Pharmacodynamics and
`Drug Development
`Perspectives in
`Clinical Pharmacology
`
`Editecf by
`
`Neal R. Cutler
`Caiifawzia Cfirzical Tz1}:z!s, 8%-s2:‘Iy Hilis, Ctmfomicz, U521
`
`John J. Sramek
`Caf£fa:'m’a Ciirzicczf Triafs, Beverb: Efiffs, Calsfomio, USA
`
`Prem K. Narang
`Pizcmnacia Acfricz, Cfiaical P§sar222acoZ0g}-jPfzamzaco:%i22e£2'es, Cofiunzfms, Ohio, USA
`
`IQHN WILEY 8: SONS
`Chichester - New York - Brisbane ° Toronto - Singapore
`
`|nnoPharma Exhibit 10290001
`
`

`

`Copyright
`
`1994 by Iohri Wiley 3: Sons Ltd,’‘
`Baffins Lane, Chiczhester,
`West Sussex PO19 IUD, England
`Telephone:
`Chichester {(3243} ?‘?9’???
`National
`International +44 243 ?'?9?"??
`
`"except Chapter 12 which is in the public domain.
`
`All rights rese1'ved.
`
`No part of this book may be reproduced by any means?
`or transmirtecl, or translated into a machine language
`without the written permission of the publisher.
`
`Otlzer ll’/Way Editorial Offices
`
`Iolm Wiley fir Sons, loo, 605 Thirtl iwenue,
`New York NY 101580012, USA
`
`Jacaranda Wiley Ltd, 33 Park Road, Milton,
`Queensland 4064, Australia
`
`john Wiley 3: Sons (Canada) Ltd, 22 Worcester Road,
`Rexclale, Ontario M9\X’ 1L1, Canada
`
`John Wiley 8: Sons {SBA} Pte Ltd, 3'?’ Jalan Pemimpin ;%0S-04
`Block B, Union Industrial Building, Singapore 2035?
`
`Library of Czmgress Catczirygirzg-irz-Paciviicatirm Data
`
`Pharmaeodynamiee and drug development : perspectives in clinical
`pharmacology} edited by Neal R. Cutler, john I. Sramek and Pram K.
`Narang.
`cm.
`p.
`Includes bibliographical references and index.
`ISBN 0 4'31 95052 1
`
`1. Drugsmlfiiysiological effect.
`Prem K.
`III. Sramek, John I.
`EDNLM: l. Pharrnarsology, Clinical. QV 38 P3318 1994}
`RM3G{).P48
`1994
`6lS'.?——clc20
`
`I. Cutler, Neal R.
`
`II. Narang,
`
`DNLMHDLC
`for Library of Congress
`
`946103
`{ZIP
`
`British Liizrary Gatafeguirrg in Pztbfieatioza Sam
`
`3‘; catalogue record for this book is available from the British‘ Library
`
`ISBN 0 4?} 950 521
`
`Typeset in 10;‘ 12 pt Plantirt by
`Mathematical Corttposition Setters Ltd, Salisbury, \5i"iltshi1‘e
`Printecl and bouncl in Great Britain by
`Bookeraft (Bath) Ltd, Midserner Norton, Avon
`
`|nnoPharma Exhibit 1029.0002
`
`

