Maximum likelihood estimation of cardiac fiber bundle orientation from arbitrarily spaced diffusion weighted images.

We propose an estimation scheme for local fiber bundle direction in the left ventricle directly from gray values of arbitrarily spaced cardiac diffusion weighted images (DWI). The approach is based on a parametric and space-dependent mathematical representation of the myocardial fiber bundle orientation and hence the diffusion tensor (DT) for the ventricular geometry. By solving a nonlinear inverse problem derived from a maximum likelihood estimator, the degrees of freedom of the fiber and DT model can be estimated from the measured gray values of the DWIs. The continuity of the DT model allows to relax the restriction to the individual DWIs to match spatially like for voxelwise DT calculation. Hence, the spatial misalignment between image slices with different diffusion encoding directions, that is encountered in-vivo cardiac imaging practice can be integrated into the estimation scheme. This feature results then in a negligible impact of the spatial misalignment on the reconstructed solution. We illustrate the methodology using synthetic data and compare it against a previously reported fiber bundle reconstruction technique. To show the potential for real data, we also present results for multi-slice data constructed from ex-vivo cardiac diffusion weighted measurements in both mono- and bi-ventricular configurations.