Pharmaeodynamics and
`Drug Development
`Perspectives in
`Clinical Pharmacology
`
`Ediiea‘ by
`
`Neal R. Cutler
`Cahfomia Clinical may, Beoei‘e‘y High, Cahfomia, {ISA
`
`John j. Sramek
`Cafflromia Ciirzim? fiiais, Bever‘bs E3535, Calsfomio} USA
`
`Prem K. Narang
`PSzmmacia Adria, Chaim! PfiannacoiogyjPharmacokizzesies, Cofiumfms, Ohio, USA
`
`ISBN WILEY 8: SONS
`Chiehester - New York - Brisbane ' Toronto - Singapore
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`Cepyright re 1994 by 30in: Wiley & Sons Leif
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`*except Chapter 12 which is in the public demairi.
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`All rights reserved.
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`Library of Ceagress Caraiegiizgwin-Pubfica55m: Data
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`Pharmaeodynamiee and drug development : perspectives in clinical
`pharmacology! edited by Neal R. Cutler, Icahn I. Sramek and Prem K.
`Narang.
`cm.
`p.
`Includes bibliographical references and index.
`{SEN 0 4’31 95052 1
`
`1. DrugsmPliysielogical effect.
`Prem K.
`III. Sramek, John I.
`[DNLM1 l. Phermaeelogy) Clinical. QV 38 P3318 1994]
`RM300.P48 1994
`615'.?—dc20
`
`I. Cutler> Neal R.
`
`II. Nai‘ang,
`
`DNLMIDLC
`fer Library of Congress
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`94’6103
`{ZIP
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`31 catalogue record for {his book is available from the British Library
`
`ISBN 0 4?} 950 521
`
`Typeset in 10; 12 pt Plantiri by
`Mathematical Compesitien Setters Ltd1 Salisbury, Wiitshire
`Printed and l'JGuI'lCi in Great Britain by
`Beekeraft (Bath) Ltd, Midsmner Norton, Avon
`
`InnoPharma Exhibit 1029.0002
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`

`

`
`
`
`List of Contributors
`
`‘
`
`.5
`
`Foreword ,
`Lesfie Z. Benet
`
`’
`
`I OVERVIEW OF PHARMACODYNAMICS
`
`1 Basic Pharmacodynamic Concepts and Modem
`Raisers}. W535
`
`2 Simultaneous l’harmacakinetia!l’harmacodynamic Modeling
`Wayne A. Gallium (emf Mickaef A. 8355922
`
`3 Factors Influencing Variability in Kinetics and Dynamics
`Pram K. Narmg cam? Ronald C. Li
`
`4 Populatiomfiased Approaches to the Assessment of
`Pharmacokinetics and l’harmacodyflamics
`‘
`30362)}: C. Ffeislzakgr and Edward 5’. Anmé
`
`:3 General Perspectives on the Role of Metabolites in
`Pharmacokinetics and Pharmacodynamics
`Raizdalf D. 56932:?
`
`6 Enantioselectivity in Drug Action and Drug Metabolism:
`Influerzce on Dynamics
`Hey; K. Kroemer, Amaze 8. Grass and Miclzei Eidzeiéaam
`
`? Regulatory Perspective: The Role of Pharmacokinetics and
`Pharmacodynamics
`Lawreme 1283225: am? Roger L. Wie’fiams
`
`1! APPLICATION OF PHARMACODYNAMICS IN SELECTEI)
`THERAPEUTIC DOMAINS
`
`8 Theoretical Models for Developing Anxiolyfics
`P. V. Nz‘ckefi and “1320mm W. Ufche
`
`9 Pharmacodynamics of Antidepressants
`Karma Dawkim, Husseini K. Marzji and Wifiz'am Z. Posse?
`
`3.
`
`xiii
`
`3
`
`19
`
`45
`
`’33
`
`89
`
`103
`
`l 15
`
`133
`
`15?
`
`InnoPharma Exhibit 1029.0003
`
`