`

`
`Contents I
`
`
`
`List of Contriirgutors
`
`0
`
`0
`
`_
`
`Fareword t
`Lesfie Z. Benet
`
`’
`
`I OVERVIEW OF PHARMACODYNAMICS
`
`1 Basic Pharmacodynamic Concepts and Modem
`Raisers} ii’/E535
`
`2 Simultaneous i’harmacakinetic,{1’harmacociynamic Modeling
`Wayrze A. Coiinmz am? Mickaef A. Efdan
`
`3 Factors Influencing Variability in Kinetics and Dynamics
`Pram K. Ncmmg am!‘ Ronaia’ C. Li
`
`4 Populatiomfiased Approaches to the Assessment of
`Phatmacokinetics and Pharmacodynamics
`‘
`Eosepiz C. FZe2'332a}aez* and Ekiward 5'. zinicré
`
`S Generai Perspectives on the Role of Metabolites in
`Pharmacokinetics and Pharmacodynamics
`Rcmdaff D. Seéferz
`
`6 Enantioselectivity in Drug Action and Drug Metabolism:
`Influeace on Dynaanics
`Hey: K.
`I<'2‘0eme:*, Amzetze S. Grass med Micfzei }_3Iic?zeZ£:amrz
`
`’? Regulatory Perspective: The Role of Pharmacokinetics and
`Pharmacodynamics
`Lawrence Lesfea (ma? Roger L. Wéffiams
`
`1! APPLICATION OF PHARMACODYNAMICS IN SELECTED
`THERAPEUTIC DOMAINS
`
`8 Theoreticai Models for Developing Anxiolytics
`P. V. Nickefi and Wzamczs W’. Ufzcfe
`
`9 Pharmacodynamics of Antidepressants
`Karon Dawkém, Husseini K. Marzji and if/éifiam 2. Poster
`
`2:
`
`xiii
`
`3
`
`19
`
`45
`
`‘F3
`
`39
`
`103
`
`1 15
`
`133
`
`15?
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`

`

`vi
`
`CONTENTS
`
`Pharmaccedynamics of Antipsychotic Drugs in
`Schizophrenia
`3033?: 3’. Smmeie and George M. Simpson
`
`11
`
`Pharmacodynamic Modeis Useful in the Evaluation of
`Drugs for Cognitive Impairment
`Micizaefi F. Murphy, Kiazsdizzs R. Sieg,f}*s'ec2’, F. facoia Hujffnnd
`Neai R. Cutie?
`
`181
`
`201
`
`Alzheimer’s Disease: Assessment of Chnlinomimetic Agents
`Scat: A. Reines
`
`225
`
`Antihypertensive Drugs
`L. Micfiznes? P:~is¢:m and Aiber-3 A. Cam‘
`
`Pharmacodynamics of Calcium Antagonist Drugs
`Dawefi R. Abemezizy czmi Nabii S. Andmrwis
`
`Agents in Congestive Heart Failure
`Edmund V. Capparefli
`
`Antiarrhythmic Drugs
`Eanice B. Sclzzuezrzz
`
`Antibiotic Pharmacodynamics
`30322: C. Rotscizafer, 1'<'cm’::z 3’. Waifzer, Kilt‘? 3’. K3555» cmci
`C}m'szop?2er ff. Szefiitscziz
`
`Pharmacodynamics of Antineoplastic Agents
`G233}: L. Rosszer and Mczzrfe 3'. Retain
`
`Controlling the Systemic Exposure of Anticancer Drugs:
`The Dose Regimen Design Problem
`Dania! Z. D’Args2rzio and fofzzvz H. Redraw:
`
`20
`
`Virology and Antiviral Drug Development
`Mficfzaef A. z"i??3€I?IE€<.Z,
`_§*::mzes R. Minor anti Stepizen E.’ Sirens
`
`Ill
`
`FRONTIERS IN PHARMACODYNAMICS: INSIGHT FROM
`MOLECULAR APPROACHES
`
`21
`
`ozvfidrencceptors and their Subtypes: Plaarmacological
`Aspects
`P. 2%. mm Zwieterz
`
`241
`
`253
`
`26?‘
`
`291
`
`315
`
`345
`
`363
`
`3??
`
`409
`
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`

