Linear versus nonlinear pharmacokinetics

A general understanding of the definitions of linear and nonlinear will be helpful when discussing drug input into the body, whether that dose or input is delivered by classic delivery means or by novel controlled release delivery systems. Linear and nonlinear pharmacokinetics are differentiated by the relationship between the dose and the resulting drug concentration. A linear pharmacokinetics system exhibits a proportional relationship between dose and Cp for all doses, whereas nonlinear pharmacokinetics systems do not. 

Linear pharmacokinetics. For a simple linear pharmacokinetics case, the body can be modeled as a single drug compartment with first-order kinetic elimination—where the dose is administered and drug concentrations are drawn from the same compartment. For an intravenous bolus dose, the expected drug plasma concentration Cp versus time curves are shown in Fig. 1.10. The kinetics for this system are described by Eq. (1.6). The well-known solution to this equation is given by Eq. (1.7), and a linearized version of this solution is given in Eq. (1.8) and shown graphically in Fig. 1.13. 

If for the same one-compartment model the input is changed from an intravenous bolus to first-order kinetic input (e.g., gut absorption), the expected Cp versus time curves are shown in Fig. 1.14. The kinetics for this system are described by 

Although Eq. (1.10) is linear with respect to dose, it is not linear with respect to its parameters (ka and K). The definition of linear and nonlinear pharmacokinetic models is based on the relationship between Cp and dose, not with respect to the parameters. 

Nonlinear pharmacokinetics. Nonlinear pharmacokinetics simply means that the relationship between dose and Cp is not directly proportional for all doses. In nonlinear pharmacokinetics, drug concentration does not scale in direct proportion to dose (also known as dose-dependent kinetics). One classic drug example of nonlinear pharmacokinetics is the anticonvulsant drug phenytoin.38 Clinicians have learned to dose pheny-toin carefully in amounts greater than 300 mg/day above this point, most individuals will have dramatically increased phenytoin plasma levels in response to small changes in the input dose. 

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Factors analogous to those affecting gut absorption also can affect drug distribution and excretion. Any transporters or metabolizing enzymes can be taxed to capacity—which clearly would make the kinetic process nonlinear (see Linear versus Nonlinear Pharmacokinetics ). In order to have linear pharmacokinetics, all components (distribution, metabolism, filtration, active secretion, and active reabsorption) must be reasonably approximated by first-order kinetics for the valid design of controlled release delivery systems. 

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