`

`10
`
`11
`
`12
`
`13
`
`14
`
`15
`
`16
`
`I?
`
`18
`
`19
`
`20
`
`Antihypertensive Drugs
`L. Miciznei Prisms: and A551??? 53. Cam
`
`Pharmaeodynamics of Calcium Antagonist Drugs
`Darrefi R. Aber‘neflzy emf Nabifi S. Andr‘awis
`
`Agents in Congestive Heart Failure
`Edmund V. Capparez’li
`
`Antiarrhythmie Drugs
`Ennice B. Sclzwm‘iz
`
`Antibiotic Pharmacodynamics
`303m C. Roiscizafer, Ken’n 3. Waiker, Km? 3’. K353}: and
`Ckrz'szopker ff. Suiiiwn
`
`Pharmacodynamics of Antineoplastie Agents
`Gm}! L. Renter and Maria 3'. Remix
`
`Controlling the Systemic Exposure of Anticancer Drugs:
`The Dose Regimen Design Problem
`Dania! Z. D’Argeizio and 30m; H. Redraw:
`
`Vimlogy and Antiviral Drug Bevelnpment
`Michele? A. Amamea, games R. Minor and 8:33)?an ES Swans
`
`Ill
`
`FRONTIERS IN PHARMACGDYNEXMICS: INSIGHT FROM
`MOLECULAR APPROACHES
`
`21
`
`aafidreneeeptors and their Subtypes: Pharmacological
`Aspects
`P. A. we Zwieten
`
`vi
`
`CONTENTS
`
`Pharmaeodynamies of Antipsychotic Drugs in
`Schizophrenia
`3033?: 3’. Smmefia and George M. Simpson
`
`’
`
`Pharmacodynamic Modeis Useful in the Evaluation of
`Drugs for Cognitive Impairment
`Me’ckaei F. Murphy, Kiazedizes R. Siegfl‘ied, F. 35:50.5 Huffand
`Neal? R. Cage?
`
`181
`
`201
`
`Alzheimer’s Disease: Assessment of Chelinamimetie Agents
`8501336. Reines
`
`225
`
`241
`
`253
`
`26?
`
`291
`
`315
`
`345
`
`363
`
`339
`
`409
`
`InnoPharma Exhibit 1029.0004
`
`

`

`CONTENTS
`
`22 Mumarinic Receptors: Pharmacologicai Subtypes,
`Structure.) Function and Regulation
`Lira Mei, Wifiz'am R. Roesé‘ee and Henry I. Yamamm‘a
`
`23 Serotonin Receptor Subtypes
`503m: B. Pritchest
`‘
`
`Index
`
`Vii
`
`433
`
`4-5?
`
`475
`
`InnoPharma Exhibit 1029.0005
`
`

`

`
` This material may be protected by Copyright law (Title 17 U.S. Code)
`
`
`
`2 Simultaneous Pharmacokinetic/
`Pharmaeodynamic Modeling
`
`
`warns A. COLBURN AND MICHAEL a. ELDON
`
`the use of
`Simultaneous pharmacoldnetic/pharmacodynatnic modeling is
`integrated pharmacolcinetic and pharmacodvnarnic models to interpret and
`extrapolate the temporal relationship between some sampled drug concentration
`and observed drug effect. The basis for such modeling is the need to analyze
`and describe measurable concentration—effect data, as well as to males clinically
`relevant extrapolations from experimental conditions to therapeutic conditions.
`Investigation of drug action using pharmacokinetie or dosewresponse models is
`well established in clinical pharmacology; the linking of these tools through
`specific mathematical models is relatively new.
`ing a
`Pharmacokinetics contributes to clinical pharmacology by provi
`means to characterize drug distribution and elimination.
`its usefulness is
`predicated on the assumption that measurable drug concentrations are related
`to drug effect in some manner,
`thereby forming the basis for deterr ining
`concentration-effect relationships {pharmacodynamics} and employing thera-
`peutic drug monitoring. In recent years, significant advances have been made
`in technologies to measure drug and metabolite concentrations in bio ogical
`matricesg further advancing the use of pharmacoitinetics as an adjunct
`to
`optimizing drug therapy. Concurrent advances in the ability to quantita e and
`understand drug effects have similarly promoted the stud}; and use of
`pharmacodynamics.
`Pharmacokineticfpharmacodynamic relationships have been investiga ed in
`two general approaches. The first approach involves the determination of drug
`effect and concentration over a series of doses administered to a relatively large
`patient population. Correlation of concentration and effect
`is performed
`retrospectively) usually resulting in the determination of target plasma drug
`concentration ranges which are thought to provide some level of drug effect
`while minimizing the risk of toxicity (1). Unfortunately,
`this approach is
`relatively imprecise due to its
`sensitivity to inter-subject variability in
`pharmaeokinetic as well as pharmacological factors. It is the imprecision and
`non-specificity of this method which requires the study of large numbers of
`
`patients to determine a therapeutic dose range} and even then may lead to
`
`
`
`Phomacmiwmmirs and 3mg Development: Perspectives in Clinical Pharmacology-
`Edited by N. R. Cutlerg I. I. Sramek and P. K Narang
`'3”) 1994 lohn ’Wiley 8{ Sons Ltd
`
`InnoPharma Exhibit 1029.0006
`
`

