A coupled diffusion approximation for spatiotemporal hemodynamic response and deoxygenated blood volume fraction in microcirculation

Background and Objective: This proof of concept study investigates mathematical modeling 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: Numerical analysis reveals how simulated hemodynamic responses influence DBV and TBV fractions, highlighting the complex interactions between blood flow dynamics and oxygen transport. The results demonstrate the model's effectiveness in estimating blood volume fractions, showing its potential in mathematical spatiotemporal modeling of hemodynamic responses, which is in a key role in medical imaging modalities such as blood oxygenation level dependent functional MRI and near infrared spectroscopy. Conclusions: This study utilizes spatiotemporal modeling integrated into a realistic head model derived from high-resolution 7 Tesla-MRI to investigate the intricate relationships among cerebral blood flow, oxygen transport, and brain tissue dynamics. This approach not only enhances understanding of cardiovascular conditions but also improves the accuracy of simulations, providing valuable insights into physiological and hemodynamic responses within the human brain. The model's applicability to MRI-based head segmentations suggests potential clinical utility for developing targeted medical interventions.