Robust constrained weighted least squares for in vivo human cardiac diffusion kurtosis imaging

Cardiac diffusion tensor imaging (cDTI) can investigate the microstructure of heart tissue. At sufficiently high b-values, additional information on microstructure can be observed, but the data require a representation such as diffusion kurtosis imaging (DKI). cDTI is prone to image corruption, which is usually treated with shot rejection but which can be handled more generally with robust estimation. Unconstrained fitting allows DKI parameters to violate necessary constraints on signal behavior, causing errors in diffusion and kurtosis measures.

We developed robust constrained weighted least squares (RCWLS) specifically for DKI. Using in vivo cardiac DKI data from 11 healthy volunteers collected with a Connectom scanner up to b-value $1350s/m{m}^2$ , we compared fitting techniques with/without robustness and with/without constraints.

Constraints, but not robustness, made a significant difference on all measures. Robust fitting corrected large errors for some subjects. RCWLS was the only technique that showed radial kurtosis to be larger than axial kurtosis for all subjects, which is expected in myocardium due to increased restrictions to diffusion perpendicular to the primary myocyte direction. For $b=1350s/m{m}^2$ , RCWLS gave the following measures across subjects: mean diffusivity (MD) $1.68\pm 0.050\times 10^{-3}{\text{mm}}^2/s$ , fractional anisotropy (FA) $0.30\pm 0.013$ , mean kurtosis (MK) $0.36\pm 0.027$ , axial kurtosis (AK) $0.26\pm 0.027$ , radial kurtosis (RK) $0.42\pm 0.040$ , and RK/AK $1.65\pm 0.19$ .

Fitting techniques utilizing both robust estimation and convexity constraints, such as RCWLS, are essential to obtain robust and feasible diffusion and kurtosis measures from in vivo cardiac DKI.