Rate parameters, pharmacokinetic model

Physiologically Based Pharmacokinetic (PBPK) Model—is 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. 

Absorbed lead is distributed in various tissue compartments. Several models of lead pharmacokinetics have been proposed to characterize such parameters as intercompartmental lead exchange rates, retention of lead in various pools, and relative rates of distribution among the tissue groups. See Section 2.3.5 for a discussion of the classical compartmental models and physiologically based pharmacokinetic models (PBPK) developed for lead risk assessments. 

PBPK and classical pharmacokinetic models both have valid applications in lead risk assessment. Both approaches can incorporate capacity-limited or nonlinear kinetic behavior in parameter estimates. An advantage of classical pharmacokinetic models is that, because the kinetic characteristics of the compartments of which they are composed are not constrained, a best possible fit to empirical data can be arrived at by varying the values of the parameters (O Flaherty 1987). However, such models are not readily extrapolated to other species because the parameters do not have precise physiological correlates. Compartmental models developed to date also do not simulate changes in bone metabolism, tissue volumes, blood flow rates, and enzyme activities associated with pregnancy, adverse nutritional states, aging, or osteoporotic diseases. Therefore, extrapolation of classical compartmental model simulations... 

While these models simulate the transfer of lead between many of the same physiological compartments, they use different methodologies to quantify lead exposure as well as the kinetics of lead transfer among the compartments. As described earlier, in contrast to PBPK models, classical pharmacokinetic models are calibrated to experimental data using transfer coefficients that may not have any physiological correlates. Examples of lead models that use PBPK and classical pharmacokinetic approaches are discussed in the following section, with a focus on the basis for model parameters, including age-specific blood flow rates and volumes for multiple body compartments, kinetic rate constants, tissue dosimetry,... 

In pharmacokinetics empirical models are for example compartment models where the body is sub-divided into one or more compartments and the drug is assumed to distribute and be eliminated with first-order rate constants. Typical model parameters are the rate constants and the volumes of the compartments. The compartmental models reflect the physiological reality only to a very limited degree. Despite this limitation compartment models are essential in drug development and have received considerable attention and showed huge utility and impact on the labeling of drugs on the market [4]. 

The use of distributed pharmacokinetic models to estimate expected concentration profiles associated with different modes of drug delivery requires that various input parameters be available. The most commonly required parameters, as seen in Equation 9.1, are diffusion coefficients, reaction rate constants, and capillary permeabilities. As will be encountered later, hydraulic conductivities are also needed when pressure-driven rather than diffusion-driven flows are involved. Diffusion coefficients (i.e., the De parameter described previously) can be measured experimentally or can be estimated by extrapolation from known values for reference substances. Diffusion constants in tissue are known to be proportional to their aqueous value, which in turn is approximately proportional to a power of the molecular weight. Hence,... 

Reaction rate parameters required for the distributed pharmacokinetic model generally come from independent experimental data. One source is the analysis of rates of metabolism of cells grown in culture. However, the parameters from this source are potentially subject to considerable artifact, since cofactors and cellular interactions may be absent in vitro that are present in vivo. Published enzyme activities are a second source, but these are even more subject to artifact. A third source is previous compartmental analysis of a tissue dosed uniformly by intravenous infusion. If a compartment in such a study can be closely identified with the organ or tissue later considered in distributed pharmacokinetic analysis, then its compartmental clearance constant can often be used to derive the required metabolic rate constant. 

The three major parameters examined in urinary excretion bioavailability studies are the cumulative amount of drug excreted unmetabolized in the urine ( Xu)-, the maximum urinary excretion rate (ERmax) and the time of maximum excretion rate (Tmax)- In simple pharmacokinetic models, the rate of appearance of drug in the urine is proportional to the concentration of drug in the systemic circulation. Thus, the values for Tmax and ERmax for urine studies are analogous to the Tmax and Cmax values derived from blood level studies. The value of r ax decreases as the absorption rate of the drug increases, and increases as the... 

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... 

The principal parameter used to indicate the rate of drug absorption is Cmax, even though it is also influenced by the extent of absorption the observed fmaX is less reliable. Because of the uncertainty associated with Cmax, it has been suggested (Endrenyi Yan, 1993 Tozer, 1994) that Cmax/AUCo-loq/ where AUCo-loq is the area under the curve from time zero to the LOQ of the acceptable analytical method, may more reliably measure the rate of drug absorption, except when multiexponential decline is extensive. Estimation of the terms should be based on the observed (measured) plasma concentrationtime data and the use of non-compartmental methods rather than compart-mental pharmacokinetic models. MRTs, from time zero to the LOQ of the analytical method, for the test and reference products can be compared, assuming that first-order absorption and disposition of the drug apply (Jackson Chen, 1987). 

Unlike the estimates of dosage rates and average steady-state plasma concentrations, which may be determined independently of any pharmacokinetic model in that systemic clearance is the only pharmacokinetic parameter used, the prediction of peak and trough steady-state concentrations requires pharmacokinetic compartmental model assumptions. It is assumed that, (i) drug disposition can be adequately described by a one-compartment pharmacokinetic model, (ii) disposition is independent of dose (i.e. linear pharmacokinetics apply), and (iii) the absorption rate is much faster than the rate of elimination of the drug, which is always valid when the drug is administered intravenously. For clinical applications, these assumptions are reasonable. 

Pharmacokinetic models to describe, as a function of formaldehyde air concentration, the rate of formation of formaldehyde-induced DNA-protein cross links in different regions of the nasal cavity have been developed for rats and monkeys (Casanova et al. 1991 Heck and Casanova 1994). Rates of formation of DNA-protein cross links have been used as a dose surrogate for formaldehyde tissue concentrations in extrapolating exposure-response relationships for nasal tumors in rats to estimate cancer risks for humans (EPA 1991a see Section 2. 4.3). The models assume that rates of cross link formation are proportional to tissue concentration of formaldehyde and include saturable and nonsaturable elimination pathways, and that regional and species differences in cross link formation are primarily dependent on anatomical parameters (e g., minute volume and quantity of nasal mucosa) rather than biochemical parameters. The models were developed with data from studies in which... 

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