Function for computing DTI and DKI spherical harmonics from diffusion and kurtosis tensors

designer.tractography.odf.dkiodfcartesian(odf, x, y, z)

Convert DKI ODF coefficients at voxel to Cartesian form.

Parameters

  • odf (array_like(dtype=float64)) – ODF coefficients at a voxel. There are 29 coefficients for DKI ODFs

  • x (array_like(dtype=float64)) – Cartesian x coordinates

  • y (array_like(dtype=float64)) – Cartesian y coordinates

  • z (array_like(dtype=float64)) – Cartesian z coordinates

Returns

cart – ODF in cartesian form

Return type

array_like(dtype=float64)

designer.tractography.odf.dkiodfspherical(odf, phi, theta)

Convert DKI ODFs coefficients at voxel to spherical form.

Parameters

  • odf (array_like(dtype=float64)) – ODF coefficients at a voxel. There are 29 coefficients for DKI ODFs

  • phi (array_like(dtype=float64)) – Polar phi angles

  • theta (array_like(dtype=float64)) – Polar theta angles

Returns

spherical – ODF in spherical form

Return type

array_like(dtype=float64)

designer.tractography.odf.dtiodfspherical(odf, phi, theta, radial_weight=4)

Convert DTI ODFs coefficients at voxel to spherical form.

Parameters

  • odf (array_like(dtype=float64)) – ODF coefficients at a voxel. There are 29 coefficients for DKI ODFs

  • phi (array_like(dtype=float64)) – Polar phi angles

  • theta (array_like(dtype=float64)) – Polar theta angles

  • radial_weight (float) – Radial weighting power for detecting directional differences (Default: 4)

Returns

spherical – ODF in spherical form

Return type

array_like(dtype=float64)

class designer.tractography.odf.odfmodel(dt, kt=None, mask=None, scale=None, res='med', l_max=6, radial_weight=4, nthreads=None)

Bases: object

DTI/DKI tractograpy class for computing ODFs and preparing spherical harmonics for DTI or DKI fiber tracking.

dkiodf(form='spherical', fa_t=0.9)

Computes DKI ODFs for the whole brain.

Parameters

  • form (str; optional; {‘spherical’, ‘cartesial’, ‘coefficient’}) – Form of ODF to return in (Default: ‘spherical’)

  • fa_t (float64; optional) – In rare cases the diffusion tensor may be extremely isotropic with very small eigenvalues, causing the kurtosis dODF to have erratic behavior with very large values, as the kurtosis dODF evaluates the inverse of D. Setting a threshold removes negative eigenvalues while preserving principal orientation in voxels where FA >= threshold (Default: 0.95)

Return type

DKI ODF in defined form

dkiodfhelper(dt, kt, radial_weight=4, fa_t=None, form='spherical')

Computes DKI fODF coefficient at a voxel. This function is intended to parallelize computations across the brain.

Parameters

  • dt (array_like(dtype=float)) – Diffusion tensor containing 6 elements

  • kt (array_like(dtype=float)) – Kurtosis tensor containing 15 elements

  • radial_weighing (float; optional) – Radial weighting power for detecting directional differences (Default: 4)

  • fa_t (float64) – In rare cases the diffusion tensor may be extremely isotropic with very small eigenvalues, causing the kurtosis dODF to have erratic behavior with very large values, as the kurtosis dODF evaluates the inverse of D. Setting a threshold removes negative eigenvalues while preserving principal orientation in voxels where FA >= threshold

  • form (str; optional; {‘spherical’, ‘cartesian’, ‘coefficient’}) – Form of ODF to return in (Default: ‘spherical’)

Returns

odf – DKI ODFs in either coefficient, spherical, or cartesian form

Return type

array_like(dtype=float)

dtiodf(form='spherical')

Computed DTI ODFs for the whole brain (ellipsoids)

Parameters

form (str; optional; {‘spherical’, ‘cartesian’, ‘coefficient’}) – Form of ODF to return in (Default: ‘spherical’)

Return type

DTI ODF in defined form

dtiodfhelper(dt, form='spherical')

Computes DTI fODF coefficient at a voxel. This function is intended to parallelize computations across the brain. Use only for diffusion ellipsoids.

Parameters

  • dt (array_like(dtype=float)) – Diffusion tensor containing 6 elements

  • radial_weighing (float; optional) – Radial weighting power for detecting directional differences (Default: 4)

  • form (str; optional; {‘spherical’, ‘coefficient’}) – Form of ODF to return in (Default: ‘spherical’)

Returns

odf – DKI ODFs in either coefficient, spherical, or cartesian form

Return type

array_like(dtype=float)

odf2sh(odf)

Converts whole-brain ODFs to spherical harmonics sampled at direction set specified by resolution. Only the real portion is returned.

Parameters

odf (4D ODF file containing spherical ODFs)

Returns

sh – Shperical harmonic expansion of ODF

Return type

array_like(dtype=float64)

odf2shhelper(odf, B, scale)

Helper function to parallelize computation spherical harmonic expansion at a voxel.

Parameters

  • odf (array_like(dtype=float64)) – Spherical ODF values at a voxel

  • B (array_like(dtype=complex)) – Spherical harmonic basis set to compute expansion

  • scale (float64) – Value of dMRI metric to multiply ODF with to control stopping criteria in tractography

Returns

sh

Return type

Shpherical harmonic expansion of ODF at voxel

odfmaxhelper(odf)

Find local maxima of ODF over spherical grid at voxel

Parameters

odf (array_like(dtype=float64)) – Spherical ODF values at a voxel

Returns

  • odfmax (array_like(dtype=float64)) – Local maxima of ODF over spherical grid in descending order

  • dirmax (array_like(dtype=float64)) – Corresponding direction vector where local ODF maxima occur

savenii(var, path)

Write out NifTI output of associated spherical harmonic file

Parameters

  • var (array_like) – variable to write out

  • path (str) – Path to output file

Return type

None; writes out file

designer.tractography.odf.shbasis(deg, phi, theta, method='scipy')

Computes shperical harmonic bases for all orders (even and odd), using functions defined by scipy, Tournier, or Descoteaux.

Parameters

  • deg (list of ints) – Degrees of harmonic

  • phi (array_like) – (n, ) vector denoting polar coordinates

  • theta (array_like) – (n, ) vector denoting azimuthal coordinates

  • method (str; optional; {scipy, tournier, descoteaux}) – Define method for SH basis set

Returns

Harmonic samples at theta and phi at specified order

Return type

complex array_like