Multiscale modelling of brain tissue oxygen and glucose dynamics in tortuous capillary during ischaemia-reperfusion

Abstract

Brain ischaemia causes reduction of cerebral blood flow, which interrupts the transport of oxygen and glucose to brain tissue. These transport inefficiencies have also been associated with the complex cerebral microvasculature. In this study, the importance of cerebral capillary complexity and tissue interstitial porosity in oxygen and glucose transport and metabolism during brain tissue ischaemia is investigated using an asymptotic expansion homogenization method. Applying this technique produces new macroscale governing equations with associated microscale cell problems. Solving the latter on the brain tissue microstructural geometry will obtain parametric tensors, namely the conductivities of the capillary, K and interstitial space, E; and the diffusivities of a substrate in the capillary, DM,c, and in interstitial space, DM,t. From the microscale simulations, increasing the capillary tortuosity resulted in a decrement of K and DM,c, but no significant changes in E and DM,t. Meanwhile, increasing the capillary radius resulted in the decrease of all parameters except K. Then, the parametric tensors obtained are used to solve the macroscale governing equations on a one-dimensional brain model under ischaemia-reperfusion conditions. From the macroscale simulations, changing the capillary tortuosity affects the uptake and metabolism of oxygen and glucose during brain ischaemia-reperfusion. In addition, in more tortuous capillaries, oxygen and glucose are utilized rapidly at tissues proximal to the capillary during the reperfusion process, leaving only a small amount of these substrates for distal tissues. This could be associated with severe stroke outcome. It is thus proposed that the capillary tortuosity of a patient could potentially be used as an additional indicator in determining the severity of ischaemic stroke.