`

`20
`
`OVERVIEW OF PHARMACODYNAMICS
`
`inappropriate conclusions that drug effect and blood or plasma drug concen-
`trations are ‘not correlated’.
`The relevant question is not whether concentration and effect are related for
`a given drug> but rather how are they related and what is necessary to elucidate
`the relationship. Answering these questions is the goal of the second approach,
`which involves correlation of graded pharmacological responses with circulating
`drug concentration in a smaller number of patients. This more specific approach
`allows investigation of the nature of drug effect and its relationship to drug
`concentration, while minimizing the impact of pharmacokinetic and pharmaco-
`dynamic inter~snhject variability.
`This chapter is concerned with the latter approach and gives an overview
`of key developments during evolution of simultaneous pharmacokinetic}
`pharmacodynamic modeling, a review of contemporary methods, and goals for
`future refinement of the topic. Detailed discussion of pharmacokinetic theory
`and practice will not be given here. The reader is directed to excellent references
`on the topic (2,3) for further information.
`
`EVOLUTION T0 THE PRESENT
`
`PHARMACOKINETIC nPPROhCl-IES
`
`The evolution to simultaneous modeling was based on the desire to refine
`understanding of drug action. This was expressed in 196? by Brodie (4} when
`he observed that fewer patients were required to determine antimalarial activity
`if drug effect was correlated to plasma concentration rather than dose. In
`retrospect, this observation could most likely he attributed to the reduction
`of
`intensabiect variability in the pharmacokinetic component of
`the
`dosewresponse relationship. During this stage of evolution: Levy {5) proposed
`that for many drugs, the intensity of effect was linearly related to log concen»
`tration over the range of 20-80% of the maximum possible effect (Emax).
`He suggested the following equation to describe the concentration~effect
`relationship after intravenous drug dosing:
`
`Ezm‘logA-I—e
`
`.
`
`(1}
`
`where E is the effect intensity, A is the amount of drug present (which may he
`represented by concentration values}; in is the slope of the linear plot of E versus
`log fl, and e is the intercept of that plot. This equation is based on the assump-
`tion that effect is directly related to drug concentration at the site of action and
`is rapidly reversible. However; the log transformation is only pseudo-linear over
`the 20430554} effect range3 owing to the underlying sigmoid nature of the
`dose-response relationship.
`
`InnoPharma Exhibit 1029.000?
`
`

