Blood flow simulation and uncertainty quantification in extensive microvascular networks: Application to brain cortical networks

Spatially resolved simulation models of microcirculatory blood flow facilitate a detailed understanding of microcirculatory phenomena at the micrometer scale by capturing heterogeneity in blood flow. These models combine physical laws, empirical descriptions of the blood's complex rheological behavior, and in-vivo/ex-vivo imaging of the microvasculature. However, imaged areas often only partially represent self-contained tissue regions, leading to numerous vessels crossing boundaries and strongly influencing simulated blood flows through imposed boundary conditions. Selecting appropriate boundary conditions is challenging due to the heterogeneity of pressures and blood flows, resulting in significant uncertainties. This study addresses two key methodological aspects of spatially resolved blood flow simulations: selecting appropriate boundary conditions and quantifying the impact of boundary condition uncertainties on simulated hemodynamic variables. An adaptive method for assigning appropriate pressure boundary conditions is proposed and rigorously evaluated in extensive brain cortical networks against reference data from an established blood flow simulation model. A probabilistic approach is adopted to assess the impact of boundary condition uncertainties on blood flow simulations. The adaptive method is further integrated into a Bayesian calibration framework, inferring distributions over thousands of unknown pressure boundary conditions and providing uncertainty estimates for blood flow simulations. The adaptive method, which is straightforward to implement and scales well with extensive microvascular networks, produces hemodynamic simulations consistent with reference data, yielding depth-dependent pressure profiles and layer-wise capillary blood flow profiles consistent with previous studies. These phenomena are demonstrated to generalize also to biphasic blood flow simulation models incorporating in-vivo viscosity formulations. The uncertainty analysis further reveals a novel spatially heterogeneous and depth-dependent pattern in blood flow uncertainty. It is anticipated that the adaptive method for pressure boundary conditions will be useful in future applications of both forward and inverse blood flow modeling, and that uncertainty quantification will be valuable in complementing hemodynamic predictions with associated uncertainties.