Directional analysis of cardiac motion field based on the Discrete Helmholtz Hodge Decomposition

Abstract

The analysis of LV rotational motion could provide insights into myocardial dysfunction and predict the outcome of interventions, and this analysis could be performed more simply in separate rotational and radial components. In this study we present an automatic method for decomposing the cardiac motion field into radial and rotational components using the Discrete Helmholtz Hodge Decomposition (DHHD). The DHHD was applied to the following 3D motion fields (i) Synthetic complex motion fields, created by applying curl and gradient operators to Gaussian potentials, to determine numerical accuracy; (ii) Synthetic motion field from the 4D Extended Cardiac-Torso (XCAT) phantom (v2.0), to validate the use of the DHHD in decomposing cardiac motion fields. Decomposition error was found to decrease with increasing smoothness of the fields, while keeping motion field components small at the boundary of the motion field domain. The DHHD was seen to separate radial and rotational cardiac motion, allowing possible simplification ofmotion analysis.