Pharmacokinetic/pharmacodynamic modeling of corticosteroids and systemic effects

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Title:
Pharmacokinetic/pharmacodynamic modeling of corticosteroids and systemic effects
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x, 181 leaves : ill. ; 29 cm.
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English
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Stark, Jeffrey G., 1964-
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Subjects / Keywords:
Research   ( mesh )
Budesonide -- pharmacology   ( mesh )
Budesonide -- pharmacokinetics   ( mesh )
Hydrocortisone -- metabolism   ( mesh )
Lymphocytes -- drug effects   ( mesh )
Models, Chemical   ( mesh )
Models, Biological   ( mesh )
Department of Pharmaceutics thesis Ph.D   ( mesh )
Dissertations, Academic -- College of Pharmacy -- Department of Pharmaceutics -- UF   ( mesh )
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bibliography   ( marcgt )
non-fiction   ( marcgt )

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Thesis:
Thesis (Ph.D)--University of Florida, 2001.
Bibliography:
Bibliography: leaves 168-179.
Statement of Responsibility:
by Jeffrey Glen Stark.
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Typescript.
General Note:
Vita.

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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aleph - 002712798
oclc - 52536069
notis - ANJ0517
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Full Text










PHARMACOKINETIC/PHARMACODYNAMIC MODELING
OF CORTICOSTEROIDS AND SYSTEMIC EFFECTS













By

JEFFREY GLEN STARK


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

UNIVERSITY OF FLORIDA


2001














ACKNOWLEDGMENTS


I would first like to thank my advisor Dr. Guenther Hochhaus for both his

guidance and his patience as I worked my way through these studies. We approached

these projects with different backgrounds and from different perspectives and,

consequently, we often had vastly different opinions regarding the directions they should

take. He allowed me the freedom to flesh out new ideas and he provided insight as to how

these ideas could be fully developed. I would also like to thank him for his continual

efforts to bring me out of the theoretical realm and into the physical domain. At times, he

was successful. Without this facet of our student-advisor relationship, many of my ideas

would have remained on the yellow legal pad on which they were initially formulated.

I would also like to give special thanks to Dr. Hartmut Derendorf. As a student in

his course, I realized that the field of pharmacokinetics was where I belonged. For many

years, I knew that I belonged somewhere, I was just unaware of where that "somewhere"

was. He always encouraged me despite my many efforts to reinvent the wheel. He

reminded me that the hours I spent redressing all the basic theories in pharmacokinetics

were never the waste of time I, at times, believed they were.

In the latter stages of my work, I found myself asking Dr. Jeffrey Hughes many

questions. With his training as both a pharmacist and a researcher, he was uniquely

qualified to supply me with the knowledge I lacked. Jeff's door was always open and I

appreciate his willingness to share his knowledge and his opinions. It is because of him








that I will always remember the interrogative phrase, "Where's the data?"

Special thanks go to Dr. Charles Wood for his willingness to serve as the external

member of my committee. He provided the insight I needed to continue and complete

some of the facets of this project. Speaking with Dr. Wood was always refreshing and his

enthusiasm for his work was both contagious and encouraging. I would also like to thank

Dr. Nicholas Bodor, a member of my advisory committee during the first phase of my

graduate education in pharmaceutics. In addition to principles of drug design, he taught

me that a pair of chopsticks is an excellent substitute for a misplaced laser pointer.

The fine folks in the Department of Pharmaceutics became a surrogate family to

me during the last few years. My first official contact in the department was with Jim

Ketcham, a man who can wrestle alligators, counsel and encourage the downhearted,

record and report course grades, bring to life characters in a play, and type without

looking at the keys. I admire and respect him. Patricia Khan, the master of the web, was

always willing and able to assist me with banners, journal articles, and all of the

instructional material I prepared for the students in the College of Pharmacy. Without

her, my diagrams would still be floating purposelessly over the text and the students

would still be trying to read my handwriting. We made a good team. With Vada Taylor

handling the ordering and bookkeeping in the department, I always had the supplies

necessary to continue my research and I had no excuse not to be busy in the lab. She also

made sure that all of the paperwork was signed for me to receive my assistantship. I

would like to thank Yufei Tang for the assistance, coaching, and training she gave me in

instrumental analysis. Her reputation as an experienced and knowledgeable chemist is

overshadowed only by her reputation as a kind and gentle spirit.








I must give special recognition to the senior-most member of both my research

group and the Department of Pharmaceutics, Marge Rigby. In addition to experiences in

the lab, Marge and I shared many meaningful conversations about life in general. At

times, I was tempted to attribute Marge's wisdom and candor to her age. However, I

believe she has always been the wonderfully astute and straightforward person I had the

pleasure of knowing. Without Marge, it is just another day in the lab.

The members of the Hochhaus research group (Sandra, Suliman, Jim, Vikram,

Intira, Yaning, and Adam, who we adopted) and I shared many good times in our course

work and our day-to-day interactions in the lab. Along the way, the "Dutchies" (Arsia,

Ester, Patsy, Han, Marrit, and Ramin) and the German boys (Markus, Richard, and Erol,

who tried to convince us that dancing in the lab was perfectly acceptable) joined us and,

for six months at a time, became very important parts of our lives. Special thanks go to

Han and Marrit for coming into my life at just the right time. Likewise, the Derendorfers,

including my encourager Julia, her cohorts Olaf and Petra, Raj, Ram, and many more

shared our days in the lab and have a special place in my heart. I thank the entire group

for tolerating my cartoons and my renditions of "My Funny Valentine" and an occasional

Mozart bass aria. We came from various backgrounds, different disciplines, and distant

lands with diverse cultures, yet grew to accept our differences, recognize our similarities,

and gain an appreciation for both as we worked, at times, in very close quarters,

functioning on too little sleep and too much caffeine, shared our meals, music, thoughts,

opinions, and dreams, laughed and learned, lost our tempers and found resolution, and,

trough all of this, revealed and discovered the strengths and weaknesses of each other and

ourselves. I would have had it no other way.








Last but not least, I would like to thank my parents, Marvin and Barbara, my

brother and sister-in-law, Greg and Leslie, and the kiddos, Lauren and Ryan, for their

love, support, and encouragement as I continued my education. The rumor that Lauren

and Ryan act just like I used to is quite untrue. I still act the same.















TABLE OF CONTENTS

page
ACKNOW LEDGM ENTS ....................................................................................... ii

ABSTRACT ............................................ ............................................................... ix

CHAPTERS

1 COMBINING PHARMACOKINETICS AND PHARMACODYNAMICS .......... 1
Introduction ................................................................................................ 1
M echanisms of Action .................................................................................. 2
Pharmacokinetics ................................................................................................ 3
Pharmacokinetic/Pharmacodynamic M odels ........................................ ........... 5
Physiological M odels .......................................................................................... 7
Surrogate M arkers .............................................................................................. 8
Surrogate M arkers for Systemic Effects of Corticosteroids .................................... 10
Cortisol Suppression ..................................................................................... 10
Lymphocyte Reduction ............................................................................... 11
Lymphocyte Subsets ..................................................................................... 11
Combined Effects of Endogenous and Exogenous Corticosteroids ................... 14
Budesonide ......................................................................................................... 16
Additional Therapeutic Corticosteroids .............................................................. 17
Hypotheses ......................................................................................................... 18

2 BINDING TO TISSUES AND PLASMA PROTEINS ......................................... 18
Background ........................................................................................................ 18
Objectives .......................................................................................................... 26
Tissue Partitioning .............................................................................................. 27
M methods ........................................................................................................ 27
Results and Discussion ................................................................................. 29
Binding to Plasma Proteins ................................................................................. 31
M methods ........................................................................................................ 31
Results and Discussion ................................................................................. 35
Summary and Conclusions ................................................................................. 36

3 PHARMACOKINETICS OF HYDROCORTISONE .......................................... 40
Background Information and Theory .................................................................. 40
Binding to Plasma Proteins ........................................................................... 41
Clearance ................................................................................................. 43
Volume of distribution ............................................................................ 44









The volume of distribution of the central compartment .......................... 46
The volume of distribution at steady-state ............................................. 47
Distribution Kinetics and Compartmental Models .......................................... 50
The two-compartment model .................................................................. 50
Compartmental models and nonlinearity .................................. ............ 52
Purpose .............................................................................................................. ....... 54
M methods ............................................................................................................ ....... 54
Preliminary Calculations ............................................................................... 54
Compartmental Models with Linear and Nonlinear Pharmacokinetics ......... 55
Simulations with the Gradient-Based Distribution Model ............................. 58
Endogenous Cortisol ..................................................................................... 58
D ata Fitting ................................................................................................... 59
Results and Discussion ....................................................................................... 60
Preliminary Calculations ............................................................................... 60
Compartmental Models with Linear and Nonlinear Pharmacokinetics ......... 63
Simulations with the Gradient-Based Distribution Model ............................. 66
Endogenous Cortisol ..................................................................................... 70
Conclusions .............................................. ......................................................... 71

4 PHARMACOKINETIC/PHARMACODYNAMIC MODELING OF TOTAL
LYMPHOCYTES AND SELECTED SUBTYPES AFTER BUDESONIDE ... 74
Introduction .............................................. ......................................................... 74
Clinical Procedures ............................................................................................. 76
Pharmacokinetic/Pharmacodynamic Modeling of Blood Lymphocytes ................. 77
Budesonide Concentrations .......................................................................... 77
Circadian Rhythm of Cortisol ....................................................................... 78
Cortisol Suppression ..................................................................................... 79
Nonlinear Binding to Plasma Proteins .......................................................... 80
Lymphocytes after Placebo ........................................................................... 81
Lymphocytes after Budesonide ..................................................................... 81
Multi-Step Modeling Procedure ................................................................... 82
Noncompartmental Analysis ............................................................................... 83
R results ...................................................................................................................... 84
Conclusions and Discussion ............................................................................... 88
B udesonide .................................................................................................... 88
Cortisol after Placebo ................................................................................. 95
Cortisol after Oral Budesonide ..................................................................... 96
Lymphocytes after Placebo ........................................................................... 97
Lymphocytes after Budesonide ..................................................................... 97

5 FACTORS INFLUENCING LYMPHOCYTE REDUCTION .............................101
Introduction ................................................. ...................................................... 101
M methods .................................................. ..........................................................102
Lymphocyte-Time Profiles ...........................................................................102
Noncompartmental Pharmacokinetic/Pharmacodynamic Parameters ...............103
Input Parameters ...........................................................................................103









Dose, Frequency, and Disposition .................................................................104
Corticosteroid Potency ....................................... ............... ......................... 105
Results and D discussion ......................................... ............... ............................105
D ose .......................................................................................................... 105
Adm inistration Tim e ............................................................. .....................106
Dosing Frequency ........................................ ................. .............................109
Circadian Rhythm of Cortisol ..........................................................................113
Potency ................................................................... .................................... 115
C conclusions ........................................................................................................119

6 CON CLU SION S ................................................................................................ 124

APPENDICES

A A TWO-COMPARTMENT MODEL WITH GRADIENT-BASED
DISTRIBU TION ........................................................... ..............................129

B BUFFERING EFFECT OF CORTISOL SUPPRESSION ON
THE REDUCTION OF BLOOD LYMPHOCYTES .......................................136

C PHARMACOKINETIC/PHARMACODYNAMIC CONSIDERATIONS IN
DESIGNING A DOSING REGIMEN ...........................................................141
D NOVEL NONCOMPARTMENTAL PARAMETERS IN
PHARMACOKINETIC/PHARMACODYNAMIC ANALYSIS ....................146
Introduction ................................................. ...................................................... 146
C concepts ............................................................................................. ........... ..........147
M ean Residence Tim e .........................................................................................152
Statistical Moments in Pharmacokinetics ...........................................................156
Mean Residence Time ................................................................................156
W eighted Average Concentration .................................................................1...57
Statistical Moments in Pharmacokinetics/Pharmacodynamics ..............................158
The Linear Effect M odel ................................... ............................................160
The Em ax Effect M odel ...................................... ............................................161
A Special C ase .............................................................................................. 164

REFEREN CES ........................................................................................................ 168

BIOGRAPHICAL SKETCH .............................................................................. 180














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

PHARMACOKINETIC/PHARMACODYNAMIC MODELING
OF CORTICOSTEROIDS AND SYSTEMIC EFFECTS

By

Jeffrey Glen Stark

May 2001

Chair: Guenther Hochhaus
Major Department: Pharmaceutics

Corticosteroids are often prescribed for chronic conditions. Diseases such as

rheumatoid arthritis and asthma require long-term drug therapy and, regardless of the

disease or route of administration, both the desired and undesired effects must be

weighed. In some cases, systemic activity is necessary and side effects are unavoidable.

Pharmacokinetic/Pharmacodynamic (PK/PD) models may be constructed to assess and

predict the degree of systemic effects of corticosteroids. Blood lymphocytes were chosen

as surrogate markers for systemic activity since their decline is directly related to possible

immunosuppression in chronic corticosteroid therapy. Total lymphocytes and selected

subtypes were monitored in a clinical study. Lymphocyte counts are suppressed by

corticosteroids, endogenous and exogenous, while endogenous cortisol itself is

suppressed by the exogenous corticosteroid administered. All of these interactions were

included in a PK/PD model. Since nonlinear binding of cortisol to plasma proteins

influences both its elimination and distribution, a new pharmacokinetic model based on








the flux of unbound cortisol was developed to describe these phenomena and

incorporated into the lymphocyte module of the PK/PD model.

The PK/PD analysis of total lymphocytes and selected subtypes revealed that total

lymphocytes were suppressed by 10% after 9 mg oral budesonide. Suppression of CD4

and CD19 was greater and that of CD8 was minimal. Based on these results, there is no

apparent benefit in monitoring subtypes over total lymphocytes solely for obtaining an

adequate surrogate marker. PK/PD simulations of total lymphocytes using parameters

obtained from clinical data showed that the degree of systemic effects after one dose per

day depends on administration time. Effects on lymphocytes are least for 4 AM

administration and greatest for 4 PM. If cortisol is monitored as the surrogate marker, the

opposite trend is observed. Lymphocyte reduction is inversely related to cortisol

suppression. Since cortisol is suppressed by exogenous corticosteroids, there is less total

corticosteroid present and no net effects on lymphocytes are predicted for bioavailable

budesonide doses of 0.1 to 0.8 mg or less. This buffering capacity is most apparent when

the potency of the drug on cortisol is three or more times greater than the potency on

lymphocytes.














CHAPTER 1
COMBINING PHARMACOKINETICS AND PHARMACODYNAMICS

Introduction

This research focused on various aspects of the theory, development, and

application of the pharmacokinetics and pharmacokinetic/pharmacodynamic (PK/PD)

modeling of corticosteroids. Anti-inflammatory corticosteroids are used to treat a variety

of chronic conditions including rheumatoid arthritis, Crohn's disease, and asthma. Since

chronic diseases require long-term drug therapy, the degree of both the desired effects

and the undesired side effects must be weighed. Potential side effects include glaucoma,

hypertension, hyperglycemia, cortisol suppression, osteoporosis, and peptic ulcers

(Caldwell and Furst 1991; Howland 1996; Sorkness 1998; Lipworth 1999; Tripathi,

Parapuram et al. 1999). The most important therapeutic actions are the anti-inflammatory,

immunosuppressive, and lympholitic effects of these drugs.

The use of inhaled corticosteroids for asthma allows, in effect, local delivery of

the drug to the lung. The goal of inhaled corticosteroids is to produce long-lasting

therapeutic effects at the pulmonary target site and to minimize systemic effects by rapid

clearance of the absorbed drug (Derendorf, Hochhaus et al. 1998). However, despite this

local delivery, the entire inhaled dose reaching the lung (as well as the fraction of the

swallowed portion of the inhaled dose not eliminated during first-pass metabolism) will

ultimately enter systemic circulation. Similarly, delayed release oral formulations may

allow for local delivery of the drug for the treatment of inflammatory bowel disease.








In the treatment of rheumatoid arthritis with oral corticosteroids, systemic activity

is necessary and undesired side effects are often unavoidable. This is due to the fact that,

unlike many classes of drugs, both desired and undesired effects of corticosteroids are

mediated by the same drug-receptor interaction (Hochhaus, Mollmann et al. 1997).

Mechanisms of Action

Corticosteroids contribute to a broad array of physiological and biochemical

processes such as carbohydrate, protein, and lipid metabolism as well as the electrolyte

and water balance (Kragballe 1989; Jusko 1994). Receptor/gene-mediated, receptor/non-

gene-mediated, and nonspecific effects are attributed to corticosteroids. The main

mechanism of action of corticosteroids is generally accepted to be via interaction with

specific receptors, which results in an increase or decrease in gene transcription. These

are characterized by slow onset and slow dissipation of the effects. Examples of such

receptor/gene-mediated effects include anti-inflammatory activity and the induction of

the hepatic enzyme tyrosine aminotransferase (Xu, Sun et al. 1995).

The glucocorticoid receptor is found mainly as a water-soluble protein within the

cell rather than as an integral part of the cell membrane. However, membrane binding

sites have been found in several tissues with a chemical similarity to the cytosolic

corticosteroid receptor. Both appear to cooperate for the modulation of cellular events.

The majority of mammalian cells have been found to contain corticosteroid receptors, in

agreement with the importance of corticosteroids for the regulation of energy metabolism

and immune and anti-inflammatory response (Hochhaus, Mollmann et al. 1997).

In addition to the classical receptor/gene-mediated mechanism, a nucleus-

independent cytosolic receptor-mediated effect has also been proposed. These are








characterized by an immediate onset after drug administration and include steroid-

induced cortisol suppression and the redistribution of lymphocytes (Balow, Hurley et al.

1975; Fauci 1975; Matsuse, Shimoda et al. 1999; Meibohm, Derendorfet al. 1999). The

obstruction of calcium influx and the interference with c-AMP-dependent protein kinase

are two examples of the modes of action for non-gene-mediated corticosteroid effects.

Clinical efficacy of high doses of corticosteroids may not always be explained by

receptor interactions because these doses result in plasma and tissue concentrations far

exceeding those for receptor saturation. High doses are indicated for spinal cord injury,

arthritis, and for the inhibition of rejection during organ transplant (van den Brink, van

Wijk et al. 1994; Ferraris, Tambutti et al. 2000). High doses of flunisolide have been

proposed for treatment of acute asthma attacks (Rodrigo and Rodrigo 1998). Despite

these common clinical applications, not much is known about the mode of action for

these nonspecific effects.

