Activity
Like other local anesthetics, tetracaine is highly surface active. Surface
activity was determined by three independent methods: surface tension, specific
conductivity, and pH. For all three phenomena, a discontinuity in the measured
quantity versus concentration indicates the formation of micelles.
Using surface tension and conductivity, we found that tetracaine acid salt
forms micelles in aqueous solution while tetracaine free base probably does not
(pages 65 and 68). The specific conductivity of aqueous tetracaine free base
indicated the presence of micelles, but at unrealistically low concentrations (page 69).
Tetracaine free base is not soluble enough to accumulate sufficient free molecules
in solution to aggregate.
Three independent methods were used to study the surface activity of 60%
tetracaine free base, 40% tetracaine acid salt mixtures (w/w) in solvents of propylene
glycol and saline. Surface tension and conductivity measurements indicated that
these tetracaine mixtures form micelles in solvents of 20% to 60% propylene glycol
(pages 66 and 69). The critical micelle concentrations (CMC) from these two
methods agree very well (within 33%). Critical micelle concentrations determined


194
GOSUB 200 INTEGRATION AND VARIANCE
ITER% = ITER% + 1
IF DEST > MID(O) THEN
TEMP(O) = LOW(O)
TEMP(l) = LOW(l)
LOW(O) = MID(O)
LOW(l) = MID(l)
MID(O) = DEST
MID(l) = VARIANCE
ELSE TEMP(O) = HIGH(O)
TEMP(l) = HIGH(l)
HIGH(O) = MID(O)
HIGH(l) = MID(l)
MID(O) = DEST
MID(l) = VARIANCE
END IF
GOTO 10
99 CLS
LOCATE 14, 1
PRINT "Solution Reached, Calculating Final Values"
PRINT #1, "Solution Reached, Calculating Final Values"
PRINT #1, "Time C2
C2(MOD)


94
Figure 47 shows the cumulative flux of scopolamine through hairless-mouse
skin as a function of time for skin treated two different ways. In one case, the skin
Fresh
Hydrated and
Preserved
Time (hrs)
Figure 47: Diffusion of aqueous scopolamine through fresh and chemically
preserved hairless-mouse skin
is mounted in the diffusion cell and allowed to contact a solution of 0.1% (w/w)
formaldehyde on both sides for 48 hours. In the other case, the skin is fresh and
untreated. For a preliminary experiment, the quality of the data is good and shows
the validity of the technique and the reliability of the HPLC as a method for
determining trace concentrations of scopolamine. The error is due to the differences
between individual mice. Hydration and preservation of the skin have a strange
effect on the diffusion of scopolamine. This single experiment could only establish
that the processes of hydration and preservation increase flux. The source of the


141
magnitude below the estimated molecular diffusivity of tetracaine in a liquid.65 This
could be a result of the parameters used in the model which are certainly naive
(pathlength = skin thickness, diffusion area = application area, skin = homogeneous
barrier).
Diffusion of Hydrocortisone Through Synthetic Membranes
The addition of a skin swelling routine to the quasi-steady state model
improves its ability to simulate experimental, in vitro, transdermal diffusion data. It
is possible that this phenomenon has nothing to do with skin swelling and simply
reflects a fundamental flaw in the theoretical model. Comparing model curves and
experimental data obtained from a non-swelling system can help make the distinction.
The diffusion of aqueous hydrocortisone through synthetic, polycarbonate
membranes (nominal pore diameter of 0.22 ^m) was modelled to determine which
modelling conditions best represented the experimental data (Figure 96-Figure 98).
Donor-phase concentrations were not held constant in the model because there was
Figure 96: Model fits for hydrocorti- Figure 97: Model fits for hydrocorti
sone in a stagnant cell sone in a poorly stirred cell


83
Figure 38: pH of tetracaine in 20% Figure 39: pH of tetracaine in saline
propylene glycol and 80% saline (v/v)
% Propylene Glycol (v/v)
Figure 40: Micelle diameter of tetracaine (60% free base, 40% acid salt, 0.36 M)
in propylene glycol and saline by QELS
cannot be determined with these methods: micelle size. Micelle size can be
accurately determined with light scattering techniques. Figure 40 shows the diameter
of micelles made of 40% acid salt (w/w) and 60% free base (w/w) at a concentration