`CONTENTS
`
`22 Muscarinic Receptors: Pharmacologicai Subtypes,
`Stmcmrea Function and Regulation
`Lire Mei, Wi§§£a:;z R. Roesiee and‘ Hemy I. Ycmza;~mm:z
`
`23 Serotmiin Receptor Subtypes
`Doknz B. Pritcizest
`A
`
`Index
`
`Vii
`
`433
`
`4-57"
`
`475
`
`|nnoPharma Exhibit 10290005
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`This material may be protected by Copyright law (Title 17 U.S. Code)
`
`2 Simultaneous Pharmacokineticf
`Pharrnacodynamic Modeling
`
`warns A. cotsuan AND MICHAEL a. ELDON
`
`the use of
`Simultaneous pharmacolcineticfpharmacodynarnic modeling is
`integrated pharrnacolcinetic and pharrnacodynamic 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 make ciinicaiiv
`relevant extrapolations from experimental conditions to therapeutic conditions.
`Investigation of drug action using pharniacokinetic or dose-response models is
`well established in clinical pharmacology; the linking of these tools through
`specific mathematical models is relatively new.
`ing a
`Pharrnacokinetics contributes to clinical phartnacolog1g 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 {pharmacodynarnics) 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
`matrices, further advancing the use of pharrnacoltinetics as an adjunct
`to
`optimizing drug therapy. Concurrent advances in the abiiity to quantita e and
`understand drug effects have similarly promoted the stud}; and use of
`pharmacodynaniics.
`Pharmacokineticfphartnacodynamic 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 zniniinizing the risk of toxicity (1). Unfortunately,
`this approach is
`relatively imprecise due to its
`sensitivity to inter--subiect variability in
`pharmacokinetic 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
`
`Pleczmmcmiwramirs and ilimg Deaelopmem: Perspectives in Clinical Pf:am:a::ofag;-
`Edited by N. R. Cutlery I. I. Sramek and I’. K. Narang
`'33) 1994 lohn Willey‘ 8t Sons Ltd
`
`|nnoPharma Exhibit 10290006
`
`

`

`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 comtentration and effect are related for
`a given drug, but rather how are they reiated 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 minirnizing the impact of phartnaeoirinetie and pharmaco-
`djrnantic inteosubject variability.
`This chapter is concerned with the latter approach and gives an overview
`of key developments during evolution of simultaneous pharrnaeoltineticf
`pharmacodynamic modeling, a review of contemporary methods, and goals for
`future reiinetnent of the topic. Detailed discussion of pharrnaeokinetic 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 EKPPROACI-{ES
`
`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 deterrnine antirnalarial activity
`if drug effect was correlated to plasma concentration rather than dose. In
`retrospect, this observation could most likely be attributed to the reduction
`of
`intersabject variability in the pharmacokinetic cornponent of
`the
`dose—response relationship. During this stage of evolution, Levy (5) proposed
`that for many drugs, the intensity of effect was linearly related to log eoncen-
`tration over the range of 20-80% of the maximum possible effect (Emx).
`He suggested the following equation to describe the cor1<:entration~effe»:t
`relationship after intravenous drug dosing:
`
`E-»m‘logA+a
`
`»
`
`{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 21, 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 2(}-m80% effect range} owing to the underlying sigrnoici nature of the
`dose—response relationship.
`
`|nnoPharma Exhibit 1029.000?
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`

`

`PHARMACO Kl Ni;ITlC,? PHtXR3s’l:\CODYNAMIC MODKLING
`
`2 1
`
`the drug exhibited a oneconipartment pharrnacoltinetic
`Assuming that
`profile, Levy further proposed the following equation to describe the decline of
`effect after intravenous drug administration (5):
`
`§=Eg~(K'??1)[2.3°£
`
`(2)
`
`where B’; is the initial effect intensity, K is the apparent iirsvorder elimination
`rate constant} 2* 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 exponentially following
`bolus drug administration. The practice of relating effect to log concentration
`data was a logicai 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
`(i.e., zero effect when no drug is present), provide a means to estimate Emmi,
`or accommodate the existence of baseline effect. While the log transformation
`may be appiicable for specific drugs,
`it
`is not a suitable substitute for
`characterizing the entire range of the dose or con<:entration—effect relationship
`as later ciescribed in the sections on parametric anci semi-parametric methods.
`Additionally, 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 site, 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 1.
`
`Concentration
`
`50
`
`80
`
`
`-«Mt.»O-O‘O 10
`
`12
`Time
`
`20
`30
`40
`Concentration
`
`(a) Theoretical -plasma concentration (solid line) and effect (dashed line)
`Figure I.
`profiles versus time following extravasculat drug aclzninistration. {la} Corresponding
`cottnterclockwise hysteresis plot of effect versus plasma concentration data front (a)
`
`|nnoPharma Exhibit 10290008
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`

