Assessment of Myocardial Heterogeneity Using the Supertoroid-based Representation of Dt-mri

INTRODUCTION The supertoroid-based representation of cardiac DT-MRI was previously shown to enhance cardiac myofiber structure characterization compared to ellipsoids, superquadrics and toroids [1]. The supertoroidal model is an evolution of the toroid-based representation and provides a new index of diffusivity the toroidal volume (TV) [2,3] and a new coefficient of anisotropy the toroidal curvature (TC). TV has been shown to characterize the cardiac remodeling process post-MI [4]. The purpose of this study is to establish the normal myofiber structure of the left ventricle (LV) using our new toroid-based indices (TV and TC) and traditional diffusion indices mean diffusivity (MD) and fractional anisotropy (FA) in normal porcine hearts. METHODOLOGY Diffusion anisotropy is classically quantified by the FA, which represents the eccentricity of the ellipsoidal tensor representation. Using the supertoroidal model, one can derive a new anisotropy coefficient based upon the curvature of the toroidal surface. This new coefficient, the toroidal curvature (TC), quantifies the maximal Gaussian curvature of the toroidal surface and is defined as: