Figure 1.
The general overview of DMS simulation procedure and module parameters.
Figure 2.
An illustration of the octree structure implemented in DMS.
In this simple example, we created groups of fiber bundles and star-shaped cells inside a simulation space which was partitioned using Nx×Ny×Nz of 4×4×1 (left) and 8×8×1 (right). For a water molecule (represented by the blue sphere) diffusing from r to r’, the need to check for the possible interactions along the path of diffusion can be reduced to the local subvolumes, as shown by the regions colored in green. The number of potential interacting objects to be processed, i.e. the cells indicated by the red arrows, can be decreased systematically.
Table 1.
The list of available NMR sequences in DMS.
Figure 3.
The 3D renderings of the bending (left) and beading (right) axon models.
Figure 4.
Modeling the neural medium using DMS.
The image at the center shows the immunostaining of neural tissues, and the others are the 3D renderings of simulated glial cells (colored in red) at different time points. The cell gradually expanded due to the effect of dynamic morphological evolution function. Dark blue spheres and light blue curves represented the diffusing particles and their motion trajectories.
Table 2.
The elapsed times (mean ± standard deviation) for the MC simulations using different dimensions of spatial subvolumes.
Figure 5.
(a) The transverse view of the hexagonal network of mesh-based cylindrical fibers, which had a diameter of 19 µm. (b) A snapshot of the MC simulation scene illustrating the zoomed area within the green square in (a), where the dark blue spheres and light blue curves are the diffusing particles and their corresponding diffusion trajectories, respectively. (c) Plots of the diffusion diffraction patterns obtained from single and double PGSE pulse sequences. (d) Plots of dMRI signal attenuation under different Np.
Figure 6.
The DMS simulation of water diffusion in virtual neuronal cells.
(a) A transverse section of the simulation scene which contains a hexagonal network of cells modeled by spheres (R = 2.58 µm). (b) A global view of the simulation space illustrating the arrangement of the cells. (c) A zoomed region of (a) showing the 3D rendering of cells (colored in red), diffusing particles (the spheres in deep blue) and their motion trajectories (the curves in light blue). (d) The ADCs estimated using the DT model for the case of constant diffusivity (red circle) and biphasic water diffusion model (blue cross).
Table 3.
Biexponential fitting parameters (mean ± standard deviation) for the case of constant diffusivity (D = 1.2×10−3 mm2/s).
Table 4.
Biexponential fitting parameters (mean ± standard deviation) for the case of biphasic water diffusion model (Dfast = 1.2×10−3 & Dslow = 0.4×10−3 mm2/s).
Figure 7.
We used DMS to combine two networks of fibers (colored in green and orange) for mimicking crossing (left), kissing (middle), and branching (right) WM fibers of human brains.
Dark blue spheres and light blue curves illustrated a subset of diffusing particles and their motion trajectories.
Figure 8.
Fiber tractography of the simulated crossing (left) and kissing (right) fibers.
The fiber tracts were represented by cylinders colored in blue, and the SDT-fODFs were color-coded depending on orientations (red: left-right, green: top-down, blue: inferior-superior).
Figure 9.
Fiber tractography of the simulated branching fibers.
(a) The DT-FA map and the regions of interests defined for clustering the fiber tracts. (b) Fiber tracking using the deterministic method. (c) Fiber tracking using the probabilistic method. The SDT-fODFs were colored in yellow.