Pharmacokinetic link model

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

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. 

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

As is implicit from all the above, the measured concentration in plasma is directly linked to the observed effect for these simple mechanistic, pharmacokinetic-dynamic models. Accordingly, these models are called direct-link models since the concentrations in plasma can be used directly in (10.6) and (10.7) for the description of the observed effects. Under the assumptions of the direct-fink model, plasma concentration and effect maxima will occur at the same time, that is, no temporal dissociation between the time courses of concentration and effect is observed. An example of this can be seen in the direct-fink sigmoid Emax model of Racine-Poon et al. [418], which relates the serum concentration of the anti-immunglobulin E antibody CGP 51901, used in patients for the treatment of seasonal allergic rhinitis, with the reduction of free anti-immunglobulin E. 

When a lag time of E (t) is observed with respect to the c (t) time course, the use of a combined pharmacokinetic-dynamic model, the indirect-link model, is needed to relate the drug concentration c (t) to the receptor site drug concentration y (t) (which cannot be measured directly) and the y (t) to the pharmacological response E (t).1... 

When one looks into the basic functions of the link and indirect response models, it is clear that one of the differences resides in the input functions to the effect and the receptor protein site, respectively. For the link model a linear input operates in contrast to the indirect model, where a nonlinear function operates. For the link model the time is not directly present and the pharmacological time course is exclusively dictated by the pharmacokinetic time, whereas the indirect model has its own time expressed by the differential equation describing the dynamics of the integrated response. 

The model described above has been successfully applied to characterize the in vivo concentration effect relationships of several 5-HT1A agonists including flesinoxan and buspirone [558,559]. This model has also linked with the operational model of agonism into a full mechanism-based pharmacokinetic-dynamic model [560]. 

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. 

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

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. 

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. 

Mitomycin C is an alkylating agent that forms cross-links with DNA to inhibit DNA and RNA synthesis. The pharmacokinetics of mitomycin C are best described by a two-compartment model, with an a half-life of 8 minutes and a terminal half-life of 48 minutes.31 Liver metabolism is the primary route of elimination. Mitomycin C has shown clinical activity in the treatment of anal, bladder, cervix, gallbladder, esophageal, and stomach cancer. Side effects consist of myelosuppression and mucositis, and it is a vesicant. 

Figure 2 Individual organ representations for a three-subcompartment (A), two-subcompartment (B), or typical membrane-linked and blood flow-limited (C) physiologically based pharmacokinetic model. See text for definition of symbols.

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. 

Figure 2.12 Three-compartment pharmacokinetic model with a linked effect compartment.

Chlorpyrifos provides an example of the utility of human pharmacokinetic models to estimate daily dose from biomonitoring data for a rapidly cleared pesticide. The urinary metabolite trichloro-2-pyridinol (TCP) is used in the NHANES study to monitor population exposure to chlorpyrifos (CDC 2005). Several epidemiologic studies have linked chlorpyrifos exposure to adverse birth outcomes through associations between urinary and blood biomarkers and have demonstrated maternal exposure and physiologic measurements in the neonate (Berkowitz et al. 2003, 2004 Whyatt et al. 2004 Needham 2005). 

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