210
83. R.D. Void and M.J. Void, Colloid and Interfacial Chemistry. Addison-
Wesley, Reading, PA, 590-1 (1983).
84. K.A. Walters, Penetration enhancers and their use in transdermal
therapeutic systems, in Transdermal Drug Delivery: Developmental Issues
and Research Initiatives. J. Hadgraft and R.H. Guy (eds), Marcel Dekker,
New York, 197-246 (1989).
85. K.A. Walters. Surfactants and percutaneous absorption, in Prediction of
Percutaneous Penetration Proceedings. April 1989, R.C. Scott, R.H. Guy,
and J. Hadgraft (eds), IBC Technical Services, London, 148-62 (1990).
86. A.J.I. Ward, Kinetic considerations in the design of surfactant-based topical
formulations, in Topical Drug Delivery Formulations. D.W. Osborne and
A.H. Amann (eds), Marcel Dekker, New York, 127-41 (1989).
87. A.J.I. Ward and R. Talln, Penetration enhancer incorporation in bilayers,
in Topical Drug Delivery Formulations. D.W. Osborne and A.H. Amann
(eds), Marcel Dekker, New York, 47-67 (1989).
88. J. Wepierre, O. Doucet, and J.P. Marty, Percutaneous Absorption of Drugs
In Vitro: Role of transepidermal and transfollicular routes, in Prediction
of Percutaneous Penetration Proceedings. April 1989, R.C. Scott, R.H.
Guy, and J. Hadgraft (eds), IBC Technical Services, London, 129-34 (1990).
89. R.C. Wester and H.I. Maibach, Dermal decontamination and percutaneous
absorption, in Percutaneous Absorption: Mechanisms. Methodology. Drug
Delivery. R. Bronaugh and H. Maibach (eds), Marcel Dekker, New York,
327-33 (1985).
90. R.C. Wester and H.I. Maibach, In vitro testing of topical pharmaceutical
formulations, in Topical Drug Delivery Formulations. D.W. Osborne and
A.H. Amann (eds), Marcel Dekker, New York, 213-20 (1990).
91. R.C. Wester and H.I. Maibach, Interrelationships in the dose response of
percutaneous absorption, in Percutaneous Absorption: Mechanisms,
methodology, drug delivery. R. Bronaugh and H. Maibach (eds), Marcel
Dekker, New York, 347-58 (1985).
92. R.C. Wester and H.I. Maibach, Structure activity correlations in
percutaneous absorption, in Percutaneous Absorption: Mechanisms,
methodology, drug delivery. R. Bronaugh and H. Maibach (eds), Marcel
Dekker, New York, 107-24 (1985).


117
% (w/v)
O 20 40 60 80 100 120 140
Figure 61: Dose response for 50% tetracaine free base and 50% acid salt (w/w)
in 40% propylene glycol and 60% saline (v/v) through human skin in vivo
reliably in a clinical setting. Unfortunately, such high concentrations of tetracaine
cause erythema (local redness) in most human subjects making this formulation
unsuitable.
The last system investigated consists of 60% tetracaine free base, 40% acid
salt (w/w) in 40% propylene glycol and 60% saline (v/v). This system also produces
very high scores, but at much lower concentrations. Figure 62 shows that the
response plateau is achieved at only 0.3 M (8.4% w/v) tetracaine. This concentration
is sufficiently low to make erythema rare.


200
TIME = h
FOR i = 0 TO M%
C(i, 0) = 0 RESET ARRAY
NEXT i
C(0, 0) = Cl INITIAL BOUNDARY CONDITIONS
C(M%, 0) = C2
COMPVAL(O) = C(M%, 0)
FOR j = 1 TO N
IF CONSTSKN = 0 THEN GOSUB 300 CALCULATE SKIN
THICKNESS
IF CONSTTOP = 0 THEN
C(0, 1) = C(0, 0) (1 h A D / VI / k) + C(l, 0) h A D / VI /
k
ELSE C(0, 1) = Cl
END IF
TIMEH = TIME / 3600
FOR i = 1 TO M% 1
C(i, 1) = r C(i 1, 0) + (1 2 r) C(i, 0) + r C(i + 1, 0)
NEXT i
C(M%, 1) = C(M%, 0) (1 h A D / V2 / k) + C(M% 1, 0) h *
A D / V2 / k
FOR ii = 0 TO M%


