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

Abstract

0.1Spatially 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 bloods 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. 0.2 Author summaryThis research focuses on improving the accuracy of blood flow simulations in tiny blood vessels, known as microvascular networks. These simulations help understand how blood moves through the smallest vessels in the body, crucial for studying various health conditions. However, accurately simulating blood flow is challenging because imaged areas often dont capture entire tissue regions, leading to uncertainties. I developed an adaptive method for setting boundary conditions in these simulations. Due to its adaptive nature, the method can be applied to microvascular networks from various types of tissue, making it broadly applicable. This method was tested extensively using data from brain cortical networks and produced reliable results, proving its validity and scalability to extensive networks. Additionally, probabilistic approaches were used to assess how uncertainties in boundary conditions affect the simulations. A key contribution is the integration of the adaptive method into a Bayesian calibration framework. This framework assimilates simulations with observations and infers distributions over thousands of unknown boundary conditions, providing uncertainty estimates for blood flow simulations. The proposed adaptive method and uncertainty analysis are expected to be valuable for future studies of microvascular blood flow, improving both the accuracy of the simulations and the understanding of the associated uncertainties.