Tensor estimation for double‐pulsed diffusional kurtosis imaging

Abstract

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.

JOURNAL CLUB: Evaluation of Diffusion Kurtosis Imaging of Stroke Lesion With Hemodynamic and Metabolic MRI in a Rodent Model of Acute Stroke

“…[35] More advanced DKI approach such as double diffusion encoding and symmetrized double pulsed field gradient MRI may provide novel insights of diffusion and kurtosis changes following stroke, which shall be investigated in the future. [47, 48]…”

In vivo microscopic diffusional kurtosis imaging with symmetrized double diffusion encoding EPI

“…In studies aiming to address this need, it has been shown that techniques that correlate diffusion over multiple displacements can detect features such as microscopic anisotropy that intra‐voxel averaging may obscure . Briefly, double diffusion encoding (DDE) (also referred to as double pulsed field gradient [double‐PFG]) MRI may yield microstructural information beyond conventional single diffusion encoding MRI . We have developed a symmetrized DDE (s‐DDE, previously referred to as sd‐PFG) NMR sequence that isolates microscopic kurtosis signal from diffusional heterogeneity and demonstrated its use in porous media .…”

Comparison of two types of microscopic diffusion anisotropy in mouse brain

“…A basic idea behind DP-DKI is that these two 3D vectors can be conveniently concatenated into a single six-dimensional (6D) displacement vector e s s 1 , s 2 ð Þ, where we use a tilde to signify a 6D quantity. 8,11,12,20 The distribution of displacements for the ensemble of diffusion molecules is then fully described by a single 6D probability density function. Associated with this 6D probability density function are a 6D diffusion tensor e D and a 6D kurtosis tensor f W, which are defined in analogy with the usual 3D case that applies to single diffusion encoding.…”

“…The noise bias correction was based on the standard method proposed by McGibney and Smith 39 and by Miller and Joseph 40 generalized to multiple channel coils, as described in Appendix B. The 6D diffusion and kurtosis tensors were obtained using in house software that implemented the method of Shaw and coworkers, 12 which employs a constrained weighted least squares fitting algorithm similar to ones routinely used for DKI. 41,42 Parametric maps of μFA 0 were then constructed by applying Equations ( 7)- (10).…”

“…In order to estimate μFA and μFA′, we apply a double diffusion encoding (DDE) 10 MRI method known as double‐pulsed diffusional kurtosis imaging (DP‐DKI) 8,11,12 . The study of MA has been one of the main applications of DDE MRI, 10 and DP‐DKI is a specific version based on an extension of the formalism of conventional (i.e., single diffusion encoding) diffusional kurtosis imaging 13,14 …”