139
Conditions
Conditions
Figure 94: Model variance for 70% Figure 95: Model variance for 70%
propylene glycol (young mice #1) propylene glycol (young mice #2)
9 g/1).* If the true concentration in the system is less than or equal to 9 g/1, then
the flux in these systems would be so small as to be negligible (overall concentration
is 0.36 M). Since measurable fluxes were obtained, it seems reasonable to assume
that the concentrations in these solutions were greater than the measured CMC
(assuming micelles do not contribute significantly to the flux). Therefore, the
formation of micelles in these systems is unlikely and the indication by the model
that solutions of saline, 5%, 20%, and 30% propylene glycol do not form micelles
(i.e., donor-phase concentration is not constant) makes sense.
At 10% propylene glycol, the best model assumes skin does not swell and the
concentration does vary (b). This result is unique among all the data on in vitro
diffusion through hairless-mouse skin. Coupled with the fact that the experimental
data themselves are anomalous (cf. Chapter 4, Figure 53, page 102), it is likely that
this system either has unique properties or the data are subject to some systematic
The system of 5% propylene glycol does not show a CMC, 20% propylene glycol
does show a CMC, and 30% propylene glycol was not tested.


LIST OF FIGURES
Figure 1: General schematic of skin structure 12
Figure 2: Molecular structure of hydrocortisone, scopolamine, lidocaine,
and tetracaine 35
Figure 3: Schematic of high pressure liquid chromatograph 42
Figure 4: Sacrifice of hairless mouse 46
Figure 5: Securing hairless mouse 47
Figure 6: First incision 48
Figure 7: Second incision 49
Figure 8: Mounting skin to cell cap 50
Figure 9: Franz diffusion cell 51
Figure 10: Schematic of rat tail Flick-o-meter 52
Figure 11: Application of drug formulation to skin patch 54
Figure 12: Skin patch on arm of volunteer 55
Figure 13: Testing response of volunteer to pain stimulus 56
Figure 14: Tetracaine solubility in propylene glycol and saline 58
Figure 15: Tetracaine (60% free base, 40% acid salt w/w) partitioning into
1-octanol 61
Figure 16: Tetracaine (60% free base, 40% acid salt w/w) partitioning into
n-octane 63
Figure 17: Product of 1-octanol partitioning and solubility data 64
xi


135
Time (hr)
Figure 72: Model fits for 20% propyl
ene glycol (old mice)
Figure 74: Model fits for 40% propyl
ene glycol (young mice)
0 2 4 6 8
Time (hr)
Figure 76: Model fits for 50% propyl
ene glycol (young mice)
Time (hr)
Figure 73: Model fits for 30% propyl
ene glycol (old mice)
0 2 4 6 8
Time (hr)
Figure 75: Model fits for 40% propyl
ene glycol (old mice)
Time (hr)
Figure 77: Model fits for 50% propyl
ene glycol (old mice)


208
63. D.W. Osborne and D.A. Hatzenbuhler, The influence of skin surface lipids
on topical formulations, in Topical Drug Delivery Formulations. D.W.
Osborne and A.H. Amann (eds), Marcel Dekker, New York, 69-86 (1990).
64. D.W. Osborne, A.J.I. Ward, and K.J. ONeill, Surfactant association
colloids as topical drug delivery vehicles, in Topical Drug Delivery
Formulations. D.W. Osborne and A.H. Amann (eds), Marcel Dekker, New
York, 349-79 (1990).
65. R.H. Perry and C.H. Chilton, Chemical Engineers Handbook 5th ed.,
McGraw-Hill, New York, (1973).
66. B.J. Poulsen and G.L. Flynn, In vitro methods used to study dermal
delivery and percutaneous absorption, in Percutaneous Absorption:
Mechanisms. Methodology. Drug Delivery. R. Bronaugh and H. Maibach
(eds), Marcel Dekker, New York, 431-60 (1985).
67. G. Ridout and R.H. Guy, Structure-penetration relationships in
percutaneous absorption, in Pesticide Formulations Innovations and
Developments. B. Cross and H.B. Scher (eds), ACS, Washington D.C.,
(1988).
68. G. Ridout, J. Hadgraft, and R.H. Guy, Model membranes to predict
percutaneous absorption, in Prediction of Percutaneous Penetration
Proceedings. April 1989, R.C. Scott, R.H. Guy, and J. Hadgraft (eds), IBC
Technical Services, London, 84-92 (1990).
69. W.A. Ritschel and P.M. Nayak, Evaluation in vitro and in vivo of
dimeticone transdermal systems, Influence of propylene glycol on drug
release, Drug Res., 37(3), 302-6, (1987).
70. M.S. Roberts, R.A. Anderson, and J. Swarbrick, Permeability of human
epidermis to phenolic compounds, J. Pharm. Pharmacol., 29, 677-83 (1977).
71. A. Rougier, D. Dupuis, C. Lotte, R. Roguet, and H. Schaefer, In vivo
correlation between stratum corneum reservoir function and percutaneous
absorption, J. Inv. Derm., 81(3), 275-8 (1983).
72. A. Rougier, D. Dupuis, C. Lotte, R.C. Wester, and H.I. Maibach, Regional
Variation in Percutaneous Absorption in Man: Measurement by the
stripping method, Arch. Dermatol. Res., 278, 465-9 (1986).