Since effects are mediated via a single receptor type, corticosteroids with different

receptor binding affinities do not differ in their qualitative or quantitative effects.

However, the concentrations necessary to achieve the desired effects will be different. In

general, lower receptor affinity may be overcome by increasing the dose, an indication

that high pharmacodynamic activity is not necessarily the most critical factor in

corticosteroid therapy. It has been suggested that the pharmacokinetic properties of the

drug may be the most important considerations for optimizing the therapeutic index

(Hochhaus, Mollmann et al. 1997).

Pharmacokinetics

The treatment of asthma has been significantly improved as a result of the








introduction of corticosteroids such as fluticasone propionate (FP) and budesonide (BUD)

having improved therapeutic ratios compared to other drugs such as hydrocortisone (HC),

predisolone (P), and dexamethasone (DEX). Although there is a marked increase in the

relative receptor binding affinity (RRA), this improvement is mainly due to optimized

pharmacokinetic properties (Derendorf, Hochhaus et al. 1998). Pharmacokinetic and

pharmacodynamic parameters of some selected corticosteroids are contained in the table

below. The corticosteroids BUD and FP are characterized by a high clearance (CL) and a

low oral bioavailability (Forai). These are especially useful for treating asthma since the

swallowed portion of the dose undergoes significant first-pass metabolism and the drug

entering systemic circulation by oral or pulmonary absorption is rapidly cleared.

However, modem corticosteroids differ in volume of distribution (Vd) and, therefore,

half-life (tl/2). Fluticasone propionate has one of the largest steady-state volumes of

distribution.

Table. Pharmacokinetic and pharmacodynamic properties of selected corticosteroids.
Drug RRA f, CL (L/h) VdYs(L)} Fra %)
HC 9 20 18 34 96
P 16 25 6 93 82
DEX 100 23 17 57 80
FLU 180 20 58 96 20
TA 233 29 37 103 23
BUD 935 12 84 183 11
FP 1800 10 69 318 <1
RRA=Relative receptor affinity (compared to dexamethasone, defined as 100),
fu=fraction unbound in plasma, CL-total body clearance, Vdss=steady-state volume of
distribution, Foral=bioavailability after oral administration.
HC=hydrocortisone, P=prednisolone, DEX=dexamethasone, FLU=flunisolide,
TA-triamcinolone acetonide, BUD=budesonide, FP-fluticasone propionate.
Parameter values were obtained from previous publications (Rohdewald, Rehder et al.
1987; Derendorf, Mollmann et al. 1991; Rohatagi, Hochhaus et al. 1995; Derendorf 1997;
Derendorf, Mollmann et al. 1997; Hochhaus, Mollmann et al. 1997; Rohatagi, Barth et al.
1997; Derendorf, Hochhaus et al. 1998; Meibohm, Hochhaus et al. 1999).








The degrees of plasma protein and tissue binding are also important

considerations. Binding is important from a pharmacokinetic perspective (since CL may

be influenced by plasma protein binding and Vdss is determined by both plasma protein

and tissue binding) and from a pharmacodynamic perspective (since only the unbound

fraction of the drug is pharmacologically active). Most corticosteroids have a high degree

of binding to plasma proteins with a small unbound fraction in plasma (f,). For high

extraction drugs, fu is a factor determining oral bioavailablity. In general, overall tissue

binding is difficult to determine. However, tissue binding or the fraction unbound in

tissues (f,t) may be estimated indirectly using the steady state volume of distribution

(Vdss) since this term is dependent on the ratio of f:fut. Due to the importance of binding

properties, these will be discussed in depth and correlated to other physicochemical

properties such as solubility and lipophilicity. Discrepancies between previously

published values of fu (flunisolide) and nonlinear plasma protein binding (hydrocortisone)

will also be addressed.

Pharmacokinetic/Pharmacodynamic Models

Corticosteroid dosing for different therapeutic outcomes is usually determined

empirically and is subject to considerable debate. The goal in designing a dosing regimen

for corticosteroids (or any drug, for that matter) is to provide a dose sufficient to achieve

the desired therapeutic effect while keeping side effects to a minimum. Even for

local/topical administration, undesired systemic (and local) side effects are possible if not

completely likely. Although equally applicable to local effects, the following discussion

is geared mainly towards systemic activity, whether desired or adverse.

In order to both assess and predict the degree of systemic effects of








corticosteroids, mathematical relationships may be constructed. These relationships,

usually referred to as models, are often complex since they must include both

pharmacokinetics, the time course of the drug in the body, and pharmacodynamics, the

effect observed at certain drug concentrations. More formally, pharmacokinetics

describes the fate of drugs in the body over a period of time, including their absorption,

distribution, localization in tissues, biotransformation, and elimination or excretion. A

more complete definition of pharmacodynamics is the study of the biochemical and

physiological effects of drugs and the mechanisms of their actions. By combining the

two, pharmacokinetic/pharmacodynamic (PK/PD) models enable the effects of a drug to

be described as a function of time. In addition to describing clinical data, PK/PD models

may be used to predict the effects of corticosteroids having different kinetic and dynamic

properties and to identify important considerations for future studies, thereby enabling the

design of more informative and cost-effective clinical trials. Other goals in PK/PD

modeling include testing competing hypotheses for differences observed in the efficacy

of drugs, predicting responses under new conditions such as various doses and

administration times, and estimating inaccessible model parameters such as the

amplification factor in a biochemical cascade yielding the observed effect after receptor

activation. It should be noted that most therapeutic effects of corticosteroids are receptor-

mediated and there seems to be no substance-specific difference in the post-receptor

reaction cascade (Derendorf, Mollmann et al. 1997). Therefore, the extent and duration of

the effects and side effects depend only on receptor occupancy determined by the

availability of the drug at the receptor site and its affinity to the receptor (Hochhaus,

Mollmann et al. 1997), making corticosteroids ideal candidates for PK/PD modeling.








As stated by Dirac (Dirac and Dalitz 1995), the physical laws necessary for the

mathematical theory of a large part of physics and the whole of chemistry are completely

known and the difficulty is only that the exact application of these laws leads to equations

too complex to be solved. This is especially true when attempting to construct

mathematical models to describe biological systems or, in the present case, the fate and

action of drugs in the body. Due to the complexity of some kinetic and dynamic

phenomena, some proposed models are entirely theoretical without close correlation to

physiological/biochemical events occurring in vivo. Examples of this include describing

the complex distribution and elimination of corticosteroids using compartmental models

consisting of poly-exponential equations and describing their effects in terms of cosine

functions, harmonic oscillations, and Fourier series (Chakraborty, Krzyzanski et al.

1999). The present study was not approached with this philosophy and every attempt was

made to apply models based on the physiological elimination, distribution, and mode of

action as well as the physicochemical properties of the drug.

Physiological Models

The goal of the present study was not to construct mathematical models that

simply describe data sets but rather to adapt or develop physiologically based models that

are also sound mathematically. By doing so, it is not only possible to describe kinetic and

dynamic data but also to obtain a better understanding and appreciation of the complex

events occurring in vivo, thereby bridging the gap between mathematical description and

physiological reality. The PK/PD models used in this study may best be described as

semi-empirical in that some aspects of the models are based on physiological

observations while others are based on the straightforward application of established








physical principles to biological systems. Examples of such physiological PK/PD models

for corticosteroids include those for the circadian rhythm of cortisol (Rohatagi, Hochhaus

et al. 1995), the reduction of blood lymphocytes (Meibohm, Derendorfet al. 1999), and

pulmonary targeting (Hochhaus, Mollmann et al. 1997) or deposition (Gonda 1981).

According to Gibaldi (Gibaldi and Perrier 1982), the kinds of information

required by the model can be classified as anatomical (organ and tissue volumes),

physiological (blood flow rates and enzyme reaction parameters), thermodynamic (drug-

protein binding isotherms), and transport (membrane permeability). The PK/PD models

in the present study allow the inclusion of parameters such as plasma protein binding,

tissue partitioning, and receptor binding affinities obtained in vitro. In addition,

absorption and distribution may be described by diffusion processes, including membrane

permeability, and elimination may be described in terms of physiological models such as

the Wilkinson-Shand expression for hepatic clearance, including enzyme activity

(Wilkinson and Shand 1974).

Surrogate Markers

Clinical trials are the standard scientific method for evaluating a new drug,

device, or procedure for the treatment or prevention of disease. The phase three clinical

trial is designed to evaluate the clinical benefit and possible side effects of a new drug

which often requires many participants to be followed for a long period of time. The

primary endpoint should be clinically relevant to the patient and examples include death,

loss of vision, symptomatic events of acquired immunodeficiency syndrome (AIDS), the

need for ventilatory support, and other events causing a reduction in quality of life

(Fleming, Prentice et al. 1994). There has recently been great interest in using surrogate








endpoints such as tumor shrinkage, changes in cholesterol levels, blood pressure, white

blood cell counts, or other laboratory measures to reduce the cost and duration of clinical

trials (Fleming 1994; Fleming, Prentice et al. 1994). Surrogate markers are objective

observations that reliably serve as early indicators for clinically meaningful endpoints

and there should be a demonstrable linkage between the surrogate and the ultimate

endpoint. Surrogate markers are only useful when meaningful correlations with clinical

events are well-established. However, it is a misconception that if a measurable

observation correlates to the desired clinical outcome, then it may be used as a valid

surrogate endpoint. Proper justification for such a replacement requires that the effect of

the drug on the surrogate end point may be used to predict the clinical outcome. Criteria

have been developed to validate surrogate endpoints in clinical trials (Boissel, Collet et

al. 1992). These criteria essentially require that the surrogate must be a correlate of the

true clinical outcome and fully capture the net effect of the drug on the clinical outcome.

Thus, the greatest potential for validating a surrogate is that the surrogate is in the only

contributory pathway of the disease process and that the entire effect on the true clinical

outcome is mediated through its effect on the surrogate.

Although this strict definition leads to the identification of the best possible

surrogate marker, in practice the mechanisms of drugs are often complex or poorly

understood and the validity of a surrogate endpoint may rarely be rigorously established

using these criteria. Thus, it may be argued that such a strict definition of surrogates

limits the information to be gained in a clinical study and that surrogate markers should

be thought of in broader terms. Surrogates can not only predict efficacy but can also be

used to characterize toxicity or undesired effects and these may not necessarily correlate








to the same pathophysiologic process as the effect on the true clinical outcome. Such

surrogates may be termed biochemical markers or "biomarkers" (Colburn 1995; Lee,

Hulse et al. 1995; Colbum 1997; Colburn 2000). Identifying biomarkers enhances the

ability to find more effective and less toxic therapies more accurately and efficiently.

Surrogates for Systemic Effects of Corticosteroids

Surrogate markers are particularly important in the study of corticosteroids since

many corticosteroid effects, desired or otherwise, are either difficult to quantify or

indeterminate during short-term observation. Two such markers have been identified f

the systemic effects of corticosteroids: endogenous cortisol ( ohata Hochhaus et al.

1995) and blood lymphocytes (Meibohm, Derendorf et al. 199 These are easily

measured in blood samples.

Cortisol Suppression

Cortisol is very sensitive to the presence of exogenous corticosteroids and the

release of serum cortisol is often dramatically suppressed after drug administration.

Cortisol suppression has been used as an indication of the amount of corticosteroid

entering systemic circulation after inhalation and has been suggested as a surrogate

marker for the effects on the hypothalamic-pituitary-adrenal axis (Meibohm, Hochhaus et

al. 1997; Meibohm, Hochhaus et al. 1999). However, cortisol is not necessarily a

preferred marker for systemic activity. As stated previously, there should be a close

correlation between a surrogate marker and the relevant effects of the drug. Although the

lack of cortisol can alter the body's regulation of protein, carbohydrate, and fat

metabolism, blood sugar levels, and inflammatory responses as observed in Addison's

disease, when cortisol suppression is induced by the administration of an exogenous








corticosteroid, the presence of the exogenous corticosteroid may compensate for the lack

of endogenous cortisol in systemic circulation. In this case, cortisol is merely replaced by

another corticosteroid, albeit a more potent one in most circumstances.

Lymphocyte Reduction

In this study, the decline in blood lymphocytes was chosen as the surrogate

marker for the systemic activity of corticosteroids. This is an appropriate choice since the

decline in lymphocytes is directly related to the suppression of the immune system often

observed in chronic corticosteroid therapy, whether it be an undesired side effect (Cupps,

Edgar et al. 1984; Pytsky 1991; Wilckens and De Rijk 1997) or the desired clinical

outcome (Wofsy 1990; Dupont, Huygen et al. 1985). Unless stated otherwise, the

discussion of lymphocytes and lymphocyte subsets below is a compilation of information

obtained from general immunology texts and review articles (Hildemann 1984; Paul

1989; Eisen 1990; Kuby 1997; Peakman and Vergani 1997).

The two key features of lymphocytes are specificity and memory. Lymphocytes

are involved in the specific immune defense system and can distinguish foreign cells and

antigens, having mechanisms for selecting a precisely defined target. The second feature

of lymphocytes is memory, allowing immunization and resistance to reinfection with the

same microorganism. Lymphocytes constitute between 25% and 40% of all white blood

cells. Less than 1% of all lymphocytes circulate in the blood, most being found in tissues.

Lymphocyte Subsets

The effects of corticosteroids on lymphocyte subsets were also investigated. Since

different subtypes play different roles in regulating the body's immune response, there is

some interest in the effects of corticosteroids on subtypes, particularly helper T cells








(CD4) and suppressor T cells (CD8) and their ratio (Gerblich, Urda et al. 1985;

Tornatore, Venuto et al. 1998; Gergely 1999). It is generally accepted that proper

regulation of the immune system requires CD4 and CD8 cells be present in a 2:1 ratio.

Lymphocytes are divided into two main classes, bone-marrow-derived (B) and

thymus-derived (T) lymphocytes. Natural killer (NK) cells, a small population of

lymphocytes, do not express characteristics of either T or B cells. Although

morphologically similar, T and B cells are distinguishable by their different cell-surface

components and are classified on the basis of these surface markers. The NK cells may

also be distinguished by these markers.

The cluster designation (CD) is based on surface antigens (designated by

numbers) that can be recognized by specific antibodies. Mature T cells have CD3/CD4

(helper cells) or CD3/CD8 (suppressor or cytotoxic cells), B cells have CD19-CD22, and

NK cells have CD16 and/or CD56. Of the mature lymphocytes in circulation, 20-30% are

B cells, 65-75% are T cells, and less than 5% are NK or null cells.

The B lymphocytes mature in the marrow and migrate directly to the spleen and

the lymph nodes. They are then ready to react to foreign substances (antigens). The

principal function of B cells is to synthesize and secrete antibodies for a rapid response to

extracellular and mucosal microorganisms, including viruses (if part of their life cycle is

spent in the extracellular fluid). When these cells are stimulated by encountering a

foreign antigen, they go through several cycles of cell division and then differentiate into

specialized antibody-secreting plasma cells. Each B cell is programmed to make one

specific antibody. The secreted antibodies typically interact with circulating antigens

such as bacteria and toxic molecules.









The T lymphocytes migrate from the bone marrow to the thymus where they

mature before migrating to the peripheral lymphoid organs (spleen and lymph nodes).

Several subsets of T cells exist and they serve two roles. The first is as the coordinator of

other immune responses, accomplished by their production of a wide variety of cytokines

and surface cell signals (helper and suppressor T cells). The second is as a responder to

long-term intracellular infections and cancerous cells (cytotoxic T cells). The T

lymphocytes do not secrete a single major protein such as immunoglobulin but carry out

their function primarily by direct contact with other cells.

Helper T cells (CD4) recognize foreign peptides on cell surfaces and secrete

factors that stimulate other cells involved in the immune response. For example, CD4

cells stimulate to B cells to bring about proliferation and the secretion of antibodies. The

CD4 cells also activate cytotoxic T cells and natural killer cells. The helper T cells are

central players in most immune responses and are the targets of human

immunodeficiency virus (HIV), the retrovirus that causes acquired human

immunodeficiency (AIDS). The CD4 subset is a common surrogate marker for the

progression of this disease since the loss of helper T cells causes failure of the immune

system.

Suppressor T cells (CD8) can switch off antibody production by suppressing the

action of other cells in the immune system, notably B cells and helper T cells. Suppressor

cells are important for terminating a response to a foreign pathogen but may also prevent

inappropriate immune responses to self-antigens (autoimmunity).

Cytotoxic T lymphocytes also have the CD8 surface marker and have the simplest

mode of action of all T cells. They recognize and kill cells that have foreign peptides on








their surfaces, for example, fragments of viral proteins on the surface of a virus-infected

cell. Tumor cells are also recognized, having proteins that do not normally constitute the

cell. Cytotoxic T cells kill infected or tumor cells by a lysis mechanism or by initiating

programmed cell death (apoptosis) in the target cell and are responsible for the rejection

of tissue and organ grafts.

Null cells or natural killer (NK) cells are large granular lymphocytes derived from

stem cells in bone marrow and are able to kill cells through a mechanism known as

antibody dependent cellular cytotoxicity, similar to cytotoxic T lymphocytes. The NK

cells are spontaneously cytotoxic to a variety of targets, including certain cancer cells.

Combined Effects of Endogenous and Exogenous Corticosteroids

As will be discussed, the degree of systemic activity as indicated by a decrease in

lymphocyte counts depends on the pharmacokinetic disposition of the drug, the potency

of the drug, and the interaction of the drug with endogenous compounds, namely cortisol.

Diurnal variations were previously reported for lymphocytes and subsets (Signore,

Cugini et al. 1985) and later correlated to the circadian rhythm of cortisol (Milad, Ludwig

et al. 1994; Meibohm, Derendorf et al. 1999). Lymphocyte counts are influenced by both

endogenous cortisol and the exogenous administered drug. In addition, exogenous

corticosteroids suppress the release of endogenous cortisol. Thus, to adequately describe

the effects of corticosteroids on lymphocytes with a PK/PD model, both cortisol

concentrations and cortisol suppression by an exogenous corticosteroid must be

considered. A schematic diagram of this model is shown in Figure 1-1.

