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.

翻译：背景与目标：本概念验证研究探讨了脑微循环中血流与氧输送的数学建模，重点在于理解血流动力学响应。通过耦合氧输送模型与血流动力学，本研究旨在预测时空血流动力学响应及其对血氧水平的影响，特别是在脱氧血容量与总血容量分数（DBV与TBV）的背景下。方法：利用菲克定律描述扩散，结合由阻尼波动方程导出的血流动力学响应函数，建立了一个耦合时空模型。菲克定律中的扩散系数基于哈根-泊肃叶流，动脉血流则通过压力-泊松方程进行数值近似。随后采用有限元方法对这些方程进行数值求解。数值实验基于高分辨率7特斯拉磁共振成像头部分割数据集进行，该数据集有助于区分动脉血管与不同脑组织分区。结果：通过利用7特斯拉磁共振成像头部分割数据集进行数值实验，进一步验证了该模型的适用性，该数据集促进了动脉血管与多种脑组织分区的区分。通过模拟血流动力学响应并分析其对体积DBV与TBV的影响，本研究为脑组织与血流的时空建模提供了有价值的见解。结论：本研究利用高分辨率7特斯拉磁共振成像头部数据进行时空建模，以探索脑血流、氧输送及脑动力学。该研究增强了对心血管疾病的理解，提高了模拟精度，并为靶向干预提供了潜在的临床应用前景。