Kinetics and the Link to Mathematics

Substances in a biological system are constantly undergoing change. These changes can include transport (e.g., transport via the circulation or transport into or out from a cell) or transformation (e.g., biochemically changing from one substance to another). These changes and the concomitant outcomes form the basis for the system in which the substance interacts. 

How can one formalize these changes, and, once formalized, how can one describe their quantitative nature Dealing with these questions involves an understanding and utilization of concepts related to kinetics. 

The kinetics of a substance in a biological system are its spatial and temporal distribution in that system. The kinetics are the result of several complex events, including entry into the system, subsequent distribution (which may entail circulatory dynamics), transport into and from cells, and elimination (which usually requires biochemical transformations). Together these events characterize the substance and the system in which it resides. 

While the substance can be an element such as calcium or zinc, or a compound such as amino acids, proteins, or sugars that exist normally in the body, in this chapter, it will be assumed to be a drug that is not normally present in the system. Thus, in this chapter, the pharmacokinetics of a drug is defined as its spatial and temporal distribution in a system. Unlike substances normally present, input of drugs into the system occurs only from exogenous sources. In addition, unless otherwise noted, the system under consideration will be the whole body. It should be noted that this definition of pharmacokinetics differs somewhat from the more conventional definition given in Chapter 1. The reason for this is seen in the following section. 

From the spatial component of the definition, location in the system is important. From the temporal component of the definition, it follows that the amount of substance at a specific location is changing with time. The combination of these temporal and spatial components leads to partial derivatives. 

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