`

`PHARMACO Kl NETIC; lirIrXRMACODYNAMIC MODKLING
`
`2 1
`
`the drug exhibited a oneacompartment phsrrnscohinetic
`Assuming that
`profile) Levy further proposed the following equation to describe the deciine of
`effect after intravenous drug administration {5):
`
`EngmiK-tny23't
`
`(2)
`
`where E; is the initial effect intensity, K is the apparent first-order elimination
`rate constant5 t is time, and all other parameters are as previously defined. These
`equations predict that the intensity of effect is linearly related to log concen-
`tration, and that effect declines linearly rather than exponentiaiiy following
`bolus drug administration. The practice of relating effect to log concentration
`data was a logicsi extension of analysing dose—response relationships using the
`log transform. The log transform does compress the dose or concentration range
`and linearize the concentration-effect relationship over the inner 20—80% of the
`effect range. However, as discussed by Holford and Sheiner (6), this method of
`data analysis does not explain effect at the extremes of the concentration range
`(is, zero effect when no drug is present), provide a means to estimate 3mm,
`or accommodate the existence of baseline effect. While the log transformation
`may be applicable for specific drugs,
`it
`is not a suitable substitute for
`characterizing the entire range of the dose or concentration-effect relationship
`as later described in the sections on parametric and semi-parametric methods.
`Additionaliy, Equations 1 and 2 do not permit assessment of the deiay in onset
`of drug effect following administration by routes requiring drug absorption or
`distribution before reaching the effector site3 or the persistence of effect when
`drug is no longer present in plasma. This delay in drug equilibration between
`the sampled biofluid and the responding tissue gives rise ‘to hysteresis in the
`effect versus concentration plot as shown in Figure l.
`
`
`
`t
`
`1
`
`s
`
`5
`
`-.‘i
`
`.s
`
`.5
`
`‘4
`
`s
`«1“:
`L”
`
`2
`
`.2‘
`
`..(_._.
`
`V
`N we”:/
`
`/
`////
`
`/
`
`l
`
`//
`,/ /r
`
`an
`
`50
`
`c: (to
`3%
`{9230
`0
`5 ,
`<2 £0
`m
`
`{a} Q
`
`ta
`
`7
`
`M”“_o
`12
`24
`
`Time
`
`o
`(m o
`
`to
`
`so
`so
`20
`Concentration
`
`so
`
`so
`
`Figure I. {3) Theoretical plasma concentration (soiid line) and effect (dashed line)
`profiles versus time following extrsvascnlar drug administration.
`(is) Corresponding
`counterclockwise hysteresis plot of effect versus plasma concentration data from (2%}
`
`InnoPharma Exhibit 1029.0008
`
`

`

`22
`
`OVERVIEW OF PHARMACODYNAMICS
`
`
`
`levy at all. (3") addressed the problem of equilibration delay by extending the
`relationships described by Equations 1 and 2 to include mnlticompartment
`harmacokinetic models and empiricallj,T comparing pharmacokinetic and drug
`effect profiles. This approach was used to investigate the relationship between
`ental performance test scores and predicted lysetgic acid diethylamide (LSD)
`pharmacokinetics from work by Aghaianian and Bing (8}. Figure 2 shows
`harmacokinetic and effect profiles from this experiment. Based on a two«
`compartment pharmacokinetic model, effect {reduction in performance score}
`did not appear to be directly related to central compartment (plasma) concen-
`rations> but rather to the time course of drug in the second or tissue compattw
`meat. However, counterclockwise hysteresis was still evident in the plot of
`erformance score versus fraction of close in the tissue compartment, as shown
`in Figure 3. Accordingly, a third compartment representing slowly equi—
`librating tissne was added to the pharmacokinetic model. This modification of
`the model resulted in a linear plot of performance score versus fraction of dose
`in the slowly equilibrating compartment, shown in Figure 4, indicating that the
`observed equilibration delay between plasma LSD concentration and effect
`could be explained by the effector compartment being pharmacokinetically
`distinct from the plasma compartment.
`The phat‘macokinetic compartment approach is limited in that it is dependent
`on identifying a potentially complex pharmacokinetic model with concentrations
`
`28
`
`Fractionofdose
`
`Time (it)
`
`EU
`
`
`
`
`
`80
`
`100Periotmancetestscore
`
`Figure 2. Observed {o} and predicted {upper curve} amounts of LSD in the central
`compartment, predicted amounts in the tissue compartment
`(lower curve) of a
`twocompartment model, and performance test
`scores
`(0}
`following intravenous
`administration of LSD to normal subjects (From reference ’3) with permission)
`
`InnoPharma Exhibit 1029.0009
`
`

`

`PHARMACOKINETIC}PHAREVEACODYNAMIC MODELING
`
`23
`
`23
`
`Pattormance
`
`035
`
`0.49
`0.20
`9.13
`Fraction at dose
`
`Figure 3. Reiationship between performance scores and thc fractional amount of LSD
`in the tissue compartment of the nan-compartment pharmacokinetic model (From
`reference '5”, with permission}
`
`Performance
`
`20
`
`b‘23
`
`so
`C x
`.30
`
`./
`3/ 120
`
`_
`
`
`
`0.05
`
`0.025
`
`0.15
`0.10
`Fraction of dose
`
`{3.20
`
`Figure 4. Relationship between perfcxrmance acorns and the fractional amount of LSD
`in the slowly equilibrating tissue compartment of a three~cnmpartment pharmacokinetic
`model {From reference ’3, with permission)
`
`in at least one compartment correlatable with the effect profile. In many casres,
`pharmacokinetic compartments are not readily recognizable as distinct body
`tissues which may be of interest, and therefore may nnt contribute to any real
`understanding of the effector site. An extension of this concept will be
`addressed later in this chapter.
`
`InnoPharma Exhibit 1029.0010
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`