The ultimate goal of this research was to adapt and apply a previously developed

physiological model for describing the combined effects of endogenous and exogenous



















A PK/PD model for the combined effects of corticosteroids


on blood lymphocytes

ECSs suppress the release,*
EIN, of endogenous cortisol
)I.=


Exogenous Corticosteroids (ECSs)

Direct Effect: ECSs inhibit>
the influx of lymphocytes\
into the blood from the
extravascular space


Lymphocytes exhibit a
circadian rhythm inversely
proportional to that of cortisol
S Indirect Effect: Cortisol
suppression by ECSs results
in less cortisol present to
influence lymphocyte influx


effects of cortisol and an exogenous corticosteroid on blood lymphocytes.


Figure 1-1. A schematic diagram of the PK/PD model for describing the combined








corticosteroids on blood lymphocytes (Meibohm, Derendorf et al. 1999) and subtypes. As

will be discussed, the degree of immunosuppression after the administration of

corticosteroids may be assessed (and later predicted using the PK/PD model) by

monitoring blood lymphocytes, total and subtypes, satisfying many of the criteria for the

validation of surrogate markers stated previously.

Budesonide

Most of the research presented in this dissertation involved budesonide (BUD), a

highly potent corticosteroid indicated for the treatment of lung diseases (Newhouse,

Knight et al. 2000) and other inflammatory conditions such as Chrone's syndrome

(Friend 1998) and psoriasis (de Jong, Ferrier et al. 1995).

As shown in Figure 1-2, budesonide contains an asymmetric 16a, 17a-acetal

group and exists as a 1:1 mixture of the two epimers, 22R and 22S, that have the same

qualitative pharmacologic effect. The 22R epimer is two to three times more potent than

22S (Ryrfeldt, Edsbacker et al. 1984).


CH20H
I CH2CH2CH3

---0

CH3



0//
Figure 1-2. Chemical structure of budesonide.

The clearance of BUD has been reported to be 83.7 L/h, a value close to liver

blood indicating that BUD is a high extraction drug, with a half life of 2.8 h, a steady








state volume of distribution of 183 L, and an oral bioavailability of 10.7% (Ryrfeldt,

Andersson et al. 1982; Thorsson, Edsbacker et al. 1994). The plasma protein binding of

BUD is 88% without affinity to transcortin (Ryrfeldt, Andersson et al. 1982). The major

metabolites are 6p-hydroxy budesonide and 16a-hydroxy prednisolone and there appears

to be no extra-hepatic biotransformation to these metabolites (Edsbacker, Jonsson et al.

1983). However, it has been hypothesized that BUD undergoes reversible conjugation

with fatty acids in vivo to yield palmitates and oleates via an ester linkage (Tunek, Sjodin

et al. 1997; Miller-Larsson, Mattsson et al. 1998). The conjugates could then serve as a

reservoir, providing sustained release of BUD. If these conjugates are present in

sufficient quantities, BUD may exhibit improved lung retention after inhalation and an

improved pharmacological profile with prolonged anti-inflammatory effects in the lung

and a greater local-to-systemic effect ratio (Wieslander, Delander et al. 1998).

Additional Therapeutic Corticosteroids

Other corticosteroids such as triamcinolone acetonide (TA), fluticasone

propionate (FP), and flunisolide (FLU) were investigated to a lesser degree. However, a

considerable amount of effort was invested in describing the pharmacokinetics of

hydrocortisone (HC) or endogenous cortisol. The reason for this is that hydrocortisone

exhibits nonlinear binding to plasma proteins and it was believed that this could effect

both the clearance and distribution of this drug. Various compartmental models were

investigated and a new model was proposed based on the distribution of free drug

between compartments. This model was designed to describe both nonlinear clearance

and nonlinear distribution (a new concept) attributed to the concentration-dependent free

fraction of hydrocortisone in systemic circulation.








Hypotheses

The following hypotheses were tested using either experimental methods,

compartmental analysis of clinical kinetic data, PK/PD modeling procedures for clinical

kinetic and dynamic data, or PK/PD simulations:

1. Corticosteroid binding to plasma proteins and tissues may be determined using in
vitro experimental procedures. These binding phenomena follow the same trends
established for solubility and lipophilicity.

2. The nonlinear binding of hydrocortisone to plasma proteins is responsible for both
nonlinear elimination and nonlinear distribution. For large doses, no singular CL or
Vd term is sufficient for adequately describing the concentration-time profile. The
pharmacokinetics of hydrocortisone may be described for any given dose by using a
free concentration gradient-based distribution model in conjunction with the
Wilkinson-Shand expression for hepatic clearance, which is a function of the
unbound fraction in plasma. This model may be integrated numerically and used to
describe and predict nonlinear pharmacokinetics with various input parameters.

3. The reduction/redistribution of blood lymphocytes may be used as a surrogate marker
for the systemic activity of corticosteroids. The pronounced first-pass metabolism of
budesonide (BUD) precludes the realization of substantial systemic effects for normal
oral doses. However, differential effects may be observed for lymphocyte subtypes.
Systemic effects may be quantified by comparing the area under the effect-time
profiles after placebo to that after budesonide administration.

4. Administration time, potency, pharmacokinetic disposition, the circadian rhythm of
cortisol, and cortisol suppression affect the degree of systemic activity (as measured
by the reduction in blood lymphocytes) observed after corticosteroid administration.
Minimal systemic effects are observed when the administered dose entering systemic
circulation is counterbalanced by the steroid-induced cortisol suppression.
Theoretically, an exogenous corticosteroid may be administered at a dose such that no
net systemic effects are observed.














CHAPTER 2
BINDING TO TISSUES AND PLASMA PROTEINS

Background

Physiological pharmacokinetic models have been used to quantitatively describe

the distribution and elimination of drugs (Chen and Gross 1979). These models differ

from conventional compartmental models in that many (or all) of the parameters have an

anatomical, physiological, or physicochemical basis. One of the most important

parameters in these models is the partition coefficient (Kp). Partition coefficients are

sometimes referred to as distribution coefficients and usually defined as the ratio of drug

concentration in tissue to that in plasma or blood, which is used to estimate the

disposition of the drug (Poulin and Theil 2000). The value of Kp is directly proportional

to the volume of distribution at steady-state and it has been suggested that Kp influences

clearance in addition to distribution (Lam, Chen et al. 1982). The proposed relationship

between Kp and clearance was not considered in the present study and may be subject to

debate.

In addition to describing drug distribution, the degree of tissue binding is

important because, for a given dose, it determines the amount of free drug in the tissue

available for pharmacological activity as only unbound drug may interact with receptors.

One of the best examples of this is the local activity in the lung after corticosteroid

inhalation. It has been suggested that lung tissue partitioning is a critical pharmacokinetic

parameter and the term "pulmonary volume of distribution" has been coined, relating the








amount of drug deposited in the lung to the pharmacologically active free drug

concentration within lung tissue immediately after inhalation (Hochhaus, Mollmann et al.

1997). The pulmonary volume of distribution (Vdpul) is a necessary parameter in the

pharmacokinetic/pharmacodynamic (PK/PD) model used to assess the pulmonary

selectivity of inhaled corticosteroids under ongoing development in our research group.

This model is shown in Figure 2-1. The free concentration of drug in the lung, C(lung),

after inhalation is

D,nh Dnh
Cf (lung) -Dh D -h Eq. 2-1
VdP,, Vng,, K, (lung)

where Dinh is the inhaled dose deposited in the lung, Viung is the volume of the lung, and

Kp is the partition coefficient of the drug into lung tissue. Human lung volume is 1.17 L

(Davies and Morris 1993).

There is no general consensus on the most appropriate method for the

determination of Kp values; Both in vivo and in vitro procedures have been used and good

correlations were observed between the two methods (Kato, Hirate et al. 1987). Although

algorithms have been proposed for assessing Kp values after various routes of

administration (Chen and Gross 1979), the most straightforward experimental design

involves the constant-rate infusion of the drug until steady-state is reached, the time at

which free levels in the plasma and tissue are equal. In vivo partition studies have been

performed for loteprednol etabonate (LE) in rats (Hochhaus, Chen et al. 1992) and for

prednisolone (P) in laboratory rabbits and rats ( Khalafallah and Jusko 1984a and 1984b;

Mishina and Jusko 1994a and 1994b). Fthe LE study in rasnificantly higher levels

were found in liver and kidney compared to other tissues.

































Figure 2-1. Pharmacokinetic/Pharmacodynamic model for assessing pulmonary
selectivity of inhaled corticosteroids.
kdiss-the dissolution rate of drug deposited in the lung after inhalation, Vdpul-the
pulmonary volume of distribution, ka,pul-the absorption rate of drug from the lung into
sustemic circulation, ka,ol-the absorption rate of the swallowed portion of the dose from
the GI tract (gastrointestinal tract) into systemic circulation, CL-total body clearance of
the drug, Vd-the volume of distribution, kr-the first order elimination rate constant.
Roughly 20% of an inhaled dose is deposited in the lung and the remaining
portion is swallowed and subject to first-pass metabolism prior to entering systemic
circulation. The drug deposited in the lung dissolves and the resulting free concentration
in the lung (initially treated as an isolated one-compartment system) is determined by the
pulmonary volume of distribution, dependent on the degree of binding to tissue. Free
drug may interact with corticosteroid receptors in the lung or be absorbed into systemic
circulation. In animal studies, pulmonary selectivity has been defined as the difference in
receptor occupancy between lung and systemic tissues (Hochhaus, Mollmann et al.
1997).








For the steady-state infusion experiment in rabbits, the total P concentration in lung tissue

was 2.9 times greater than the unbound concentration in plasma (Khalafallah and Jusko

1984a).

Few in vivo studies have been reported for human tissue partitioning of

corticosteroids and these involved the inhalation of a drug prior to lung resection surgery.

After budesonide inhalation, the concentration in lung tissue was 8 times greater than that

in plasma (total rather than unbound concentrations) (Van den Bosch, Westermann et al.

1993). After the inhalation of fluticasone propionate, central lung concentrations ere 3

to 4 times greater than peripheral lung concentration", whi"h, nt",m were 10 times
to times

greater than serum levels (Esmailpour, Hogger et al. 1997).
~~-- -- ~*.
In vitro studies have been performed using both human and rat tissues and it was

found that partitioning of aromatic compounds into rat adipose tissue is predictive of

partitioning into human adipose tissue (Pierce, Dills et al. 1996). In order to reach steady-

state conditions during in vitro experiments, sufficient incubation times must be allowed

for complete distribution of drug into the tissues and equilibrium between the tissue and

the surrounding drug solution. These partitioning experiments are commonly performed

by placing a tissue sample in a buffer solution (pH 7.4) containing the drug and

incubating the tissue/solution for 18 to 24 h at 370C (Jepson, Hoover et al. 1994).

Related in vitro experiments have been described for human lung tissue (Hogger

and Rohdewald 1998). Flunisolide (FLU), beclomethasone dipropionate (BDP),

beclomethasone monopropionate (BMP), hydrocortisone (HC), BUD, and FP were

considered in this experiment. In this study, human lung tissues samples were placed in

corticosteroid solutions (0.3 pg/mL) for 1 h. The tissues were then placed in human








plasma for re-equilibration of drug between tissue and plasma. The results were reported

qualitatively and the uptake of drug into tissue exhibited the following rank order:

FP > BDP > BMP > BUD > FLU > HC.

From viewing the diagrams in this publication, the uptake of FP appears to be roughly 2.5

times greater than that of BUD. Tissue concentrations after re-equilibrium in human

plasma exhibited the following rank order:

BDP = BMP < FP < BUD = HC < FLU.

A possible drawback in the design of these experiments is that the solutions used for the

initial uptake of FP and BDP into lung tissue exceeded the aqueous solubilities of these

two drugs. It is not possible to directly compute and compare Kp values from these results

to those in other publications and those in the present study because total rather than

unbound plasma concentrations were reported, tissue concentrations were reported in

units of ug drug/g of tissue (preventing Kp from being expressed as a unitless parameter),

and the experiments were conducted at ambient room temperature rather than at 370C.

In addition to predicting the distribution and free fractions of drugs in tissues,

partition coefficients are of key interest in the design of new therapeutic agents. It has

been shown that the partition coefficient of drugs in a two-phase system of octanol and

water (normally expressed as the log of the partition coefficient, logP) is related to

biological activity (Dunn and Hansch 1974), uptake into tissues (Comford 1982), and

solubility (Valvani, Yalkowsky et al. 1981). Traditionally, the relationship to activity has

been explained in terms of thermodynamics. One the driving forces for the drug-receptor

interaction is the so-called hydrophobic interaction. In the systems involving water as the

polar phase, the hydrophobic effect is always the driving force that governs the








distribution process irrespective of the interacting or noninteracting nature of the

substances studied (Ruelle 2000). For lipophilic drugs in an aqueous environment,

complexation with a receptor results in a favorable change in the Gibb's free energy. This

favorable change (a negative change since energy is released) is often due to an increase

in entropy rather than a decrease in enthalpy.

Estimations of Kp values of new drug candidates using conventional in vitro

and/or in vivo methods is time and cost intensive. For this reason, octanol-water or olive

oil-water is often used to calculate partition coefficients. It has been shown that the

solubility in phospholipids is a function of solubility in octanol-water (Poulin and

Krishnan 1995) and tissue partitioning equations have been developed in which the only

compound-dependent input parameters are the lipophilicity parameters, such as olive oil-

water or octanol-water partitioning, and/or unbound fraction in plasma, fu, determined in

vitro (Poulin, Schoenlein et al. 2001).

Partition coefficients are used in the selection of compounds for further

development. Biological activity was related to lipid-water partition coefficients as early

as 1901 and most modem quantitative structure-activity relationships (QSAR) are based

on octanol-water partition coefficients (Van Valkenburg and American Chemical Society.

Division of Pesticide Chemistry. 1972; Hansch and Leo 1979). The "Hansch approach"

to understanding drug action is based on the assumption that physicochemical properties

governing drug transport and drug-receptor interaction can be factored into electronic,

hydrophobic, and steric components. One of the most widely used equations for relating

biological activity (BA) to these physicochemical properties within a series of

structurally related compounds is








[1i
BA ~ log I =-a. (logP)2 +b logP + p o-+ E, +c Eq. 2-2
SEC50 o

where EC50 is the drug concentration producing 50% of the maximal response, P is the

octanol-water partition coefficient (the hydrophobic factor), a is an electronic factor, Es is

related to steric interactions, and a, b, p, 8, and c are constants (Van Valkenburg and

American Chemical Society. Division of Pesticide Chemistry. 1972; Dunn and Hansch

1974). The expression above is written as a quadratic equation in terms of logP to

account for any nonlinear dependence of drug activity on the hydrophobic character of

the molecule. This is not always the case and a simplified equation,


BA- = a.log P + b, Eq. 2-3


is often sufficient for QSARs (Van Valkenburg and American Chemical Society.

Division of Pesticide Chemistry. 1972; Hansch and Leo 1979). In the case of lipophilic

molecules (such as most therapeutic corticosteroids), relative lipid content (logP) has

been shown to be the sole mechanistic determinant of tissue-plasma partition coefficients

(Haddad, Poulin et al. 2000). To aid in assessing the hydrophobic factors in these

expressions, various empirical and semi-empirical algorithms have been proposed (Flynn

1971; Bodor and Huang 1992a; Bodor and Huang 1992b; Poulin and Theil 2000; Ruelle

2000).

As stated, the degree of plasma protein binding, often expressed as the fraction

unbound (fu), impacts the pharmacokinetic disposition of drugs by modulating the

primary pharmacokinetic parameters, clearance and volume of distribution. In addition, fu

is important from a pharmacodynamic perspective because only free drug is

pharmacologically active. Thus, f, is necessary in most PK/PD modeling procedures.








Objectives

The steady state tissue partitioning of selected corticosteroids was initially

assessed in vitro using lung tissue (rat) to obtain an estimate of the pulmonary volume of

distribution, an important consideration in the pharmacokinetic/pharmacodynamic

(PK/PD) modeling of inhaled corticosteroids. Budesonide (BUD) and triamcinolone

acetonide (TA) were considered because these two corticosteroids were used in previous

animal studies in our group and the data obtained in the present study may be

incorporated into the pharmacokinetic/pharmacodynamic (PK/PD) model used in the

previous studies.

Values of logP were calculated using a semi-empirical quantum mechanical

program and compared to the experimentally determined tissue and plasma binding. This

was done in order to determine the correlation between binding/partitioning phenomena

and other physicochemical properties (stemming from molecular size, shape, structure,

and functional groups) such as aqueous solubility.

Plasma protein binding was determined for various corticosteroids in rat and

human plasma in order to allow total drug concentrations to be converted into

pharmacologically active free levels in the PK/PD model.

In previous animal studies and applications of the PK/PD model for assessing

pulmonary selectivity, receptor binding was used as a surrogate marker for local (lung)

and systemic (various tissues) effects. In these receptor binding studies, receptor

occupancies were reported under the assumption that all binding represented binding to

the corticosteroid receptor and that non-specific binding was minimal. Thus, non-specific

binding in lung cytosol was assessed to validate this assumption.








Tissue Partitioning

Methods

Sprague-Dawley male rats were sacrificed by decapitation. Tissues (lung, liver,

kidney, spleen, brain, heart, and thigh muscle) were immediately removed and excess

blood was removed by blotting the tissues with paper towels. Portions of these tissues

(roughly 0.5 g) were accurately weighed and tissue volumes were determined for these

tissues (n=8) by displacement using phosphate-buffered saline solution (PBS: 24 g

dibasic sodium phosphate, 4 g monobasic sodium phosphate, 4 g sodium chloride in 4 L

distilled water, pH 7.4) in a 10 ml graduated cylinder. The degree of drug partitioning

was determined by placing the weighed tissue samples in 15 ml Falcon tubes and adding

10 mL corticosteroid solution in PBS of known concentration. For BUD, the number of

replications was n=14 and for TA, n=6. Tubes were placed in a rotating rack in an oven

preheated to 370C. Due to the fact that the liver is a metabolizing organ, partitioning into

liver tissue was assessed at 40C to minimize enzyme activity. Tissue samples were

incubated at constant temperature with rotation for 18 h. Tissues were removed and

homogenized in 5 mL distilled water. Portions (1 mL) of the tissue homogenates,

solutions in which the tissues were incubated, and corticosteroid solutions (incubated for

18 h at 370C without the addition of any tissue samples) were extracted with two 2-mL

volumes of ethyl acetate. Extractions were evaporated under nitrogen gas (Meyer N-Evap

analytical evaporator, model no. 112, Organomation Associates, Inc.) and reconstituted in

0.5 mL acetonitrile/water (50:50). Concentrations were determined using reverse-phase

HPLC with a C-18 column (Zorbax SB-C18, 4.6 mm x 7.5 cm, PN866953.902) and a

mobile phase of acetonitrile/water/trifluroacetic acid (50/49.07/0.03). Samples (50 iL)








were injected via an auto sampler (Perkin-Elmer auto sampler model ISS-100). The flow

rate of mobile phase was ImL/min (Milton Roy multiple solvent delivery system

CM4000). Detection was set at 254 nm (Milton Roy programmable wavelength detector

SM4000) and the results were recorded using a Hewlett Packard integrator (model HP

3394A). Calibration standards (1, 2, 5, 10, 25, 50 pig/mL) were prepared from a stock

solution of the drug in methanol.

