Diffusion time dependency of extracellular diffusion

Purpose: To quantify the variations of the power-law dependences on diffusion time t or gradient frequency (Formula presented.) of extracellular water diffusion measured by diffusion MRI (dMRI). Methods: Model cellular systems containing only extracellular water were used to investigate the (Formula presented.) dependence of (Formula presented.), 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(D₂O, deuterium oxide) dispersed in regular water (H₂O). (Formula presented.) was obtained over a broad (Formula presented.) range (∼1–1000 ms) and then fit power-law equations (Formula presented.) and (Formula presented.). Results: Both simulated and experimental results suggest that no single power-law adequately describes the behavior of (Formula presented.) over the range of diffusion times of most interest in practical dMRI. Previous theoretical predictions are accurate over only limited (Formula presented.) ranges; for example, (Formula presented.) is valid only for short times, whereas (Formula presented.) or (Formula presented.) is valid only for long times but cannot describe other ranges simultaneously. For the specific (Formula presented.) range of 5–70 ms used in typical human dMRI measurements, (Formula presented.) matches the data well empirically. Conclusion: The optimal power-law fit of extracellular diffusion varies with diffusion time. The dependency obtained at short or long (Formula presented.) 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.