Representing unsegmented vessels using available vascular data for bioheat transfer simulation

A primary challenge with any voxel domain generated from imaging data is limited voxel resolution. Due to the dimensional scale of blood vessels, not all vessels are captured and the loss of segmentable vascular data results in discontinuous blood vessels. The pre-capillary vessels, like arterioles, provide the highest resistance to blood flow. Due to the resolution limitations, these pre-capillary vessels are modeled with the tissue as a porous domain. This results in a loss of information that could have been modeled if the pre-capillary vessels were segmented and thus distinct from capillary bed. These vessels can only be modeled if a very high image resolution is used, increasing the imaging and computational simulation cost. Instead, a mathematical representation of the pressure drop induced in these unsegmented blood vessels is used. This paper provides equations to predict the flow resistance of unsegmented vasculature with reference to flow resistance of available segmented vascular data. These equations provide deeper insight into vascular resistances. The effect of using equations of flow resistance on bioheat transfer is analyzed by simulating a 3D vascular domain of 32 terminal vessels and five generations of bifurcation. Each generation is successively removed and substituted with the new flow resistance equations to analyze the error in heat transfer due to a lack of segmentation data. Two methods are proposed and demonstrated to show considerable error reduction in bioheat transfer.