Development and application of a one-dimensional blood flow model for microvascular networks

Although there are many studies available in the literature on time domain modelling of one-dimensional network blood flow, the rheological properties of blood in this modelling framework have often been disregarded through the inviscid assumption. While such a simplification may be suitable for studying the larger vessels of the circulatory system, this approach cannot be taken when modelling flow in the vessels of microcirculation in which viscous effects are much more significant. In this study, a one-dimensional network blood flow model was extended to incorporate experimentally characterized properties of the non-Newtonian blood rheology, namely the reduction in the effective viscosity in thin vessels (the Fahraeus-Lindqvist effect) and the non-proportional splitting of red blood cells at junctions (phase separation). The numerical implementation was based on the high-order finite element technique with implicit time integration, necessitated by the decreasing length of vessels on this scale. Investigations in small networks indicated that the diameter dependence of viscosity has a major impact on the overall flow and should be included in small vessel networks. However, since phase separation effects are significant only in small arterioles of diameter less than 40 microm and require significant additional complexities in computation, they may be neglected for networks that do not contain these vessels without causing a large error. The proposed technique was applied to a coronary vascular subnetwork extracted from micro computed tomography scans of a rat heart consisting of approximately 2500 segments and proved to be computationally efficient, thus providing a potential foundation for applying this model to future physiological investigations.