Numerical Simulation of Fluid and Heat Transfer in a Biological Tissue Using an Immersed Boundary Method Mimicking the Exact Structure of the Microvascular Network

摘要

The aim of this study is to develop a model of fluid and heat transfer in a biological tissue taking into account the exact structure of the related microvascular network, and to analyze the influence of structural changes of such a network induced by diabetes. A cubic region representing local skin tissue is selected as the computational domain, which in turn includes two intravascular and extravascular sub-domains. To save computational resources, the capillary network is reduced to a 1D pipeline model and embedded into the extravascular region. On the basis of the immersed boundary method (IBM) strategy, fluid and heat fluxes across a capillary wall are distributed to the surrounding tissue nodes by a delta function. We consider both steady and periodic blood pressure conditions at the entrances of the capillary network. Under steady blood pressure conditions, both the interstitial fluid pressure and tissue temperature around the capillary network are larger than those in other places. When the periodic blood pressure condition is considered, tissue temperature tends to fluctuate with the same frequency of the forcing, but the related waveform displays a smaller amplitude and a certain time (phase) delay. When the connectivity of capillary network is diminished, the capacity of blood redistribution through the capillary network becomes weaker and a subset of the vessel branches lose blood flow, which further aggravates the amplitude attenuation and time delay of the skin temperature fluctuation.