Chapter 8
`Foundations of Pharmacodynamic
`Systems Analysis
`
`William J. Jusko
`
`Abstract The pillars of pharmacodynamic modeling are the pharmacokinetics of
`the drug, the nature of the pharmacology that underlies drug interactions with their
`targets, and the physiology of the system considering molecular to whole body
`levels of organization and functioning. This chapter provides a general assessment
`of the fundamental components and some interactions of each of these pillars
`indicating how they serve as building blocks for systems models. Key elements of
`pharmacokinetics include the operation of Fick's Laws for diffusion and perfusion
`along with the often nonlinear mechanisms of drug distribution and elimination.
`Target- binding relationships in pharmacology evolve from the law of mass action
`producing capacity -limitation in most operative control functions. Mammalian
`physiology and pathophysiology feature a wide breadth of turnover rates for bio-
`logical compounds, structures, and functions ranging from rapid electrical signals to
`lengthy human lifespans, which often determine the rate -limiting process and basic
`type of model to be applied. Appreciation of the diverse array, mechanisms, and
`interactions of individual components that comprise the pillars of pharmacody-
`namics can serve as the foundation for building more complex systems models.
`
`Keywords Fick's laws
`Target- binding Drug- biological interface Affinity
`Turnover Homeostasis
`Substrate control Operational efficacy
`Capacity
`Gaddum equation
`
`8.1
`
`Introduction
`
`The three pillars of pharmacodynamics (PD), as depicted in Fig. 8.1, are the
`pharmacokinetics (PK) of the drug, the pharmacology and mechanism of the
`drug- biological interface, and the physiology or pathophysiology of the system
`
`W.J. Jusko (2)
`Department of Pharmaceutical Sciences, University at Buffalo,
`404 Kapoor Hall, Buffalo, NY, USA
`e -mail: wjjusko @buffalo.edu
`
`© American Association of Pharmaceutical Scientists 2016
`D.E. Mager and H.H.C. Kimko (eds.), Systems Pharmacology and Pharmacodynamics,
`AAPS Advances in the Pharmaceutical Sciences Series 23,
`DOI 10.1007/978-3-319-44534-2_8
`
`161
`
`Page 1
`
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`KVK v. SHIRE
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`162
`
`W.J. Jusko
`
`Computation
`
`Mathematics
`
`N
`
`:N=
`co
`
`a
`Lq
`O
`t?
`
`_L
`0i
`_c
`
`'
`
`.
`Statistics
`
`C?
`' o ,
`Ó
`v
`co
`
`L
`a
`._
`
`Fig. 8.1 The palace of pharmacodynamics with its foundation, structural components, and three
`pillars
`
`being altered by the drug (Mager et al. 2003; Jusko 2013). Each can contribute to
`the extent and time -course of observed pharmacodynamic responses depending on
`their intrinsic properties and rate -limiting step(s). The foundations of systems
`analysis will be explored by delineating the basic "rules of biology" for the major
`components that govern each of the pillars of pharmacodynamics. Along with the
`determinants of PK, two general principles, namely capacity -limitation and turn-
`over, form the basis for a variety of commonly used PK/PD and systems models.
`Genomics is included in Fig. 8.1 as the presence, location, and functioning of
`determinants of PK/PD are governed by genomics and genetics. The quantitative
`skills of mathematics, statistics, and computation are needed to identify relation-
`integrate them into models, analyze experimental data, and perform
`ships,
`simulations.
`
`8.2 Pharmacokinetics
`
`Common approaches for analyzing pharmacokinetic data utilize noncompartmental,
`compartmental (mammalian), and physiological concepts and methods, with
`ascending degrees of complexity. Physiologically -based PK (PBPK) models pro-
`vide mechanistic and insightful separation of drug and systems properties as well as
`their interfaces and interactions. Three key relationships that underpin drug distri-
`butional processes in PBPK models are:
`
`Page 2
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`

`

`8 Foundations of Pharmacodynamic Systems Analysis
`
`163
`
`Fick's Law of Diffusion:
`
`dA = PS(Ch - Cl)
`dt
`
`where the rate of drug movement (Amount/time, dA/dt) from higher (Ch) to lower
`(C1) concentrations is governed by the permeability -surface area (PS) coefficient
`(Fick 1855). Permeability (P) is governed by molecular size and lipid solubility of
`the compound along with the nature of the biological membrane and its surface area
`(S). This equation is often invoked to describe small molecule (drug) absorption
`rates, movement between interstitial fluids (ISF) and cell water spaces, and has been
`adapted to account for biophase distribution of drugs.
`
`Fick's Law of Perfusion: d = Q(Ca - C)
`
`where the rate of organ uptake (dA/dt) is governed by arterial (Ca) and venous (Cr)
`drug concentrations and organ blood flow (Q) (Teorell 1937). The ratio of
`(Ca - C,,) /Ca is also termed the Extraction Ratio (ER). This equation is commonly
`used in PBPK models to describe drug distribution to various organs and tissues via
`blood flow.
`
`Convection: d = L(1 - a) C = fL Q(1 - 6) C
`
`where organ uptake of molecules is determined by water movement equaling lymph
`flow (L) and the vascular reflection coefficient (a) associated with water flux across
`capillary membranes into ISF (Renkin 1979). Lymph flow is usually assumed as a
`small fraction (fL = 0.02 -4 %) of blood flow to each organ or tissue as determined
`by the Starling (1896) approximation, while the reflection coefficient varies with
`type of organ capillaries (some `leaky' such as liver, some `tight' such as muscle).
`This equation is used in PBPK models of monoclonal antibodies (mAbs) and other
`large molecules to describe their limited and slow movement from plasma to ISF
`(Cao et al. 2013). Glomerular filtration rate is primarily a convection process as
`well.
`The joint roles of blood flow and permeability for control of the distribution of
`molecules from blood to tissues is termed Distribution Clearance (CLd) in PK and
`quantified as:
`
`CLd=fdQ=Q(1 -e-PS/Q)
`
`where fd is the fraction of Q accounting for organ uptake of drug, PS is the
`rate -limiting factor when Q is small, and Q is the rate -limiting factor when PS is
`large (Stec and Atkinson 1981).
`The array of nonlinear protein binding, metabolism, transport, and clearance
`relationships commonly encountered in PK are listed in Table 8.1 (Jusko 1989).
`
`Page 3
`
`

`

`Wilkinson and Shand (1975)
`
`ConcentrationRowland et al. (1973) and
`
`CLbu: Intrinsic clearance
`
`Goldstein, (1949)
`
`KA: Equilibrium Association constantDf free drug
`
`Shannon (1939)
`Menten (1913)
`ConcentrationMichaelis and
`Substrate
`
`Concentration
`
`References
`
`Km
`
`Km
`
`Affinity
`
`Q: Blood Flow
`Pt: Protein Conc.
`n: No. Binding Sites
`
`Vtt
`
`Vt t,,
`
`Capacity
`
`Q +cL
`Q.c"
`
`=
`
`CL
`
`Clearance
`
`Organ clearance
`
`b = 1 /KA +Df
`
`nPeD1
`K + C
`v,,,x'c
`
`D
`
`dt
`dAT
`
`ar - m +c
`'c
`
`v
`
`a
`
`Equation
`
`Bound drug
`
`Protein binding
`
`Flux
`formation rate
`Metabolite (M)
`Function
`
`Transport
`
`Metabolism
`Process
`
`Table 8.1 Common capacity -limited functions in pharmacokinetics
`
`4,
`
`Page 4
`
`

`

`8 Foundations of Pharmacodynamic Systems Analysis
`
`165
`
`They all evolve from the law of mass action where the limited quantity of binding
`substances, metabolic enzymes, or transporters results in capacity -limited pro-
`cessing of drugs and other substrates. At low drug concentrations, the functions
`operate linearly, such as with the common relationship for intrinsic clearance,
`CLint = Vm/Km, pertaining to drug metabolism. Often the preferred or operative
`drug concentration is the free or unbound drug in either plasma or in tissues. These
`distributional and elimination relationships are components of full PBPK models
`and are presented here partly owing to their fundamental value in PK, but also
`because they are helpful in describing the kinetics of physiological substances or
`biomarkers when analyzed in PK/PD and systems models. For example, the PK/PD
`modeling of cortisol as an indicator of adrenal suppression and of nitrate as a
`biomarker of inflammation is best handled by considering their intrinsic kinetics
`(Krzyzanski and Jusko 2001; Sukumaran et al. 2012).
`
`8.3 Pharmacology
`
`The interaction of drugs (D) with their biophase targets (R) is the interface that
`controls the array of subsequent genomic, proteomic, biochemical, and physio-
`logical changes. These targets may be receptors, enzymes, transporters, ion chan-
`nels, and/or DNA. A common feature is that the concentration or quantity of such
`targets is limited and can be described with the law of mass action:
`
`as described by:
`
`D
`
`+R DR
`k-
`
`kopf
`
`dR
`dt
`
`k0riDR-k0ffDR
`
`where k0n is the association rate constant, keis the dissociation rate constant and, at
`equilibrium, the equilibrium dissociation constant is KD = k0yk0n. This type of
`interaction leads to a nonlinear relationship that the author calls "The Equation of
`Life ":
`
`Function =
`
`Capacity Substrate
`Affinity -I- Substrate
`
`In this fashion, Capacity, Affinity, and Substrate control numerous biological pro-
`cesses: those involved in PK as listed in Table 8.1 and those describing many
`pharmacological actions as listed in Table 8.2. These pharmacologic processes or
`
`Page 5
`
`

`

`and Ko (1994)
`Dayneka et al. (1993) and Jusko
`
`)
`
`(
`
`Concentration
`
`SC50
`
`Sma,
`
`=1 +^uu+C
`Numerical change
`
`Scso
`
`C
`
`Jusko and Ko (1994)
`Dayneka et al. (1993),
`Zhi et al. (1988)
`Jusko (1971),
`
`Black and Leff (1983)
`
`Hill (1910)
`
`Clark (1933)
`References
`
`Concentration
`n: Power Coefficient
`concentration
`[AR]: Agonist- receptor
`y = Hill Coefficient
`C or C v
`
`Di. free drug
`Substrate
`
`Concentration
`
`IC50
`
`Constant
`KE: Transducer
`
`EC50
`
`Ema,
`
`KD orkt
`13,,
`CapacityAffinity
`
`Imp
`
`K
`
`Em
`
`Fractional Change
`
`Ics0 + c
`'max 'C
`
`1
`
`=
`
`removal
`Altered input or
`
`removal
`Altered input or
`
`Stimulation
`
`Inhibition
`
`Kc50 +c
`Km,. c
`
`dr
`ax
`
`CytotoxicityKilling rate
`
`KÉ + [R]
`E - [ARln'Em
`
`TransductionEffect
`
`=Eqo + 0
`= Kp +Df
`
`Eÿ' CY
`
`Db
`
`Equation
`
`Bound drug
`Function
`
`PD effects
`binding
`Receptor
`Process
`
`E
`
`Direct effect
`
`Table 8.2 Common capacity -limited functions in pharmacology
`
`Page 6
`
`

`

`8 Foundations of Pharmacodynamic Systems Analysis
`
`167
`
`mechanisms include receptor binding, transduction, cytotoxicity, inhibitory and
`stimulatory changes, as well as simple directly observed drug effects.l
`It is important to appreciate the need for sufficiently high doses or drug con-
`centrations to attain an observed maximum response (Capacity) and the occurrence
`of the Affinity constant at concentrations when responses equal one -half of
`Capacity. Such conditions facilitate operation of all PK/PD models and assist in
`resolution of the parameter values (Dutta et al. 1996; Krzyzanski et al. 2006). Some
`of the relationships include a power coefficient (n, y) accompanying the concen-
`tration and Affinity terms. Although this power coefficient may not have a mecha-
`nistic basis, it sometimes adds flexibility in fitting pharmacological data. Of special
`note is that the Affinity term in the equations is of the nature that lower, rather than
`higher, concentration values reflect greater potency of the drug.
`The simple pharmacologic relationships listed in Table 8.2 have been applied for
`a vast array of drugs and response measures. However, pharmacology textbooks
`may offer additional more complex relationships that have usually evolved from
`in vitro systems (Kenakin 1997). One of note is the Adair equation (1925) relevant
`for biphasic or hormesis drug effects:
`
`E=
`
`EmCaC
`EC50 + C + K2 C2
`
`where K2 is a secondary binding coefficient. This equation produces a bell- shaped
`Effect (E) versus concentration (C) relationship. Cao et al. (2012) applied this
`equation to describe the effects of GLP -1 on stimulating insulin secretion for a wide
`range of doses examined in rats.
`Another complex relationship of considerable value is the Black and Leff (1983)
`equation for nonlinear transduction of the effects of an agonist:
`
`Em Tn Cn
`Effect = (KD + Cr + 2n Cn
`
`where i is Operational Efficacy defined as Bmax/KE (Other symbols are defined in
`Table 8.2). Resolution of all parameters in this equation may require assessment of
`both nonlinear drug- receptor binding (Bmax, KD) as well as nonlinear responses (Em,
`KE) in relation to receptor occupancy. This equation is of great value as the PK and
`drug- receptor interactions are usually specific for individual compounds, while the
`subsequent events yielding an effect are controlled by the biological transduction or
`signaling system. One applied example is where the plasma concentrations of
`methylprednisolone were found to control receptor binding while the receptor
`
`'The author tells his students that this equation will also predict their future success in pharma-
`cometrics: a function of the combination of brain capacity (IQ), affinity for mathematics, statistics,
`and computation, and the relevant assimilated information (coursework and studies).
`
`Page 7
`
`

`

`168
`
`W.J. Jusko
`
`binding of free and liposomal- incorporated drug served as the basis for the
`time -course of immunosuppression for lymphocytes in the spleen of rats (Mishina
`and Jusko 1994).
`
`8.4 Physiology
`
`Nearly all mechanistic PD models are based on the concepts of turnover and
`homeostasis (Mager et al. 2003; Jusko 2013). Biological compounds (biomarkers),
`structures, and functions are continually being produced and degraded. The starting
`condition or baseline of most PD models is thus the steady -state that exists in the
`organism. Numerous physiological controls can be invoked to maintain home-
`ostasis of the system and factor being measured.
`Figure 8.2 provides a listing of many biological entities that have served as PD
`measures. Their time -frames for turnover range from very fast (electrical signals) to
`very slow (human lifetimes). The factors in the upper part of the list are often
`biomarkers of body processes while the lower components may require clinical
`measures of major organ or system functioning (e.g., arthritis or depression
`symptom scores). Of course, patient survival is a key endpoint in cancer
`chemotherapy where measurements are made in a population sense.
`The turnover rate may determine which type of PK/PD model applies. For very
`rapid turnover processes, direct effect or biophase models are relevant as the PK of
`the drug will be rate - limiting in controlling observed responses. When the pro-
`duction (kin) and loss (kout) rates of the biological factors are slower and directly
`altered by drugs, indirect response models pertain. As systems become more
`complex with multiple controls, then transduction, multi- component, or systems
`models are needed. These time -frames also determine study designs as slow pro-
`cesses need lengthier monitoring of the response measures.
`
`SY STEM S M ODE l
`
`.
`S
`
`Fig. 8.2 Diversity of
`turnover rates and models
`(adapted from Mager and
`Jusko 2008)
`
`Biological Turnover Rates of Structures or Functions
`Fast Electrical Signals (msec) -,
`Neurotransmitters (msec)
`¡ á
`Chemical Signals (min)
`¡ o
`Mediators, Electrolytes (min) : n
`R
`Hormones (hr)
`1 K
`mRNA (hr)
`(
`)
`Proteins / Enzymes (hr)
`Cells (days)
`
`Direct
`Effect
`Models
`
`Turnover
`Models
`
`Tissues (mo)
`Organs (year)
`Person ( .8 century)
`
`V
`Slow
`
`1 E
`R
`I s
`I
`
`--J
`--%c
`1 Ì
`1 N
`1 1
`
`1 ñ
`-- L
`
`Transduction
`Models
`
`Page 8
`
`

`

`8 Foundations of Pharmacodynamic Systems Analysis
`
`169
`
`Table 8.3 Basic types of turnover models or components used in pharmacodynamics
`
`Model type
`
`Diagram
`
`Indirect response
`
`k
`
`i-r
`
`Precursor -indirect
`
`kp
`
`P
`
`R
`
`kout
`
`->
`
`Cytotoxiciry
`
`Irreversible
`
`Transit
`
`kg
`
`kin
`
`t
`
`Feedback
`Tolerance (Tol)
`
`kt
`--->
`
`k,
`
`R
`
`k°t
`k1
`
`ti
`
`kt
`
`x
`
`Receptor binding
`Target- mediated
`
`k5,.n 1
`
`C
`
`+
`
`R
`
`k,°ss
`
`kon
`
`k
`
`°"
`
`CR
`
`Input
`function
`kin (drug
`modified)
`Zero -order
`
`kp P (drug
`modified)
`First -order
`
`kg
`First -order
`
`kin
`Zero -order
`
`Loss
`function
`km (drug
`modified)
`First -order
`
`knot
`First -order
`
`k1 C (drug
`modified)
`Second -order
`k1 C (drug
`modified)
`Second -order
`
`First -order
`1/i
`kt
`First -order
`knn C R
`Second -order
`
`First -order
`1/r
`kt
`First -order
`
`ko ff CR
`First -order
`
`References
`
`Dayneka
`et al. (1993),
`Jusko and
`Ko (1994)
`Sharma et al.
`(1998)
`
`Jusko,
`(1971), Zhi
`et al. (1988)
`Yamamoto
`et al. (1996)
`
`Sun and
`Jusko (1998)
`Friberg et al.
`(2002)
`
`Shimada
`et al. (1996),
`Mager and
`Jusko (2001)
`
`R
`
`I Usually nonlinear inhibition: (1
`
`.150
`
`ic +cc
`Usually nonlinear stimulation: (1-I- SCSO+c)
`I Drug- induced loss may be simple 2nd -order k1 C R or nonlinear: (xmc
`
`)
`
`KC50 + C
`
`Turnover and homeostasis are part of most of the basic PD models or compo-
`nents currently known.2 Homeostasis reflects the baseline and final steady -state
`condition of body systems before and after drug administration and the diverse
`feedback and set -point mechanisms that help maintain normal functioning. The
`primary PD turnover models are depicted in Table 8.3 with indication of input and
`loss functions, types of rate processes, and commonly associated pharmacological
`functions. In the receptor and target- mediated models, turnover may be viewed as
`drug binding and dissociating from receptors particularly when kon is relatively
`slow (Swinney 2009). The synthesis (k,) and degradation (kdeg) rates of the
`receptors also contribute to the PD, particularly for longer studies. The Precursor
`model and Feedback component are often employed to account for tolerance and
`rebound phenomena.
`
`2Here turnover is generalized to include any process where the response or control factor is
`affected by production and loss. Some authors consider only basic indirect response models as
`turnover models.
`
`Page 9
`
`

`

`170
`
`W.J. Jusko
`
`The listings in Table 8.3 provide the most basic models or components. Various
`complexities can be added to any model such as transit steps, feedback, additional
`compartments, circadian baselines (Krzyzanski et al. 2000a), disease -altered base-
`lines (Lepist and Jusko 2004), life -span loss ( Krzyzanski et al. 2000b), and/or
`physiological limits in responses (Yao et al. 2006).
`
`8.5 Disease Progression
`
`Disease progression models often reflect the time- course of disturbance of PD
`baselines, turnover components, or subsystems with changes in homeostasis
`(Mould et al. 2007; Earp et al. 2008a, b). A classic disease model for cell prolif-
`eration and tumor growth is the `resistance to death' Gompertz function (1825) as
`shown in the modern convenient form:
`
`N = NSS e- No e
`
`]nNss
`
`-kg.t
`
`where kg is a first -order growth constant, N0 is the initial number, and NSS is the
`steady -state number of cells, tumor size, and/or body mass. This equation accounts
`for early exponential growth with an ultimate attainment of a plateau value.
`The simpler, preferred equation used for size measures or numbers of cells in
`many chemotherapy studies is the logistic function (Robertson 1923):
`
`Growth Rate = kg 1 - N° N
`
`NSS
`
`Cell proliferation rates have also been modeled with an adaptation of the
`Michaelis -Menten equation (Meagher et al. 2004). All of these growth or disease
`models are "Equations of Life" in a somewhat different format as they are nonlinear
`and exhibit capacity -limitation.
`
`8.6 Drug Interactions
`
`The wealth of existing drug -drug interactions and quantitative methods are
`well- appreciated in pharmacokinetics. When two or more drugs are administered,
`additional interactions can occur owing to either the nature of their pharmacological
`mechanisms or their alteration of the same or convergent turnover process or both.
`The isobolograph approach based on Loewe Additivity (1926) is often used in
`assessing pharmacologic interactions of two agents (Gessner 1974). However, this
`and most drug interaction methodology in pharmacology has involved measure-
`ment of a static endpoint and do not take into account the PK/PD time- course of
`
`Page 10
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`

