Dependence of apparent diffusion coefficients on axonal spacing, membrane permeability, and diffusion time in spinal cord white matter

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Abstract
We used a numerical simulation of water self‐diffusion among permeable cylinders to predict the dependence of MR‐based apparent diffusion coefficients in white matter on axonal separation, barrier permeability, and diffusion time (T). The transverse apparent diffusion coefficient (tADC), calculated with simulated diffusion‐sensitizing gradients perpendicular to the axon fibers, remains a function of T down to diffusion times as short as .1 μsec for a range of diffusion barrier permeability. As the diffusion time lengthens, the response of tADC depends on axon diameter, with decreases in tADC occurring earliest, and most dramatically, for the smallest fiber diameter simulated (2 μm). For a given axonal separation, asymptotic values of ADC are determined by permeability alone and are the same for 2‐μm and 11‐μm fibers of equal membrane permeability. The effect of increased relative intracellular volume is manifested primarily in a decrease in tADC at short T. Increases in interaxonal spacing increase the tADC at asymptotically long diffusion times and reduce the dependence on permeability. However, at the widest plausible axonal separations, permeability remains an important determinant of tADC. These simulations may enhance interpretation of measured tADC in the context of the underlying physiologic and structural changes at the cellular level that accompany white‐matter disease.