The pharmacokinetics of cyclosporin (CsA) are unusual because of several heterogeneous features which include the presence of more than one conformer, considerable accumulation, in erythrocytes and lipoproteins, extensive plasma protein binding, distribution into deep tissues, biliary secretion and hepatic clearance involving a large number of metabolites. In this study, a stochastic compartmental model was developed to describe the heterogeneous elimination kinetics of CsA. This new approach relies on a probabilistic transfer model with a gamma distributed probability intensity coefficient for drug elimination. For comparative purposes both the stochastic model and compartmental deterministic models were fitted to real post infusion data from patients receiving CsA as a 2-hr intravenous infusion. The criteria for selecting the best model showed that the stochastic model, although simpler than the compartmental deterministic models, is more flexible and gives a better fit to the kinetic data of CsA than the compartmental deterministic models. The stochastic model with a random rate intensity coefficient adequately describes the heterogeneous pharmacokinetics of CsA.

Purpose, To develop the physiologically sound concept of fractal volume of drug distribution, nu (f) and evaluate its utility and applicability in interspecies pharmacokinetic scaling. Methods, Estimates for nu (f) of various drugs in different species were obtained from the relationship: nu (f) = (nu - V-pl) V-ap-V-pl/V-ap + Vpl where nu is the total volume of the species (equivalent to its total mass assuming a uniform density 1g/mL), V-pl is the plasma volume of the species and V-ap 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, V-c. the steady state volume of distribution, V-ss, and the volume of distribution following pseudodistribution equilibrium, V-z). 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 nu (f) 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.

The theory of nonlinear dynamical systems (chaos theory), which deals with deterministic systems that exhibit a complicated, apparently random-looking behavior, has formed an interdisciplinary area of research and has affected almost every field of science in the last 20 years. Life sciences are one of the most applicable areas for the ideas of chaos because of the complexity of biological systems. It is widely appreciated that chaotic behavior dominates physiological systems. This is suggested by experimental studies and has also been encouraged by very successful modeling. Pharmacodynamics are very tightly associated with complex physiological processes, and the implications of this relation demand that the new approach of nonlinear dynamics should be adopted in greater extent in pharmacodynamic studies. This is necessary not only for the sake of more detailed study, but mainly because nonlinear dynamics suggest a whole new rationale, fundamentally different from the classic approach. In this work the basic principles of dynamical systems are presented and applications of nonlinear dynamics in topics relevant to drug research and especially to pharmacodynamics are reviewed. Special attention is focused on three major fields of physiological systems with great importance in pharmacotherapy, namely cardiovascular, central nervous, and endocrine systems, where tools and concepts from nonlinear dynamics have been applied.