Tissue masses were converted to volumes using previously determined densities

for each of the selected tissues except muscle. Muscle density was not determined

experimentally and a density of 1.0 g/mL was used for skeletal muscle, as in other studies

(Khalafallah and Jusko 1984b). This enabled the tissue partition coefficients, Kp, to be

determined as a unitless parameter. The Kp values were calculated directly from

experimentally determined tissue and incubation solution concentrations and defined as

K = 7Cissue (ug / mL)2
SCsolUo (pg / mL)

where Ctissue is the drug concentration in the tissue and Csolution is the final concentration

in the incubation solution. The fraction of drug bound to non-water components in each

tissue, reported as a percent (%fbt), was calculated using

K -f,
% fb, =100. K Eq. 2-5
K,

where Kp is the tissue partition coefficient and fw is the fractional water content in tissue,

averaging 0.761 for the tissues considered in this study (Khalafallah and Jusko 1984b).

The percent of total drug that is unbound (%fut) and pharmacologically active drug in the

tissue is

%fu, = 100- fb,. Eq. 2-6








For comparison, octanol-water partition coefficients (expressed as logP) were

predicted for various corticosteroids using a semi-empirical method relating logP to the

structure, size, shape, and functional groups of a molecule (Bodor and Huang 1992a). In

this user-friendly program, the chemical structure of the molecule is entered using a

graphical interface and logP values are generated automatically after optimization of the

ground-state structure of the molecule, based on semi-empirical quantum mechanics and

molecular orbital theory.

Results and Discussion

The results of the density experiments are shown in Table 2-1. Densities were

very close to unity for most tissues. Lung density was slightly less and this value is likely

due to the air content in the tissue immediately after excision.

Calculated Kp values for BUD and TA are shown in Table 2-2 and the calculated

fbt values (expressed as a percentage) are shown in Table 2-3. Previously published

results for prednisolone (P) (Khalafallah and Jusko 1984b) are also included for

comparison. In the experiments conducted in this study, smallest Kp values were

observed for muscle tissue, largest values were observed for liver (BUD) and kidney

(TA). Similar results have been reported for other corticosteroids in vivo with a lesser

degree of partitioning into muscle for P (Khalafallah and Jusko 1984b) and a greater

degree of partitioning into liver and kidney for loteprednol etabonate (Hochhaus, Chen et

al. 1992). The larger standard deviation for liver tissue binding, observed in the present as

well as other published studies, is likely due to the loss of drug through enzymatic

activity (Khalafallah and Jusko 1984b). No distinct trends were observed for partitioning

of BUD, TA, and P into other tissues.








Table 2-1. Densities of selected tissues.
Tissue Density (g/mL)
Lung 0.72 0.12
Liver 1.08 0.06
Kidney 1.07 + 0.21
Spleen 0.94 0.17
Brain 0.98 0.15
Heart 1.07 0.16
Muscle *
*Muscle density was not determined experimentally.


Table 2-2. Partition coefficients (K,) for budesonide (BUD), triamcinolone
acetonide (TA), and prednisolone (P) in selected tissues.
Tissue Kp(BUD) K(TIA Kp (P)
Lung 8.60 2.95 3.01 1.08 2.86
Liver 12.20 + 7.16 7.82 2.64 0.38-4.47
Kidney 8.49 4.01 6.02 + 1.65 2.91
Spleen 7.72 3.30 4.19 1.45 1.16
Brain 5.50 3.21 3.96 1.11 ---
Heart 9.26 3.06 4.71 1.35 2.92
Muscle 2.11 0.44 --- 1.54
Values of Kp for BUD and TA were calculated according to Eq. 2-4 with n=14 and n=6,
respectively. Values for P are previously reported results from other researchers
(Khalafallah and Jusko 1984b).


Table 2-3. Tissue binding (%fbt) for budesonide (BUD), triamcinolone
acetonide (TA), and prednisolone (P) in selected tissues.
Tissue %fbt (BUD) %fbt_(TA) %fbt (P)
Lung 91.2 28> 74.7 26.8 72.6
Liver 93.8 55.0 90.3 30.5 58.7-84.3
Kidney 90 430 J 87.4 24.0 72.8
Spleen 90.1 38.6 81.8 28.3 34.9
Brain 6.2 +500.3 80.8 22.6 59.3
Heart 91.8-3r3 83.8 24.0 72.9
Muscle 63.9 6.8 --- 50.3
Values of %fbt were calculated using Eq. 2-5 and based on the values of partition
coefficients (Kp, Table 2-2) determined experimentally and previous published values of
the fractional water content in each tissue (Khalafallah and Jusko 1984b).








Interestingly, the partitioning of TA into lung tissue was somewhat less than the

partitioning into other tissues. This trend was not observed for BUD and it is possible that

the larger Kp for BUD in lung tissue is be due to the formation of fatty acid conjugates, as

was hypothesized in other publications (Miller-Larsson, Mattsson et al. 1998;

Wieslander, Delander et al. 1998). However, the conjugates were not assayed in the

present study and the importance of these conjugates may not be stated conclusively. In

comparison to TA, a larger uptake of BUD was also observed in vitro in previous human

lung tissue studies (Hogger and Rohdewald 1998).

Predicted octanol-water logP values for various corticosteroids are shown in

Table 2-4. Consistent with the results obtained in the in vitro tissue partitioning

experiments, larger logP values were observed for BUD. With the exception of BMP, the

predicted logP values followed the same trend as drug uptake into human lung tissue

(Hogger and Rohdewald 1998).

Table 2-4. Predicted logP values for selected corticosteroids.
Corticosteroid LogP
TA 1.03
BMP 2.42
Fluticasone 2.63
BUD 3.24
FP 3.89
Values of LogP for octanol-water partitioning were not determined experimentally. The
reported values were calculated using a previously developed semi-empirical quantum
mechanical method (Bodor and Huang 1992a).


Binding to Plasma Proteins

Methods

Whole blood from Sprague-Dawley rats was collected into heparinized tubes

immediately after decapitation or cardiac puncture. Tubes containing whole blood were








centrifuged at 3000 rpm (DYNAC II centrifuge, Clay Adams/a division of Becton,

Dickson, and Company) for 20 min at room temperature to precipitate blood cells.

Plasma was removed with a pipette and placed in borosilicate tubes and refrigerated at

4C while preparations were made to continue the experiment (not more than two hours).

Corticosteroid solutions in rat plasma were prepared using a stock solution of the

drug in methanol to yield a final plasma solution of drug in 0.1% methanol. Dilutions

were also performed with phosphate buffered saline (PBS) solution to provide control

solutions. All solutions were warmed to 370C before filtration. Free drug was separated

from the protein-bound drug by ultrafiltration (Centrifree micropartition device for in

vitro diagnostic use, 30 Kdal cutoff, Amicon Bioseparations, Millipore Corporation).

Three 1-mL portions of the plasma solution and the controls were pipetted into Centrifree

micropartition devices. These were placed into a centrifuge (Beckman Centrifuge model

JA-20) that had been pre-warmed to 37C and centrifuged for 10 min at 4000 rpm (a

force of 1935 g). Less than 20% of the total plasma volume was filtered to prevent

dramatic changes in free concentrations. An optimal filtration time of 10 min was

previously determined by filtration rate experiments as shown in Figure 2-2. Portions of

all solutions were retained unfiltered in order to assess total concentrations. All binding

experiments were performed in triplicate.

Calibration standards, plasma solutions (filtered and unfiltered), and PBS

solutions (filtered and unfiltered) were subjected to the same preparation procedure

before analysis. The procedure was as follows:

Aliquots (100 pL) of each solution to be analyzed were placed in heavy walled

borosilicate culture tubes. Dexamethasone (DEX, 20 ptg/mL in methanol) was used as an









Plasma filtered vs time

100
80
60
E 40-_

0
20 I


0 20 40 60
Time (minutes)

Figure 2-2. Filtration rate of human plasma through Centrifree partition devices.


internal standard (IS) for TA and FLU samples and TA (10 ng/mL in methanol) was used

as an IS in BUD samples. The IS (100 pL) and 800 uiL PBS were added to the samples to

produce a total volume of 1 mL. The TA and FLU samples were extracted with 2 mL of

ethyl acetate, capping and shaking for 15 min in an Eberbach shaker set on low. Tubes

were then centrifuged at 3000 rpm for 10 min. Ethyl acetate was taken off the top of each

tube with disposable glass pipettes and placed into borosilicate culture tubes. The

extraction procedure was performed twice. Samples were evaporated under nitrogen gas

until dry and residues were reconstituted in 100 pL acetonitrile/water (50:50).

The DEX and TA/FLU contents of each sample were determined using reverse-

phase HPLC analysis. The calibration curves for TA and FLU were constructed using

calibration standards in methanol (1, 4, 10, 20, 50 utg/mL). The mobile phase used was

30% acetonitrile and 0.03% trifluoroacetic acid in distilled water. The HPLC system used

for analysis was the same as that described in the previous section regarding drug

concentrations in tissue extractions.








The BUD samples were analyzed separately by a liquid chromatography-mass

spectrometry (LC-MS) assay following solid phase extraction (Lindberg, Paulson et al.

1987; Kronkvist, Gustavsson et al. 1998; Krishnaswami, Mollmann et al. 2000).

Retention of the corticosteroids by the membrane in the filtration device was determined

by comparing concentrations of filtered and unfiltered solutions of the drug in PBS

solution.

A similar method for determining the protein binding of TA, BUD, and FLU in

human plasma was performed using human plasma purchased from Civitan Regional

Blood Center (Gainesville, FL). Experiments were performed within 24 h of obtaining

plasma from the blood center. Plasma was kept under refrigeration and never frozen.

Nonspecific binding of TA and BUD in rat lung cytosol was also determined by

ultrafiltration. The cytosol was prepared according to previously published methods

(Hochhaus, Rohdewald et al. 1983). The binding of TA was determined in undiluted

cytosol and that of BUD was determined in diluted cytosol, cytosol:water (1:3).

The tissue and plasma protein binding data may be combined to estimate the

volume of distribution at steady state (Vdss). This volume term is proportional to the ratio

of the unbound fraction of drug in plasma to that in tissue,


Vds = Vp +V, Eq. 2-7


where Vp is the volume of plasma (-3 L), Vt is the volume of tissue water (-38 L), f, is

the unbound fraction in plasma, and fut is the unbound fraction in tissue. The fraction of

drug bound to plasma proteins (fb) is related to the free (unbound) fraction (fu) by

f, = -fb Eq. 2-8

The unbound fraction in tissue may be calculated using Eq. 2-4 through Eq. 2-6.








Values for Vdss calculated using the f,t determined in the present study would

most certainly underestimate the actual volumes of distribution at steady-state. The

reason for this is that, in general, corticosteroids exhibit pronounced partitioning into

fatty tissues. Since adipose tissue partitioning was not assessed, absolute values of Vdss

may not be calculated accurately. Instead, the ratio of tissue-to-plasma protein binding

was calculated and compared to previously reported Vdss values. Values of the Vdss (and

tissue-to-plasma protein binding ratios) and other relevant parameters for BUD and TA

were correlated. The parameter values for BUD were normalized to those for TA in order

to facilitate comparisons.

Results and Discussion

The results of plasma protein binding in rat and human plasma, expressed as a

percent of the fraction bound (fb), are shown in Table 2-5. Nonspecific binding in cytosol

is given in Table 2-6. There was no significant binding to the filter or the filtration tube

when PBS solutions containing the corticosteroids were filtered.

Table 2-5. Plasma protein binding (% f) of selected corticosteroids.
Species TA BUD FLU
Rat 87.2 5.2 --- ---
Human 68.8 1.8 89.2 + 2.3 71.5 + 3.9


Table 2-6. Nonspecific binding in rat lung cytosol of TA and BUD.
Corticosteroid Cvtosol dilution % fb
TA Undiluted 18.57 3.94
BUD 1:3 16.12 + 7.56

Plasma protein bindings are in close agreement with previously published values

of 71% for TA (Rohatagi, Hochhaus et al. 1995) and 88% for BUD (Ryrfeldt, Andersson

et al. 1982). The fb of 71.5% for FLU is more plausible than the 20% bound reported in

diluted human plasma (Tomlinson, Runkel et al. 1982). Nonspecific binding of








corticosteroids of less than 20% in cytosol is not predicted to be of any consequence in

the interpretation of previously acquired receptor binding data. The reason for this is that

at least 80% of the drug exists as free drug inside the cell and is able to interact with the

receptor. If significant binding occurred, the receptor occupancies determined in previous

studies would need to be corrected for the non-specific binding. This is not the case and it

is likely that any perturbation due to non-specific binding in the receptor binding assay is

within typical experimental error.

Summary and Conclusions

For BUD and TA, there is a very close correlation between the tissue partition

coefficient, solubility, octanol-water partitioning, and receptor affinity. These and other

parameters (normalized to the values for TA) are shown in Figure 2-3. This suggests that

these parameters be strongly influenced by the hydrophobic character (logP) of the

molecules. Thus, although electronic and steric factors can not be completely neglected,

these are not determining factors for tissue distribution and solubility. Trends for receptor

binding and solubility have already been correlated to lipophilicity (Hogger and

Rohdewald 1998). However, these have been established on a qualitative rather than

quantitative basis. From viewing the values tabulated in Figure 2-3, there is a roughly a

3-fold difference in the tissue partitioning/binding, solubility, lipophilicity, and receptor

affinity values between BUD and TA. The larger difference in the RRA ratio suggests

that either TA has some steric hindrance in interacting with the receptor or that BUD has

a more favorable electronic interaction, yielding a more negative change in enthalpy (and

therefore Gibb's free energy) upon receptor binding.

The difference between fu values for BUD and TA is not as great as that between









Normalized Parameters for TA and BUD

A


4


STA
O BUD


RRA Kp logP 1/Sol 1/fut 1/fu fu/fut Vdss

Figure 2-3. Normalized partitioning, binding, and distribution parameters for
triamcinolone acetonide (TA) and budesonide (BUD).
RRA-relative receptor affinity, Kp-experimentally determined tissue partition
coefficient (lung), logP-estimated octanol-water partition coefficient, 1/Sol-inverse
of the aqueous solubility, 1/fut-inverse of the experimentally determined unbound
fraction in tissue (lung), 1/fu-inverse of the experimentally determined unbound
fraction in plasma, Vdss-the volume of distribution at steady-state. Parameter
values not determined in this study were obtained from tabulated data in previous
publications (Rohatagi, Hochhaus et al. 1995; Hochhaus, Mollmann et al. 1997;
Derendorf, Hochhaus et al. 1998; Hogger and Rohdewald 1998).








logP and, therefore, protein binding may not be explained solely on the basis of the

hydrophobic interaction or lipophilicity. There is, however, a very close correlation

between the degree of plasma protein binding and the experimental tissue binding-to-

protein binding ratio as well as the Vdss values obtained from clinical data. This suggests

that despite the inability to calculate absolute values of Vdss directly from the data

acquired in the present study, the in vitro tissue experiments provided an excellent

estimate of the relative overall tissue partitioning of BUD and TA.

It should be noted that the in vitro procedures conducted in this study only reflect

the permeability and/or affinity of the drug to a particular tissue. Perfusion was not a

factor. This is of no consequence when these parameters are used in the PK/PD model for

assessing pulmonary selectivity because the binding in the lung immediately after

inhalation does not depend on perfusion. The Kp value for lung tissue may be used to

convert the amount of an inhaled dose deposited in the lung to the respective free

concentration. By knowing both the concentration and the affinity to the corticosteroid

receptor, initial receptor occupancy may be calculated for a given dose. The decline in

receptor occupancy is proportional to the decline in drug concentration in the lung as the

drug is absorbed into systemic circulation. As stated, there is a 3-fold difference in both

Kp and RRA between BUD and TA. For the same dose, initial free concentrations in the

lung will be 3 times lower for BUD compared to TA. However, the RRA for BUD is

roughly 3 times greater than that for TA. Thus, for a given dose, the same initial receptor

occupancy will be observed for both drugs and any differences in pulmonary selectivity

between BUD and TA are due to the degree of lung deposition, retention of drug in the

lung, the bioavailability of the swallowed fraction of the dose, and the half-life of the








drug once it is absorbed into systemic circulation. Sample calculations are provided in

Figure 2-4 for a 10 pg dose and the inhibition of T cell proliferation. In this example, the

initial effects for BUD and TA were almost identical, at 71% and 70%, despite the

difference in potency (RRA). The dependence of pulmonary selectivity on

pharmacokinetics (namely clearance) has been addressed in previous studies (Hochhaus,

Mollmann et al. 1997) and the results of the present study further support this hypothesis.


Pulmonary Effects of BUD and TA

Anti-Inflammatory Response: Inhibition ofT Cell Proliferation
Inhaled Dose (ug) Cone (ug/L) Effect (%)

BUD: 10 ug C,,, = g ( 1.1 )(8.6) ug/L
S(0fe(1.17)(8.6) (6-----)
n(100%) (.ug / L)
(0.4ug/L + .Oug/L)


Vd, = V,, K
pul lung


TA:


Effect= Emax nc
EC5, + Cone


S(00%) -(2.8ug / L)
(1.2ug / L + 2.8ug / L)

g_/L 0,/


C = 10ug 2.8u
Cfree (1.17L).(3.0)


The pharmacologically free concentration in the lung is determined by the
pulmonary volume of distribution for the drug, budesonide (BUD) or triamcinolone
acetonide (TA). Lung volume (human) is 1.17 L; KP is the partition coefficient of
the drug. Effects (anti-inflammatory response) were calculated using an Ema model.
Figure 2-4. Pulmonary effects for the same dose of budesonide (BUD) and
triamcinolone acetonide (TA) on the inhibition of T cell proliferation.
Calculations were performed using experimentally determined partition coefficients for
BUD and TA into lung tissue of 8.6 and 3.0, respectively, from Table 2-2, a lung volume
of 1.17 L (Davies and Morris 1993), and previously reported EC50 values for the
inhibition of T cell proliferation (Hogger and Rohdewald 1998). A value of 100% was
used as the maximal effect, Emax.


