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The effects of some simplifications of numerical schemes are also shown through numerical examples, such as linearization, simple average of diffusion coefficient, and approximate treatment for the coupling between radiation and material.
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MD (10−3 mm s−1) reflects a combined average of axial diffusion (diffusion along the principal axis) and radial diffusion (diffusion along the orthogonal direction), and FA reflects the extent to which diffusion within biological tissue is anisotropic, or constrained along a single axis, and can range from 0 (fully isotropic) to 1 (fully anisotropic).
For each average of diffusion-weighted images, six images without diffusion weighting (b = 0 sec/mm2) were also acquired with matching imaging parameters.
The majority of studies have used the metric of mean diffusivity (MD), which assesses the average degree of diffusion in all directions, as opposed to quantifying directionality.
Essential to successful modelling is the ability to determine reasonable estimates of the critical parameters, the growth rate ρ and the average diffusion coefficient D (an average of the diffusion coefficients in white matter D w and grey matter D g).
D is the diffusion parameter of the model: it is proportional to the average number of diffusion steps taken by a cell per each competitive interaction it is engaged in.
The average value of diffusion coefficient of the drug, Mdrug, is 4.13 × 10−6 cm s−1.
Thirty cases have been simulated to get the accurate average value of diffusion coefficients.
Meanwhile, thirty MD simulations with the same initial conditions have been performed to achieve the accurate average value of diffusion coefficient.
In each case, three averages of diffusion-weighted data were acquired using a 3D-segmented echo planar imaging sequence (echo time/repetition time = 122/530 ms, bandwidth = 789 Hz/pixel, matrix size: 168 × 192 × 120, resolution 0.94 × 0.94 × 0.94 mm).
Corresponding diffusion measurements for the binaries appeared to show a weighted average of the diffusion coefficients of the pure components.
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