75
X (nm)
Figure 27: Ultraviolet absorbance spectrum of lidocaine
This HPLC method was originally obtained from a Supelco chromatography catalog
as a method for detecting lidocaine, but it also worked well for scopolamine and
tetracaine. The solvents in the original method were acetonitrile (90%) and aqueous
0.02 M, buffered phosphoric acid (10%) at a flowrate of 1.00 ml/min with a C8
column (a C8 carbon chain covalently bonded to a silica matrix). This method
evolved in subsequent analyses to become 72% acetonitrile, 18% 0.02 M buffered
phosphoric acid, and 10% methanol. This solvent mix minimized the retention time
of the drugs while providing adequate resolution. The identities of the peaks were
established by calibration with pure sample and noting which peak varied with the
concentration of the drug in the sample. The retention times of the drugs varied
with the batch of the phosphoric acid buffer, although Figure 29-Figure 31 show


23
Radial diffusion. For a topically applied formulation in vivo, diffusion is not
limited to one direction. Radial diffusion can be a significant factor.38 In an in vitro
diffusion cell, radial transport is impossible since the drug cannot diffuse through the
walls of the diffusion cell or laterally through the skin.
Receptor phase. The choice of receptor phase can affect the ability of the
diffusing substance to partition from the skin into the receptor compartment. In
addition, the solubility of the diffusing substance in the receptor fluid can affect
interpretation of results if an infinite sink is assumed. Bronaugh and Stewart12 varied
the receptor fluid for the diffusion of two lipophilic fragrance chemicals. They found
that increasing the lipophilicity of receptor phase increased the flux of the fragrances
through the skin.
Recommendations. Wester and Maibach90 suggested ways to help match in
vivo conditions of humans using an in vitro diffusion cell.
Membranes Human skin should be used if possible
Cell design A large receptor volume minimizes the effects of
low solubility in the receptor phase
Temperature Circulating temperature should be 37C (results
in a skin temperature of 32C, average for skin in
vivo)


200 PRINT #1, USING "###.### #####.### #####.###
#.########"; G; Cl; C2; D: LPRINT G, Cl, C2, D210 PRINT #1,
LPRINT
LPRINT "Time (hr) Concentration (ug/ml) Thickness (cm)"
LPRINT" Donor Receptor"
LPRINT
LPRINT
240 GOSUB 1000
LPRINT USING "###.### ######.### #####.####
##.### Z; Cl; C2; L;
PRINT #1, USING "###.### ######.### #####.####
##.###"; Z; Cl; C2; L
LPRINT FILES
TIME = G
241 TOP(O) = TOP(l): BOT(O) = BOT(l)
250 GOSUB 350
260 TOP(l) = TOP(O) + G*D*A/L/V1* (BOT(O) TOP(O) + 2 *
TOPSER)
IF CONSTTOP = 1 THEN TOP(l) = Cl
270 BOT(l) = BOT(O) + G*D*A/L/V2* (TOP(O) BOT(O) + 2 *
BOTSER)
271 TTME% = TIME / G


Figure 7: Second incision
buffered saline injected by a syringe through the upper sample port. (To insure that
no air was drawn into the receptor compartment, the sample volume extracted was
less than the volume in the upper sample port arm.)
The concentrations obtained from HPLC were used to calculate the total mass
transferred through the skin. The following mass balance accounts for the sampling
process.


