Pharmacokinetics complex models

To date, however, present several computational approaches have been reported to predict the important subprocesses for oral availability. This chapter will present some examples for the prediction of such pharmacokinetic properties, starting from the three-dimensional (3D) structure of the drug candidates. In our experience it is much better to develop and use a number of different simple local models, than to use a unique complex model that depends on a multitude of poorly understood subfactors. 

Pharmacokinetics and Drug Dosage Regimen Design—A Possible Application Requiring Construction and Manipulation of a Complex Model and Data Base with an Expert System... 

Ariens [432] was the first to describe drug action through indirect mechanisms. Later on, Nagashima et al. [433] introduced the indirect response concept to pharmacokinetic-dynamic modeling with their work on the kinetics of the anticoagulant effect of warfarin, which is controlled by the change in the prothrombin complex synthesis rate. Today, indirect-response modeling finds extensive... 

These studies show that it is possible to predict the time course of drug effects in vivo in situations in which complex homeostatic control mechanisms are operative. As such, they form the basis for the development of an entirely new class of pharmacokinetic-dynamic models. These models are important for the development of new drugs and the application of such drugs in clinical practice. For example, on the basis of this kind of model, it becomes possible to predict whether withdrawal symptoms will occur on cessation of (chronic) drug... 

Other approaches have been used for more complex models. These include curve stripping or the method of residuals,either manually or using a computer program such as CSTRIP and ESTRIF. These techniques can separate a multiexponential curve into its component parts for initial estimates. Other techniques include deconvolution methods specific to the one and two compartment pharmacokinetic models. The objective of the deconvolution method is to mathematically subtract the results obtained after IV administration from the oral or extravascular data. This results in information about the input or absorption process alone. More general methods have been presented by various researchers that do not rely on a particular compartmental model. ... 

Pharmacokinetic/pharmacodynamic modeling is a complex, iterative process involving multiple steps. Once data are collected, exploratory graphic analyses of the raw data are usually carried out to 1) detect outliers 2) explore distribution of variables and 3) assess... 

Dose-response models describe a cause-effect relationship. There are a wide range of mathematical models that have been used for this purpose. The complexity of a dose-response model can range from a simple one-parameter equation to complex multicompartment pharmacokinetic/pharmacodynamic models. Many dose-response models, including most cancer risk assessment models, are population models that predict the frequency of a disease in a population. Such dose-response models typically employ one or more frequency distributions as part of the equation. Dose-response may also operate at an individual level and predict the severity of a health outcome as a function of dose. Particularly complex dose-response models may model both severity of outcome and population variability, and perhaps even recognize the influence of multiple causal factors. 

This chapter reviews some of the in silico attempts to predict oral bioavailability. However, bioavailability is a complex property, and various pros and cons of current quantitative structure-activity relationship (QSAR) based approaches will be discussed here. As an alternative, physiologically-based pharmacokinetic (PBPK) modeling is discussed as a promising approach to predict and simulate pharmacokinetics (PK), including estimating bioavailability. 

Biomarker models that integrate pharmacokinetics, pharmacodynamics, and biomarkers are complex because they are based on sets of differential equations, parts of the models are nonlinear, and there are multiple levels of random effects. Therefore, advanced methods from numerical analysis and applied mathematics are needed to estimate these complex models. When the model is estimated, one seeks a model that is appropriate for its intended use (see Chapter 8). 

Ludden et al. (1994) have compared the ability of the AIC calculated using Eq. (1.45), BIC calculated using Eq. (1.47), and F-test to select the correct pharmacokinetic model using Monte Carlo simulation. They did not examine the use of AICc in model selection, which is unfortunate, since that would have been a more relevant criteria than AIC. They showed that the three tests do not always agree in their choice for the correct model, which is expected. The F-test tends to select the simplest model more often than does the AIC or BIC, even if the more complex model is the correct model. The AIC tends to select the complex model more often than the BIC when the complex model is correct. But the BIC... 

With the complexity of modern pharmacokinetic-pharmacodynamic models, analytical derivation of sensitivity indexes is rarely possible because rarely can these models be expressed as an equation. More often these models are written as a matrix of derivatives and the solution to finding the sensitivity index for these models requires a software package that can do symbolic differentiation of the Jacobian matrix. Hence, the current methodology for sensitivity analysis of complex models is empirical and done by systematically varying the model parameters one at a time and observing how the model outputs change. While easy to do, this approach cannot handle the case where there are interactions between model parameters. For example, two... 

Pharmacokinetic-pharmacodynamic models are becoming increasingly complex through the incorporation of covariate information, effect mechanisms, and lower quantification limits of assays which reveal compartments not previously known to exist. With sparse data collected during Phase 3 trials it may not be possible to develop and support such complex models because of... 

PBPK/PD models refine our understanding of complex quantitative dose behaviors by helping to delineate and characterize the relationships between (1) the external/exposure concentration and target tissue dose of the toxic moiety, and (2) the target tissue dose and observed responses (Andersen et al. 1987 Andersen and Krishnan 1994). These models are biologically and mechanistically based and can be used to extrapolate the pharmacokinetic behavior of chemical substances from high to low dose, from route to route, between species, and between subpopulations within a species. The biological basis of... 

What are called physiologically based pharmacokinetic (PBPK) and pharmacodynamic (PBPD) models are more mechanistically complex and often include more compartments, more parameters, and more detailed expressions of rates and fluxes and contain more mechanistic representation. This type of model is reviewed in more detail in Section 22.5. Here, we merely classify such models and note several characteristics. PBPK models have more parameters, are more mechanistic, can exploit a wider range of data, often represent the whole body, and can be used both to describe and interpolate as well as to predict and extrapolate. Complexity of such models ranges from moderate to high. They typically contain 10 or more compartments, and can range to hundreds. The increase in the number of flux relationships between compartments and the related parameters is often more than proportional to compartment count. 

Pharmacokinetics is closely related to pharmacodynamics, which is a recent development of great importance to the design of medicines. The former attempts to model and predict the amount of substance that can be expected at the target site at a certain time after administration. The latter studies the relationship between the amount delivered and the observable effect that follows. In some cases the observable effect can be related directly to the amount of drug delivered at the target site [2]. In many cases, however, this relationship is highly complex and requires extensive modeling and calculation. In this text we will mainly focus on the subject of pharmacokinetics which can be approached from two sides. The first approach is the classical one and is based on so-called compartmental models. It requires certain assumptions which will be explained later on. The second one is non-compartmental and avoids the assumptions of compartmental analysis. 

Readers interested in such advanced topics are referred to a number of texts that describe these more complex pharmacokinetic models in detail [1-5] and to the website http //www.boomer.org/pkin/. 

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