'"














CHAPTER 3
PHARMACOKINETICS OF HYDROCORTISONE


Background Information and Theory

The suppression of endogenous cortisol has been used as a biomarker (discussed

in Chapter 1) in pharmacokinetic/pharmacodynamic (PK/PD) studies of exogenous

corticosteroids (Derendorf, Mollmann et al. 1997). Cortisol is also an important

component in the PK/PD model describing the reduction of blood lymphocytes observed

after the administration of corticosteroids because the number of lymphocytes circulating

in the blood is modulated by the total plasma concentration of corticosteroid, endogenous

plus exogenous (Meibohm, Derendorf et al. 1999). Thus, in order to describe the effects

of exogenous corticosteroids on lymphocytes adequately using a PK/PD model, cortisol

and cortisol suppression must be included in the model. In addition to the usual

pharmacokinetic properties, the cortisol module of the PK/PD model must describe its

circadian rhythm. This has been accomplished using a variable production (or release)

rate of cortisol (Rohatagi, Hochhaus et al. 1995). The degree of cortisol binding to

plasma proteins must also be included because not only does this determine the free

fraction of cortisol that is pharmacologically active (on lymphocytes), as will be

discussed, it may also influence the pharmacokinetic disposition of cortisol.

Both endogenous cortisol and exogenous hydrocortisone were considered this

facet of the present PK/PD study. Determining the effects of nonlinear binding on

pharmacokinetics using only endogenous cortisol data (after placebo) is problematic due








to the variable release rate of cortisol. However, by suppressing the release of

endogenous cortisol with dexamethasone prior to hydrocortisone administration, the

pharmacokinetics of cortisol/hydrocortisone may be assessed in the absence of any

diurnal variations (Derendorf, Mollmann et al. 1991). Therefore, pharmacokinetic models

for hydrocortisone will be discussed prior to addressing the more complex expressions

needed to describe and predict endogenous cortisol levels.

Binding to Plasma Proteins

Hydrocortisone, or endogenous cortisol, exhibits saturable, nonlinear binding to

transcortin and linear binding to albumin (Ballard 1979a and 1979b). This is due to the

high affinity of hydrocortisone to transcortin, a plasma protein present in much lower

concentrations than albumin, and the low affinity of hydrocortisone to albumin. Thus, the

pharmacologically free concentration is not constant but concentration-dependent.

Assuming that hydrocortisone binds only to albumin and transcortin and that there is only

one binding site per protein, the total hydrocortisone concentration may be written as

K, QTr C,
Crota = +I KAIb QAlb C + Cf Eq. 3-1
1+ Kr C,

where Cf is the concentration of free (unbound) hydrocortisone, KTc is the affinity

constant for transcortin (3.0 x 107 L/mol), KAIb is the affinity constant for albumin (5.0 x

103 L/mol), and QTc and QAlb are the normal physiological concentrations of transcortin

and albumin, 0.7 gumol/L and 550 pmol/L, respectively (Ballard 1979b). This expression

may be rearranged to give a quadratic equation in terms of Cf, the free concentration.

After solving the quadratic for Cf, the fraction unbound, fu, may then be determined by

C
f,= 'Eq. 3-2
f,-Cro~o










In order to determine the concentrations at which transcortin saturation occurs, values of


fu were calculated for a large concentration range using these formulae and the nonlinear

binding is shown in Figure 3-1. Total and free concentrations for a smaller range of


concentrations are provided in a separate plot in which nonlinear binding is compared to


a constant binding of 95%.


Unbound fraction of Hydrocortisone
0 .3 ... ........................... ......................
0.3 --- -

0.25

0.2

fu 0.15

0.1

0.05

0
1 10 100 1000 10000 100000
Cp (nglmL)


3J
E


0


Free Hydrocortisone Concentration

14
12 _
10 A
8]


6


S2 j
0 ...

0 50 100 150 200
Total Cone (nglmL)

L--- Nonlinear binding A- Linear binding (95%)
--- J


Figure 3-1. Nonlinear binding of hydrocortisone to plasma proteins.
Values of the unbound fraction (fu) were calculated from total concentrations and average
plasma protein concentrations and binding affinities according to Eq. 3-1 and Eq. 3-2. For
comparison, free concentrations were also predicted using a linear binding of 95%.



For concentrations less than 100 ng/mL, the fraction unbound is relatively

constant, roughly 0.05 (5%). This is apparent in the second plot in which free


concentrations were determined with both nonlinear and linear binding: The predicted


free levels are equal for total hydrocortisone concentrations below 100 ng/mL. However,

for larger concentrations, the nonlinearity is pronounced and the concentration of free


drug rises sharply with increasing total concentrations, reaching a plateau of just over


0.25 (25%) for concentrations above 10,000 ng/mL (10 pg/mL), the concentration at


r
C----- ----~-~--:I'----~r`- i








which transcortin binding sites are saturated and hydrocortisone exhibits linear binding to

albumin. Thus, for a concentration between 0.1 and 10 pg/mL, plasma protein binding is

nonlinear and the pharmacologically active free fraction is concentration-dependent.

Pharmacokinetic Considerations

It has been suggested that nonlinear protein binding leads to dose-dependent

pharmacokinetics of hydrocortisone (Toothaker and Welling 1982; Derendorf, Mollmann

et al. 1991). The same is true for prednisolone, which binds to both albumin and

transcortin (Boekenoogen, Szefler et al. 1983; Rohdewald, Rehder et al. 1987; Rohatagi,

Hochhaus et al. 1995). Nonlinear binding may modulate the pharmacokinetics of

hydrocortisone in two ways.

Clearance. Perhaps the most obvious way by which pharmacokinetics are

dependent on plasma protein binding is by affecting the clearance and, in fact, increased

clearance values have been observed with higher doses. The total body clearance of

hydrocortisone after a 20 mg IV bolus dose (n=8) was reported as 18.2 4.2 L/h

(Derendorf, Mollmann et al. 1991). Noncompartmental analysis of unpublished data after

100 mg hydrocortisone IV (n=5) produced a larger total body clearance, 21.9 3.0 L/h.

These clearance values indicate that hydrocortisone is a low extraction drug with a

variable hepatic extraction ratio. For low extraction drugs, the Wilkinson-Shand equation

for hepatic clearance (Wilkinson and Shand 1974),


CL = QH"CLit Eq. 3-3
QH + CLif,

may be simplified to

CL = CLi,. f, Eq. 3-4









where QH is hepatic blood flow, f, is the unbound fraction of the drug, and CLint is the

intrinsic clearance, a measure of enzyme activity. According to Eq. 3-4, it is obvious that

if fu increases, then CL will increase proportionally. Of course, determining CL for

hydrocortisone presents a complex problem because fu is not constant for concentrations

between 0.1 and 10 utg/mL. To illustrate the dependence of total CL on fu, clearance

values were predicted for a large range of total hydrocortisone concentrations. Values of

CL were calculated using Eq. 3-3 with QH of 90 L and CLint of 365 L/h (estimated using a

total CL of 18.2 L/h and a free fraction of 0.05, the value at low concentrations). The

predicted clearance values are plotted versus hydrocortisone concentrations in Figure 3-2.

In order to illustrate the changes in clearance at lower concentrations, a second plot is

provided with concentration expanded logarithmically. The predicted clearance at 10,000

ng/mL (10 glg/mL) is about four times greater than that at 100 ng/mL (0.1 ptg/mL).



Total Clearance of Total Clearance of
Hydrocortisone 60 Hydrocortisone

60 50
50 40
S40 _


Conc (ngmL) 1 10 100 1000 10000
Cone (ng/mL)

Figure 3-2. Predicted clearance ofhydrocortisone at various concentrations.
Clearance values were calculated using Eq. 3-3. The value of intrinsic clearance (CLint)
was estimated from the published CL value of 18.2 L/h (Derendorf, Mollmann et al.
1991) and fu of 0.05.

Volume of distribution. The second manner in which nonlinear binding may

modulate the pharmacokinetics of hydrocortisone is by affecting the volume of


30 30 -o
S20 20
d 20 J/-- ------------- ~ II 20d?
10
0 10---20 --3----- 510
0 1000 2000 3000 4000 5000 0








distribution. By definition, the volume of distribution is the volume that relates the

amount of drug in the body to the concentration found in the plasma. Assessing the

changes in this pharmacokinetic parameter is somewhat complex because most drugs,

including hydrocortisone, exhibit a distribution phase after IV bolus administration and,

consequently, several volume terms may be defined. Two of these, the volume of

distribution of the central compartment (Vc) and the steady-state volume of distribution

(Vdss) are discussed below.

Both perfusion and permeability control drug distribution. Since most therapeutic

corticosteroids are lipophilic and unionized such that membranes to not present a barrier

for distribution, the distribution of these drugs is perfusion-limited rather than

permeability-limited. If drug distribution is related to blood flow, then highly perfused

organs and tissues such as the liver and kidney should be in rapid distribution equilibrium

with the blood (or plasma). The plasma and well-perfused tissues are often treated as a

homogenous unit generally referred to as the central compartment. This is shown in the

distribution diagram, Figure 3-3. Kinetic homogeneity does not necessarily mean that the

drug concentrations in all tissues of the central compartment are the same at a given time

point. However, it is assumed that any changes in the plasma levels will be reflected

(quantitatively) by changes in central compartment tissue levels (Gibaldi and Perrier

1982). In contrast, drug levels in poorly perfused tissues require a finite time to reach

equilibrium with those in the central compartment. Drug levels in poorly perfused tissues

first increase, reach a maximum, and then decline. After some time, pseudo-equilibrium

is attained between the highly perfused tissues and fluids of the central compartment and

the poorly perfused tissues. Distribution of drug into the poorly perfused tissues may








occur at different rates and, for this reason, poorly refused tissues are often grouped

together into a single peripheral compartment. As shown in Figure 3-3, the hypothetical

peripheral compartment is, at best, a hybrid of several physiologic units (Gibaldi and

Perrier 1982).


Perfusion-limited drug distribution may be described in
terms of physiologic units based on the degree of perfusion
Figure 3-3. Perfusion-limited drug distribution.


The volume of distribution of the central compartment. From a purely

physiological viewpoint, the initial volume of distribution after an IV bolus injection is

the volume of plasma (3.22 L for a 70 kg man) or, if the drug binds to erythrocytes, the

volume of whole blood (5.25 L for a 70 kg man) (Gibaldi and McNamara 1977; Davies

and Morris 1993). In practice, however, there is normally rapid distribution into well-

perfused tissues and initial distribution volumes are larger than 3.22 L when determined

experimentally with a practical lower limit of 7-7.5 L (Gibaldi and McNamara 1978;


Peripheral


Central








Rowland and Tozer 1995). (The apparent volume of plasma proteins, about 7.5 L for

albumin, is a better estimate of the volume of distribution for drugs highly bound to

plasma proteins but not bound to tissues. This volume term is larger since plasma

proteins, and, therefore, protein-bound drugs, equilibrate between plasma and other

extracellular fluids. However, if the drug is restricted to the plasma due to a very high

molecular weight, the volume of distribution tends to approximate the volume of plasma,

about 3 L, Rowland and Tozer 1995). The volume of distribution of the central

compartment, Vc, relates the drug concentration immediately after an IV bolus injection

to the observed plasma concentration. Of course, it must be assumed that no elimination

has taken place and that distribution is minimal. A Vc of 23.9 4.8 was previously

reported for hydrocortisone after a 20 mg IV bolus dose (Derendorf, Mollmann et al.

1991).

Although often overlooked, the experimentally determined Vc may depend on the

degree of binding to plasma proteins. The reason for this is that, despite the rapidity of

the early distribution phase, the extent of distribution into the well-perfused tissues

constituting the central compartment is determined by the ability of the drug to distribute

into tissues, the degree of binding in the well-perfused tissues, and fu (because only

unbound drug can cross membranes). For example, if two drugs differ only in the degree

of protein binding, the drug with the larger fu, i.e., the drug having a greater free fraction

for the same dose, will have a larger Vc after IV bolus. In the present case of

hydrocortisone with saturable protein binding, a larger dose yields a larger fu and Vc is

dose-dependent. Thus, an increase in the dose does not necessarily produce a proportional

increase in the initial concentration observed after IV bolus administration.








The volume of distribution at steady-state. Possibly the best approach to

assessing the effects of nonlinear binding on drug distribution is to consider the steady

state volume of distribution, Vdss. By definition, Vdss is the volume of distribution

(during distribution) at which the free concentration in the central compartment is equal

to the free concentration in the peripheral compartment. In the case of linear kinetics, the

value of Vdss is between Ve and Vdp, the volume of distribution in the terminal phase

(Gibaldi 1969). For most drugs, Vdss and Vdp differ by less than 10% (Gibaldi, Levy et

al. 1978). Although this volume term is short-lived in its ability to relate the amount of

drug in the body to the concentration observed in the plasma after a single dose, under the

assumption that passive diffusion is the primary means of drug transport, Vdss is the

apparent volume of distribution during a constant IV infusion at steady state. The Vdss is

easily calculated from concentration-time data by noncompartmental analysis and may

also be defined in terms of physiological volumes as


Vd, = V + ,- Eq. 3-5


where Vp is the plasma volume (central compartment), Vt is the volume of tissue water

into which the drug distributes (peripheral compartment), fu is the fraction unbound in the

plasma, and fut is the fraction unbound in the tissue. From this expression, Vdss is directly

proportional to the unbound fraction in plasma and inversely proportional to the unbound

fraction in peripheral tissues. The Vt depends on the ability of the drug to cross

membranes and the degree to which drug molecules gain access to intracellular fluids

(Rowland and Tozer 1995). For lipophilic drugs that cross membranes easily, Vt is often

taken to be total body water minus the plasma volume, 38.71 L for a 70 kg man. Without

this assumption, fut and Vt may not be considered independently and only their ratio may








be used in Eq. 3-5. To illustrate how varying the unbound fraction influences the steady

state volume of distribution, Vdss was calculated over a wide range of fu values after

defining fu, as 0.3, estimated from the published Vdss of 33.7 L for hydrocortisone

(Derendorf, Mollmann et al. 1991) and assuming fu is 0.05. See Figure 3-4. (This is a

general illustration of Vdss-dependency on fu with f, varying between 0.001 and 1.0 rather

than the range of hydrocortisone of 0.05 and 0.25 shown in Figure 3-1).

If fu is not a constant, no singular value of Vdss may be used to characterize the

distribution of the drug. Thus, the volume of distribution during a constant rate infusion

for a drug with nonlinear protein binding depends on the infusion rate. Under the

assumptions used to generate Figure 3-3, the Vdss of hydrocortisone (0.05 < fu < 0.25)

may range between 9 and 40 L.



Predicted Volume of Distribution at
Steady State

140
120
100
V,, 80
Vdss60
40
20
0 .- .-.---
0 0.25 0.5 0.75 1
Free Fraction (fu)

Figure 3-4. Steady state volume of distribution with changing f_.
Steady-state volumes of distribution (Vdss) were calculated according to Eq. 3-5 using
fut=0.3 and Vt=38.71 L. Values corresponding to free fractions (fu) of 0.05 and 0.25 are
highlighted to indicate the range of possible Vdss values for hydrocortisone, based on
nonlinear binding to plasma proteins.








Distribution Kinetics and Compartmental Models

The most common approach to the pharmacokinetic characterization of a drug is

to represent the body as a system of compartments and to assume that the transfer of drug

between the compartments and drug elimination may be described using first-order rate

constants (linear kinetics) (Gibaldi and Perrier 1982). The simplest model depicts the

body as a single, homogeneous unit. Thus, this model is commonly referred to as the one-

compartment body model. Portraying the body as a single compartment may be useful for

laying the foundation ofpharmacokinetics, but this is usually an inaccurate representation

for the events that follow drug administration. The basic assumption of the one-

compartment distribution model is that equilibration of drug between blood and tissues

occurs spontaneously (instantaneously) (Rowland and Tozer 1995). In reality, however,

distribution takes time. As mentioned previously, the time required for distribution

depends on tissue perfusion, permeability characteristics of the drug, and the partitioning

between tissue and blood. To account for this time factor in drug distribution, multi-

compartments models are often used, the two-compartment model being the most favored

one based on physiologic considerations (Rowland and Tozer 1995).

The two-compartment model. Although a one-compartment model has been used

to describe the concentration-time profile of hydrocortisone after oral administration

(Toothaker, Sundaresan et al. 1982), a two-compartment model was required to describe

clinical data after IV bolus administration (Toothaker and Welling 1982; Derendorf,

Mollmann et al. 1991). This was due to the pronounced distribution phase observed after

IV administration. For a single IV bolus dose, the two-compartment model may be

written as a simple biexponential curve,








C(t)= A-e-"a +B-e -C' Eq. 3-6

where ac and 3 are macroconstants characterized by the first-order rate constants for drug

transfer out of and into the central compartment, k12 and k21, respectively, and the first-

order rate constant for drug elimination from the central compartment, klo,

2 I
a=(k,1 +k,2 +k2,)+ (k1o +k,2 +k2)2 -4.kko .k21,
2

S)I
S(ko + k,2 + k2,)- {(k, +k,2 +k2 ,)2 4. ko k21
2

and A and B are pre-exponential factors defined in terms of the dose, Vc, and k21,

D (k21-a)
A=
V, ( a)

B D (k2,-l)
Vc (ao P)

A diagram of this model is shown in Figure 3-5.


Compartment 1


Compartment 2


k10
( 1st order elimination rate constant)


Figure 3-5. Two-compartment pharmacokinetic model.


I


I








The two-compartment model adequately described the concentration-time profiles

of hydrocortisone for the dose and dosage forms considered (Derendorf, Mollmann et al.

