Myelin represents a significant barrier to water diffusion in white matter, and this phenomenon has been used in many models to describe diffusion-weighted MRI (DWI) signal in white matter in terms of its microstructural compartments^1,2. As models of DWI signal become more complex, an open question is whether the presence of water within myelin and the movement of water between compartments can influence DWI measurements.

In this abstract, we use a Monte Carlo simulation to assess the role of myelin water diffusion and myelin content on the apparent diffusion coefficient (D_app) and kurtosis (K_app) measured by clinical DWI.

A Monte Carlo simulation of water diffusion was created that accounts for myelin, while allowing water to diffuse within myelin and exchange with the surrounding compartments. Simulations were performed in a geometry of 200 myelinated axons, represented as two concentric circles. An example geometry is given in Fig 1 with a myelin volume fraction (v_m) = 0.36, and an intra-axonal volume fraction (v_i) = 0.35. The biophysical properties of water in white matter were characterized by 5 parameters—the unhindered diffusion coefficient of water in intra- and extra-axonal spaces (D₀ = 3.0 μm²/ms), the apparent diffusion coefficient of water in myelin (D_m), the transverse relaxation time-constants of water in the intra- and extra-axonal spaces (T_2ie = 80 ms) and in myelin (T_2m = 15 ms), and the relative density of water in myelin compared to the intra- and extra-axonal spaces (p_m = 0.5). Simulations were implemented in CUDA, wrapped into MATLAB, and run on a Linux computer with a GeForce GTX TITAN GPU.

A pulsed gradient spin echo diffusion experiment (∆=40ms, δ=20 ms, t_e = 100 ms, G_max = 0-60 mT/m) was simulated. To test the sensitivity of D_app and K_app to myelin water diffusion, simulations were run over a range in D_m = 0, 10^-5, 10^-4, 10^-3, 10^-2, 10^-1 µm²/ms. The mean axon radius was also varied, R = 0.25, 1, and 4 µm.

Another simulation was used to test if the set of D_app and K_app values are uniquely sensitive to the amount of myelin present in a geometry. Using the same diffusion experiment at D_m = 10^-3 µm²/ms and R = 1 µm, simulations were run with v_m = 0.36 and 0.10. Since a change in v_m requires a corresponding change in intra- & extra-axonal volume, geometries were generated with 6 different values in the relevant range of v_i between 0.50 and 0.60.

D_app and K_app are plotted vs D_m in Figure 2. As D_m increased from 0, there was an initial slight decrease in D_app followed by an increase. Conversely, K_app increased slightly with an increase in D_m, followed by a rapid decrease. The initial decrease in D_app and increase in K_app observed here is due to an increased amount of signal that has resided in the slowly diffusing myelin compartment. Some studies³ have suggested that the physiologic value of D_m is around 10^-3 µm²/ms. The subtle changes observed in D_app and K_app in this range of D_m could have an important impact on more complex models of DWI signal.

To test the influence of v_m, relative differences in D_app (blue) and K_app (red) calculated as

$$\Delta D_{app}=\frac{D_{app}\left(v_m=0.1\right)-D_{app}\left(v_m=0.36,v_i=0.35\right)}{D_{app}\left(v_m=0.36,v_i=0.35\right)}\cdot100\%$$

$$\Delta K_{app}=\frac{K_{app}\left(v_m=0.1\right)-K_{app}\left(v_m=0.36,v_i=0.35\right)}{K_{app}\left(v_m=0.36,v_i=0.35\right)}\cdot100\%$$

are plotted in Figure 3 in the cases of D_m=0 and 10^-3 µm²/ms. When myelin water diffusion was neglected, this simulation indicates that ∆D_app and ∆K_app were uniquely affected by the change in myelin content, as a change in v_m resulted in either a change in D_app, a change in K_app, or a change in both parameters. However, this sensitivity to myelin content is diminished when myelin water diffusion is considered, as both ∆D_app and ∆K_app crossed zero near v_i ≈ 0.57.

This simulation study suggests that myelin water and exchange of water between microstructural compartments has the potential to subtly influence DWI results. As models of DWI signal become more complex, there is the potential for models that neglect these mechanisms to be biased.