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

TL;DR

This study develops a coupled mathematical model to simulate blood flow and oxygen transport in the brain's microcirculation, providing insights into hemodynamic responses and blood volume changes using high-resolution MRI data.

Contribution

It introduces a novel coupled diffusion and hemodynamic response model for cerebral microcirculation, integrating MRI data for high-resolution spatiotemporal analysis.

Findings

The model accurately predicts blood volume fractions in brain tissue.

Numerical experiments demonstrate the model's applicability to high-resolution MRI data.

Insights into cerebral blood flow dynamics and oxygen transport mechanisms.

Abstract

Background and Objective: This proof of concept study investigates mathematical modelling of blood flow and oxygen transport in cerebral microcirculation, focusing on understanding hemodynamic responses. By coupling oxygen transport models and blood flow dynamics, the research aims to predict spatiotemporal hemodynamic responses and their impact on blood oxygenation levels, particularly in the context of deoxygenated and total blood volume (DBV and TBV) fractions. Methods: A coupled spatiotemporal model is developed using Fick's law for diffusion, combined with the hemodynamic response function derived from a damped wave equation. The diffusion coefficient in Fick's law is based on Hagen-Poiseuille flow, and arterial blood flow is approximated numerically through pressure-Poisson equation (PPE). The equations are then numerically solved with the finite element method (FEM). Numerical experiments are performed on a high-resolution 7-Tesla Magnetic Resonance Imaging (MRI) dataset for head segmentation, which facilitates the differentiation of arterial blood vessels and various brain tissue compartments. 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: This study utilizes spatiotemporal modelling with high-resolution 7 Tesla-MRI head data to explore cerebral blood flow, oxygen transport, and brain dynamics. It enhances understanding of cardiovascular conditions, improves simulation accuracy, and offers potential clinical applications for targeted interventions.