Three-Dimensional Prolate Spheroidal Extrapolation for Sparse DTI of the In-Vivo Heart

Nicolas Toussaint¹, Christian Stoeck², Maxime Sermesant, ^1,3, Sebastian Kozerke, ¹², Philip Batchelor¹

We propose to extrapolate sparsely distributed cardiac DTI using prolate spheroid coordinate system. For this, a segmented shape of the left ventricle is mapped to the closest truncated prolate spheroid using a non-linear diffeomorphic registration algorithm. Thereby, the tensor components and spatial positions can be expressed in prolate spheroid coordinates. After extrapolation, dense tensors are mapped back using the symmetric transformation. Comparison with the classic Cartesian extrapolation shows better consistency of the tensor field at unknown positions. It is demonstrated that this shape-based extrapolation method gives robust estimation of the in-vivo fibre architecture of the left ventricle.