Theoretical Model for Water Diffusion in Tissues

TLDR

Tissue is modeled as a periodic array of cells with partially permeable membranes, where intra‑ and extracellular diffusion coefficients differ. The study aims to analytically and numerically investigate water diffusion in this tissue model, including the impact of T2 relaxation differences and application to ischemic brain changes. Analytical expressions for apparent diffusion coefficients in isotropic and anisotropic tissues were derived and benchmarked against Monte Carlo simulations, while also examining T2 relaxation effects and ischemic alterations. The derived ADCs differ from the fast‑exchange formula, and the observed diffusion changes are unlikely due to reduced membrane permeability but rather to combined shifts in cellular volume fraction and intra‑/extracellular diffusion.

Abstract

Abstract Water diffusion in a tissue model is studied both analytically and numerically. Tissue is regarded as a periodic array of boxes surrounded by partially permeable membranes (cells), embedded in an extracellular medium, intracellular and extracellular diffusion coefficients may differ. Expressions for the apparent diffusion coefficients (ADC) in isotropic and noniso‐tropic tissues are derived and compared with Monte Carlo simulations. Calculated ADCs disagree with values obtained from the widely used “fast exchange” formula. Effects of differences between intracellular and extracellular T 2 relaxation times on measured values of ADC and T 2 are discussed. The general analysis is specifically applied to the changes occurring in ADC following ischemic insults to brain tissue. It is found that although membranes affect ADC significantly, the observed changes in diffusion cannot be due to reduced membrane permeabilities. They may result from the combined effect of changes in cellular volume fraction, extracellular and intracellular diffusion.