`22
`
`OVERVIEW’ OF PHARMACODYNAMICS
`
`Levy et ai. if’) addressed the problem of equilibration delay by extending the
`elationships described by Equations 1 and 2 to include multicompartment
`harmacokinetic models and empiricalijs comparing pharmacokinetic and drug
`effect profiles. This approach was used to investigate the relationship between
`ental performance test scores and predicted lysergic acid diethylamide (LSD)
`pharrnacokinetics from work by Aghaianian and Bing (8). Figure 2 shows
`harmacokinetic and effect profiles from this experiment. Based on a two
`compartment pharrnacokinetic 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 cotnpart~
`merit. However, counterclockwise hysteresis was stiil evident in the plot of
`erformance score versus fraction of dose in the tissue compartment, as shown
`in Figure 3. Accordingly, a third compartment representing slowly equi—
`lihrating tissue 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
`couid be explained by the effector compartment being pharmacokineticaliy
`distinct from the plasma compartment.
`The pharmacol-zinetic compartment approach is limited in that it is dependent
`on identifying a potentialiy complex pharinacokinetic mode} with concentrations
`
`28
`
`score
`
`
`
`Performancetest
`
`Fractionofdose
`
`EU
`
`80
`
`100
`
`Time {it}
`
`Figure 2. Observed {o} and predicted {upper curve} amounts of LSD in the central
`compartment, predicted amounts in the tissue cornpartnient
`(lower curve) of a
`twocompartment model, and performance test
`scores
`{0}
`following intravenous
`aclniinistration of LSD to normal subjects (From reference ?, with permission)
`
`|nnoPharma Exhibit 10290009
`
`

`

`PHAIIMACGKJNETIC,‘1’HAR£\=lACODYNAMIC MODELING
`
`23
`
`23
`
`Perforrnanee
`
`£1.05
`
`0.49
`0.20
`0.10
`Fraction of dose
`
`Figure 3. Relationship between performance scores and the fractional amount of LSD
`in the tissue compartment of the two-compartment phsrmaeolcinetie model (From
`reference '3, with permission}
`
`Performance
`
`30
`
`55£23
`
`so
`9 ,»
`.30
`
`./
`3/ 120
`
`K
`
`
`
`0.05
`
`0.015
`
`0.15
`0.10
`Fraction of dose
`
`0.20
`
`Figure 4. Relationship between péi1‘f(}l'I113£1C(2 scores and the fractional amount of LSD
`in the slowly equilibrating tissue compartment of a three~eompartment pharmacokinetis:
`model {From reference 3’, with permission}
`
`in at least one compartment correlstsble with the effect profile. In many cases,
`pharmaeokinetic cornpartments are not readily recognizable as distinct body
`tissues which may be of interest, and therefore may not contribute to any real
`understanding of the effector site. An extension of this concept will be
`addressed later in this chapter.
`
`|nnoPharma Exhibit 10290010
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`