1991). However, because of the nonlinear processes taking place, parameters obtained

from fitting data to this model must be regarded as dose-specific and may not be used to

predict the disposition of hydrocortisone for other doses. This is especially true if the

distribution- or a-phase is to be accurately described since saturable protein binding is

most apparent at the high concentrations achieved immediately after injection.

Compartmental models and nonlinearity. After considering the potential dose-

dependency of both CL and Vd, new models were tested in which Eq. 3-3 was used to

describe the clearance and Eq. 3-5 was used to describe Vd as each of these equations

allows fu to be treated as a separate variable. These models were based on a one-

compartment system,


C(t) = .e',
Vd

where D is the dose, Vd is the volume of distribution, and ke is the rate of elimination,

QH CLint f
CL QH + CLint f
ke Eq. 3-7
Vd V + V. f


Using the one-compartment model allowed distribution to be described in terms of the

nonlinear fu. (The two-compartment model is formally defined only in terms of Vc, the

volume of the central compartment). Although Eq. 3-5 for Vdss is only true at steady-state

for pharmacokinetic models with distribution, under the assumption that a dynamic

equilibrium is established immediately after drug administration, Vdss is equal to Vd in a

one compartment system. By incorporating the physiologically based expressions for CL








and Vd, intrinsic clearance and overall tissue binding for hydrocortisone may be

determined from concentration-time data.

This model allowed for any deviation from linear pharmacokinetics due to

changes in fu, the data were well-described in the elimination phase, and this model

offered a slight improvement over the usual one-compartment model having constant

values of CL and Vd. However, early time points were severely underestimated due to the

lack of any distribution phase. Several other models were constructed by starting with a

one-compartment system yet allowing Vd to expand. These pseudo-one-compartment

models dramatically improved fitting of the data and although they were interesting

conceptually, they were somewhat empirical, based more on intuition than on sound

physical or mathematical principles.

The two-compartment model was revisited with the first order elimination rate

constant, kio, defined by the Wilkinson-Shand equation for hepatic clearance and the

physiological expression for volume of distribution, Eq. 3-3 and Eq. 3-5, respectively.

This model performed well for individual data sets but the same distribution rate

constants, k12 and k21, could not be used to describe hydrocortisone after different doses

(data after 20 and 100 mg IV bolus doses).

Although some of these models may have worked in practice, they were all

flawed in theory since nonlinear conditions were imposed on functions derived under the

assumption that all processes, namely distribution and elimination, are strictly linear. It

was concluded that Eq. 3-3 was useful for describing nonlinear elimination but that the

distribution characteristics were too complex to be fully described using traditional

pharmacokinetic models. Ultimately, a new model was derived based on the distribution








of free drug by passive diffusion that allowed for nonlinear processes.

Purpose

The objectives of this project were as follows:

1. To investigate the possible nonlinear pharmacokinetics of hydrocortisone;
2. To determine whether or not such nonlinear processes are important for describing
the concentration-time profile of endogenous cortisol in the physiological
concentration range; and
3. To construct a physiological pharmacokinetic model that could produce good fits of
concentration-time profiles as well as provide some insight as to how nonlinear
binding affects these profiles.

Methods

Data from a previously published clinical study of hydrocortisone (single IV

bolus doses of 20 mg administered to eight volunteers) were obtained (Derendorf,

Mollmann et al. 1991). Unpublished data after single IV bolus doses of 100 mg to five

volunteers were also obtained.

Preliminary Calculations

Before compartmental analysis, preliminary calculations were performed to

determine the variability in the unbound fraction (f,,) and other parameters such as the

volume of distribution using concentration-time data after a 20 mg IV bolus dose (n=8).

(In the remainder of this chapter, the unbound fraction of drug in plasma is denoted ful,

designating the central compartment, compartment 1, as a subscript. The overall unbound

fraction in tissues is denoted fu2 rather than fut, indicating the second, or peripheral,

compartment. This notation is used to distinguish between compartment- and time-

dependent parameters, t being the most appropriate symbol for time).

In order to test the hypothesis that nonlinear binding greatly affects the initial

distribution phase of hydrocortisone, values of ful were calculated for each time point for








each subject, averaged, and plotted for each time point with standard deviations. The

volume of distribution was also calculated for each time point, averaged, and plotted. By

definition, the volume of distribution relates the amount of drug in the body at any given

time (Xt) to the concentration observed in the plasma (Cp),

X,
C, (t)
V'

which may be rearranged to give

X,
V, Eq. 3-8
C, (t)

where Vt is the apparent volume of distribution at time t. By relating the amount of drug

eliminated at time t to the area under the curve from time-zero to time t (AUCt), Eq.3-8

may be expressed as

SD. (AUC AUC,)
V, = Eq. 3-9
C, (t) AUC,

where AUCoo is the total AUC (extrapolated to infinity) (Chiou 1972; Niazi 1976a; Niazi

1976b; McNamara, Slattery et al. 1979).

Compartmental Models with Linear and Nonlinear Pharmacokinetics

Individual and average hydrocortisone-time data after IV administration, 20 mg

hydrocortisone to eight patients and 100 mg to five patients, were fitted to different

pharmacokinetic models. The two-compartment model, Eq. 3-6 using microconstants,

was compared to a new two-compartment model having free concentration gradient-

based distribution. (When the conventional two-compartment model was used, the dose,

20 mg or 100 mg, was factored out of the pre-exponential parameters, A and B, and

entered as a constant for each data set). A complete derivation and discussion of the








gradient-based distribution model is provided in Appendix A. In integrated form (suitable

only for linear binding and linear pharmacokinetics), this model is

C,(t) = Ae-a' + B e- Eq. 3-10

where

D(K-f2 -a
A= V2 a Eq. 3-11
V,-(8-a)

and


= V, )
B= V--Eq. 3-12
V,-(a-,p)

In these equations, D is the dose, K is the diffusion coefficient, V1 is the volume of the

central compartment (formally defined as the plasma volume, 3.22 L), and fu2 is the free

fraction of drug in the periphery. The rate constants a and ( are functions of the free

fraction in the central compartment (ful), fu2, VI, and V2, the volume of the peripheral

compartment (formally defined as 38.71 L). From viewing the integrated form of this

new model, it is apparent that there is a close structural similarity to the conventional

two-compartment model. In fact k21, the rate constant in the conventional two-

compartment model describing the transfer of drug into the central compartment from the

peripheral compartment is present in the gradient-based distribution model. However, in

the latter, it is defined in terms of the diffusion coefficient, tissue binding, and the volume

of the peripheral compartment. From Eq. 3-6 and Eq. 3-10 through Eq. 3-12,


k2 K 2
V2


Likewise,









k


This similarity regarding kl2 is found in the expressions included in Appendix A.

Due to the fact that fu, is not constant in the present application to hydrocortisone

data, no integrated solution for the gradient-based distribution model is possible in closed

form. The differential form was used for all hydrocortisone data fitting procedures. The

differential equations are

dC, K- f,,, K.f4
S- _K-f +ko -C, + .C2 Eq. 3-13
dt V, V,

and

dC2 K fI K. fu2
CI C2. Eq. 3-14
dt V2 V,2

where CI is the concentration in the central compartment and C2 is the concentration in

the peripheral compartment. Values of fu, were calculated at a given concentration using

Eq. 3-1 and Eq. 3-2. The values of K and fu2 were variables determined in fitting the data

to the model. The elimination rate from the central compartment (klo) was variable and

defined in terms ofEq. 3-3 and V1 as

QH CLin f-ul
CL Q, + CL,, f,l
k QHCL Eq. 3-15
V, V,

The intrinsic clearance, CLint, was determined in fitting the data to the model and QH was

fixed at an average hepatic blood flow of 90 L (Rowland and Tozer 1995).

The gradient-based distribution model was incorporated into an ExcelTM

spreadsheet to allow simulations to be performed. The model was entered in differential

form and is integrated numerically over 2000 intervals. This allows nonlinear processes,








either clearance or distribution, to be simulated. Two sets of input parameters may be

entered to generate two concentration-time profiles for each simulation. This

comprehensive spreadsheet includes (1) variable simulation times, (2) on/off functions

for linear and nonlinear binding to plasma proteins (albumin and transcortin) with

variable plasma concentrations and binding affinities, (3) on/off functions for hepatic

and/or renal clearance with variable hepatic and/or renal function, (4) plots for plasma

and tissue concentrations (total and free), (5) plots for clearance, volume of distribution

(calculated at each time point using a noncompartmental algorithm), and the unbound

fraction in plasma, and (6) a complete noncompartmental analysis of the simulated

concentration-times profiles. The current version of this spreadsheet is limited to IV

bolus administration and tissue binding is assumed to be linear for all doses.

Simulations with the Gradient-Based Distribution Model

After fitting clinical data (hydrocortisone, 20 mg IV to eight volunteers) to the

gradient-based distribution model in the SCIENTIST program, the fitted parameters were

entered into the numerically integrated model in the ExcelTM spreadsheet in order to

conduct simulations specifically for hydrocortisone. Of particular interest was the time-

dependent volume of distribution. Simulated Vd-time profiles were compared to those

generated from the actual data using the noncompartmental algorithm in Eq. 3-9.

Endogenous Cortisol

The pharmacokinetics of endogenous cortisol were also investigated for future

incorporation into the PK/PD model describing the effects of exogenous corticosteroids

on blood lymphocytes. The circadian rhythm of cortisol was described using a linear

release model (Rohatagi, Bye et al. 1996; Derendorf, Mollmann et al. 1997),









dCon
dC Rc k C C Eq. 3-16
dt o

Rm Rm tmi
R = mx Rma mn tmax < t < tmin Eq. 3-17
Vd (tm. -tmin -24) Vd *(tmax t,, -24)
R max Rmin a tmin

R R t
Rc = m t ma n tmin < t < tmax Eq. 3-18
Vd (tmax min ) Vd (tmax min

where the release rate of cortisol is described by two linear functions (Rc) between the

maximum cortisol release (Rmax) at tmax (6-10 AM) and a minimum release at tmin (8 PM-

2 AM), keCO" is the elimination rate of cortisol, and Vd is the volume of distribution

(Rohatagi, Hochhaus et al. 1995). Cortisol concentration-time data after placebo (n=12)

were fitted to a modified linear release model with gradient based distribution and

nonlinear elimination. This modified model was based on Eq. 3-16 through Eq. 3-18 with

the assumption that cortisol is released into the central compartment (Vd=Vc=3.22 L) and

eliminated by hepatic metabolism (keco"=klo) according to Eq. 3-13 through Eq. 3-15.

For comparison, the same data set was fitted to the linear release model (one-

compartment) used in previous publications with a fixed volume of distribution (33.7 L)

and a first-order elimination rate constant, keCO" (Rohatagi, Bye et al. 1996).

Data Fitting

All data fitting procedures were performed using SCIENTIST (Micromath, Salt

Lake City, Utah), a program that allows models to be entered in either analytic or

differential form. The integrity of the models was compared using the Model Selection

Criteria (MSC), a modified Akaike information criterion generated in the statistics option

in this program. In general, a larger MSC value is indicative of a better description of the

data. The complexity of the model and the number of parameters needed to construct the









model are also factors in determining the MSC.

Results and Discussion

Preliminary Calculations

The results of the preliminary calculations of the unbound fraction in plasma (fl)

for hydrocortisone (HC) data after 20 mg (single IV bolus doses to eight volunteers) are

shown in Figure 3-6.



Free fraction (fu) after 20mg HC (IV)

0.25 ----------------------

0.2

0.15 -

0.1 -

0.05

0 ,
0 2 4 6 8
Time (hr)

Figure 3-6. Free fraction (fi1) of hydrocortisone in plasma.


From comparing these values to those in Figure 3-1, it is apparent that complete

saturation of transcortin does not occur after a 20 mg dose, f"i not having reached the

plateau of 0.25. At roughly five hours after injection, a sufficient amount of

hydrocortisone has been eliminated to allow a dynamic equilibrium to be established

between free and bound drug and ful becomes relatively constant at just under 0.05.

The volume of distribution at various time points is shown in Figure 3-7. In linear

kinetics, the volume of distribution rises from the initial value, Vc, to that in the

elimination phase, Vdp, with the steady state value situated somewhere between Vc and









Vdp. This is clearly not the case for this dose of hydrocortisone wherein Vd rises and then

declines toVdp. The same trend was observed when Vd was simulated using the gradient-

based distribution model and parameters obtained from the analysis of clinical data (20

and 100 mg hydrocortisone, IV bolus administration). The rise in Vd may be explained by

the fact that the large initial ful allows for rapid distribution of free drug into the

periphery where tissue binding occurs. Based on Eq. 3-8, there is a disproportional

decline in plasma concentration in comparison to the amount of drug remaining in the

body, which may be described only by an increase in the volume of distribution.




Vd after 20mg HC (IV) Simulated Vd after 20mg HC (IV)
50 o 50
40 40

Z 30 30
>20 20 --
10 o 10 -
0 o
0 1 2 3 4 0 1 2 3 4
Time (hr) Time (hr)
Time (hr)

Figure 3-7. Calculated volume of distribution after 20 mg hydrocortisone.
For the plot on the left, a noncompartmental algorithm (Eq. 3-9) was used to calculate the
volume of distribution (Vd) at each data time point after the IV bolus administration of 20
mg hydrocortisone (n=8). These were averaged and plotted along with the standard
deviation. For the plot on the right, the volume of distribution was calculated using the
same algorithm for a simulated concentration-time profile. This simulation was
performed using the gradient-based distribution model (Eq. 3-13) with parameters
obtained from fitting clinical data to the model (20 mg doses, n=8).

A large unbound fraction also yields a rapid hepatic elimination at early time

points. The influence of ful on CL was illustrated in Figure 3-2. After reaching steady

state, the time at which free levels in the central and peripheral compartments are equal,








drug begins to flux back into the central compartment where it is tightly bound to

transcortin. The amount of drug removed from the central compartment is

counterbalanced by the amount of drug returning from the peripheral compartment and,

for a brief period, plasma concentrations are relatively constant. In fact, expanding the

ful-time profile logarithmically reveals a slight plateau corresponding to the time at which

the peak Vd is observed. This plot is provided in Figure 3-8.




Log-Log plot of the free fraction (fu)
after 20mg hydrocortisone



Plateau
0.1



0.01
0.1 1 10
time (hr)

Figure 3-8. Free fraction of hydrocortisone in plasma (fu) expanded logarithmically.
The unbound fraction (ful) of hydrocortisone was calculated from clinical data (n=8) and
population average values of protein concentrations and binding affinities. These were
averaged for each time point and plotted along with the standard deviation. Values of ful
were relatively constant at time points around 0.5 h.


In this scenario, there is a disproportional decline in the amount of drug remaining

in the body and the plasma concentration leading to a smaller apparent volume of

distribution. It may then be hypothesized that the binding of hydrocortisone to plasma

proteins, specifically transcortin, is much greater than its affinity to tissues. Similar trends

were observed when the 100 mg data was subjected to this type of analysis. Again, there








was a slight plateau at approximately 0.5 h with very little change in ful from 0.3 to 0.7 h.

Compartmental Models with Linear and Nonlinear Pharmacokinetics

The results of simultaneously fitting hydrocortisone data after a 20 mg or 100 mg

IV bolus dose to a two-compartment model are shown in Table 3-1. This model is

described in Eq. 3-6 in terms of macroconstants. These results may be compared to those

obtained from fitting the same data sets to the new two-compartment model described in

Eq. 3-13 and Eq. 3-14. Parameter values obtained from the gradient-based distribution

model are shown in Table 3-2.


Table 3-1. Parameters obtained from simultaneously fitting 20 mg andl00 mg
hydrocortisone data to a two-compartment model with macroconstants.
Parameter Value SD*
A (ng/ml) 24.9 2.6
B (ng/ml) 16.0 0.7
a (l/h) 6.2 0.8
P (1/h) 0.35 0.02
MSC 2.7
*Standard deviations were generated using the statistics option in SCIENTIST. Clinical
data after 20 and 100 mg hydrocortisone (IV bolus administration) were fitted
simultaneously to a two-compartment model (Eq. 3-6). A single set of parameters was
obtained since the dose was entered as a separate constant, 20 or 100 mg.


Table 3-2. Parameters obtained from simultaneously fitting 20 mg and 100 mg
hydrocortisone data to a two-compartment model with
gradient-based diffusion.
Parameter Value SD*
K (l/h) 223.7 10.4
CLint (L/h) 93.6 4.1
fU2 0.30 0.01
MSC 4.2
*Standard deviations were generated using the statistics option in SCIENTIST. Clinical
data after 20 and 100 mg hydrocortisone (IV bolus administration) were fitted
simultaneously. A single set of parameters was obtained since the dose was entered as a
separate constant, 20 or 100 mg.


A larger MSC value was obtained using the gradient-based distribution model, 4.2









compared to 2.7 for the normal two-compartment model. When the 20 mg and 100 mg

data were analyzed separately (simultaneously fitting 8 data sets after 20 mg and 5 data

sets after 100 mg), the differences in MSC values between the two models were even

greater, at 6.1 and 5.2, respectively, for the gradient-based distribution model compared

to 2.4 and 2.3 for a conventional two-compartment model.

Visibly better fits were obtained using the gradient-based distribution model,

particularly at early time points. This is shown in both Figure 3-9 and Figure 3-10. The

latter is an enlargement of the fitted 100 mg data illustrating that a brief plateau, between

0.5 and 1.5 h, precedes the elimination phase.


Model 20 mg 100 mg
2-Comp '-0m HC after 20 mg IV/2-comp model HC after 100 mg IV/2-comp model
]0- -2500
Model 1
Conventional 750-so 2








2-Comp p a 20 H Cp after 100mg HC V
250
and 500-
K1-

,
Time(h i 2 4n 6
Time ( ) Time (hr)
2-Comp Cp after 20mg HC IV Cp after 100mg HC IV
Model/
Nonlinear 120da we 2500 t t t- t -
Distribution 1ol o 5, o o
and con800cent n
Elimination 6W C IO
S400 CL o10 .
200 500
o0 0.. '
0 2 4 6 8 0 2 4 6 8
Time (hr) Time (hr)


Figure 3-9. Fitted hydrocortisone data after 20 mg and 100 mg.
Hydrocortisone data were fitted to the conventional two-compartment model Eq. 3-6 and
a new distribution model, Eq. 3-13 through Eq. 3-15, based on the flux of free drug down
a concentration gradient.









