Negative power functions of time in pharmacokinetics and their implications

Abstract

When a clearance curve in pharmacokinetic studies--and in tracer kinetics in general--is well fitted by a sum of negative exponentials of time, in very many cases the data would also be well fitted over much or all of the same period by a function of time consisting mainly of a negative power or by a gamma function. There are also instances where two such power functions can be observed in the same clearance curve. Examples are given from numerous reanalyses of published results. These facts have not been explained, except as being fortuitous, by any existing theory or model based on two or more homogeneous compartments. Theoretical and practical implications are outlined and some general recipes are put forward with a view to replacing multicompartmental analysis.