A Coupled Diffusion Approximation for Spatiotemporal Hemodynamic Response and Deoxygenated Blood Volume Fraction in Microcirculation

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.