Atlases of cardiac fiber differential geometry

Studies of intra-species cardiac fiber variability tend to focus on first-order measures such as local fiber orientation. Recent work has shown that myofibers bundle locally into a particular type of minimal surface, the generalized helicoid model (GHM), which is described by three biologically meaningful curvature parameters. In order to allow intra-species comparisons, a typical strategy is to divide the parameters of the generalized helicoid by heart diameter. This normalization does not compensate for variability in myocardial shape between subjects and makes interpretation of intra-species results difficult. This paper proposes to use an atlas of rat and dog myocardium, obtained using diffeomorphic groupwise Log-demons, to register all hearts in a common reference shape to perform the normalization. In this common space the GHM is estimated for all hearts and compared using an improved fitting method. Our results demonstrate improved consistency between GHM curvatures within a species and support a direct relation between myocardial shape and fiber curvature in the heart.