Advection and diffusion of substances in biological tissues with complex vascular networks

For highly diffusive solutes the kinetics of blood-tissue exchange is only poorly represented by a model consisting of sets of independent parallel ca pillary-tissue units. We constructed a more realistic multicapillary networ k model conforming statistically to morphometric data. Flows through the to rtuous paths in the network were calculated based on constant resistance pe r unit length throughout the network and the resulting advective intracapil lary velocity held was used as a framework for describing the extravascular diffusion of a substance for which there is no barrier or permeability lim itation. Simulated impulse responses from the system, analogous to tracer w ater outflow dilution curves, showed flow-limited behavior over a range of flows from about 2 to 5 ml min(-1) g(-1) as is observed for water in the he art in vivo. The present model serves as a reference standard against which to evaluate computationally simpler, less physically realistic models. The simulated outflow curves from the network model, like experimental water c urves, were matched to outflow curves from the commonly used axially distri buted models only by setting the capillary wall permeability-surface area ( PS) to a value so artifactually low that it is incompatible with the experi mental observations that transport is flow Limited. However, simple axially distributed models with appropriately high PSs will fit water outflow dilu tion curves if axial diffusion coefficients are set at high enough values t o account for enhanced dispersion due to the complex geometry of the capill ary network. Without incorporating this enhanced dispersion, when applied t o experimental curves over a range of flows, the simpler models give a fals e inference that there is recruitment of capillary surface area with increa sing flow. Thus distributed models must account for diffusional as well as permeation processes to provide physiologically appropriate parameter estim ates. (C) 2000 Biomedical Engineering Society. [S0090-6964(00)01003-1].