Theorems on log-convex disposition curves in drug and tracer kinetics

Conventionally, analysis of the dynamic behaviour of substances in the whole organism is based on the multiexponential paradigm (compartmental model). Alternatively the use of power functions has been proposed. In this paper a unified view is developed investigating the implications of observed log-convexity of disposition (clearance) curves. Using a non-compartmental approach it is proved that the disposition residence time distribution corresponding to a log-convex impulse response (blood concentration-time curve) belongs to the DFR (decreasing failure rate) class, implying that (1) the disposition curve has an exponential tail and (2) the relative dispersion of residence times is greater than or equal to one. This class of disposition curves includes multiexponential and power functions as special cases. In terms of the underlying biophysical principles the DFR property is discussed as a consequence of a dominant role of passive distribution processes of particles in the organism. The paper also deals with the corresponding properties of a recirculatory model using renewal theoretic concepts.