`

`24
`
`OVERVIEW OF PEIARMACODYNAMECS
`
`PHfiRMfiCOUYNAMIC APPROACHES
`
`In l968, 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 paraineterized for analysis of
`in aim and in vino concentration-effect relationships as the sigmoid En.“ model
`shown below:
`
`E
`
`_ Ema:-; ' C?
`-I Ecsgl -1? CW
`
`{3}
`
`where E is intensity of effect, Em“ is the maximum possible effect in the system
`being studied, C is the drug concentration, EC” is the steadywstate drug concen-
`tration evoking 50% of Ema, and qr is the sigmoidieity parameter indicating
`the slope and shape of the curve. Note that when the value of ~,« is l, the
`c:oncentration——effect curve is a simple ll§;‘ps‘3rl3{}l8. and the model is termed the
`Em,“ model. A typical sigmoid effectmconeentration 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 Em“ models to receptor binding theory (10). Clark {l 1)
`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 einpiricall§; reasonable since they describe the
`Widely observed phenomena that as
`the maximum response (effect)
`is
`approaelied, increasing levels of stinmlation (concentration) are required to
`teach the niaxitnnm. The Em“ models offer advantages over the logarithmic
`model suggested by Levy (5) in that they predict effect over the entire COI1C€I1~
`tration range, including zero effect when concentration equals zero, and the
`tnasirnutn possible effect (Emit).
`Wagner (9) also proposed inserting eoncentrationwtime data predicted from
`pharmacokinetie models into the Hill equation to predict the time course of in
`nine response, based on its similarity to in nine experiments where the concen-
`tration in the bath solution could be varied to study response. This approach
`has been expanded to simultaneously fitting phatmacoltinetic and pharmaco-
`djgmamic models to concentration--effect data as detailed in the Present methods
`section of this chapter.
`Several other pharniacodynamic models and modifications of the Emx model
`have been used to describe concentration—effeet relationships. Examples of
`these are as follows.
`
`The linear model
`
`E -~ 3 ~ C + £5};
`
`_
`
`{4}
`
`where S is the slope of the linear effect versus coiicentration plot, Es is the effect
`
`|nnoPharma Exhibit 1029.0011
`
`

`

`l3l~Ir’lRMAC{)KINETlC,?l“l"IARl‘vl:&(3()DYNAMlC l‘viODELIl‘~lG
`
`25
`
`Effect
`
`' o
`
`1 o
`
`3 0
`2 o
`Concentration
`
`ft 0
`
`5 0
`
`Figure 5. Plot of drug effect versus concentration simulated using the sigmoid Emx
`model given in Equation 3 (parameter values: Sam =0.}’9, EC“: = l0, and ~,« m3}
`
`intensity when no drug is present, and E and C are as previously defitled. 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
`
`E~E::==
`
`«Emax ' CY
`EC50? + Q
`
`(5)
`
`This model is based on the assumption that E0 can be subtracted from the effect
`data, leaving the 0—l00°/E; response curve intact. This may not be the case when
`endogenous substances bind to the receptor or interaszt 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.
`
`|nnoPharma Exhibit 10290012
`
`

`

`Z6
`
`OVERVIEW OF PHARMACODYNAMlCS
`
`The baseline inclusion model
`
`Emmi - {C -1- Cg)"‘
`E :'?““.“j"""“""""'".
`Ecsgl + (C+ C9)?
`
`(6)
`
`where 8;} is the concentration of drug which would be required to generate
`baseline effect such that E includes the baseline effect. The concepts and appli-
`cations of the baseline subtraction and inclusion models have been previously
`described (12).
`
`The inhibitory Emx model
`
`E~—~i3o-
`
`Emax °
`lC5(;“’ 'i'
`
`('2?)
`
`where K353 is the drug concentration causing 50% inhibition of Emx. 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 tnaxiniutn and minimum effects occurring at zero and the
`maximum concentration value. Reviews of these and other pharmacodynannc
`models O5,1Z,l3) and examples of their application {6,l4,1S) have recently been
`published. In addition, Colburn (12) has discussed many considerations of
`phartnacolcineticfphartnacodynamic study design, including selection of dosing
`routes and regimens and corresponding pharmacodynatnic 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 pharmacolcineticfpharmacodjgnainic 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
`pararneterized pharrnacoltinetic and pharmacodynaniic models linked by a
`parametric model. Recent advances have been made where both pharmaco-
`kinetic and pharmacodjznatnic data are analyzed non-pararnetrically, that is,
`without assuming that the correct nnderlying 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.
`Althottgh the term parametric was not originally applied to the first simul-
`taneous pharrnacokineticfpharmacodynannc models, it has come into use since
`the advent of the semi—pat‘ametric methods.
`
`|nnoPharma Exhibit 10290013
`
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`