The conventional two-compartment model was able to accurately describe part of

the concentration-time profile of the 100 mg data set. However, as seen in Figure 3-10,

the predicted profile deviates from the actual data values in the post-distribution phase.


Conventional 2-Compartment Model Gradient-Based Distribution Model

HC after 20 and 100 mg IV CpTotal after 100mg HC IV
2-Comp Model Gradient-Distr Model

10000 10000



I 1000 1000



100 100
0012345
30 1 2 3 4 5
0 1 2 3 4 5
Time (h) Time (hr)


Figure 3-10. Fitted hydrocortisone data after 100 mg IV using a two-compartment model
with gradient-based distribution.
Hydrocortisone data were fitted to the conventional two-compartment model Eq. 3-6 and
a new distribution model, Eq. 3-13 through Eq. 3-15, based on the flux of free drug down
a concentration gradient.


The deviation observed using the conventional two-compartment model is not

observed in the fitted profile using the gradient-based distribution model. In general,

either the 20 or 100 mg data could be described using a conventional two-compartment

model using weight factors but both could not be described simultaneously with the same

set of parameters. In addition to describing the data, this model provided an estimate of

the intrinsic clearance of hydrocortisone and the overall tissue binding, principle

objectives in this study. The unbound fraction in the peripheral compartment (fu2) of 0.3

indicates that the affinity of hydrocortisone to tissues is roughly the same as that to








albumin. Interestingly, this value had been predicted in the preliminary calculations using

the previously reported volume of distribution at steady-state (Vdss) of 33.7 L and a

fraction unbound in plasma of 0.05 (for low concentrations). Using this value for fu2 and

0.26 for ful (the unbound fraction of hydrocortisone in plasma after total saturation of

transcortin), the predicted Vdss is 36.7 L (calculated from Eq. 3-5). This is very close to

the maximum observed in the time-dependent volume of distribution in Figure 3-6. It

may be hypothesized that the maximum Vd in Figure 3-6 corresponds to the steady-state

volume of distribution (formally defined as the Vd at the time when free concentrations in

the central and peripheral compartments are equal).

Although diffusion coefficients are defined in different terms depending on the

application, the value of K determined in this pharmacokinetic model is certainly related

to the membrane permeability of hydrocortisone and logP (Chapter 2). As

discussed in Appendix A, the diffusion coefficient in the gradient-based distribution

model has units of volume-per-time. For this reason, K may be thought of as the

clearance of the drug from the peripheral compartment, assuming drug metabolism

occurs only in the central compartment. With knowledge of the physiological parameters

determined in the analysis of clinical data (diffusion coefficients, enzyme activity, and

tissue binding) and the affinity constants for plasma proteins, it should be possible to

accurately predict the pharmacokinetic disposition of hydrocortisone all doses.

Simulations with the Gradient-Based Distribution Model

To illustrate the usefulness of the gradient-based distribution model, simulations

were performed for two different scenarios. These are shown in Figure 3-11 and 3-12 and

the user interface of the ExcelTM spreadsheet is shown in Figure 3-13.










Total Concentration (Central) Total Concentration (Peripheral)
10000 --- --
S...... .. ....60 -...... ....60--.


o 20
g 1000 50

o o 10
1 0 Q---------------
4 8 10
0.1 .---.. .----- ....... .... ... 0 4 8 12
Time (hr) Time (hr)

Casel -Case2 Casel Case2

Figure 3-11. Simulated concentration-time profiles for different values of K.
These profiles were generated using the gradient-based distribution model. The diffusion
coefficient for Casel was 1 and that for Case2 was 10. All other input parameters and
plasma protein binding characteristics are identical and equal to those for hydrocortisone.


The first scenario is a rather straightforward example illustrating how different

diffusion coefficients (based on the physicochemical properties of the drug as discussed

in Chapter 2) modulate the disposition of the drug. In Figure 3-11, all input parameters

were equal to those obtained in the analysis of clinical data for hydrocortisone (20 and

100 mg IV, Table 3-2) except for the diffusion coefficients. The values for K differ by a

factor of 10 (1 for Casel and 10 for Case2). The smaller diffusion coefficient for Casel

caused a slow partitioning of drug into the peripheral compartment after IV bolus

administration and, as a result, drug concentrations were low (but rather constant) in the

peripheral compartment while the drug was rapidly eliminated from the central

compartment. The concentration of drug in the peripheral compartment for Case2,

however, rose rapidly and showed a rapid decline as well due to the relatively free

partitioning between the central and peripheral compartments. This is a general example

for drugs exhibiting distribution phases and the same would be predicted whether or not

nonlinear distribution or elimination occurs.



































Figure 3-12. Simulated concentration-time profiles for different values of fu.
These profiles were generated using the gradient-based distribution model. The unbound
fraction in tissues for Casel was 0.1 and that for Case2 was 0.9. All other input
parameters and plasma protein binding characteristics are identical to those for
hydrocortisone.


In Figure 3-12, a somewhat more complex scenario is presented. Here, the only

difference is found in the fraction unbound in the tissues (or peripheral compartment)

with all other input parameters equal to those obtained from the analysis of

hydrocortisone data after 20 and 100 mg IV bolus doses. For Casel fu2 equals 0.1 and for

Case2, 0.9. As predicted from general pharmacokinetic principles, the greater degree of

tissue binding in Casel (having a lower unbound fraction) in comparison to Case2 results

in larger concentrations in the peripheral compartment and a larger volume of










distribution. Likewise, this drug exhibits a longer terminal half-life (observed in the


terminal slope of the concentration-time profile for the central compartment), which may


be explained by the high degree of tissue binding and the large volume of distribution.


Although the nonlinear protein binding affects the volume of distribution to some degree


(in that Vd for Casel rises and then declines as was observed for hydrocortisone), the


nonlinear kinetics are much more evident in the clearance.


Two-Compartment Model with Gradient-Based Distribution
An Application of Fick's 1" Law of Diffusion
Hepatic andlor Renal Clearance Linear andlor Nonlinear Binding


^A single diffusion coefficient
Clearance Terms
Lint (L/hr) 100 100
Qhep(L/hr) 90 90
GFR (mlmin) 130 130
Volume Terms
Central: V1 (L) 3.22
Peripheral: V2 (L) 38.71
DAveraoe nhvsiolonical values (70knl


P1 (umo/L) 0.71 0.71 (0.71)}
kal (L/mol^) 30 30 (30)
P2 (umol/L) 573 573 (573)
ka2 (uLmol^-3) 0.005 0.005 (0.005)
Mol wt 362.47 362.47 (362.47)


Transcortin: Low [...], Large ka, Nonlinear
Albumin: High [...], Small ka, Linear
EValues f... for hvdrocortisone binding


fQuick Calc ICtotal I ful Free Conc
Casel (ng/ml) 5000 0.246 1227.72
Case (na/ml 100 0.054 5.37


. v' r---'t ... ....---- --- I
Fful. C(free) based on chosen binding criteria
Terminal Half-Lifes
Casel Case2 Units
Central: Total 3.590 1.210 (hr)
Peripheral 2.878 1.134 (hr)
Central: Free 2.951 1.179 (hr)
Noncompartmental Parameters
Casel Case2 Units
AUC:Central 2.082 1.619 ^3(ng/ml/hr)
AUC:Peripheral 0.787 0.267 ^3(ng/m/hr)
AUC:Central-free 0.235 0.232 '3(ng/ml/hr)
MRT:Central (hr)
MRT:Peripheral (hr)
Vdss (L)
Vdarea 49.77 21.56 (L)
DistributionRate
T to steady state (hr)
CL-average 9.61 12.35 (L/hr)


r


Total Concentration (Peripheral)

250
200
E
,150
100
0 50

0.01 0.1 1 10
Time (hr)
[- Casel --Case2-


Figure 3-13. Interface for the gradient-based distribution model spreadsheet.


. _... i. .. .. [ .. .








In this scenario, a change in the tissue binding indirectly affected the clearance of

the drug from the central compartment by prolonging the time during which there is

nonlinear binding to plasma proteins. Of course, clearance is concentration-dependent

rather than time-dependent and the clearance values of both drugs (Casel and Case2) are

equal for a given concentration. This is evident from viewing the concentration-time

profiles for the central compartment and the clearance profile (immediately below that for

concentration at roughly 2.5 h). For Case2, there is pronounced nonlinearity in the

clearance at early time points, becoming linear at just over 4h. For Casel, however, a

larger fraction of the administered dose partitions into the tissues, reentering the central

compartment over a long period of time, and clearance does not become constant until

roughly 12 h after the dose was given.

Endogenous Cortisol

The results of fitting endogenous cortisol data to the linear release model with and

without the introduction of a second compartment with nonlinear distribution and

elimination are shown in Table 3-3 and plots are contained in Figure 3-14.


Table 3-3. Parameters obtained from modeling endogenous cortisol after placebo.
Parameter Linear Release Model' Linear Release Model2
(normal) (modified)
Rmax (pg/h) 3309.2 2288.1
tmax (h) 20.6 21.9
tmin (h) 18.5 19.1
cort (h-) 0.7 ---
fut --- 0.7
K (L/h) --- 4139.1
MSC 2.1 2.4
'The normal linear release model is a one compartment model with first-order
elimination. See Eq. 3-16 through Eq. 3-18.
2The linear release model was modified to include gradient-based distribution
into the periphery and nonlinear hepatic clearance. See Eq. 3-13 and Eq. 3-15.










Despite having one additional fitted parameter, slightly better fits were obtained

with the gradient-based distribution model compared to the normal linear release model.

However, it may not be necessary to use this model considering that the normal

physiological concentrations of cortisol are much lower than the concentrations of

hydrocortisone analyzed in this study after the 20 and 100 mg IV bolus doses. In

addition, since exogenous corticosteroids suppress the release of cortisol, it is predicted

that the concentrations of cortisol are sufficiently low as to render the inclusion of

nonlinear processes an unnecessary complication in modeling procedures.



Linear release model (normal) Linear release model (modified)
A one compartment model with A two compartment model with gradient-
first-order elimination based distribution, nonlinear elimination
Cortisol after Placebo Cortisol after Placebo
200 200 ... .

160 -i 160

S120 120-
C -
L 80- 80 -

40 40

0 0i i i i
24 30 36 42 48 24 30 36 42 48
Time (hr) Time (hr)
Figure 3-14. Fitted endogenous cortisol data after placebo.
In these fitting procedures, average cortisol concentrations after placebo were used (n=6).
In the gradient based distribution model, it was assumed that cortisol was released into
and eliminated from the central compartment.



Conclusions

Better model selection criteria (MSC) values were obtained when the two-

compartment model was redefined to allow nonlinear distribution and elimination.

Accordingly, the nonlinear model provides better fits of the data, particularly at early








time points. The ful values for hydrocortisone calculated from the total concentrations

and predicted free levels range from 0.04 to 0.19 for a 20 mg dose and up to 0.24 for a

100 mg dose. The results obtained from the preliminary calculations and from the

analysis of clinical data indicate that the nonlinear plasma protein of hydrocortisone is

responsible for nonlinear pharmacokinetics.

In regard to comparisons between the newly developed model and the familiar

two-compartment system, it should be noted that the commonly used two-compartment

body model (Eq. 3-6, Figure 3-5) provides a distribution phase only via the rate constants

ct and p. The pre-exponential factors A and B are defined in terms of Vc and no change

in Vd is taken into consideration per se. However, in the nonlinear model with gradient-

based distribution, Eq. 3-13 and Eq. 3-14, the apparent volume of distribution changes

over time and may be viewed as an inherent component of the model since ful, fu2, VI,

and V2 determine flux from one compartment to the other. Previous models for

describing changes in volume of distribution were based on Eq. 3-5, including either

nonlinear binding in plasma or tissue (Gibaldi and Perrier 1982). As found in the

preliminary calculations and data analysis in the present study, such models are an

improvement over conventional models with constant values for CL and Vd but fail to

describe the distribution phase after IV bolus administration. The manner in which

nonlinear distribution is described in the gradient-based distribution model proposed in

this chapter is unique. Furthermore, this model is unique in its ability to describe both

nonlinear elimination and distribution simultaneously.

Assuming that ful may be calculated using affinity constants for drug binding to

plasma proteins, this model has the distinct advantage of describing nonlinear processes






73


as well as predicting overall tissue binding (or Vt/fu2) and enzyme activity, should hepatic

metabolism be a major elimination pathway. In the event that the drug under

consideration exhibits linear binding to plasma proteins such that ful is constant, the

integrated form of this model may be used and fui treated a fitted parameter. Thus, the

new model allows both distribution into the periphery and elimination to be defined in

terms of physiological properties and established physical principles.














CHAPTER 4
PHARMACOKINETIC/PHARMACODYNAMIC MODELING OF TOTAL
LYMPHOCYTES AND SELECTED SUBTYPES AFTER BUDESONIDE

Introduction

As stated in previous chapters, pharmacokinetic/pharmacodynamic (PK/PD)

models enable the effects of a drug, whether local or systemic, desired or undesired, to be

predicted as a function of time. Systemic effects monitored in previous clinical trials

include decreased bone density and growth (Prummel, Wiersinga et al. 1991; Doull,

Freezer et al. 1996; Allen 1998; Efthimiou and Barnes 1998), blood eosinophil counts

(Pincus, Humeston et al. 1997), hypertension and effects on the cardiovascular system

(Sholter and Armstrong 2000; Maxwell, Moots et al. 1994; Yunis, Bitar et al. 1999),

psychotic symptoms (Curtis, Fogel et al. 1970; Seifritz, Hemmeter et al. 1994), and

cushingoid appearance (Wilson, Blumsohn et al. 2000). Since many of these effects are

often difficult to assess and quantify, the application of PK/PD models in clinical studies

often relies on easily measured surrogate markers, or, in broader terms, biomarkers in the

blood. Two commonly used surrogate markers for the systemic effects of coricosteroids

are cortisol suppression (Derendorf, Hochhaus et al. 1993) and reduction of blood

lymphocytes resulting from their redistribution into peripheral tissues (Fauci 1979).

In the present study, the systemic effects of budesonide (BUD) were monitored

after oral administration. The two formulations considered were Budenofaulk (BF) and

Entocort (EC). BF is a pH-modified delayed release formulation that, in effect, achieves

local delivery of the drug after oral administration for the treatment of inflammatory








bowel diseases and EC is as sustained release formulation. The decline in blood

lymphocytes was chosen as the surrogate marker for the systemic activity of BUD since

this is directly related to the suppression of the immune system often observed in chronic

corticosteroid therapy and is, therefore, clinically relevant. Lymphocytopenia has been

monitored as both a necessary outcome in the treatment of allergic inflammation (Oneda

1999) and an indication of undesired systemic activity in the treatment of asthma

(Fokkens, van de Merwe et al. 1999) or colitis (Van Gossum, Schmit et al. 1998). There

is some indication that successful therapy of asthma results in changes in the ratios of

helper and suppressor T-lymphocytes in both systemic circulation and bronchoalveolar

lavage fluid (Milgrom 1991) although no direct correlation has been found for T cell

downregulation and disease state indices (Majori, Piccoli et al. 1997).

From Chapter 1, subclasses of lymphocytes play different roles in regulating the

immune system. Knowledge of how corticosteroids influence the number of cells in

circulation could allow immunosuppression to be monitored and predicted more

effectively. Pharmacokinetic-phamacodynamic (PK/PD) modeling has been used to fit

and predict cortisol levels and total lymphocyte counts following corticosteroid

administration (Derendorf, Hochhaus et al. 1993). Although lymphocyte subsets have

been monitored in various clinical trials (Boss, Neeck et al. 1999; Fokkens, van de

Merwe et al. 1999; Milner, Kent et al. 1999), previous PK/PD studies of lymphocyte

subpopulations were limited to CD4 and CD8 after methylprednisolone (Milad, Ludwig

et al. 1994) and CD3 and CD8 after prednisone (Imani, Jusko et al. 1999). Since

lymphocytes are modulated by both endogenous and exogenous corticosteroids, the

present PK/PD study was conducted to assess the combined effects of budesonide and








cortisol on total lymphocytes and all relevant subclasses. Representative subpopulations

were chosen for total T cells (CD3), helper T cells (CD4), suppressor T cells (CD8), B

cells (CD19), and natural killer or NK cells (CD56 and/or CD16).

Clinical Procedures

Single doses of budesonide, Budenofalk (BF) and Entocort (EC), and placebo

were administered at 8 AM to the same group of volunteers. Five subjects received 3 mg

BF, four received 9 mg BF, and five received 9 mg EC. Placebo capsules were

administered to six subjects in the study. A commercially available radioimmunoassay

(RIA) was used to determine cortisol concentrations and BUD concentrations were

determined by HPLC/RIA analysis with a sensitivity of 0.133 ng/mL (Hochhaus,

Froehlich et al. 1998). Cortisol levels and lymphocyte counts (described below) were

determined at the Medical Clinic Bergmannsheil, University of Bochum, Bochum,

Germany and quantitative analysis of BUD was performed at the Department of

Pharmaceutics, University of Florida, Gainesville, FL.

The Blood samples were collected into tubes containing EDTA for total

lymphocyte counts and containing heparin for subset analysis. Total leukocyte counts and

percentages were measured using an automated cell counter (Coulter STKR).

Lymphocyte subsets were analyzed by flow cytometry (FACSCalibur and Simulset

software, Becton Dickinson). Each blood sample had a concurrent sample containing

CD54 FITC and CD14 PE analyzed to insure proper gating techniques. An isotypic

control was utilized to identify any non-specific binding attributed to the monoclonal

antibodies used. Total T cells were measured using anti-CD3. The CD4+ cells were

defined by dual staining with anti-CD3 and anti-CD4 and CD8+ cells were defined using








anti-CD3 with anti-CD8. The number of B cells was measured using anti-CD19. Natural

killer cells were CD3-expressing CD56/CD16. The CD56 and CD16 subsets were

measured collectively. Aliquots of blood were incubated with antibody pairs for dual

staining for 15 min at room temperature. Erythrocytes were lysed and fixed using FACS

Lysing solution and cells were analyzed within 4 h after fixation. All monoclonal

antibodies were obtained from Becton Dickinson.

Pharmacokinetic/Pharmacodynamic Modeling of Blood Lymphocvtes

Various aspects of the PK/PD model describing the combined effects of

endogenous and exogenous corticosteroids on lymphocytes were discussed in preceding

chapters. The complete model is presented here. A modular assembly concept was used

to construct the PK/PD model and each of the procedures is discussed below.

