Constrained spherical deconvolution


Constrained Spherical Deconvolution (CSD) [Tournier2007] estimates a white matter fibre Orientation Distribution Function (fODF) based on an estimate of the signal expected for a single-fibre white matter population (the so-called response function). This is used as the kernel in a deconvolution operation to extract a white matter fODF from dMRI signal measured within each voxel.

User guide


Constrained Spherical Deconvolution as defined in [Tournier2007] relies on single-shell high angular resolution diffusion imaging (HARDI) data, containing at least one non-zero b-value. Ideally, the b-value used should be in the region of 2,500 – 3,000 s/mm² (at least for in vivo human brains), although good results have sometimes been obtained using b = 1000 s/mm² data.

In addition, this command expects that a suitable single-shell single-tissue response function has already been computed. Please refer to the Response function estimation page for details.


Constrained Spherical Deconvolution can be performed as:

dwi2fod csd dwi.mif response.txt fod.mif


  • dwi.mif is the dwi data set (input)

  • response.txt is the response function (input)

  • fod.mif is the resulting fODF (output)

Typically, you will also want to use the -mask option to avoid unnecessary computations in non-brain voxels:

dwi2fod csd -mask mask.mif dwi.mif response.txt fod.mif

The resulting WM fODFs can be displayed together with the mean fODF amplitude map using:

mrview fod.mif -odf.load_sh fod.mif