Bilinear Models for Spatio-Temporal Point Distribution Analysis: Application to Extrapolation of Whole Heart Cardiac Dynamics

Abstract

In this work we introduce the usage of bilinear models as a means of factorising the shape variation induced by subject variability and the contraction of the human heart. We show that it is feasible to reconstruct the shape of the heart at a certain point in the cardiac cycle if we are given a small number of shapes representing the same heart at different points in the same cycle, using the bilinear model. Depending on pathology and the ratios between healthy and pathological hearts in the training set, RMS reconstruction errors measured between 1.39 and 16.58 millimetres, with a median of 6.79 and 90th percentile of 9.95 millimetres.

Bilinear point distribution models for heart motion analysis

“…The resulting dataset consisted of 15 image volumes (temporal phases) obtained using retrospective ECG gating [8] with voxel dimensions of 0.4×0.4×2.0 mm 3 per subject. For more details about the data set and the segmentation method, the reader can refer to [9,10].…”

“…Please, see Hoogendoorn et al [9,10] for further details. Bilinear models cannot be computed from a single individual's data.…”

“…Such models were first presented by Tenenbaum and Freeman [11], with the objective of separating style from content. Since then, they have been successfully used in a variety of applications, such as separation of face anatomical characteristics from expression (see Mpiperis et al [12]), or, as used in the scope of this paper, anatomical characteristics of the heart from motion variations (Zhu et al [13,14] and Hoogendoorn et al [9,10]). In this latter application, a generic motion model for the whole population was computed through bilinear models, and it was used to extrapolate cardiac dynamics from a small number of frames of a volumetric cardiac sequence.…”

“…In order to find the most typical volumetric curve, we have computed the maximum contraction point (MCP) and the maximum deceleration point (MDP) of each patient. It is important to emphasize that MCP and MDP are computed with the volumetric data (already segmented data), and not with cross-correlation of the heart images as it was performed by Hoogendoorn et al [10] , in order to have consistency with the data used to create the model and to estimate the most common behavior. Fig.…”

Bilinear Models for Spatio-Temporal Point Distribution Analysis

“…To the best of our knowledge, our previous work (Hoogendoorn et al 2007) was the first to model individual and temporal variations of cardiac shape as two different sources of variability within the same set of data. Before, inter-subject variation and dynamics were not decoupled at all Mitchell et al 2002;Hamarneh and Gustavsson 2004).…”