Tensor estimation for double-pulsed diffusional kurtosis imaging

NMR Biomed. 2017 Jul;30(7). doi: 10.1002/nbm.3722. Epub 2017 Mar 22.


Double-pulsed diffusional kurtosis imaging (DP-DKI) represents the double diffusion encoding (DDE) MRI signal in terms of six-dimensional (6D) diffusion and kurtosis tensors. Here a method for estimating these tensors from experimental data is described. A standard numerical algorithm for tensor estimation from conventional (i.e. single diffusion encoding) diffusional kurtosis imaging (DKI) data is generalized to DP-DKI. This algorithm is based on a weighted least squares (WLS) fit of the signal model to the data combined with constraints designed to minimize unphysical parameter estimates. The numerical algorithm then takes the form of a quadratic programming problem. The principal change required to adapt the conventional DKI fitting algorithm to DP-DKI is replacing the three-dimensional diffusion and kurtosis tensors with the 6D tensors needed for DP-DKI. In this way, the 6D diffusion and kurtosis tensors for DP-DKI can be conveniently estimated from DDE data by using constrained WLS, providing a practical means for condensing DDE measurements into well-defined mathematical constructs that may be useful for interpreting and applying DDE MRI. Data from healthy volunteers for brain are used to demonstrate the DP-DKI tensor estimation algorithm. In particular, representative parametric maps of selected tensor-derived rotational invariants are presented.

Keywords: DKI; MRI; brain; double diffusion encoding; kurtosis; least squares; microscopic diffusion anisotropy; tensor.

MeSH terms

  • Algorithms*
  • Anisotropy
  • Brain / anatomy & histology*
  • Brain / diagnostic imaging*
  • Data Interpretation, Statistical*
  • Diffusion Tensor Imaging / methods*
  • Female
  • Humans
  • Image Enhancement / methods
  • Image Interpretation, Computer-Assisted / methods*
  • Male
  • Reproducibility of Results
  • Sensitivity and Specificity
  • Young Adult