Power-law kinetics of tracer washout from physiological systems.

Recent studies suggest that the tail of the washout of tracer-labeled substances from physiological systems can exhibit power-law behavior. In this work we develop a theoretical interpretation of the power-law behavior of the flow-limited washout of tracer-labeled water from the myocardium. Using minimal assumptions concerning the complicated structure of the coronary network we show that the washout from a heterogeneous flow system is given by h(t) approximately equal to A x p1 (V/t)(-beta), where beta is close to 3, p1 is the probability density of flows through the system, V is a constant volume associated with each pathway, and A is a constant. This prediction fits observed power-law washout behavior of tracer water in the heart. This theory is general enough to lead us to speculate that close examination of transport in other heterogeneity-perfused systems is likely to reveal similar power-law behavior.