`24
`
`OVERVIEW OF PHARMACODYNAMICS
`
`PHARMfiCODYNAMIC APPROACHES
`
`In 1968, Wagner (9) proposed using the Hill equation to model the hyperbolic
`relationship between drug effect and dose or concentration. This proposal has
`been Widely adopted and the model has been parameteriaed for analysis of
`in vino and it: also concentration—effeet relationships as the sigmoid Em“ model
`shown below:
`
`E
`
`_ Ema); ‘ {fr
`- ECSO’Y 'i' Cr};
`
`(3}
`
`Where E is intensity of effect, Emax is the maximum possible effect in the system
`being studied, C is the drug concentration, ECgs is the steady~state drug concen-
`tration evoking 50% of Email and ’y is the sigmoidicity parameter indicating
`the slope and shape of the curve. Note that when the value of y is 19 the
`concentration—effect curve is a simple hyperbole and the model is termed the
`Emx model A typical sigmoid effectmeoneenttation curve depicting parameters
`of this model is shown in Figure 5.
`Hyperbolic models have been used to describe various binding phenomena
`such as Michaelis~Menten enzyme kinetics and protein binding,
`thereby
`linking the use of the Emax models to receptor binding theory (l0). Clark {l1}
`also proposed the use of a similar equation to model dose-response relationship
`as an application of mass action theory. The use of hyperbolic models to
`represent biological processes is empirically reasonable since they describe the
`Widely observed phenomena that as
`the maximum response (effect)
`is
`approached} increasing levels of stimulation (concentration) are required to
`reach the maximum. The Emu models offer advantages over the logarithmic
`model suggested by Levy {5) in that they predict effect over the entire eoneen~
`tration range, including zero effect when concentration equals zero> and the
`maximum possible effect (Emax).
`Wagner (9) also proposed inserting concentrationwtime data predicted from
`pharmacokinetie models into the Hill equation to predict the time course of in
`also response, based on its similarity to in nine experiments where the coneenw
`tration in the bath solution could be varied to study response. This approach
`has been expanded to simultaneously fitting pharmacokinetie and pharmaco—
`dynamic models to concentration—effect data as detailed in the Present methods
`section of this chapter.
`Several other pharmaeodynatnie models and modifications of the Emax model
`have been used to describe concentration—effect relationships. Examples of
`these are as follows.
`
`The linear model
`
`a ~.~ s~ o + to
`
`,
`
`{4)
`
`where S is the slope of the linear effect versus concentration plot, Es is the effect
`
`InnoPharma Exhibit 1029.0011
`
`

`

`PHIKRMACQKINETIQPlifiRi‘tlfiCQDYNAMlC MODELING
`
`25
`
`Effect
`
`' e
`
`1 o
`
`3 0
`a e
`Coneenttation
`
`51 o
`
`5 0
`
`Figure 5. Plot of drug effect versus concentration simulated using the sigmoid Enmx
`model given in Equation 3 (parameter values: 8mm =0.79, RC” = 10, and «,e wB}
`
`intensity when no drug is present, and E and C are as previously defined. The
`linear model has limited application, usually to defined segments of the true
`response curve:
`since it predicts
`that effect
`increases with increasing
`concentration without limit;
`
`The baseline subtraction model
`
`5-333:
`
`Emmi ' CW
`Elissa/Y + Cl
`
`(5)
`
`This model is based on the assumption that Ea can be subtracted from the effect
`data, leaving the O—lOG% response curve intact. This may not be the case when
`endegenous substances bind to the receptor or interact biochemically to main-
`tain the baseline effect. In this situation: the baseline effect should be included
`in the model as given below in Equation 6.
`
`InnoPharma Exhibit 1029.0012
`
`

