Diffusion time dependency of extracellular diffusion

To quantify the variations of the power-law dependences on diffusion time t or gradient frequency $$ of extracellular water diffusion measured by diffusion MRI (dMRI).

Model cellular systems containing only extracellular water were used to investigate the $$ dependence of $$ , the extracellular diffusion coefficient. Computer simulations used a randomly packed tissue model with realistic intracellular volume fractions and cell sizes. DMRI measurements were performed on samples consisting of liposomes containing heavy water(D₂ O, deuterium oxide) dispersed in regular water (H₂ O). $$ was obtained over a broad $$ range (∼1-1000 ms) and then fit power-law equations $$ and $$ .

Both simulated and experimental results suggest that no single power-law adequately describes the behavior of $$ over the range of diffusion times of most interest in practical dMRI. Previous theoretical predictions are accurate over only limited $$ ranges; for example, $$ is valid only for short times, whereas $$ or $$ is valid only for long times but cannot describe other ranges simultaneously. For the specific $$ range of 5-70 ms used in typical human dMRI measurements, $$ matches the data well empirically.

The optimal power-law fit of extracellular diffusion varies with diffusion time. The dependency obtained at short or long $$ limits cannot be applied to typical dMRI measurements in human cancer or liver. It is essential to determine the appropriate diffusion time range when modeling extracellular diffusion in dMRI-based quantitative microstructural imaging.