Three-dimensional Prolate Spheroidal Extrapolation for Sparse DTI of the In-vivo Heart

We propose to extrapolate sparsely distribut ed cardiac Diffusion Tensor Image data usi ng the prolate spheroidal coordinate syst em. To this end, a segmented shape of the left ventricle myocardium is ma pped to the closest truncated prolate spheroid using a non-linear symmetric diffeomorphic registration algorithm. Thereby, the tensor compone nts and spatial position can be expressed in prolate spheroida l coordinates. After extrapolation, dense tensor data are mapped back using th e symmetric transformation. Comp arison with the classic Cartesia n extrapolation shows better consistency of the tensor field at unknown positions. It is demonstrated that this shape-based extrapolation metho d allows for robust 3D estimation of the in-vivo fibre architecture of the left ventri cle in human hearts, as the pr olate spheroidal coordinates in trinsically contain the symmetry properties of cardiac fibres.