Understanding SH-Order in MRtrix: dwi2response, dwi2fod, shconv, amp2sh

Hello everyone,

I’ve been playing with the MRtrix toolkit, particularly commands like dwi2response, dwi2fod, for Constrained Spherical Deconvolution (CSD) and have been finding it to be incredibly powerful. Thank you to everyone involved for your hard work!

I do have some questions that might seem naive, but they’re puzzling me. My current work involves using only 6 diffusion MRI measurements (6 directions), which meet the minimum requirement for SH-order 2. However, I noticed that the dwi2response command can calculate response function SH coefficients up to order 10 (its default order), and dwi2fod csd can generate SH-order 8 Fiber Orientation Distribution Functions (fODFs), which effectively have 45 channels. Following this spherical deconvolution, I used the shconv command on the response function and fiber ODF to perform a spherical convolution, resulting in an SH-order 8 image of the “reconstructed” signal. This is where I’m confused – my original data is only SH-order 2, yet the reconstructed signal appears to contain much more detailed data. Also, when I tried to use the amp2sh command to transform my 6 measurements into SH-order 8 data, it was unsuccessful, stating that transformation is only possible to SH-order 2, the maximum l_max value. (I also tried using Dipy for this projection, but it yielded poor results with anomalously high values at higher orders, which seems illogical.)

  1. How should I understand what’s happening in this process and interpret the results from higher-order reconstructions when starting with minimal data? Is it valid to consider the original SH-2 data and the reconstructed SH-8 data equivalent?

  2. Are there methods to effectively & directly generate an SH-8 data projection from just 6 measurements? And how do we assess the accuracy and reliability of higher-order spherical harmonic projections/reconstructions?

Thank you in advance for your insights!

Best regards,