  Background and Objective: This article concerns a diffusion-based
mathematical model for analyzing blood flow and oxygen transport within the
capillaries, emphasizing its significance in understanding the physiological
and biochemical dynamics of the cerebrovascular system and brain tissue. The
focus of this study is, in particular, on neurovascular coupling and the
spatiotemporal aspects of blood flow and oxygen transport in microcirculation.
Methods: By adopting a coupled modelling approach that integrates the
hemodynamic response function (HRF) with Fick's law and the Navier-Stokes
equations (NSEs), we provide a computational framework for the diffusion-driven
transport of deoxygenated and total blood volume fractions (DBV and TBV),
essential for understanding blood oxygenation level-dependent functional
magnetic resonance imaging (fMRI) and near-infrared spectroscopy (NIRS)
applications. Results: The applicability of the model is further demonstrated
through numerical experiments utilizing a 7 Tesla magnetic resonance imaging
(MRI) dataset for head segmentation, which facilitates the differentiation of
arterial blood vessels and various brain tissue compartments. By simulating
hemodynamical responses and analyzing their impact on volumetric DBV and TBV,
this study offers valuable insights into spatiotemporal modelling of brain
tissue and blood flow. Conclusions: By integrating spatiotemporal modelling
within a realistic head model derived from high-resolution 7 Tesla-MRI, we
analyze the complex interplay between blood flow, oxygen transport, and brain
tissue dynamics. This inclusion of a realistic head model not only enriches the
accuracy of our simulations but is also beneficial for understanding the
physiological and hemodynamic responses within the human brain.
