Tensor estimation for double-pulsed diffusional kurtosis imaging

Calvin B. Shaw, Edward S. Hui, Joseph A. Helpern, Jens H. Jensen (Corresponding Author)

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Article numbere3722
JournalNMR in Biomedicine
Issue number7
Publication statusPublished - Jul 2017
Externally publishedYes


  • brain
  • DKI
  • double diffusion encoding
  • kurtosis
  • least squares
  • microscopic diffusion anisotropy
  • MRI
  • tensor

ASJC Scopus subject areas

  • Molecular Medicine
  • Radiology Nuclear Medicine and imaging
  • Spectroscopy


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