Theorems and implications of a model-independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions. IV. Exact relationship between the terminal log-linear slope parameter beta and drug clearance

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Abstract
An exact formula relating the terminal log-linear beta parameter and the drug clearance is derived. The expression is valid for drugs with a linear, polyexponential disposition kinetics. The formula is useful for calculating the clearance when the clearance has changed between drug administrations and requires only drug level data from the terminal, log-linear elimination phase in addition to data from a single separate i.v. administration in the same subject. Data from an i. v. administration are necessary in order to apply the disposition decomposition technique to isolate and uniquely define the distribution kinetics in terms of the distribution function h(t).The different clearances can then be calculated from the beta values of the log-linear terminal drug level data and the parameters of h(t).The theoretical basis of the method and its assumptions and limitations are discussed and various pertinent theorems are presented. A computer program enabling an easy implementation of the proposed method is also presented. The mathematical and computational procedures of the method are demonstrated using kinetic data from i.v. and oral administrations of cimetidine, diazepam, and pentobarbital in human subjects. The classical V. beta method of approximating the clearance as the product of volume of distribution and beta is considered for comparison. For the three drugs considered the V. beta method which assumes a single exponential disposition kinetics leads to excessive errors when applied in absolute clearance comparisons. However, when applied in relative comparisons in the form of the “beta correction” the errors cancel out to some extent depending on the magnitude of the distribution kinetic effect. Whenever possible it is advisable to apply the proposed method to avoid such errors.