Title Page
 Table of Contents
 List of Tables
 List of Figures
 Materials and methods
 Physical properties of drug...
 Drug diffusion in vitro
 Drug diffusion in vivo
 Recommendations for future...
 Derivation of the full numerical...
 Computer programs
 Biographical sketch

Title: Interfacial diffusional theoretical, and clinical aspects of topical local anesthetic formulation
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00090184/00001
 Material Information
Title: Interfacial diffusional theoretical, and clinical aspects of topical local anesthetic formulation
Series Title: Interfacial diffusional theoretical, and clinical aspects of topical local anesthetic formulation
Physical Description: Book
Creator: Miller, Kenneth James.
 Record Information
Bibliographic ID: UF00090184
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 001717488
oclc - 25622360

Table of Contents
    Title Page
        Page i
        Page ii
        Page iii
        Page iv
        Page v
    Table of Contents
        Page vi
        Page vii
        Page viii
        Page ix
    List of Tables
        Page x
    List of Figures
        Page xi
        Page xii
        Page xiii
        Page xiv
        Page xv
        Page xvi
        Page xvii
        Page xviii
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
    Materials and methods
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
    Physical properties of drug formulations
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
    Drug diffusion in vitro
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
        Page 105
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
    Drug diffusion in vivo
        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
        Page 120
        Page 121
        Page 122
        Page 123
        Page 124
        Page 125
        Page 126
        Page 127
        Page 128
        Page 129
        Page 130
        Page 131
        Page 132
        Page 133
        Page 134
        Page 135
        Page 136
        Page 137
        Page 138
        Page 139
        Page 140
        Page 141
        Page 142
        Page 143
        Page 144
        Page 145
        Page 146
        Page 147
        Page 148
        Page 149
        Page 150
        Page 151
        Page 152
        Page 153
        Page 154
        Page 155
    Recommendations for future work
        Page 156
        Page 157
        Page 158
        Page 159
        Page 160
    Derivation of the full numerical routine
        Page 161
        Page 162
        Page 163
        Page 164
        Page 165
        Page 166
        Page 167
        Page 168
    Computer programs
        Page 169
        Page 170
        Page 171
        Page 172
        Page 173
        Page 174
        Page 175
        Page 176
        Page 177
        Page 178
        Page 179
        Page 180
        Page 181
        Page 182
        Page 183
        Page 184
        Page 185
        Page 186
        Page 187
        Page 188
        Page 189
        Page 190
        Page 191
        Page 192
        Page 193
        Page 194
        Page 195
        Page 196
        Page 197
        Page 198
        Page 199
        Page 200
        Page 201
        Page 202
        Page 203
        Page 204
        Page 205
        Page 206
        Page 207
        Page 208
        Page 209
        Page 210
        Page 211
    Biographical sketch
        Page 212
        Page 213
        Page 214
        Copyright 1
        Copyright 2
Full Text







Copyright 1991


Kenneth James Miller II

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


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.


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

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

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

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


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


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 ...................


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






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

....... 169

FNR.BAS ......

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

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

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


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


Figure 1:

Figure 2:

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:
(v/v) (

Figure 65:

Figure 66:

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) ..............














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




.......... 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



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.



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


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


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 = 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.


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

concentration to the flux with a mass balance.7

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

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

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.


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

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


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

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


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


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


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


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


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.


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.


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


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.


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).


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.


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


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


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.


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


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


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.


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.


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


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

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


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


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


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


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

overshadowed by the change in its physical dimensions.



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.


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



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









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

Figure 2:

Molecular structure of hydrocortisone, scopolamine, lidocaine, and

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


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.


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.


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 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.


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


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


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 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


(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

/< 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


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


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


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.


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


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.


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


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



Figure 8: Mounting skin to cell cap

M(tn) =C(tn) V+Vs,( C(tx))

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

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


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).


Figure 11: Application of drug formulation to skin patch


Skin patch on arm of volunteer

Figure 12:




Testing response of volunteer to pain stimulus


Figure 13:



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


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.


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


-3 h .j --- Acid Salt

--/" -- Free Base

-*-- 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

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


for systems containing more than 60% propylene glycol could not be evaluated using


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.



0 6 Single
U Phase
4 Region


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

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

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 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

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



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




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


Figure 17:

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





0.0000 '
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


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

T = 23C
70 oo% CMC = 0.1M

g 60

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.



70 -

60 I

50 T =23C \ d

10-5 10-4 10-3 10-2

C (M)

Figure 20: Surface tension of aqueous tetracaine free base


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
S80% PG

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

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%).

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


pH Range

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




(no CMC)


0.1 0.2 0.3

C (M)

Conductivity of aqueous tetracaine acid salt

Figure 22:



7 cmc 0.00003M *

0 5-

4 -



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,



0 0.2 0.4 0.6 0.8 1.0

+ Saline

A 20% PG

O 40% PG

+ 50% PG

A 60% PG

* 80% PG

V 100% PG

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^


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


pH Range

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


(no CMC)


200 300

X (nm)

Ultraviolet absorbance spectrum of hydrocortisone

Figure 25:






200 300

X (nm)

Ultraviolet absorbance spectrum of scopolamine

Ultraviolet absorbance maxima of drugs




Hydrocortisone 200 247

Scopolamine 190

Lidocaine 213

Tetracaine 311 196


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:



r 1


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


g 1


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.






1 2 3 4

Elapsed Time (min)

HPLC chromatogram of scopolamine

Table 8: Approximate HPLC retention times of drugs


Retention Time

Scopolamine 2.50

Lidocaine 2.60



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:


1600 Lidocaine


C 800

J, 400

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.



C 400 Tetracaine

S 300

0 200



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 *

79 ._-gg_7pKeA. = 8.7


7 1.19 mmol
Tetracaine HCI
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

----- Saline

12 -
S---- 20% PG

10 --- 40% PG

SFl.... .. 50% PG

S--B- 60% PG

-*-- 80% PG


% 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

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,

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
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;

University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs