Pharmacokinetic/Pharmacodynamic, link models

P. J. Williams, J. R. Lane, C. Turkel, E. Capparelli, Z. Dziewanowska, and A. Fox, Dichioroacetate population pharmacokinetics with a pharmacodynamic link model. 

Pharmacokinetic-pharmacodynamic (PKPD) modeling makes a quantitative link between the pharmacokinetic profile of the drug and the concentration required to significantly occupy the target receptor and drive efficacy. The free... 

Lin, S. and Ghien, Y.W., Pharmacokinetic-pharmacodynamic modeling of insulin comparison of indirect pharmacodjmamic response with effect-compartment link models, J. Pharm. Pharmacol, 54, 791-800, 2002. 

Duffull, S.B. and Aarons, L., Development of a sequential linked pharmacokinetic and pharmacodynamic simulation model for ivabradine in healthy volunteers, Eur. J. Pharm. ScL, 10, 275-284, 2000. 

Risk Assessment. This model successfully described the disposition of chloroform in rats, mice and humans following various exposure scenarios and developed dose surrogates more closely related to toxicity response. With regard to target tissue dosimetry, the Corley model predicts the relative order of susceptibility to chloroform toxicity consequent to binding to macromolecules (MMB) to be mouse > rat > human. Linking the pharmacokinetic parameters of this model to the pharmacodynamic cancer model of Reitz et al. (1990) provides a biologically based risk assessment model for chloroform. 

Population pharmacokinetics can be extended to pharmacodynamics and PK/PD modeling using a link model like an effect compartment (Sheiner et al. 1979). In huge clinical trials only a limited number of patients can be included in a pharmacokinetic satellite study. The model is developed in this satellite. Knowing the demographic covariates of the patients in the whole study, concentration time curves and even effect time curves can be predicted. 

FIGURE 20.1 The relationship between pharmacokinetics, link model, and pharmacodynamics. 

The approach involves a semimechanistic or mechanistic model that describes the joint probability of the time of remedication and the pain relief score (which is related to plasma drug concentrations). This joint probability can be written as the product of the conditional probability of the time of remedication, given the level of pain relief and the probability of the pain relief score. First, a population pharmacokinetic (PK) model is developed using the nonlinear mixed effects modeling approach (16-19) (see also Chapters 10 and 14 of this book). With this approach both population (average) and random (inter- and intraindividual) effects parameters are estimated. When the PK model is linked to an effect (pharmacodynamic (PD) model), the effect site concentration (C ) as defined by Sheiner et al. (20) can be obtained. The effect site concentration is useful in linking dose to pain relief and subsequently to the decision to remedicate. 

Complex pharmacokinetic/pharmacodynamic (PK/PD) simulations are usually developed in a modular manner. Each component or subsystem of the overall simulation is developed one-by-one and then each component is linked to run in a continuous manner (see Figure 33.2). Simulation of clinical trials consists of a covariate model and input-output model coupled to a trial execution model (10). The covariate model defines patient-specific characteristics (e.g., age, weight, clearance, volume of distribution). The input-output model consists of all those elements that link the known inputs into the system (e.g., dose, dosing regimen, PK model, PK/PD model, covariate-PK/PD relationships, disease progression) to the outputs of the system (e.g., exposure, PD response, outcome, or survival). In a stochastic simulation, random error is introduced into the appropriate subsystems. For example, between-subject variability may be introduced among the PK parameters, like clearance. The outputs of the system are driven by the inputs... 

What are the strengths and weaknesses of these approaches The use of intrinsic clearance in vitro permits predictions between species for the particular enzyme/route of metabolism concerned. If humans have qualitatively different routes of metabolism for any particular compound, then this will weaken the predictive value of the in vitro observation. Similarly, allometric scaling works best for compounds with a high component of non-enzymatic elimination, such as our model compound with approximately 90% excretion as unchanged drug. This prediction weakens as variations in rates of enzymatic reactions become more important. The pharmacokinetic-pharmacodynamic modelling approaches use existing in vivo data to calculate constants which can be applied to other in vivo data, but does not, in its present form, link in vitro and in vivo data. 

Exposure-response modeling can be an important component of a totality of evidence assessment of the risk of QTc prolongation. It can be evaluated in early-phase studies and as part of the conventiontil study of QTc prolongation, and may help inform further evaluation. There are many different types of models for the analysis of concentration-response data, including descriptive pharmacodynamic (PD) models and empirical models that link pharmacokinetic (PK) models (dose-concentration-response) with PD models. 

Figure 1.2 Relationship between the pharmacokinetic, link, and pharmacodynamic models.

An important aspect of PD models is the link between the pharmacokinetics and the pharmacodynamic model, i.e. which concentration drives the drug effect. For empirical models there are many different PK/PD link approaches described and the theory is presented in several review papers [33-35]. The two most popular approaches are described in the following and are also illustrated in Fig. 17.7. The direct link approach assumes that a change in the measured concentration is directly reflected in a change in the measured P D. This is most often observed if the site of PK measurement and the site of PD measurement are identical (e.g. PK measurement in plasma and clotting time as PD measurement). 

Pharmacodynamic models mathematically relate a drug s pharmacological effect to its concentration at the effect site. Examples of the types of pharmacodynamic models that have been employed include the fixed-effect model/ maximum-effect models (Emax and sigmoid Emax)/ and linear and log-linear models (11). Unlike pharmacokinetic modelS/ pharmacodynamic models are time independent. However these models can be linked to pharmacokinetic modelS/ as discussed in Chapter 19. 

The pharmacokinetics and pharmacodynamics of recombinant interleukin-2 (IL-2) in patients with human immunodeficiency virus (HIV) infection have been evaluated (75). Patients were administered IL-2 either by continuous infusion or by SC injection for 5 days over multiple cycles. Following repeated injection, soluble IL-2 receptors were substantially but transiently increased. A dose-dependent decrease in area under the concentration-time curve (AUC) between days 1 and 5 was attributed to a receptor-mediated change in clearance. Concentrations were described using an unusual model that employed an indirect stimulatory PD model to link the time-dependent changes of the pharmacokinetics with the change in IL-2 receptor density following repeated administration. 

The blood or plasma concentrations of the parent drug and/or its active metabolites (systemic exposure) may provide an important link between drug dose (exposure) and desirable and/or undesirable drug effects (8). For this reason, the modeling of parent drug and metabolite pharmacokinetics, coupled with pharmacodynamic (PD) measurements, offers an essential development tool for prediction and simulation. 

For some dmgs, we can link the parameters and equations of pharmacokinetics to those of pharmacodynamics, resulting in a PKPD model which can predict pharmacological effect over time. This concept is discussed in more detail later in this chapter. (Equation 17.7 is a typical PKPD equation.) Figure 17.3 depicts the relationship of effect versus time for the dmg albuterol (salbuta-mol) and contrasts this with a superimposed plot of plasma dmg concentration versus time. 

As stated, a number of PBPK/PD models have been developed for individual nerve agents (sarin, VX, soman, and cyclosarin) in multiple species. Chapter 58 in the current volume discusses tiie development of such models. Standalone PBPK or compartmental models have also been developed that describe the pharmacokinetics of certain countermeasures, such as diazepam (Igari et al., 1983 Gueorguieva et al., 2004) and oximes (Stemler et al., 1990 Sterner et al., 2013). However, to date, few models for specific countermeasures have been harmonized and linked to NA PBPK/PD models to be able to quantitatively describe their pharmacokinetic and pharmacodynamic interactions. This is partly due to the fact that most PBPK/ PD models developed for NAs and other OPs focus on the inhibition of ChEs as the critical endpoint. The lack of a mathematical description of the disruption of other complex biochemical pathways presents a problem for linking these NA models to those of many countermeasures. For example, the conventional NA countermeasures, atropine and diazepam, as well as many novel countermeasures, do not directly impact ChE kinetics because they act at sites distinct from the active site of the esterases, such as muscarinic, GABA, or NMDARs (Figure 69.2). 

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