Pharmacokinetics mathematical models

DWA Bourne. Mathematical Modeling of Pharmacokinetic Data. Lancaster, PA Technomic Publishing Company, 1995. 

Other major early contributions of biochemical engineering have been in the development of the artificial kidney and physiologically based pharmacokinetic models. The artificial kidney has been literally a lifesaver. Pharmacokinetic models divide the body of an animal or human into various compartments that act as bioreactors. These mathematical models have been used very successfully in developing therapeutic strategies for the optimal delivery of chemotherapeutic drugs and in assessing risk from exposure to toxins. 

When evaluating the safety of chemicals in humans, it is very important to know the fate of chemicals in the human body and the amounts of exposure in daily activity. This section reviews the metabolic reactions of pyrethroids in humans, and the biomonitoring of pyrethroid metabolites in human urine for the exposure assessment. Mathematical modeling is a useful tool to predict the fate of chemicals in humans. This section also deals with the recent advance of mathematical modeling of pyrethroids to predict the pharmacokinetics of pyrethroids. 

In order to obtain an in vitro-in vivo relationship two sets of data are needed. The first set is the in vivo data, usually entire blood/plasma concentration profiles or a pharmacokinetic metric derived from plasma concentration profile (e.g., cmax, tmax, AUC, % absorbed). The second data set is the in vitro data (e.g., drug release using an appropriate dissolution test). A mathematical model describing the relationship between these data sets is then developed. Fairly obvious, the in vivo data are fixed. However, the in vitro drug-release profile is often adjusted by changing the dissolution testing conditions to determine which match the computed in vivo-release profiles the best, i.e., results in the highest correlation coefficient. 

Auton TR, Woollen BH A physiologically based mathematical model for the human inhalation pharmacokinetics of 1,1,2-trichloro-l,2,2-trifluoroethane. Int Arch Occup Environ Health 63 133-138, 1991... 

In the physiological sense, one can divide the body into compartments that represent discrete parts of the whole-blood, liver, urine, and so on, or use a mathematical model describing the process as a composite that pools together parts of tissues involved in distribution and bioactivation. Usually pharmacokinetic compartments have no anatomical or physiological identity they represent all locations within the body that have similar characteristics relative to the transport rates of the particular toxicant. Simple first-order kinetics is usually accepted to describe individual... 

Physiologically based pharmacokinetic (PBPK) models use mathematical descriptions of the uptake and disposition of chemical substances to quantitatively describe the relationships among critical biological... 

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