`

`26
`
`OVERVIEW OF PHARMACODYNAMICS
`
`The baseline inclusion model
`
`Emax ° {C + Qt)?
`E : scat + (C+ can
`
`(6)
`
`where Ct} is the concentration of drug which would be required to generate
`baseline effect such that 15? includes the baseline effect. The concepts and appli—
`cations of the baseline subtraction and inclusion models have been previously
`described (12).
`
`The inhibitory Em“ model
`
`52333-
`
`Ema); ' G
`IC5(}Y 'i' C!"
`
`('2?)
`
`where 1850 is the drug concentration causing 50% inhibition of 5mm. This
`model is useful for investigating the effects of inhibitory drugs without trans-
`forming the data. Its use will result in an inverted effect versus concentration
`plot with the maximum and minimum effects occurring at zero and the
`maximum concentration value. Reviews of these and other pharmacodynamic
`models (6,12,13) and examples of their application {6,14,15) have recently been
`published. In addition, Colburn (12) has discussed many considerations of
`pharmacokinetic}pharmacodynamic study design, including selection of dosing
`routes and regimens and corresponding pharmacodynamic models. Alternative
`models including those for dealing with indirect effects and tolerance will be
`presented in the section on future developments.
`
`PRESENT
`
`The present state of simultaneous pharmacokineticfpharmacodynarnic modeling
`has drawn heavily on the foundations of relating effect to an accessible bioilnid
`as described in the preceding section. This too has evolved, beginning with fully
`parameterized pharmacokinetic and pharmacodynamic models linked by a
`parametric model. Recent advances have been made where both pharmaco—
`kinetic and pharmacodynamic data are analyzed non-parametrically, that is,
`without assuming that the correct underlying model and its parameters are
`known and/ or identifiable. This latter approach is perhaps better termed semi—
`parametric since the parameters of the linking model are still estimated.
`Although the term parametric was not originally applied to the first simul—
`taneous pharinacokinetic/pharmacodynamic models, it has come into use since
`the advent of the semi«pararnetric methods.
`
`InnoPharma Exhibit 1029.0013
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`

`PHARMACOKINETIQ PHARMACODYNanC MODELING
`
`2?
`
`FARAMETRIC aaraoacn
`
`Sheiner at of. (16) first proposed that the pharmacokinetic model parameters
`could be substituted into the Hill equation such that concentration and effect
`profiles could he simultaneously modeled using nonlinear regression. The
`novel aspect of their compartment model~hased approach was the inclusion of
`a theoretical effect compartment related to the central (plasma) compartment,
`but not influencing the overall pharmacokinetic profile one to its relatively small
`size. A schematic representation of the model is shown in Figure 6(a). Drug
`transfer into and loss from the effect compartment were controlled by first-order
`rate constants and drug effect was assumed to be directly related to the amount
`of drug in the effect compartment at any time. The plasma to effect compart—
`ment transfer rate constant, a”; and amount of drug transferred to the effect
`compartment were assumed to be so small that the pharmacokinetic profile
`would not be altered and that the negligible amount of drug in the effect
`compartment did not need to be returned to the central compartment. Under
`these conditions, the rate constant for drug loss from the effect compartment,
`KEG, would control the temporal relationship between effect and the concen-
`tration profile in the plasma compartment.
`Sheiner et a2. {16) evaluated the model using concentrationmeffect data
`obtained following d-tubocurarine administration as a two~stage intravenous
`infusion to healthy patients and to patients with end~stage renal failure. They
`concluded that the method was robust and could predict the equilibrium delay
`between appearance of drug in plasma and onset of effecta shown in Figure 2?.
`One of the main advantages of this approach is that it allows the characterization
`
`
`
`(bl
`
`KEG
`
`and peripheral
`{a}
`compartment
`representation of central
`Figure 6. Schematic
`compartment in) effect models used in pharmacokineric/pharmacodynamic modeling
`
`InnoPharma Exhibit 1029.0014
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`

