Tensor estimation for double-pulsed diffusional kurtosis imaging.
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.
Center for Biomedical Imaging, Medical University of South Carolina, Charleston, South Carolina, USA.|Department of Radiology and Radiological Science, Medical University of South Carolina, Charleston, South Carolina, USA.
Calvin B
CB
Shaw
Department of Diagnostic Radiology, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Pokfulam, Hong Kong, SAR, China.
Edward S
ES
Hui
Center for Biomedical Imaging, Medical University of South Carolina, Charleston, South Carolina, USA.|Department of Radiology and Radiological Science, Medical University of South Carolina, Charleston, South Carolina, USA.|Department of Neuroscience, Medical University of South Carolina, Charleston, South Carolina, USA.|Department of Neurology, Medical University of South Carolina, Charleston, South Carolina, USA.
Joseph A
JA
Helpern
Center for Biomedical Imaging, Medical University of South Carolina, Charleston, South Carolina, USA.|Department of Radiology and Radiological Science, Medical University of South Carolina, Charleston, South Carolina, USA.
Jens H
http://orcid.org/0000-0003-3219-4287
JH
Jensen
D000465:Algorithms; D016880:Anisotropy; D001921:Brain / Q000033:anatomy & histology* / Q000000981:diagnostic imaging*; D003627:Data Interpretation, Statistical; D056324:Diffusion Tensor Imaging / Q000379:methods*; D005260:Female; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008297:Male; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D055815:Young Adult
DKI; MRI; brain; double diffusion encoding; kurtosis; least squares; microscopic diffusion anisotropy; tensor