Budesonide Concentrations

The modeling of the kinetic data for the single oral doses of 3 mg BF, 9 mg BF,

and 9 mg EC was performed using a two-compartment body model with first-order

absorption and first order elimination. A lag time (Tiag) was used to describe the time

delays in absorption exhibited by the two formulations. This pharmacokinetic model is

A -a.(T-r,, B p.,+B) A B -ke-*(t-T)
C, (t)= --A .e + --. e ---+ B ]-e -
(ka a) (ka p) (k a) (ka f)

Eq. 4-1

where ka is the absorption rate constant, Tiag is the lag time between the time of

administration and the start of GI absorption, a and 3 are macroconstants defined in

terms of the microconstants (first-order rate constants for drug transfer between the

central and peripheral compartment and elimination from the central compartment), and

A and B are pre-exponential factors defined in terms of dose, bioavailability, and the









volume of distribution of the central compartment (discussed in Chapter 3). Fitted values

of ka and p were converted into the absorption half-life (tl/2abs) and elimination half-life

(t/2elim), respectively, using

ts ln[2] and ln[2]
tl/2obs k- and tl/2elim -
ko P

Individual concentration-time profiles (after administration of a given dose and

formulation) for each volunteer were fitted to this pharmacokinetic model.

Pharmacokinetic parameters for a given dose/formulation (3 mg BF, 9 mg BF, or 9 mg

EC) were averaged prior to subsequent PK/PD modeling procedures. Average parameter

values and standard deviations are reported. Although the program used in the fitting

procedures contains a statistics option, averages and standard deviations of all

pharmacokinetic parameters were calculated manually from the results obtained from

fitting individual data sets to Eq. 4-1.

Circadian Rhythm of Cortisol

The circadian rhythm of endogenous cortisol after placebo was described by a

linear release model (Rohatagi, Bye et al. 1996; Derendorf, Mollmann et al. 1997),

dCo" = Rc k Ccon Eq. 4-2
dt

R R -t*
R Rmax R max m tmin ,tmax < tmin
Vd .(tmi trin -24) Vd (tm. tmn -24) '
Rmax mmna "ma m

R R t
Rc max Rmax min tmin < t < tmax
Vd ( max -tmin ) Vd (max in

where the release rate of cortisol is described by two linear functions (Rc) between the

maximum cortisol release (Rmax) at tmax (6-10 AM) and a minimum release at tmin (8 PM-








2 AM), kco1 is the elimination rate of cortisol, and Vd is the volume of distribution fixed

at a predetermined value of 33.7 L (Derendorf, Mollmann et al. 1991; Rohatagi,

Hochhaus et al. 1995). Placebo cortisol data was averaged (n=6) and fitted to this model

in order to determine values of Rmax, tmax, tmin, and keco" for this particular group of

subjects. Standard deviations were obtained from the statistics option in the program used

for the fitting procedures (SCIENTIST, discussed below). The values of these parameters

were fixed prior to subsequent modeling procedures.

Cortisol Suppression

The expression for baseline (placebo) cortisol in Eq. 4-2 may be modified to

include the suppression of cortisol by budesonide. By incorporating an Emax-based

expression, the cortisol release after budesonide administration may be described by

dCon ( C Bud
R C I Jud kCort -Cco" Eq. 4-3
dt c EC C +CBud e

where Cfud is the free budesonide concentration in plasma, EC5oB-c is the free

budesonide concentration that reduces the release of cortisol by 50%, Ctotcor is total

cortisol concentration, and kecot is the first-order elimination rate of cortisol (Rohatagi,

Bye et al. 1996; Derendorf, Mollmann et al. 1997). Total budesonide concentrations were

converted into unbound concentrations using a fraction unbound of 0.12 (Ryrfeldt,

Andersson et al. 1982). Since most of the parameters in this model had been obtained

previously from the analysis of placebo data, ECs0Boc was the only parameter obtained in

the PK/PD analysis of treatment data (cortisol levels after the administration of BUD).

Average values and standard deviations are reported (obtained from the statistics option

in the program used for the modeling procedures). Values of ECsoB-c for a given








dose/formulation (3 mg BF, 9 mg BF9, and 9 mg EC) were determined and reported

separately in terms of the free levels.

Nonlinear Binding to Plasma Proteins

Since cortisol exhibits nonlinear binding to transcortin in the physiological

concentration range (Ballard 1979b), a nonlinear binding algorithm (Meibohm,

Derendorf et al. 1999) was used to determine unbound concentrations. This was

necessary because the pharmacologically active unbound fraction is not constant but,

rather, concentration-dependent. Cortisol binds to albumin and transcortin, and total

cortisol concentration (Ctotcot) can be described according to


Clon KTC Q, C Co KAlb Alb Cor CorC or
t 1+ KTC C" 1+KAb CCort

where KTc is the affinity constant between cortisol and transcortin (3 x 107 L/mol), KAIb

the affinity constant between cortisol and albumin (5 x 104 L/mol), QTc the total

transcortin concentration (0.7 itmol/L), QAlb the total albumin concentration (550

pmol/L) (Ballard 1979b), and Cfc0" the unbound cortisol concentration. Since binding to

albumin in the physiological cortisol concentration range is approximately linear

(KAlb-CfCOn << 1), a simplified form may be used

K c .C'cort
CcO 1 QTC + KAb .QAb Ccori Cr Eq. 4-6
1+ K, Co

Solving for Cfc" yields the unbound concentration responsible for the fluctuations in

lymphocyte counts observed for baseline (placebo) conditions. Free cortisol levels were

calculated from average cortisol data prior to modeling lymphocyte-time profiles, both

placebo and treatment.









Lymphocytes after Placebo

An indirect response model was used to characterize the transient depletion of the

lymphocytes from blood induced by the circadian rhythm of cortisol (Wald, Law et al.

1992; Mollmann, Wagner et al. 1998). In this model, the number of lymphocytes N in the

blood is described by a zero-order influx of cells (rate constant kin) and a first-order

efflux of cells (rate constant kout),

dN Em CCor
=k i. 1 -ma- k,, N
dt ECoL + cEq. 4-7


where Ema is the maximum effect of cortisol (or corticosteroids in general) and ECsoc-L

is the cortisol concentration producing 50% of Emax. Average lymphocyte-time profiles

(n=6) for total lymphocytes and the CD3, CD4, CD8, CD19, and CD56/16 subtypes after

placebo were fitted to this model. As discussed below, placebo and all treatment data for

a given lymphocyte type were fitted simultaneously. This was done in order to minimize

the error likely to occur when EC50C-L and Emax are determined from fitting only the

small effects of endogenous cortisol on lymphocytes.

Lymphocytes after Budesonide

The combined pharmacodynamic effects (Ariens 1954; Meibohm, Derendorf et

al. 1999) of budesonide and cortisol on lymphocytes was described by


dN
dt '


( 8ECBL
S B 50 -kCo
..max / EC-, L C
+ EC50 +ku N
B-4L Bud E+ B C outCor
ECso +C. + C-C'
so 1' ECS 1L


where Emax is the maximum effect of cortisol and budesonide on the influx of


Eq. 4-8








lymphocytes, Cfot is the unbound cortisol concentration, and EC50B-L and EC50C-L are

the unbound concentrations of budesonide and cortisol, respectively, which produce 50%

of Emax. Average lymphocyte-time profiles for each lymphocyte type after a given

treatment were fitted to this model simultaneously with average placebo data. For

example, average total lymphocyte data after placebo (n=6), average total lymphocyte

data after 3 mg BF (n=5), average total lymphocyte data after 9 mg BF (n=4), and

average total lymphocyte data after 9 mg EC (n=5), four average data sets in all, were

fitted simultaneously to the models in Eq. 4-7 and Eq. 4-8 in order to determine kin, kout,

Emax, EC50BL, and ECsoc-L for total lymphocytes. Both ECsoBL and ECsoc5 L values are

reported as free levels. This same procedure was used to determine these parameters for

the selected subtypes. Parameter values were reported along with the standard deviations

obtained from the statistics option in the SCIENTIST program.

Multi-Step Modeling Procedure

Absolute lymphocyte counts were converted to a percentage of the initial count at

8 AM. All fitting procedures were performed using the SCIENTIST software package

(SCIENTIST 1993). Analysis was performed step-wise, beginning with the kinetic data

and cortisol data after placebo. Cortisol data after budesonide was then analyzed to

determine the degree to which cortisol was suppressed for a particular dose and

formulation. Due to the small overall effects on lymphocytes, lymphocyte data after

budesonide (3 mg BF, 9 mg BF, and 9 mg EC) for a given type (total or subpopulation)

were analyzed simultaneously with placebo data for that type. Average values and

standard deviations for the lymphocyte module in the PK/PD model were obtained from

the statistics option in the SCIENTIST program and compared using Tuckey's multiple








comparison test with a 95% confidence interval.

Noncompartmental Analysis

The area under the curve (AUC for the concentration-time or effect-time profile)

was calculated for all pharmacokinetic and pharmacodynamic data. For the

pharmacokinetic data, AUCs were calculated using the trapezoidal rule for a 24-hour

period (the duration of the clinical study) and the terminal AUC was determined by

extrapolating the concentration-time profile to infinity using the terminal slope, obtained

from a semi-logarithmic plot (natural log of the concentration versus time) of the data.

Total AUCs were calculated, averaged, and reported with the standard deviation for each

dose/formulation of BUD. The AUCs of the pharmacodynamic data (cortisol-time and

lymphocyte-time profiles) were determined for a 24-hour period (the duration of the

clinical study) for both placebo and treatment data using the trapezoidal rule. No attempt

was made to extrapolate treatment profiles back to baseline (placebo) levels/counts. The

AUCs of the dynamic data were then used to compute the net effects of BUD on both

cortisol and lymphocytes over a 24-hour period. These cumulative effects were calculated

as follows:

The cumulative cortisol suppression (CCS) was calculated according to

AUC AUC
CCS = 100 Uplacetbo- rat Eq. 4-9
A UCplacebo

where AUCplacebo is the 24-hour AUC for placebo cortisol data and AUCreat is the 24-

hour AUC of the cortisol-time profile after budesonide administration.

The cumulative lymphocyte reduction (CLR) was calculated in a similar manner,

AUC -AUC
CLR = 100 placebo rea Eq. 4-10
AUCplacebo








where AUCplacebo is the 24-hour AUC for placebo lymphocyte data and AUCtreat is the 24-

hour AUC of the lymphocyte-time profile after budesonide administration.

Average values for CCS and CLR are reported with standard deviations. Since

these parameters are based on both placebo and treatment data, which differ in sample

size, the standard deviations (SD) were calculated using a weighted average of the sample

variances,



[ (n, -1) S + (n -21)-
SDn I S Eq.4-11
(n, + n2 2)

where Si and S2 are the standard deviations (the square root of the sample variance) of

the two quantities (in this case, the AUC of placebo data and the AUC of treatment data)

and nl and n2 are the respective sample sizes, and expressed as a percentage of the values

of CCS and CLR.

Results

Pharmacokinetic parameters (lag times, rate constants, and pre-exponential

factors) obtained from fitting budesonide-time profiles to a two-compartment model in

macroconstants are listed in Table 4-1 along with the total areas under the concentration-

time profiles extrapolated to infinity. Plots of the fitted concentration-time profiles

(average data with standard deviation) after 3 mg BF, 9 mg BF, and 9 mg EC are

provided in Figure 4-1.

From the analysis of placebo cortisol data using Eq. 4-2, kcort was 0.61 0.07 h'

and the AUC24 (the area under the cortisol-time profile over a 24-hour period) was 1521

366 ng/mL/h. The maximum release of cortisol (Rmax) was 2853 280 ng/mL/h. The

times of maximum and minimum cortisol release, tmax and tmin, were 5 AM 1.5 h and


~








1:30 AM 1.4 h, respectively.

Values of EC5oB-+ obtained from fitting cortisol data after budesonide

administration (3 mg BF, 9 mg BF, and 9 mg EC) to the PK/PD model in Eq. 4-3 are

provided in Table 4-2 along with the areas under the cortisol-time profiles (for a 24-hour

period) and the cumulative cortisol suppressions (calculated according to Eq. 4-9). For

comparison, parameters from the analysis of placebo data are included in Table 4-1. Plots

of the fitted data are shown in Figure 4-2.

Table 4-1. Pharmacokinetic parameters of budesonide.


Parameter
Tlag (h)
A (ng/mL)
B (ng/mL)
tl/2abs (h)
tl/2elim (h)
a (h-')
MSC (average)


3 mg BF*
3.47 0.55
9.15 6.17
1.98 0.74
0.12 0.05
3.15 0.92
3.09 2.33
4.11


9 mg BF*
3.24 0.65
5.78 2.16
2.98 2.19
0.09 0.05
2.48 0.31
0.89 0.74
4.93


9 mg EC*
0.78 0.25
7.12 3.95
2.55 1.57
0.36 0.16
4.56 1.17
2.96 1.49
2.71


AUCo (ng/mL/h) 12.48 6.13 16.22 4.84 15.49 8.19
*Budenofaulk (BF), Entocort (EC).
Lag times and absorption/elimination half-lives were obtained from individual fitting data
to a two-compartment, Eq. 4-1. The area under the curve (AUC) of the budesonide-time
profile was calculated using the trapezoidal rule and extrapolating to infinity. Standard
deviations were calculated manually.

Table 4-2. Parameters from the analysis of cortisol data after oral budesonide.
Parameter Placebo 3 mg BF 9 mg BF 9 mg EC
EC5os-C (ng/mL) --- 0.09 0.04 0.05 0.04 0.08 0.03
AUC24(ng/mL/h) 1521 366 1448 167 1313 126 1093 224
CCS (%) --- 4.8 + 0.9 13.7 + 2.5 28.2 6.3
Rmax (ng/mL/h) 2853 280 --- --
tmax (h)* 0500 + 1.5 -
tmin (h)* 0130 1.4 --
keco" (h-') 0.61 0.07 ---
*Military time.
PK/PD parameters of cortisol after placebo and budesonide are described in Eq. 4-2 and
Eq. 4-3, respectively. EC50B-c is expressed in terms of free BUD concentrations. The
area under the curve (AUC) was determined using the trapezoidal rule for a 24-hour
period. The cumulative cortisol suppression (CCS) was calculated according to Eq. 4-9.
Standard deviations for AUC24 and CCS were calculated manually and those for model
parameters were obtained from the statistics option in SCIENTIST.












Budesonide after 3mg BF


6 12 18 24
Time (hr)


Budesonide after 9mg BF


4 -


3-

2-

1


0


12
Time (hr)


Budesonide after 9mg EC


18 24


Time (hr)
Figure 4-1. Fitted budesonide-time profiles for 3 mg and 9 mg BF and 9 mg EC.
Two formulations of budesonide, Budenofalk (BF) and Entocort (EC), were
administered. Sample sizes were 3 mg BF (n=5), 9 mg BF (n=4), 9 mg EC (n=5).
Pharmacokinetic data were fitted to a two-compartment model with first-order absorption
and elimination, Eq. 4-1. A lag time was included to describe the delay in the release of
budesonide from the two formulations.












Cortisol concentration after placebo


6 12
Time (hr)


18 24


Cortisol concentration after 9mg BF


6 12
Time (hr)


TiFoure A4-2


18 24


0 6 12
Time (hr)


18 24


0 6 12 18
Time (hr)


ettiF d cortisol-time p .


24


Average cortisol data after placebo and oral budesonide were fitted to the linear release
model, Eq. 4-2 and Eq. 4-3, respectively. Two formulations of budesonide, Budenofalk
(BF) and Entocort (EC), were administered. Sample sizes were 3 mg BF (n=5), 9 mg BF
(n=4), 9 mg EC (n=5). Dotted lines in the 3 mg BF, 9 mg BF, and 9 mg EC plots
represent the cortisol-time profile after placebo (simulated using parameters obtained
from fitting cortisol data to Eq. 4-2).


350


Cortisol concentration after 9mg EC


P; A-


Cortisol concentration after 3mg BF








The NK subpopulation data (CD56 and/or CD16) did not fit the present PK/PD

model. All other subtypes and total lymphocytes were well-described by the model.

Parameters obtained from fitting baseline lymphocyte-time profiles (after placebo) to the

PK/PD in Eq. 4-7 are contained in Table 4-3 along with the areas under the lymphocyte-

time profiles. Fitted data are shown in Figure 4-3.

The ECsoB-L values obtained from fitting lymphocyte-time profiles after budesonide

administration to the PK/PD model in Eq. 4-8 are shown in Table 4-4. The fitted data for

total lymphocytes and subtypes (CD3, CD4, CD8, and CD19) are shown in Figure 4-4

and Figure 4-5, respectively. A general trend was observed in that the ECsoB-L value for

the CD8 subtype was larger and those for CD4 and CD19 were somewhat smaller.

However, due to the large standard deviations, these values are not statistically different.

Results for the areas under the lymphocyte-time profiles and the cumulative

lymphocyte reductions are provided in Table 4-5.

Conclusions and Discussion

Budesonide

As shown in Figure 4-1, the BF formulation exhibits a considerable lag time

before the release of budesonide, roughly 3.5 h. However, once absorption begins,

concentrations increase rapidly. The sustained release characteristics of the EC

formulation are represented in the slow rise in BUD concentrations. The differences in

these two formulations are also seen in the fitted model parameters in Table 4-1. The EC

formulation has a longer absorption half-life as well as a longer elimination half-life. It is

likely that the sustained release of BUD influenced the elimination half-life calculated

from the terminal slope.











Total after placebo CD3 after placebo CD4 after placebo



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0 24 0 12 1 24 0 6 12 IS 24
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CD8 after placebo CD19 after placebo CD56/16 after placebo




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;2 1. Ji 0 2. 50.
0 5 12 15 24 0 5 12 18 24 5
Time (hr) Time (hr) 0 6 12 IB 24
Time (hr)

Figure 4-3. Fitted lymphocyte data (total and subtypes) after placebo.
Average lymphocyte data (n=6) were fitted to the PK/PD model in Eq. 4-7 describing the
effect of the circadian rhythm of endogenous cortisol on lymphocyte counts. The
CD56/16 subtype did not fit the present PK/PD model. The data are shown here and were
subjected only to noncompartmental analysis.


















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