Figure 18: Product of n-octane partitioning and solubility data 66
Figure 19: Surface tension of aqueous tetracaine acid salt 67
Figure 20: Surface tension of aqueous tetracaine free base 68
Figure 21: Surface pressure of tetracaine (60% free base, 40% acid salt
w/w) in propylene glycol and saline 69
Figure 22: Conductivity of aqueous tetracaine acid salt 70
Figure 23: Conductivity of aqueous tetracaine free base 71
Figure 24: Conductivity of tetracaine (60% free base, 40% acid salt w/w)
in propylene glycol and saline 72
Figure 25: Ultraviolet absorbance spectrum of hydrocortisone 73
Figure 26: Ultraviolet absorbance spectrum of scopolamine 74
Figure 27: Ultraviolet absorbance spectrum of lidocaine 75
Figure 28: Ultraviolet absorbance spectrum of tetracaine 76
Figure 29: HPLC chromatogram of scopolamine 77
Figure 30: HPLC chromatogram of lidocaine 78
Figure 31: HPLC chromatogram of tetracaine 79
Figure 32: NaOH titration of aqueous tetracaine 80
Figure 33: NaOH titration of tetracaine in propylene glycol and saline ... 81
Figure 34: pH of tetracaine in propylene glycol 81
Figure 35: pH of tetracaine in 80% propylene glycol and 20% saline
(v/v) 81
Figure 36: pH of tetracaine in 60% propylene glycol and 40% saline
(v/v) 82
Figure 37: pH of tetracaine in 40% propylene glycol and 60% saline
(v/v) 82
xii


183
450 RESUME NEXT
1000 CALCULATE NEW SKIN THICKNESS
LI = .069029 + .049499 (TIME / 3600 + TIMEO) .0044692 (TIME / 3600
+ TIMEO) A 2
L2 = .18821 (TIME / 3600 + TIMEO) A .050642
IF (TIME / 3600 + TIMEO) < 4.8270328# THEN L = LI ELSE L =
L2
RETURN
PROFILE.BAS
...This program will generate the concentration profile for various times across
skin mounted in a Franz diffusion cell
ON ERROR GOTO 500
CLS
DEFDBL A-Z
PI# = 4 ATN(l)
A = 2.5 A 2 PI# / 4 Area of Diffusion
GOSUB 1000 Enter Information
DIM CONCENTR(SKINNUM%, 2), L(2)
CONCENTR(0, 2) = Cl: CONCENTR(SKINNUM%, 2) = C2
OPEN "O", #1, FILES + ".prn"
GOSUB 600
Initial Skin Thickness


3
Ficks second law of diffusion incorporates the time rate-of-change of
concentration to the flux with a mass balance.7
dC^
dt
-VJA =Dab
v2C
2
Difficulty in analyzing diffusion data is usually encountered when the second
or combined law of diffusion (Equation 2) is integrated. The boundary and initial
conditions imposed by the system geometry and experimental apparatus often
complicate integration despite simplifying assumptions.
Transdermal diffusion theory*
Transdermal diffusion consists of many phases; including, release of the solute
from the solvent, diffusion of the solute through the solvent to the membrane,
partitioning of the solute into the membrane (establish equilibrium across the phase
boundary), diffusion through the membrane, partitioning out of the membrane,
reaction, and removal by the circulatory system.
For drug diffusion through the skin, some models assumed that the
concentration gradient and, consequently, the flux were constant. One of the earliest
theoretical models for transdermal diffusion was developed by Michaels et al.60
Their model described diffusion through a homogeneous barrier with a steady state
(linear) concentration profile within the skin and negligible receptor-phase drug
*An excellent and much more complete description of the mechanics of diffusion
as they relate to transdermal diffusion can be found in B.W. Barrys Dermatological
Formulations. Percutaneous Absorption Chapter 2.4


