Optimizing Diffusion-Weighted MRI Using Electrostatic Repulsion
Optimizing Diffusion-Weighted MRI Using Electrostatic Repulsion
In diffusion-weighted MRI, the signal attenuation of the diffusion-weighted signal compared to the unweighted signal can be used to calculate the apparent diffusion coefficient (ADC) in tissue. The relevant equation is =, where is the diffusion weighting strength [1]. Because diffusion in tissue can be anisotropic, it is better to measure the diffusion in three orthogonal directions and calculate the mean diffusivity (MD), which is typically done in diffusion-weighted MRI. If the diffusion is measured in at least six different directions, the anisotropic diffusion signal can be described by a second-order tensor that also allows for the quantification of the diffusion anisotropy [2, 3]. In this case, the diffusion signal is described by =, where is the diffusion weighting gradient direction. For more advanced models, more gradient directions are needed, or the gradient directions need to be distributed over multiple shells (different values for ).
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For optimal modeling of the tissue diffusion, the diffusion gradient directions need to be evenly distributed on a hemisphere (the signal attenuation in direction will be identical to directions ). This can be done using electrostatic repulsion of particles on a sphere [4]. This method also allows for optimal multishell gradient distributions, where the shell weighting determines if the sub-shells are optimized () or the total number of directions is optimized () [5]. Multiple shells are shown using points with different colors.
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