Blood-flow limited model

Lumping compartments 1, 2, and 3 into a single homogeneous tissue compartment implies the blood flow-limited model. The tissue mass balance equation for a noneliminating organ is... 

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.

The three-compartment tissue model is ordinarily simplified by lumping all three subcompartments, lumping subcompartments 1 and 2, or lumping subcompartments 2 and 3. These simplifications result in the blood flow-limited (i.e., lumping all three subcompartments) and the membrane-limited (i.e., lumping any two subcompartments) tissue models. Differential mass balance equations for a noneliminating membrane-limited compartment are... 

A complete or global tissue distribution model consists of individual tissue compartments connected by the blood circulation. In any global model, individual tissues may be blood flow-limited, membrane-limited, or more complicated structures. The venous and arterial blood circulations can be connected in a number of ways depending on whether separate venous and arterial blood compartments are used or whether right and left heart compartments are separated. The two most common methods are illustrated in Figure 3 for blood flow-limited tissue compartments. The associated mass balance equations for Figure 3A are... 

Distinguishing Between Blood Flow-Limited and Membrane-Limited Organ Models... 

The simple assumptions that constitute blood-flow-limited PBPK models often are inadequate for characterizing the pharmacokinetics of macromolecules. Instead, a membrane- or permeability-rate-limited model is more common, where it is assumed that mass transfer across the cell membrane is rate-limiting. For these models, organ compartments are subdivided into at least two well-stirred spaces representing vascular Cry) and extravascular (Ct,ev) compartments. Such a system might be described by the following equations for a noneliminating tissue ... 

Validation of the Model. Outputs from the various models were compared to observations of blood concentrations reported from studies of oral gavage or intravenous exposures of rats to di- -butyl phthalate (NIEHS 1994, 1995). Based on the comparisons of model outputs to observed time courses for blood mono- -butyl phthalate concentrations from NIEHS (1994, 1995), Keys et al. (2000) concluded that the diffusion-limited, pH-trapping model more closely represents the empirical data. However, it is difficult to interpret this finding if the same data were used in the model optimization (see Table 4 of Keys et al. 2000). The diffusion-limited, pH-trapping model simulated reasonably well the time courses for blood concentrations of mono- -butyl phthalate reported by NIEHS (1994, 1995). A log-likelihood ratio test was used to compare the fit of the various augmented models to that of the flow-limited model. The diffusion-limited, pH-trapping model gave a better statistical fit to the empirical data than the other four models, with the next best fit achieved with enterohepatic circulation model. However, the latter model appeared to underestimate peak mono- -butyl phthalate plasma concentrations, which would be an important limitation for its use in risk assessment. 

A modification of the forcing function approach makes use of linear systems analysis for individual tissue compartments. Parametric or nonparametric fnnctions are fitted to observed blood drug concentration-time data, and then combined with tissue drug concentration-time measurements deconvolved to obtain a disposition fnnction for drug kinetics in the tissue. From the tissue disposition function, certain parameters for blood flow-limited organ models can be obtained. 

The physiological compartments of PBPK models are arranged and connected according to anatomical intercompartment blood flows, and the kinetics in each compartment is described by individual mass-balance differential equations. In the simplest case, it is assumed that mass transfer is blood flow limited and compartments are well-stirred spaces. Under this assumption, the rate of change of concentration (C) in a noneliminating tissue (T) maybe described by the following ordinary differential equation ... 

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... 

Since laminar flow itself occurs at low values of Re( = Dupl/x), the most likely situations are those characterized by low velocity (u) or high viscosity (p,), such as those involving the slow flow of polymers in extrusion reactors, or of blood in certain organs in animals. Even if not a close approximation in some cases, the predictable performance of an LFR may serve as a limiting model for actual performance. 

Although a simple bioconcentration model assumes rapid movement of a hydrophobic contaminant through an organism, distribution may be relatively slow. The predominant limiting factor in this case is the blood flow. Slow transport to lipid tissue sinks can result in lower apparent BCF values than would be the case if true equilibrium were attained. 

Fig. 17.5 Schematic representation of a physiological based model. Left figure shows the physiological structure, upper right figure shows a model for a perfusion rate limited tissue, and lower right figure shows a model for a permeability rate-limited tissue. Q denotes the blood flow, CL the excretion rate, KP the tissuerplasma distribution coefficient, and PS the permeability surface area coefficient.

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