`28
`
`OVERVIEW OF PHARMACODYNAMICS
`
`ETC infusion rate (pg! kg I min}
`
`12
`
`I68
`
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`Figure ’1". Observed d—tubocurarine piaema concentrations {a} and effect (0) during and
`foliowing intravenous infusion of the drug. Solid line: best fit of the pharmacokinetief
`phatmacodynamic model to the data {From reference loj with permission}
`
`relationship under nonwsteadystate conditions.
`of the concentrationmeffect
`Conversely, many factors of drug effect such as receptor binding and post-
`binding events are grouped and represented in the model by aningle first-order
`rate constant.
`
`Colburn (I?) investigated the model proposed by Sheiner et a3. (16) and found
`that it was able to represent a wide variety ofopharmaeokinetie and pharmaco»
`dynamic phenomena. He defined effect equations applicable to several classical
`compartment models and extended the approach to accommodate the effect
`compartment concentration being driven from a peripheral compartment as
`shown in Figure 60:»). In the interest ofmodel identifiabiiity, he recommended
`that centtni and peripheral compartment models be fit to each data set and that
`
`InnoPharma Exhibit 1029.0015
`
`

`

`PHARMnCOKINETlC}l’l‘ll’lRl‘leCODYNr-‘llvliC MODELlNG
`
`29
`
`drug be administered by several routes of administration before extrapolating
`the concentration—effect relationship beyond observed data AddltionallyS a
`model selected from fitting to singledose data should be tested for adequacy by
`studying the transition from single to multiple doses} since predicted and
`observed effects will
`systematically diverge when multiple doses
`are
`administered if an incorrect model has been chosen (iii). Potential divergence
`due to inappropriate model selection is illustrated in Figure 8.
`The peripheral compartment effect model (Figure 64:17)} can be used to explain
`apparent changes in pharmacoltineticlpharmacodynamic relationships as a
`function of route of administration, or other phenomena not explained by the
`central compartment effect model {Figure as) (14). The peripheral compart~
`merit effect model provides an additional tool for explaining non—parallelism
`between concentration and effect modeled using the central compartment effect
`model. Modeling the effect compartment as driven by a peripheral compart-
`ment may be more physiologically relevant if the effector tissue is believed to
`he a phatmacoklnetically identifiable tissue. More representative models could
`result if the pharmacokinetic compartment model is replaced with a physio
`logical flow model where the target organ thought to be the receptor}r effector site
`can be isolated (14).
`
`is
`Further refinement of the pharmacoklnetic}pharmacodynamic model
`possible using specially designed studies to isolate and identify the rate-limiting
`components of the proposed model {12). By using a varying first-order rate of
`intravenous administration,
`rate-limiting and} or controlling steps such as
`receptor binding can be isolated from the model. f‘ilternativel1vj one may find
`that diffusion to the receptor is the slowest step, and construct the model to
`reflect this. Elucidation of a robust model that can predict drug effect under a
`variety of conditions will aid in selecting dosage regimens and optimizing
`therapy.
`
`SEMI-l’nRAMETRIC AFPROACH
`
`the intrinsic
`thorough understanding of
`Parametric modeling requires
`pharmacoklnetic and pharmacodynamic models before combining them, as well
`as the ability to identify and reliably estimate each parameter of the combined
`model. This may often be difficult, depending on noise level of the pharmaco«
`kinetic and pharmacodynatnic data sets and the characteristics of the underlying
`models for a given drug. In an attempt to minimize these factors, Foseau and
`Sheiner (18} proposed that the phartnacodynainic component of the combined
`model could be modeled non-parametrically using the relationship between
`observed effect and the effect compartment drug concentration (Ce) predicted
`using a parametric pharmacokinetic model. To achieve this, it is necessary to
`assume that
`the relationship betvveen Cs and effect
`is instantaneous and
`invariant with time, i.e.,‘ tolerance and sensitization do not occur. As in the
`parametric approach, the effect compartment is modeled as receiving negligible
`
`InnoPharma Exhibit 1029.0016
`
`

`

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`Eomwwnfiumfig"SBEES950%SufiummfionvMakmfifiomEH8@838magmammSofia
`
`InnoPharma Exhibit 10290017
`
`
`