51
Figure 9: Franz diffusion cell
The total mass obtained from this equation can then be converted to a corrected
concentration by dividing by the receptor compartment volume (V) or to a flux by
dividing by the mass transfer area (diameter = 25 mm) and sampling interval.
In Vivo Diffusion
Two different in vivo procedures were used in this study: rat tail-flick testing
and clinical testing on human volunteers. Both procedures are described below as
well as their relative advantages and disadvantages.
Rat tail-flick test
i
Cursory screening of prototype anesthetic preparations was carried out by
anesthesiology department personnel associated with this project using the rat tail-


40
Skin Swelling
Since skin in contact with liquid tends to swell, the extent of swelling was
determined to learn its possible effect on drug diffusion. A skin sample of known
cross-sectional area was weighed as a function of time immersed in water. Any
increase in mass was attributed to uptake of water and a corresponding increase in
volume (using density of water = 1.0 g/ml). The change in area of the upper and
lower faces of the skin sample was assumed to be negligible compared to the
increase in skin thickness. The initial volume of the skin was calculated based on a
density of 1.0 g/ml and its thickness was calculated by considering the skin sample
to be a disk of known radius. The change in skin thickness caused by the absorption
of water was correlated for later use in the theoretical model (Chapter 6, page 131).
Conductivity
Conductivity measurements were made using a YSI conductivity bridge Model
31 with a YSI 3043 Electrode (cell constant = 1/cm). This instrument uses a
scintillation screen to indicate conductance or resistance of the solution in which the
electrode is immersed. The screens two lighted bars diverge as the calibrated dial
indicating conductance approaches the solutions conductivity. The solutions'conduc-
i
tivity is the dial reading at which the screens bars reach their maximum separation.
The instrument can measure conductivities from about 0.5 tmhos to 2 mhos


56
Figure 13: Testing response of volunteer to pain stimulus
*


66
Figure 18: Product of n-octane partitioning and solubility data
base does not form micelles like the HC1 salt, but precipitates out of solution as solid
crystals.
Similar measurements were also performed in various solvents consisting of
propylene glycol and saline with a 40% tetracaine acid salt, 60% free base (w/w)
solute. The normal surface tension of the solvent ranges from 72.4 mN/m for water
to about 30 mN/m for pure propylene glycol. In order to more clearly illustrate the
effect of added solute, the surface tension (yc) has been converted to surface pressure
(7rc); where irc = y0- yc (yG refers to C = 0 or no solute). Figure 21 shows the
surface pressure of tetracaine in propylene glycol-saline solvents. Surface pressure
rises from 0 in the pure solvent to some maximum value which depends on the
solute-solvent interaction. To determine a CMC, the location of the change in slope


19
Solute concentration
Concentration refers to molecularly dispersed substances; literature on the
effects of emulsification (i.e., systems in which the solute is not molecularly
dispersed) is reviewed on page 17. The theoretical response to increased concentra
tion is a proportional increase in flux (according to Ficks first law). Chandrasekaran
et al.17 found that the diffusion of scopolamine through human epidermis followed
such a trend. There are also accounts of deviation from this expected response (both
positive and negative).13,32,70'91 Many of these effects appear to be due to confusion
between the overall concentration and the concentration of drug molecularly
dispersed in the medium.
Effect of temperature
The thermal motion of molecules is the driving force for diffusion. Increasing
the amplitude of thermal motion (temperature) should increase the rate of diffusion
of drugs through the skin just as it increases the rate of diffusion of other solutes in
other systems. The difference in the barrier properties of skin at different
anatomical sites may at least be partially due to differences in temperature.4 Barry
also states that the effect of temperature on transdermal diffusion is usually studied
by an Arrhenius plot (log of drug permeability versus the inverse of temperature).
Such analysis has determined that the activation energies of n-alkanols (ethanol to
pentanol) are constant ( ~ 16.5 kcal/mol) between ambient and body temperature.
Heavier n-alkanols do not yield constant activation energies. It is suggested that this
may be caused by the melting or extraction of some lipids in the stratum corneum


