Been thinking about this a little more during the ISMRM Diffusion Study Group Workshop.
In the most general case, it is necessary to be able to specify an arbitrary number of fixels, where each of those fixels may have a more complex representation.
Consider for example NODDI. It is tempting to specify the solitary fibre orientation as a spherical coordinate or 3-vector image, and the Watson distribution scalar orientation dispersion as a scalar image. However if you were to attempt to extend this to multiple fixels per voxel and a Bingham distribution per fixel, this strategy quickly breaks down.
What would provide a more general solution is for a Watson distribution to be one of the listed orientation representations, with the prospect of containing multiple fixels per voxel. The NODDI model would provide one such image, with maximum one fixel per voxel, and the orientation dispersion encoded via the kappa term in the Watson distribution. Getting to a single image with a single 3-vector per voxel, and a single scalar image with ODI (which is a transformation of kappa), would then be what has previously been referred to as model-derived parameters; that is, they can be calculated from the core model fit parameters, being the solitary Watson distribution. Note in particular that this is generic encoding of a Watson distribution on S2 and is in no way DWI-specific.
Given #74, we will need to expand that list to include a symmetric rank-4 kurtosis tensor.
Indeed in this process I think that the orientation representation "param" should in fact be removed.
Been thinking about this a little more during the ISMRM Diffusion Study Group Workshop.
In the most general case, it is necessary to be able to specify an arbitrary number of fixels, where each of those fixels may have a more complex representation.
Consider for example NODDI. It is tempting to specify the solitary fibre orientation as a spherical coordinate or 3-vector image, and the Watson distribution scalar orientation dispersion as a scalar image. However if you were to attempt to extend this to multiple fixels per voxel and a Bingham distribution per fixel, this strategy quickly breaks down.
What would provide a more general solution is for a Watson distribution to be one of the listed orientation representations, with the prospect of containing multiple fixels per voxel. The NODDI model would provide one such image, with maximum one fixel per voxel, and the orientation dispersion encoded via the kappa term in the Watson distribution. Getting to a single image with a single 3-vector per voxel, and a single scalar image with ODI (which is a transformation of kappa), would then be what has previously been referred to as model-derived parameters; that is, they can be calculated from the core model fit parameters, being the solitary Watson distribution. Note in particular that this is generic encoding of a Watson distribution on S2 and is in no way DWI-specific.
Given #74, we will need to expand that list to include a symmetric rank-4 kurtosis tensor.
Indeed in this process I think that the orientation representation
"param"should in fact be removed.