A FRACTAL APPROACH TO HETEROGENEOUS DRUG DISTRIBUTION - CALCIUM PHARMACOKINETICS

Purpose. To point out the importance of heterogeneity in drug distribu tion processes and develop a noncompartmental approach for the descrip tion of the distribution of drug in the body. Methods. A dichotomous b ranching network of vessels for the arterial tree connected to a simil ar venous network was used to describe the heterogeneity of blood flow in the successive generations of the networks. The relevant kinetics of drug distribution in the well perfused and the deep tissues was con sidered to take place under well stirred (homogeneous) and understirre d (heterogeneous) conditions, respectively. Results. A ''homogeneous m odel'' with classical kinetics (which is mathematically equivalent wit h the one-compartment model) was developed for these drugs which are c onfined to well perfused (''well stirred'') spaces. A ''heterogeneous model'' was proposed for the drugs reaching understirred spaces using a decreasing with time rate coefficient (fractal kinetics) to model th e diffusion of drug under heterogeneous conditions. The analysis of th e model equations revealed that the homogeneous model can be considere d as a special case of the heterogeneous model. Concentration-time plo ts of multiexponential type were generated using the heterogeneous mod el equation. The empirically used power functions of time for the anal ysis of calcium clearance curves, were found to be similar to the equa tion adhering to the heterogeneous model. Fittings comparable to multi exponential models were obtained when the heterogeneous model equation with only one adjustable parameter was applied to six sets of long pe riod calcium data. Conclusions. The heterogeneous processes of drug di stribution in the body can obey the principles of fractal kinetics. Ca lcium clearance curves were analysed with the heterogeneous model. The validity of multicompartmental models which are based on the concept of homogeneity to describe drug distribution should be reconsidered.