In the previous post, we looked at how we can improve the speedup of fitting the simulated signal with Cython and what tweaks did we perform with the Legendre-Gauss Integration.
In this post, we will look at how the simulated signal can be visualized using the SHORE-3D Model and the GQI Model from the DIPY Library:
SHORE-3D Model: Exploits the ability of Compressed Sensing (CS) to recover the whole 3D Diffusion MRI (dMRI) signal from a limited number of samples while efficiently recovering important diffusion features such as the Ensemble Average Propagator (EAP) and the Orientation Distribution Function (ODF). Following are the crossings generated from the NODDIx model with crossings. The model helps visualize in the form of lobes:
GQI (Generalized q-sampling imaging):
Based on the Fourier transform relation between diffusion magnetic resonance (MR) signals and the underlying diffusion displacement, a new relation is derived to estimate the spin distribution function (SDF) directly from diffusion MR signals. This relation leads to an imaging method called generalized -sampling imaging (GQI), which can obtain the SDF from the shell sampling scheme used in -ball imaging (QBI) or the grid sampling scheme used in diffusion spectrum imaging (DSI). The GQI method can be applied to grid or shell sampling schemes and can provide directional and quantitative information about the crossing fibers.
The code for these visualizations can be found here.
- Continuous diffusion signal, EAP and ODF estimation via Compressive Sensing in diffusion MRI”, Merlet, Sylvain. L et al., Medical Image Analysis , Volume 17 , Issue 5 , 556 – 572