127
C2(f)-C2(0)-rd£ [((C^-C^T
2 (C2(X)-C,(X)(-l)")e vVi.yx =
^-1 13
t
C2(0)tW (C,(X)-C2(X))*
' j0
2 (C,(x)(-l)"-C2(X))e ~D"Vx/iV*
n=1
Equations 12 and 13 are numerically integrated to get the boundary concentrations
as functions of time. The integration scheme used is quite simple.
Ct+At~Ct+M()t 14
dt
Substituting Equations 12 and 13 into Equation 14 gives explicit, time dependent
expressions for the donor and receptor phase concentrations.
j-, t+At
s-i t 4A /, t *-t t
'-'1 + T, t _^1
KL
2E (c2'(-i)''-Q> ~d"v'//-2
-I
s^t+At t AD At i n i i
^2 ~ ^2 +1 V^l ^2 '
2E (Q'(-i)-qV V/2
n=l
Adopting dimensionless groups gives further simplification.
15
16
4>x-
AL K
Volume ratio (Vs = Skin Volume)


132
The model is designed to allow the donor-phase concentration to fall as drug
is transported across the skin unless otherwise specified. Drug solubility in the
solvent must be considered when modelling is attempted. If the solution is super
saturated, the concentration of the donor phase will remain constant as drug
continues to dissolve and enter the donor phase solution. For a suspension,
emulsion, or micellar solution; the actual concentration in the donor phase would be
the concentration of molecularly dispersed solute and not the overall concentration.
General Behavior of Model
Certain features distinguish the modelled systems from one another.
Qualitative comparisons of the time lag can be made between the non-swelling,
varying concentration model (Figure 66) and the other permutations of the model.
Allowing the skin to swell increases the time lag by increasing the distance between
the donor-phase and the receptor-phase. Holding the donor-phase concentration
constant (infinite source conditions) decreases the time lag because it increases the
rate of diffusion. The concentration difference across the membrane does not
decrease as rapidly as when donor-phase concentration falls, so the rate of diffusion
is greater.
The net effect of combining skin swelling and constant donor-phase
concentration depends on the rate of diffusion. If the diffusion is very slow, skin
swelling greatly increases the time lag since the drug will scarcely have penetrated
the membrane before the skin is fully swollen. The drug must then traverse a longer


77
Figure 29: HPLC chromatogram of scopolamine
Table 8: Approximate HPLC retention times of drugs
Drugs
Retention Time
(min)
Scopolamine
2.50
Lido caine
2.60
Tetracaine
3.00
tetracaine free base and HC1 (acid), varying the ratio between tetracaine salt and
tetracaine free base in solution can be studied by a standard acid-base titration.


13
Skin components. Marzulli53 separated human skin into its components to
measure their barrier properties individually. Statistical significance was only
detected between full thickness skin and the dermis, however, the sectioned skins
were generally more permeable than intact skin. Scheuplein76 found that the water
permeability of the outer layer of human skin was approximately one order of
magnitude lower than that of deeper tissue. Much later, Anderson et al.2 compared
the barrier properties of full thickness human skin to isolated stratum corneum.
They found that the isolated stratum corneum resembled the behavior of the full
thickness skin for both partitioning and diffusion. Findings such as these were
instrumental in identifying the stratum corneum as the primary resistance to
transdermal diffusion.
Damage and disease. Barry4 describes experiments investigating transdermal
diffusion as a function of skin condition. Permeability of mouse skin to hydrocorti
sone was found to increase when the mice were deficient in essential fatty acids,
exposed to UV light, exposed to vitamin A acid, exposed to 10% acetic acid in
acetone, or exposed to solvents that fluidized or extracted the stratum corneum lipids.
Abraded skin was found to be equally permeable to steroids as unabraded skin in
rats, but more permeable in monkeys.4 Tape stripping* increased the rate of water
loss to approximately that of a free water surface and also increased the permeability
of the skin to most substances. Shaving of hair from both humans and laboratory
Tape stripping refers to the removal of outer skin cells by applying and removing
adhesive tape.


