(G-276) Modeling Blood Flow Dynamics and Hematocrit Distribution in Cerebral Microvascular Networks by Tracing Red Blood Cell Movement in Capillary Networks

A complex microvascular network supplies the brain with nutrients and oxygen. It incorporates several hundred miles of blood vessels, the majority of which are capillaries. Multiple mechanisms control blood perfusion in the brain including signaling from active neurons (i.e. neurovascular coupling) that can affect tone and diameter in arterioles but also in capillaries. Neurovascular coupling and proper blood flow control is critical for normal brain function and may be compromised in neurodegenerative diseases, such as Alzheimer’s and Dementia.

Tissue perfusion by red blood cells will depend on local blood flow and hematocrit (HD) levels that can dynamically vary as vessels react to stimuli. Absence of red blood cells can often be observed in capillaries (capillary stalling) and this could impair surrounding tissue oxygenation, viability and proper function. The relative inaccessibility of the cerebral microcirculation to experimental observation makes modeling an invaluable tool for understanding regulatory mechanisms of brain perfusion in health and in disease.

In this study we use computational tools to predict dynamic changes in blood flow and hematocrit distribution in reconstructed microvascular networks of the mouse cerebral cortex. We apply a novel approach of tracing individual Red Blood Cells (RBCs) through the capillary network to predict transient changes in hematocrit, viscosity and flow as arterioles and capillaries react to vasoactive signals. The proposed model of capillary flow dynamics will be utilized to explore mechanisms of capillary stalling and assist in multiscale analysis of cellular signaling, vessel mechanics and blood flow control in the brain.

A microvascular network of the mouse cerebral cortex is reconstructed from previous data (Blinder et al., Nat. Neurosci., 2013) and contains 10⁴ vessels within 1mm³ of brain tissue. Vessels are segmented to approximately 30µm in length and the resulting network is represented using a graph object in MATLAB. Hemodynamic simulations predict pressure (P), flow (Q) and Hematocrit (HD) distributions throughout the network. In each vascular segment, flow is calculated using the Hagen-Poiseuille equation based on the pressure gradient across the segment and effective hydrodynamic resistance that depends on vessel length, diameter, and effective viscosity. Conservation of blood flow and RBC flux is enforced at network bifurcation points and the non-continuum nature of blood is accounted for via empirical formulas for the Fahraeus-Lindqvist and phase separation effects. These empirical correlations have often been used to predict HD distribution in microvascular networks as well as effective blood viscosity from local values of Diameter (D) and HD. To account for transient changes in capillary HD, we modified the method of Schmid et al. (PLoS Comput Biol, 2017) and traced individual RBCs within the capillary network. The proposed method incorporates Poisson entry times in capillary network inlets and stochastic selection of RBC path at bifurcation points in agreement with the phase-separation empirical relationship.  RBC ‘traffic jams’ are resolved as previously described. The number of RBCs in a capillary segment at a particular time point is used to calculate the effective HD and viscosity to inform predictions for P and Q distribution in the network. 

Vessels in the microcirculation including arterioles and capillaries respond to different mechanical and chemical signals by adapting their diameter. The mechanisms that enable vascular network coordination, optimize tissue perfusion, and resource utilization are not clearly understood. An integrated modeling approach will allow us to elucidate mechanisms of cerebral blood flow control in health and disease. We have previously developed a comprehensive multiscale computational approach that integrates vascular cell signaling with vessel biomechanics and hemodynamics in a first attempt to link macroscale responses of blood perfusion to the underlying cellular-level signaling in the brain.  The multiscale model, however, cannot capture local changes in hematocrit with dynamic changes in vessel diameters. To address this limitation, we adapted a previously proposed method of RBC tracking to predict local HD and effective viscosity in capillaries, transiently. Our method introduces stochastic path selection for RBCs at capillary bifurcations that at steady state will converge to the HD distribution predicted by the widely used Pries and Secomb empirical correlations.

Thus, for model validation we compare steady state solution against our previous model (Tsoukias et al., JTB 2007) and transient evolution of network hemodynamics against the method of Schmid et al. We predict network hemodynamics upon brain functional stimulation, simulated by the local dilation of arterioles and capillaries, and we examine the contribution of capillary and arterioles to functional hyperemia. Capillary segments with no RBC flux are identified to quantify capillary stalls in the network.  We identify three mechanisms that promote capillary stalling: a) The presence of White Blood Cells (WBC) obstructing flow in the network; b) The constriction of capillaries by pericytes below a critical diameter for RBC perfusion and c) Q/HD heterogeneity leading to minimally perfused segments.

This work is supported by the National Institute of Neurological Disorders and Stroke and the National Institute of Aging of the NIH under award number R01NS19971.

Blinder, P., Tsai, P., Kaufhold, J. et al. The cortical angiome: an interconnected vascular network with noncolumnar patterns of blood flow. Nat Neurosci 16, 889–897 (2013). https://doi.org/10.1038/nn.3426

Pries, A.R., Secomb, T.W., Microvascular blood viscosity in vivo and the endothelial surface layer. American Journal of Physiology-Heart and Circulatory Physiology, 289(6). (2005). https://doi.org/10.1152/ajpheart.00297.2005.

Schmid, F., et al. Depth-dependent flow and pressure characteristics in corticol microvascular networks. PLOS Computational Biology, 13(2). (2017). https://doi.org/10.1371/journal.pcbi.1005392.

Tsoukias, N.M., Goldman, D., Vadapalli, A., Pittman, R.N., Popel AS. A computational model of oxygen delivery by hemoglobin-based oxygen carriers in three-dimensional microvascular networks. J Theor Biol. (2007) Oct 21;248(4):657-74. doi: 10.1016/j.jtbi.2007.06.012.