Premium
Tensor estimation for double‐pulsed diffusional kurtosis imaging
Author(s) -
Shaw Calvin B.,
Hui Edward S.,
Helpern Joseph A.,
Jensen Jens H.
Publication year - 2017
Publication title -
nmr in biomedicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.278
H-Index - 114
eISSN - 1099-1492
pISSN - 0952-3480
DOI - 10.1002/nbm.3722
Subject(s) - kurtosis , nuclear magnetic resonance , diffusion mri , tensor (intrinsic definition) , chemistry , materials science , biological system , physics , mathematics , magnetic resonance imaging , medicine , statistics , biology , radiology , pure mathematics
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.