84
of 0.36 M overall in selected solvents of propylene glycol and saline. The largest
micelles are in the purely aqueous system and micelle size decreases rapidly as the
organic fraction increases until at 80% propylene glycol no micelles are detected.
Therefore, as the fraction of propylene glycol increases; the CMC increases and the
micelle diameter decreases. The enormous size of the micelles in the aqueous
solution suggests that the micelles may not be typical spherical micelles.
Thermal Breakdown of Tetracaine
The thermal degradation of tetracaine was measured to determine the
maximum shelf-life of a transdermal formulation containing tetracaine free base.
The concentration of tetracaine (40% acid salt, 60% free base w/w) in a solution of
40% propylene glycol and 60% saline (v/v) was measured over 14 days. The
measured concentration of solutions at 24C and 32C were scaled relative to an
identical solution stored at 5C. The remaining fraction of tetracaine in solution was
termed viability.
The thermal breakdown of tetracaine is more rapid at 32 C than at 24 C,
although there is measurable loss of drug even at room temperature (Figure 41). To
limit thermal breakdown to 10%, the maximum storage life (at room temperature)
To determine the micelle diameter using QELS the viscosity and refractive index
of the solvent were estimated. This was accomplished by linear interpolation based
on the fraction of propylene glycol. The refractive index of propylene glycol was
obtained from The CRC Handbook of Chemistry and Physics. The viscosity of
propylene glycol was calculated using a correlation in The Properties of Gases and
Liquids by Reid, Prausnitz, and Sherwood.


206
43. J. Hadgraft, G. Ridout, Development of Model Membranes for
Percutaneous Absorption Measurements: I. Isopropyl myristate, Int J
Pharm, 39, 149-56 (1987).
44. J. Hadgraft, G. Ridout, Development of Model Membranes for
Percutaneous Absorption Measurements: II. Dipalmitoyl
phosphatidylcholine, linoleic acid and tetradecane, Int J Pharm, 42, 97-104
(1988).
45. J. Hadgraft, K.A. Walters, and P.K. Wotton, Facilitated transport of
sodium salicylate across an artificial lipid membrane by azone, J. Pharm.
Pharmacol., 37(10), 725-27 (1985).
46. M. Herraez-Dominguez, O. Diez-Sales, D. Guzman-Albaich, and D. Cano-
Blanquer, Importance of the stagnant aqueous diffusion layers in
percutaneous absorption in in vitro studies, in Prediction of Percutaneous
Penetration Proceedings. April 1989, R.C. Scott, R.H. Guy, and J. Hadgraft
(eds), IBC Technical Services, London, 337-45 (1990).
47. J.D. Ingle, Jr. and S.R. Crouch, Spectrochemical Analysis. Prentice-Hall,
Englewood Cliffs, NJ, (1988).
48. J.C. Jamoulle, O. Watts, B. Martin, A. Brzokewicz, B. Martin, and B.
Shroot, Structure permeation relationships of retinoid-like substances in a
model barrier system (poster), in Prediction of Percutaneous Penetration
Proceedings. April 1989, R.C. Scott, R.H. Guy, and J. Hadgraft (eds), IBC
Technical Services, London, 346-52 (1990).
49. K.A. Johnson, Transport of micelle-solubilized compounds through
microporous membranes, Ph.D. Dissertation, University of Florida, 1987.
50. V.M. Knepp, J. Hadgraft, and R.H. Guy, Transdermal Drug Delivery:
Problems and possibilities, CRC Critical Reviews in Therapeutic Drug
Carrier Systems, 4, 13-37, (1987).
51. G.P. Kushla and J.L. Zatz, Evaluation of a noninvasive method for
monitoring percutaneous absorption of lidocaine in vivo, Pharm. Res.,
7(10), 1033-7 (1990).
52. D.E. Leahy, A.L.J. DeMeere, A.R. Wait, P.J. Taylor, J.A. Tomlinson, and
E. Tomlinson, A general description of water-oil partitioning rates using
the rotating diffusion cell, Int. J. Pharm., 50, 117-32 (1989).


118
% (w/v)
O 20 40 60 80 100
Figure 62: Dose response for 60% tetracaine free base 40% acid salt (w/w) in
40% propylene glycol and 60% saline (v/v) through human skin in vivo
Time response
The onset of analgesia is measured by testing for topical anesthesia as a
function of time. Several identical patches are applied to a subject and, at a
specified time, one patch is removed and the area tested (as in Chapter 2: Materials
and Methods, page 53). Figure 63 shows the time response curves for high drug
concentrations (1.1 M, 1.8 M); Figure 64 shows the time response curves for low to
medium concentrations (0.036 M 1.004 M). For comparison, these plots also show
the placebo effect. The formulations consist of varying concentrations of tetracaine
(40% acid salt, 60% free base w/w) in a solvent of 40% propylene glycol and 60%
saline. For high concentrations of tetracaine, the anesthetic formulations were