Pharmacokinetics mathematical basis

Studies of dmg absorption, distribution and elimination comprise what is referred to as pharmacokinetics. By contrast, the concentration of a pharmaceutical compound at the site(s) of action in relation to the magnitude of its effect(s) is referred to as pharmacodynamics. Both pharmacokinetics and pharmacodynamics have their roots in physiology, chemical kinetics, biochemistry, and pharmacology. They seek to provide a mathematical basis of the absorption, distribution, metabolisms, and... 

Dhillon and Gill (2006) defined pharmacokinetics as a fundamental scientific discipline that underpins applied therapeutics and noted that pharmacokinetics provides a mathematical basis to assess the time course of drugs and their effects in the body. Four pharmacokinetic processes that determine the concentration of a drug that has been administered are ... 

In the following sections we will review the mathematical basis of some of the important relationships that are used when pharmacokinetic principles are applied to the care of patients. The reader also is... 

One can now appreciate why conventional definitions of pharmacokinetics are a little different from the definition given here. The conventional definitions make references to events other than temporal and spatial distribution. These events are, in fact, consequences of a drug s kinetics, and thus the two should be separated. The processes of drug absorption, distribution, metabolism, and elimination relate to parameters that can only be estimated from a mathematical model describing the kinetics of the drug. The point is that, to understand the mathematical basis of pharmacokinetic parameter estimation, it is necessary to keep in mind the separation between kinetics per se and the use of data to estimate pharmacokinetic parameters. 

Stirred tank models have been widely used in pharmaceutical research. They form the basis of the compartmental models of traditional and physiological pharmacokinetics and have also been used to describe drug bioconversion in the liver [1,2], drug absorption from the gastrointestinal tract [3], and the production of recombinant proteins in continuous flow fermenters [4], In this book, a more detailed development of stirred tank models can be found in Chapter 3, in which pharmacokinetic models are discussed by Dr. James Gallo. The conceptual and mathematical simplicity of stirred tank models ensures their continued use in pharmacokinetics and in other systems of pharmaceutical interest in which spatially uniform concentrations exist or can be assumed. 

In the following sections, we will illustrate how these principles have been applied. We will highlight the fundamental mathematical models, that with increasing confidence have allowed us to identify compounds projected to exhibit good human pharmacokinetic profiles from simple preclinical data. These mathematical relationships may also provide the basis for a purely in silico prediction of human pharmacokinetics when coupled with robust in silico models of DMPK endpoints. 

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