`3?l~IARMACOKlNETlCf I’I{ARNlACOD‘1’N£9sil=1lC MODELING
`
`2?
`
`PARAMETRIC AIWROACH
`
`Sheiner at of. (16) first proposed that the pharmaeokinetic model parameters
`could be substituted into the Hill equation such that concentration and effect
`profiles could be simultaneously modeled using nonvlinear regression. The
`novel aspect of their compartment model-based approach was the inclusion of
`a theoretical effect compartment related to the central (plasma) compartment,
`but not influencing the overall pharrnacokinetic profile due 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, Em; and amount of drug transferred to the effect
`compartment were assumed to he so small that the pharznacokinetic 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,
`Kgo, would control the temporal relationship between effect and the concen-
`tration profile in the plasma compartment.
`Sheiner et
`<22.
`(16) evaluated the model using concentrationmeffect data
`obtained following of-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 effect, shown in Figure 27.
`One of the main advantages of this approach is that it allows the characterization
`
`
`
`lb}
`
`KEG
`
`and peripheral
`{a}
`compartment
`representation of central
`Figure 6. Schematic
`compartment (lo) effect models used in pharmacokineticjpharmacodynamic modeling
`
`|nnoPharma Exhibit 10290014
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`

`28
`
`OVERVIEW‘ OF PHEXRMACODYNAMICS
`
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`Figure 3". Observed a‘-tubo:>cuz‘arine plasma concentrations {9} and effect Co) during and
`foliowing ixitraxrczmus infusion of the drug. Selid line: best fit of the pharmacnkinetief
`pha1~macod:mamic model to the data {From reference 16, with permission}
`
`relationship under nonwsteady-state conditions.
`of the c0ncent1‘ation~«effect
`Conversely, many facmrs of drug effect such as receptor binding and past-
`binding events are groupeci and represented in the model by aeingle firsmnrder
`rate constant.
`
`Calburn (1?) investigated the model proposed by Sheiner ex a2. (16) and found
`that it was able to represent a wide variety ofipliarmacokinetic and pharmaco»
`dynamic phenomena. He derived effect equations applicable to several classical
`COI1’1pa2‘t11’1{'2I1[ models and extended the approach to accommodate {he effect
`compamnem c0:1centra1;i<m being driven from 21 peripheral czempartment as
`shown in Figure 603). In the interest ofmaciel isrientifiability, he recomniended
`that C{il'1U‘£ii and peripheral compartment medeis be fit (.0 each data set 311:} that
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`|nnoPharma Exhibit 10290015
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`29
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`drug be administered lay several routes of aclrninistration before extrapolating
`the concentration—effect relationship beyond observed data. rhdditioiially, a
`model selected from fitting to singlodose data should be tested for adequacy by
`studying the transition from single to multiple doses, since predicted and
`observed effects will
`sysiematically diverge when multiple doses
`are
`administered if an incorrect model has been chosen (l?}. Potential divergence
`due to inappropriate model selection is illustrated in Figure 8.
`The peripheral compartment effect model (Figure 64:13)} can be used to explain
`apparent changes in pharrnacolzineticfpharmacodynamic relationships as a
`function of route of administration, or other phenomena not explained by the
`central compartment effect model {Figure 63%) (14). The peripheral cornpart~
`merit effect model provides an additional tool for explaining nomparallclisrn
`between concentration and effect modeled using the central compartment effect
`model. Modeling the effect compartment as driven by a peripheral compart-
`ment may he more physiologically relevant if the effector tissue is believed to
`be a pharrnacokinetically 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} effector site
`can be isolated (14).
`
`is
`Further refinement of the pharmacoltineticfpharmacodynanuc model
`possible using specially designed studies to isolate and identify the rate-limiting
`components of the proposed model {I2}. By using a varying iirst~order rate of
`intravenous administration,
`rate-limiting and] or controlling steps such as
`receptor binding can be isolated from the model. Alternatively, 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-PARAMETRIC APPROACH
`
`the intrinsic
`thorough understanding of
`Parametric modeling requires
`pharmacokinetic and phartnacodynaniic 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 pharmacodynairiic data sets and the characteristics of the underlying
`models for a given drug. In an attempt to minimize these factors, Fnseau and
