Pharmacokinetic models, mass transfer

JM Gallo, FC Lam, DG Perrier. Moment method for the estimation of mass transfer coefficients for physiological pharmacokinetic models. Biopharm Drug Dispos 12 127-137, 1991. 

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. 

Conceptual models of percutaneous absorption which are rigidly adherent to general solutions of Pick s equation are not always applicable to in vivo conditions, primarily because such models may not always be physiologically relevant. Linear kinetic models describing percutaneous absorption in terms of mathematical compartments that have approximate physical or anatomical correlates have been proposed. In these models, the various relevant events, including cutaneous metabolism, considered to be important in the overall process of skin absorption are characterized by first-order rate constants. The rate constants associated with diffusional events in the skin are assumed to be proportional to mass transfer parameters. Constants associated with the systemic distribution and elimination processes are estimated from pharmacokinetic parameters derived from plasma concentration-time profiles obtained following intravenous administration of the penetrant. 

Closure. After completing this chapter, the reader should be able to define and describe molecular diffusion and how it varies with temperature and pressure, the molar flux, bulk flow, the mass transfer coefficient, the Sherwood and Schmidt numbers, and the correlations for the mass transfer coefficient. The reader should be able to choose the appropriate correlation and calculate the mass transfer coefficient, the molar flux, and the rate of reaction. The reader should be able to describe the regimes and conditions under which mass transfer-limited reactions occur and when reaction rate limited reactions occur and to make calculations of the rates of reaction and mass transfer for each case. One of die most imponant areas for the reader apply the knowledge of this (and other chapters) is in their ability to ask and answer "What if. , questions. Finally, the reader should be able to describe the shrinking core model and apply it to catalyst regeneration and pharmacokinetics. 

In 1966 experimental studies were initiated on the susceptibility of anaesthetized hamsters to decompression insult, attempting to utilize existing pharmacokinetic and toxicological modeling techniques to characterize the role of the inert gas in producing decompression sickness. The hamster model consisted of three discrete elements. First, a mass transfer model had to be developed that would describe the uptake,... 

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 ... 

Provides more detailed examples in bioheat transfer and pharmacokinetics which may be useful in modeling heat and mass transfer in the brain parenchyma. 

The mass balances used in pharmacokinetics often contain rate constants which may include overall mass transfer coefficients and interfacial areas per volume. In cases like this, the relation between drug mass transfer and the more exact engineering coefficients is not known because the geometry implied in the pharmacokinetic models may not be known. In this case, we cannot use engineering correlations to predict pharmacokinetic behavior. We can only see whether drug concentration vs. time varies in roughly the manner expected for mass transfer. 

In this section we review some of the simplest pharmacokinetic models which contain mass transfer coefficients. We do so only to illustrate the basic ideas involved more complete analyses for specific drugs are beyond the scope for this book. To begin, we consider how we can easily measure blood flow in one artery. One way is to inject a known mass M of a nonadsorbing solute into the artery and measure the downstream concentration ci spectrophotometrically as a function of time. From a mass balance... 

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