Computational Mathematics Elucidates the Dependence of Brain Perfusion on Microcirculation

This dissertation presents a comprehensive mathematical model of microcirculatory cerebrovascular blood flow and oxygen transport to cortical tissue. As available measurements for blood flow, RBC oxygenation, RBC velocity and blood flow in cerebral blood microvessels (dia<100µm) in human patients are difficult to obtain, computer simulations are necessary for quantifying measurements acquired from imaging modalities, such as CT or fMRI. A 3D model of the human cortical microcirculation is presented, including oxygen perfusion to tissue. This model is closely validated against available in vivo animal and ex vivo human measurements. The sensitivity of these models to boundary conditions is investigated as well as the apparent “flat” tissue oxygen tension gradients at deep within the cortex. This model is than augmented with a novel biphasic blood flow model, the kinetic plasma skimming model (KPSM). This novel KPSM was developed out of necessity following a comprehensive investigation of existing biphasic blood flow models which were unable to accurately reproduce the phenomena of plasma skimming observed experimentally in physiological studies of the microcirculation. This biphasic model of blood flow, coupled with an improved nonlinear oxygen dissociation model, was deployed on four murine microcirculatory networks acquired from two-photon confocal microscopy. This study demonstrated the variability of hemodynamic properties along different “paths” through the cerebral microcirculation, and that vessels of similar types and lumen diameters may exhibit a wide variation in blood pressure, flow, hematocrit, RBC velocity or RBC oxygenation. Furthermore, the majority of the microcirculatory resistance was shown to reside between the pre-capillary arterioles and the ascending venules, and not in the descending arterioles or the surface pial arteries. Finally, the pulsatile distensibility of the microcirculatory vessels was addressed. Several fluid structure interaction models were investigated, as well as candidate solvers to compute the solution of these nonlinear wave equations. A two-step Lax Wendroff solver was identified as a robust method for computing hemodynamics across a distributed blood flow network. Dynamical blood flow, pressure, velocity and vessel volume was computed across a 3D simplified microcirculatory network. Three functional hyperemia case studies were investigated as possible vasodilatory mechanisms in response to neuronal activation. In each scenario, a different vessel type was vasodilated exclusively; a pial artery, a penetrating arteriole, or a collection of pre-capillary arterioles. The passive network response to these vasodilatory mechanisms was compared against changes in CBV as measured by fMRI. It was determined that none of these mechanisms activated in isolation would be capable of reproducing measured CBV changes, therefore these mechanisms must work in concert during functional hyperemia. Overall, the models presented here demonstrate that morphologically accurate, physiologically consistent models are capable of reproducing hemodynamic measurements at the micron scale within the cerebral vasculature. Furthermore, as these measurements are impossible to obtain in a distributed fashion, these computational models provide a comprehensive picture of intracranial dynamics that would otherwise be unobtainable. This model establishes the first-principles mechanistic understanding of cerebral oxygen supply and functional hyperemia that is necessary for quantifiable fMRI.