A mathematical analysis of the influence of perfusion heterogeneity on indicator extraction

The permeability–surface-area product (PS) of an organ having heterogeneous capillary transit times can be determined by the sudden-injection, multiple-indicator dilution method from the relationship 1n[C_D(t)/C_P(t)]=(PS_c/Q_c)τ(t), where C_P and C_D are the venous concentrations of the permeating and nonpermeating indicators, respectively, and S_c/Q_c is the capillary surface-area-to-volume ratio, if the capillary transit-time function τ(t) is known. Rose and Goresky [12] analyzed the properties of τ(t) assuming that capillary and conducting-vessel transit times were coupled so that conducting vessels with short transit times serve capillaries with short transit times and conducting vessels with long transit times serve capillaries with long transit times (flow coupling). In this study, we examine the properties of τ(t) assuming random coupling of conducting vessels and capillaries by representing the organ as a convolution of the capillary transit-time distribution h(t) and the conducting-vessel transit-time distribution C(t). The results indicate that in such an organ τ(t) will be an increasing function bounded by the minimum and maximum capillary transit times and the duration of C(t). The analysis and simulations using typical h(t) and C(t) functions indicate that τ(t) can have similar properties regardless of whether flow coupling or random coupling of conducting and capillary vessels exists.