Descriptive and Intuitive Population-Based Cardiac Motion Analysis via Sparsity Constrained Tensor Decomposition

Analysing and understanding population-specific cardiac function is a challenging task due to the complex dynamics observed in both healthy and diseased subjects and the difficulty in quantitatively comparing the motion in different subjects. It was proposed to use affine parameters extracted from a Polyaffine motion model for a group of subjects to represent the 3D motion regionally over time for a group of subjects. We propose to construct from these parameters a 4-way tensor of the rotation, stretch, shear, and translation components of each affine matrix defined in an intuitive local coordinate system, stacked per region, for each affine component, over time, and for all subjects. From this tensor, Tucker decomposition can be applied with a constraint of sparsity on the core tensor in order to extract a few key, easily interpretable modes for each subject. Using this construction of a data tensor, the tensors of multiple groups can be stacked and collectively decomposed in order to compare and discriminate the motion in each group by analysing the different loadings of each combination of modes for each group. The proposed method was applied to study and compare left ventricular dynamics for a group of healthy adult subjects and a group of adults with repaired Tetralogy of Fallot.