Pharmacokinetic model process

Absorption, distribution, biotransformation, and excretion of chemical compounds have been discussed as separate phenomena. In reality all these processes occur simultaneously, and are integrated processes, i.e., they all affect each other. In order to understand the movements of chemicals in the body, and for the delineation of the duration of action of a chemical m the organism, it is important to be able to quantify these toxicokinetic phases. For this purpose various models are used, of which the most widely utilized are the one-compartment, two-compartment, and various physiologically based pharmacokinetic models. These models resemble models used in ventilation engineering to characterize air exchange. 

Physiologically based pharmacokinetic models provide a format to analyze relationships between model parameters and physicochemical properties for a series of drug analogues. Quantitative structure-pharmacokinetic relationships based on PB-PK model parameters have been pursued [12,13] and may ultimately prove useful in the drug development process. In this venue, such relationships, through predictions of tissue distribution, could expedite drug design and discovery. 

The CAT model estimates not only the extent of drug absorption, but also the rate of drug absorption that makes it possible to couple the CAT model to pharmacokinetic models to estimate plasma concentration profiles. The CAT model has been used to estimate the rate of absorption for saturable and region-depen-dent drugs, such as cefatrizine [67], In this case, the model simultaneously considers passive diffusion, saturable absorption, GI degradation, and transit. The mass balance equation, Eq. (51), needs to be rewritten to include all these processes ... 

R. Suverkrup. Discontinuous absorption processes in pharmacokinetic models. /. Pharm. Sd. 1979,... 

If we let K = (D Sa Pc/d), then, since A is present in the equation, n must equal 1, so we have a first-order rate process. Fick s law of diffusion, which is important for quantitating rates of absorption, distribution, and elimination, is thus the basis for using first-order kinetics in most pharmacokinetic models. 

In fact, physiologically based pharmacokinetic models are similar to environmental fate models. In both cases we divide a complicated system into simpler compartments, estimate the rate of transfer between the compartments, and estimate the rate of transformation within each compartment. The obvious difference is that environmental systems are inherently much more complex because they have more routes of entry, more compartments, more variables (each with a greater range of values), and a lack of control over these variables for systematic study. The discussion that follows is a general overview of the transport and transformation of toxicants in the environment in the context of developing qualitative and quantitative models of these processes. 

The discussion above provides a brief qualitative introduction to the transport and fate of chemicals in the environment. The goal of most fate chemists and engineers is to translate this qualitative picture into a conceptual model and ultimately into a quantitative description that can be used to predict or reconstruct the fate of a chemical in the environment (Figure 27.1). This quantitative description usually takes the form of a mass balance model. The idea is to compartmentalize the environment into defined units (control volumes) and to write a mathematical expression for the mass balance within the compartment. As with pharmacokinetic models, transfer between compartments can be included as the complexity of the model increases. There is a great deal of subjectivity to assembling a mass balance model. However, each decision to include or exclude a process or compartment is based on one or more assumptions—most of which can be tested at some level. Over time the applicability of various assumptions for particular chemicals and environmental conditions become known and model standardization becomes possible. 

For the sake of simplicity, simple monophasic pharmacokinetics (one compartment and one half-life) was assumed in the above example and in many other examples in this report. In real life, most chemicals express biphasic or polyphasic pharmacokinetics (several compartments and several half-lives). Squeezing a polyphasic pharmacokinetic behavior into a one-compartment model by assuming a single half-life may lead to negligible errors for some chemicals and serious misinterpretation of biomarker concentrations for others. The same can be said about nonlinear processes, such as metabolic induction, inhibition, and saturation. A good way to check the accuracy of a simple pharmacokinetic model is to verify its performance by comparing with a physiologically based pharmacokinetic (PBPK) model that may encompass the mentioned factors. 

The committee recommends that efforts be made to develop human pharmacokinetic models early in the study-design process to understand the influence of such factors as metabolism, sampling time, and population variability, that are critical to interpretation of the biomonitoring data. 

PBPK model Physiologically based pharmacokinetic model. Physiologically based compartmental model used to characterize pharmacokinetic behavior of a chemical. Available data on blood flow rates, and metabolic and other processes, which the chemical undergoes within each compartment are used to construct a mass-balance framework for the PBPK model. 

The distribution and disposition of a drug in the body result from a complex set of physiological processes and biochemical interactions. In principle, it is possible to describe these processes and interactions in mathematical terms and, if sufficient data are available, to predict the time course of drug and metabolite(s) in different species and at specific anatomic sites (15). A physiological pharmacokinetic model was developed to predict the deamination of cytosine arabinoside (ARA-C) in humans from enzyme parameters determined from homogenates of human tissue (16). ARA-C is converted to its inactive metabolite, uracil arabinoside (ARA-U) by cytidine deaminase, the activity of which varies substantially among tissues. 

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. ... 

Vancomycin is approximately 30 to 55% bound to plasma proteins. Its distribution after intravenous administration proceeds as a biphasic process and is consistent with a two or three compartment model. The half-life of the first distributive phase is approximately 0.4 hour in patients with normal renal function the second distributive phase is approximately 1.6 hours [172]. Consistent with its multicompartment pharmacokinetic modeling, vancomycin is widely distributed and penetrates into many different body fluids and... 

Physiologically based pharmacokinetic modeling (PB-PK) accurately describes nonlinear biochemical and physical processes computer hardware and... 

Bioaccumulation can be estimated by a kinetic model. In kinetic models (sometimes called physiological models or physiologically based pharmacokinetic models), consideration is given to the dynamics of ingestion, internal transport, storage, metabolic transformation, and excretion processes that occur in each type of organism for each type of chemical. In kinetic models,... 

The advantages of using non-compartmental methods for calculating pharmacokinetic parameters, such as systemic clearance (CZg), volume of distribution (Vd(area))/ systemic availability (F) and mean residence time (MRT), are that they can be applied to any route of administration and do not entail the selection of a compartmental pharmacokinetic model. The important assumption made, however, is that the absorption and disposition processes for the drug being studied obey first-order (linear) pharmacokinetic behaviour. The first-order elimination rate constant (and half-life) of the drug can be calculated by regression analysis of the terminal four to six measured plasma... 

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