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

TL;DR

This study utilizes spatiotemporal modelling with high-resolution 7 Tesla-MRI head data to explore cerebral blood flow, oxygen transport, and brain dynamics, enhancing understanding of cardiovascular conditions, improves simulation accuracy, and offers potential clinical applications for targeted interventions.

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.

Figures (9)

• Figure 1: Computational domain in cylindrical coordinates, taking into account for the axial symmetry in which blood flow in the artery domain $\Omega_\mathrm{A}$ is determined by the velocity field ${\bf u}$. Blood flowing through the boundary $\mathrm{B}$ is aligned along with normal vector $\vec{\bf n}$ and enters first arterioles with length $L$, where the pressure $p$ drops linearly, i.e., $\partial p / \partial \vec{\bf n}$ is constant, before it enters the capillary bed $\hat{\Omega}$.
• Figure 2: The vessel segmentation of this study together with the grey matter layer (left) and subcortical compartments (right) of the head model.
• Figure 3: Three different 14-mm-diameter regions of interest (ROIs) placed in (1) whitematter (WM), (2) grey matter (GM) and (3) brainstem (BS). The coronal slice of the visualization is shared by the ROIs' center points.
• Figure 4: The hemodynamic response function $\alpha(t)$ (red) and its time derivative $\alpha_{,t} (t)$ (blue) resulting from the time-mollified balloon model (Section \ref{['sec:balloon_model']}) in which the parameters have been selected as described in Table \ref{['tab:physical_parameters']}. The amplitude of about 20 % has been measured, e.g., for cat cortex kim2011temporal. The horizontal axis shows time $t$ in seconds and the vertical one shows the value of $\alpha(t)$.
• Figure 5: Time-evolution of average relative volumetric oxygenated (red) and deoxygenated (blue) blood volume (OBV and DBV) fraction with respect to their local mean values in the three different regions of interest (ROIs) of this study. The horizontal axis shows the time $t$ (s). In each case, the neural activity is modelled as a point source in the center of the ROI.