Strainger Things: Discrete Differential Geometry for Transporting Right Ventricular Deformation Across Meshes

Abstract

Cardiac dynamics have been a focus of image analysis, and their statistical models are used in a wide range of applications: generating synthetic datasets, derivation of specific biomarkers of pathologies, or atlas-based motion estimation. Current representations of dynamics, mainly based on displacements, often overlook the physiological basis of cardiac contraction. We propose to use local strain as a more accurate representation, and demonstrate this on 3D echocardiography surface meshes of the right ventricle. Our methodology, based on a differential geometry algorithm, deforms the surface mesh according to a pre-imposed strain field. This approach allows for a clearer disentanglement between cardiac geometry and dynamics, better differentiating deformation changes than those due to changes in cardiac morphology. The methodology is demonstrated in two toy examples: transporting deformation from one individual to another; and simulating the effects of a pathology on a healthy patient, namely an akinetic right ventricular outflow tract.