Fractal volume of drug distribution: it scales proportionally to body mass

Abstract

Purpose: To develop the physiologically sound concept of fractal volume of drug distribution, vf, and evaluate its utility and applicability in interspecies pharmacokinetic scaling.

Methods: Estimates for vf of various drugs in different species were obtained from the relationship: vf = (v - Vpl)(Vap - Vpl)/V + Vpl where v is the total volume of the species (equivalent to its total mass assuming a uniform density Ig/mL), Vpl is the plasma volume of the species and Vap is the conventional volume of drug distribution. This equation was also used to calculate the fractal analogs of various volume terms of drug distribution (the volume of central compartment, Vc, the steady state volume of distribution, Vss, and the volume of distribution following pseudodistribution equilibrium, Vz). The calculated fractal volumes of drug distribution were correlated with body mass of different mammalian species and allometric exponents and coefficients were determined.

Results: The calculated values of vf for selected drugs in humans provided meaningful and physiologically sound estimates for the distribution of drugs in the human body. For all fractal volume terms utilized, the allometric exponents were found to be either one or close to unity. The estimates of the allometric coefficients were found to be in the interval (0,1). These decimal values correspond to a fixed fraction of the fractal volume term relative to body mass in each one of the species.

Conclusions: Fractal volumes of drug distribution scale proportionally to mass. This confirms the theoretically expected relationship between volume and mass in mammalian species.