Diffusion time dependency of extracellular diffusion

Abstract

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

Methods: Model cellular systems containing only extracellular water were used to investigate the $t/f$ dependence of $D_{\mathrm{ex}}$ , 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). $D_{\mathrm{ex}}$ was obtained over a broad $t$ range (∼1-1000 ms) and then fit power-law equations $D_{\mathrm{ex}}\left(t\right)=D_{\text{const}}+\text{const}·t^{-{\vartheta }_t}$ and $D_{\mathrm{ex}}\left(f\right)=D_{\text{const}}+\text{const}·f^{{\vartheta }_f}$ .

Results: Both simulated and experimental results suggest that no single power-law adequately describes the behavior of $D_{\mathrm{ex}}$ over the range of diffusion times of most interest in practical dMRI. Previous theoretical predictions are accurate over only limited $t$ ranges; for example, ${\theta }_t={\theta }_f=-\frac{1}{2}$ is valid only for short times, whereas ${\theta }_t=1$ or ${\theta }_f=\frac{3}{2}$ is valid only for long times but cannot describe other ranges simultaneously. For the specific $t$ range of 5-70 ms used in typical human dMRI measurements, ${\theta }_t={\theta }_f=1$ 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 $t$ 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.

Keywords: D2O; diffusion; diffusion time; extracellular; liposome; oscillating gradient; phantom.