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

Abstract

Abstract. 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.

Statistical Analysis of Organs’ Shapes and Deformations: The Riemannian and the Affine Settings in Computational Anatomy

“…In [37,38,39], relevant factors discriminating between the motion patterns of healthy and unhealthy subjects were identified thanks to a Tucker decomposition on Polyaffine motion parameters with a constraint on the sparsity of the core tensor (which essentially defines the loadings of each mode combination). The key idea is to consider that the parameters resulting from the tracking of the motion over cardiac image sequences of a population can be stacked in a 4-way tensor along motion parameters × region × time × subject.…”

Improving Understanding of Long-Term Cardiac Functional Remodelling via Cross-Sectional Analysis of Polyaffine Motion Parameters

“…The healthy control subjects from the openly available STACOM 2011 cardiac motion tracking challenge dataset [1] (n = 15, 3 female, mean age ± SD = 28 ± 5) were used since these have already been used to validate the polyaffine cardiac motion tracking. The pathological subjects were a dataset of Tetralogy of Fallot patients (n = 10, 5 female, mean age ± SD = 21 ± 7), which were already used to analyse the polyaffine motion parameters in [10]. The Tetralogy of Fallot cohort forms a suitable testing set for this problem since there are known functional changes over time in these patients in response to poor pulmonary valve function or in the absence of a pulmonary valve.…”

Cardiac Motion Evolution Model for Analysis of Functional Changes Using Tensor Decomposition and Cross-Sectional Data

“…Previously, multilinear methods using higher-order PCA have been used for cardiac motion analysis, such as in [14], and later to compare spatial and temporal components in different populations in [15]. To our knowledge there has been no use of higher-order PLS applied to cardiac image analysis.…”

“…Tensorbased statistical analysis using higher-order decomposition (i.e. multilinear algebra) has been used for cardiac image analysis in recent years to, for example, characterise spatiotemporal motion patterns from cine-CMR [15] and to improve compressed-sensing CMR [27]. In both of these examples, unsupervised approaches were used, such as PCA or singular value decomposition (SVD), despite the fact that higher-order supervised approached exist.…”

“…Furthermore, given the low-dimensional parameterisation of the motion using this method, the parameters can be robustly compared between subjects and using this method the parameters were decomposed into spatial and temporal components using Tucker tensor decomposition, a form of higher-order principal component analysis (PCA). This method was later extended in [15] to include sparsity constraints on the core matrix to reduce the number of required combinations of spatial and temporal modes, and to build a combined comparative analysis of healthy and diseased patients.…”