`8 Foundations of Pharmacodynamic Systems Analysis
`
`171
`
`drug action. Fortunately, time -honored mechanistic equations allow the PK to be
`incorporated into their interaction relationships:
`Gaddum (1937) Equation for Competitive Interactions:
`
`EA+B
`
`EmaxA ' ECCso + EmaxB ECScBOB
`+ 1
`CA +
`
`EC DA
`
`ECSOB
`
`where CA is the concentration of agonist and CB is the concentration of a drug
`competing for the same target site. This equation is applicable for two agents
`typically having similar molecular structures and targets. The Gaddum equation
`simplifies for an antagonist when EmaxB = 0 as:
`
`Effect =
`
`Em,axA CA
`
`CA+EC50Al1+ECo$I
`
`The ability to fully resolve antagonistic drug effects requires careful assessment of
`the actions of the agonist to obtain its EmaxA and EC50A values and further
`examining the offsetting effects of the antagonist in order to calculate EC50B. It is
`difficult to do this in most in vivo studies, but Mandema et al. (1992) accomplished
`this in quantifying the agonist effects of midazolam and antagonistic action of
`flumazenil in studies in human subjects.
`Ariens et al. (1957) provided basic equations for more complex drug interactions
`such as noncompetitive, uncompetitive, and irreversible drug combinations that
`require careful enactment for experimental data. The Kenakin (1997) book provides
`highly useful instructions regarding these diverse relationships.
`If one of these basic mechanistic equations does not suffice in accounting for the
`joint effects of two agents, then an empirical drug interaction parameter (fr) can be
`introduced by multiplying it times one of the EC50 terms. Chakraborty et al. (1999)
`used the inhibitory forms of the Gaddum equation and Ariens equations and
`demonstrated how adding the * term allowed assessment of possible immuno-
`suppressive interactions between IL -10 and prednisolone for inhibiting lymphocyte
`proliferation. In fitting joint drug data, * < 1 reflects synergy and * > 1 reflects
`r does not equal 1, is that a more complex
`antagonism. Another interpretation, if
`mechanism may exist than accounted for by these basic interaction equations.
`Turnover models often allow a mechanistic approach for discernment of natural
`synergy occurring for two or more drugs. Earp et al. (2004) provided equations for
`indirect response models and demonstrated how strong synergism can result when
`there is either joint inhibition of kin and stimulation of kou,. or, conversely, stimu-
`TheThe principle that synergy or augmented drug
`lation of kin and inhibition of
`
`Page 11
`
`

`

`172
`
`W.J. Jusko
`
`effects are produced by opposing drug effects on the two sides of a turnover process
`also applies in chemotherapy when inhibition of growth along with cytotoxicity on
`the loss side occur. This was nicely demonstrated for the effects of rituximab and
`rhApo2L on tumor xenografts in a small systems model enacted by Harrold et al.
`(2012).
`
`8.7 Summary and Prospectus
`
`This compilation of PK/PD models and components provides a `toolbox' of kinetic
`processes, pharmacological functions, and turnover features of major basic models.
`Enhanced PK/PD or small to large systems models can often be assembled by
`consideration of the sequence of events leading to an observed drug effect and
`utilization of the appropriate mechanistic pieces that capture major rate -limiting
`steps. For example, Earp et al. (2008a, b) described disease progression in arthritic
`rats and inhibitory effects of dexamethasone on pro -inflammatory cytokines and
`edema with model components that included PK, receptor binding, transduction,
`competitive interactions, end organ Turnover (paw and bone), and inhibitory
`pharmacological functions. Similarly, Fang et al. (2013) assembled a small systems
`model to account for the diabetogenic effects of methylprednisolone in a
`meta- analysis of receptor, genomic, and biomarker (glucose, insulin, FFA) data
`from several studies in rats. The similarity that exists for numerous capacity -limited
`pharmacologic and disease progression functions and the fundamental nature of
`diverse turnover processes greatly facilitates the meshing of these components in
`assembling complex models.
`
`Acknowledgments This work was supported by NIH Grants GM 24211 and GM 57980 and by
`the University at Buffalo Center of Excellence in Pharmacokinetics and Pharmacodynamics.
`Technical assistance was provided by Mrs. Suzette Mis. The author greatly appreciates the
`mentorship and friendship of Gerhard Levy, deemed the "Father of Pharmacodynamies ", for his
`seminal contributions in recognizing concepts and models for simple direct drug effects (Levy
`1966), indirect responses (Nagashima et al. 1969), target -mediated drug disposition (Levy 1994),
`and many other aspects of PK/PD.
`
`References
`
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