`Sheiner (18) proposed that the pharinacodynainie component of the combined
`model could be modeled non—pararnetrically using the relationship between
`observed effect and the effect compartment drug concentration (Ce) predicted
`using a parametric pliarrnacoltinetic model. To achieve this, it is necessary to
`assume that
`the relationship between Cs and effect
`is instantaneous and
`invariant with time, i.e.,i tolerance and sensitization do not occur. As in the
`parametric approach, the effect compartment is modeled as receiving negligible
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`|nnoPharma Exhibit 10290016
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`PHARi‘~élACOKlNE"l"lC{ Pllz’:Ri\=lACODYl\lAMIC MODELINC}
`
`31
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`amounts of drug with the concentration profile determined by Kim and the
`plasma drt g concentration (Cp). In the non-parametric phartnacodynamic
`approach, ysteresis between effect and Cs is suppressed by choosing K50 such
`that the ascending and descending arms of the effect-—Ce plot are super-
`irnposable (18). The best estimate of K53 is determined using a univariate search
`method when minimizes the average squared difference between observed and
`interpolated effect Values from the hysteresis plot as shown in Figure 9.
`Fuseau and Sheiner (18) tested the nonparametric pharrnacodynamic method
`using simu ations based on hyperbolic and sigmoid Emit models as well as
`models of the g3—function {convex Ce-B relationship), tolerance, sensitization
`and non-equilibrium between Ce 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 Em“ models and the 6 function model when adequate numbers
`of data having minimal error were used. However, the non—parametric method
`could not provide accurate or precise estimates of Kg, when applied to data from
`the tolerance, sensitization or nonequilibrium simulation models. Additionally,
`performance was reduced for all simulation models when too few data or noisy
`data were used.
`
`Subsequently, Unadkat at of. (19) extended the nonparametric pharmaco-
`dynamic approach to include pliarmacolcinetic modeling such that pharn1aco~
`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/pharmaeo—
`dynamic modelling. The advantages of this approach are that fewer assumptions
`about either the underlying pharmacokinetic or pharmacodynamic model are
`
`IIIIIIIIItIIIIIIIII!
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`Figure 9. Application of the r;0n~parameI:rlc pharmacodynamie method of Fuseau and
`Sheiner (l8) to estimate K59 by minimizing the average squared difference between
`observed (Bi; and E32) and interpolated (E;m,;) effect data. Ce values are corresponding
`effect compartment concentration values estimated using a parametric pharmacoleinetic
`model {From reference 18, with permission’)
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`|nnoPharma Exhibit 10290018
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`32
`
`OVERVIEW OF PHARMACODYNAMICS
`
`(19) described this as a two-stage process where
`:12.
`required. Unadlcat st
`observed Cp values are used to model pharmacodynamics and determine the
`linlcing {<"_r;0 value. Simple linear interpolation is used to estimate Cp—time
`values if missing from the Cp-—effect data set as shown in Figure 10. The
`resultant Cp~time data set is used to estimate Ce as a function of time by
`numerically integrating the fnllowing equation for a given value of Km (19):
`
`dCe{dt = K, ~ (3,, —. Km Ce
`
`ts}
`
`Where K1 is effect compartment input rate constant (assumed to be equal to
`Kgo} and ail 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
`Km value which minimizes the area within the hysteresis loop is found.
`This approach assumes that Ce and hence effect is a function of observed (and
`interpolated) C32: as determined by the value of K503 independent of intrinsic
`pharmacokinetics. Based on a series of simulations, the authors (19) suggested
`that this approach is nearly as efficient as the parametric approach even when
`
`Plasma
`
`concentration
`
`Time
`
`Figure 19. Example of non--parametric ‘fit’of plasma concentration ((33)) versus time
`data (0). If C}; was not observed at a pharmacodynamic observation time, it is estimated
`using linear interpolation between the nearest bracketing observed values {Catt-) and
`(Ipiz +}) (From reference 19, with permission)
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`|nnoPharma Exhibit 10290019
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`PHARMACOKlNl3TlCfPl~lARi’vlACOIi)YNAhlIC MODELING
`
`33
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`the underlying models were known, but considerably more robust when the
`underlying models were rnis~speciiied.
`Shafer at tel. (20) reported a cornparison of the above method with parametric
`pharinacolcin