PBPK

Volumes and flows are based on actual measured tissue volumes and blood flows to various organs, which have been tabulated for many species [5]. The basic approach for the development of a PBPK model, including model formulation, parameterization and validation, was described in detail by Clewell et al. [1]. These authors also included discussions on technical topics ranging from numerical solutions of PBPK models to sensitivity analysis. 

PBPK models require physicochemical and biochemical parameters along with physiological parameters. Historically, PBPK models were developed using a combination of in vitro data and/or in vivo PK data for a spedflc compound, and the amount of data necessary for model development was seen as prohibitive for application in the pharmaceutical industry. However, recent PBPK modeling papers 

Another important advance adding to the value of PBPK modeling in the pharmaceutical industry are physiological, mechanistic models developed to describe oral absorption in humans and preclinical species. Oral absorption is a complex process determined by the interplay of physiological and biochemical processes, physicochemical properties of the compound and formulation factors. Physiologically based models to predict oral absorption in animals and humans have recently been reviewed [18, 19] and several models are now commercially available. The commercial models have not been published in detail because of proprietary reasons but in essence they are transit models segmenting the gastrointestinal tract 

Mechanism-based PK/PD models contain specific expressions to characterize the different stages between drug administration and clinical effects, namely target site distribution, target binding and activation, pharmacodynamic interactions. 

Often PK/PD models are developed using classic PK models to describe plasma concentrations, which is often appropriate when P K samples are obtained during the PD assay so that plasma concentrations are most accurately simulated. A PBPK/PD model may be particularly useful when P K data are not available for a given PD assay, when a PD effect is not related to free plasma concentrations but instead is related to the free concentration in a target tissue, orwhena PK/PD model must be extrapolated to humans. 

---

Physiologically Based Pharmacokinetic (PBPK)/Pharmacodynamic (PD) Models... 

The structure and mathematical expressions used in PBPK models significantly simplify the true complexities of biological systems. If the uptake and disposition of the chemical substance(s) is adequately described, however, this simplification is desirable because data are often unavailable for many biological processes. A simplified scheme reduces the magnitude of cumulative uncertainty. The adequacy of the model is, therefore, of great importance, and model validation is essential to the use of PBPK models in risk assessment. 

PBPK models improve the pharmacokinetic extrapolations used in risk assessments that identify the maximal (i.e., the safe) levels for human exposure to chemical substances (Andersen and Krishnan 1994). PBPK models provide a scientifically sound means to predict the target tissue dose of chemicals in humans who are exposed to environmental levels (for example, levels that might occur at hazardous waste sites) based on the results of studies where doses were higher or were administered in different species. Figure 3-4 shows a conceptualized representation of a PBPK model. 

Note This is a conceptual representation of a physiologically based pharmacokinetic (PBPK) model for a hypothetical chemical substance. The chemical substance is shown to be absorbed via the skin, by inhalation, or by ingestion, metabolized in the liver, and excreted in the urine or by exhalation. 

No PBPK models were identified for methyl parathion. 

Physiologically Based Phamiacokinetic (PBPK) Model—Comprised of a series of compartments representing organs or tissue groups with realistic weights and blood flows. These models require a variety of physiological information tissue volumes, blood flow rates to tissues, cardiac output, alveolar ventilation rates and, possibly membrane permeabilities. The models also utilize biochemical information such as air/blood partition coefficients, and metabolic parameters. PBPK models are also called biologically based tissue dosimetry models. 

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... 

PBPK models results in more meaningful extrapolations than those generated with the more conventional use of uncertainty factors. 

If PBPK models for endosulfan exist, the overall results and individual models are discussed in this section in terms of their use in risk assessment, tissue dosimetry, and dose, route, and species extrapolations. 

No PBPK modeling studies were located for endosulfan. 

No data were located concerning whether pharmacokinetics of endosulfan in children are different from adults. There are no adequate data to determine whether endosulfan or its metabolites can cross the placenta. Studies in animals addressing these issues would provide valuable information. Although endosulfan has been detected in human milk (Lutter et al. 1998), studies in animals showed very little accumulation of endosulfan residues in breast milk (Gorbach et al. 1968 Indraningsih et al. 1993), which is consistent with the rapid elimination of endosulfan from tissues and subsequent excretion via feces and urine. There are no PBPK models for endosulfan in either adults or children. There is no information to evaluate whether absorption, distribution, metabolism, or excretion of endosulfan in children is different than in adults. 

Simulation methods have also been developed that include physiologically based pharmacokinetic modeling (PBPK) and methods such as Cloe PK, OMPPPlus, GastroPlus , SimCYP , and others [122] that are described elsewhere in this book. It is likely that the computational metabolism predictions could be integrated with these to assist in deriving more accurate predictions of human pharmacokinetic parameters. 

Notice Approaches for the Application of Physiologically-Based Pharmacokinetic (PBPK) Models and Supporting Data in Risk Assessment E-Docket ID No. ORD-2005-0022. Fed Reg July 28, 2005 70 (144) 43692-43693. 

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. 

In PBPK models tissue blood perfusion and tissue composition can be characterized independently of the drug thus such a model can be created once and reused for many different drugs. Furthermore, because physical laws (mass conservation, diffusion, or facilitated transport mechanisms) are incor-... 

Classic parameter estimation techniques involve using experimental data to estimate all parameters at once. This allows an estimate of central tendency and a confidence interval for each parameter, but it also allows determination of a matrix of covariances between parameters. To determine parameters and confidence intervals at some level, the requirements for data increase more than proportionally with the number of parameters in the model. Above some number of parameters, simultaneous estimation becomes impractical, and the experiments required to generate the data become impossible or unethical. For models at this level of complexity parameters and covariances can be estimated for each subsection of the model. This assumes that the covariance between parameters in different subsections is zero. This is unsatisfactory to some practitioners, and this (and the complexity of such models and the difficulty and cost of building them) has been a criticism of highly parameterized PBPK and PBPD models. An alternate view assumes that decisions will be made that should be informed by as much information about the system as possible, that the assumption of zero covariance between parameters in differ-... 

---