Dear Team,

I have a question regarding the interpretation of the spherical harmonic coefficients as produced with dwi2fod in MRTrix. From my understanding, the shape of the FODs can be represented as a linear combination of the spherical harmonics. In other words, in the simplest case, the basis function Y(l,m) that most resembles the shape of the FOD will have a large coefficient. For example, I have seen this in ACPC-oriented volumes in the white matter corresponding to the corticospinal tract (Corona Radiata, Posterior Limb of the Internal Capsule, and Cerebral Peduncles) for the coefficients of the Y(2,0) basis function which just looks like a vertical dumbell. The FODs are indeed very much vertically oriented here, so a large coefficient in this area makes sense to me.

That being said, I am confused as to the coefficients of the Y(0,0) volume, which is simply a sphere. My intuition tells me that an area with a large coefficient for the sphere would represent an area with high isotropic diffusion (i.e. grey matter and ventricles). However, upon examination of the Y(0,0) volume from MRTrix (i.e. first volume of the spherical harmonic coefficients 4D volume), the contrasts seem to be completely opposite from my expectations. The white matter has a much higher coefficient than the grey matter and the ventricles which are close to being black.

Is this due to some normalization of the coefficients that I am not aware of?

In another thread, (Fod2metric), the first volume was referred to as the total apparent fiber density (AFD) map. But if the basis function for this coefficient is a sphere, why would this represent the fiber density?

My last comment may seem off-topic, but when I calculate the spherical harmonic coefficients with Dipy using the peaks_from_model function, the first volume is simply a single value brain of 0.2821âs which is literally the equation for Y(0,0) = 1/sqrt(4*pi) (http://nipy.sourceforge.net/dipy/reference/dipy.reconst.html). However, shouldnât there be a different coefficient for every voxel weighting the contribution of the Y(0,0) basis function? I will contact the developers of Dipy separately to try to understand this behavior.

My ideal goal is to process data with Dipy to generate the SH coefficient volumes and use mrregister for registration; however, due to the different behaviors of MRTrix and Dipy, I think itâs important to understand how the SH coefficient volumes are generated before naively performing registration with these volumes.

Thank you for your time and explanation,

Eric