`

`PHARMACOKINETIC; PHARMACODYNAMIC MODELING
`
`31
`
`
`
`amounts of drug with the concentration profile determined by Kim and the
`plasma drt g concentration (Cpl. In the non-paz‘ametric pharmacodynamic
`approach, ysteresis between effect and Ca is suppressed by choosing K50 such
`that the ascending and descending arms of the effect-Ce plot are sanct-
`imposable (18). The best estimate of K53 is determined using a univariate search
`method wh'ch minimises the average squared difference between observed and
`interpolated effect values from the hysteresis plot as shown in Figure 9.
`Fuseau and Sheinet (18) tested the nonparametric pharmacodynamic method
`using simu ations based on hyperbolic and sigmoid Emax models as well as
`models of the g3~function {convex Cc-E relationship), tolerance) sensitization
`and non-eouilibrlum between Ca and the receptor, the latter three which violate
`the assump ions of the method. The proposed method was found to be accep-
`table for both Ema): models and the #3 function model when adequate numbers
`of data having minimal error were used. itlowever> the non—parametric method
`could not provide accurate or precise estimates of Kgo when applied to data from
`the tolerance, sensitization or nonequilibrium simulation models. Additionally,
`performance was reduced for all simulation models omen too few data or noisy
`data were used.
`
`Subsequently, Unadkat at of. (19) extended the nonapatametric pharmaco—
`dynamic approach to include pharmacokinetic modeling such that pharmaco»
`kinetics and pharmacodynamics could be simultaneously modeled non-
`parametrically with the link model still used to estimate the parameter K50,
`thereby allowing ‘semiwparametric’ simultaneous pharmacokinetic/pharmaco
`dynamic: modelling. The advantages of this approach are that fewer assumptions
`about either the underlying pharmaeokinetie or pharmacodynamic model are
`
`lIl
`
`
`
`
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`cog?
`
`Figure 9. Application of the non—parametric pharmacodynamie method of Fuseau and
`Sheiner {18) to estimate K59 by minimizing the average squared difference between
`observed {Eu and Egg) and interpolated (53mg) effect data. Ce values are corresponding
`effect compartment concentration values estimated using a parametric pharmacoltinetlc
`model {From reference 18, with permission)
`
`InnoPharma Exhibit 1029.0018
`
`

`

`32
`
`OVERVIEW OF PHARMACODYNAMZCS
`
`required. Unadltat at of. {19} described this as a two-stage process where
`observed Ce values are used to model pharmacodynamics and determine the
`linking KEG value. Simple linear interpolation is used to estimate Cit—time
`values if missing from the Clo—effect data set as shown in Figure 10. The
`resultant (Sp-time data set is used to estimate Ce as a function of time by
`numerically integrating the following equation for a given value of Kg; (19):
`
`aegis: = K] ~ op - Kay Ce
`
`(8}
`
`Where K1 is effect compartment input rate constant (assumed to be equal to
`K50} and all other parameters are as previousiy defined. A starting estimate of
`{€59 is selected and the parameter value is increased or decreased incrementally
`depending on the direction of hysteresis and area between the limbs of the
`effect-Ce plot corresponding to each Km value. The process is iterated until the
`K50 value which minimizes the area within the hysteresis loop is found.
`This approach assumes that Cs and hence effect is a function of observed (and
`interpolated) C}? as determined by the value of K503 independent of intrinsic
`pharmacoklnetics. Based on a series of simulations, the authors (19) suggested
`that this approach is nearly as efficient as the parametric approach even when
`
`
`
`
`
`
`Plasmaconeentration
`
`Time
`
`Figure 19. Example of non-parametric ‘fit’of plasma concentration (Ce) versus time
`data {G}. If Co was not observed at a pharmacodynamic observation time, it is estimated
`using linear interpolation between the nearest bracketing observed values (8339-) and
`Cpiz +}) (From reference 19, with permission)
`
`InnoPharma Exhibit 1029.0019
`
`

`

`PHARMACOKlNETIC;PHARMACODYNAMIC MODELING
`
`33
`
`the underlying models were known, but considerably more robust when the
`underlying models were misspecitied.
`Shafcr at all. (20) reported a comparison of the above method with parametric
`pharmacokinetic/pharmacodvnamic modeling in the evaluation of the neuro-
`museular blocking drug metocurine in laboratorfi,t animals. The semi-parametric
`method was found to give results in close agreement with the parametric
`method. When results differe