Patient independent representation of the detailed cardiac ventricular anatomy

Reparameterization of surfaces is a widely used tool in computer graphics known mostly from the remeshing algorithms. Recently, the surface reparameterization techniques started to gain popularity in the field of medical imaging, but mostly for convenient 2D visualization of the information initially represented on 3D surfaces (e.g. continuous bulls-eye plot). However, by consistently mapping the 3D information to the same 2D domain, surface reparameterization techniques allow us to put into correspondence anatomical shapes of inherently different geometry. In this paper, we propose a method for anatomical parameterization of cardiac ventricular anatomies that include myocardium, trabeculations, tendons and papillary muscles. The proposed method utilizes a quasi-conformal flattening of the myocardial surfaces of the left and right cardiac ventricles and extending it to cover the interior of the cavities using the local coordinates given by the solution of the Laplace's equation. Subsequently, we define a geometry independent representation for the detailed cardiac left and right ventricular anatomies that can be used for convenient visualization and statistical analysis of the trabeculations in a population. Lastly we show how it can be used for mapping the detailed cardiac anatomy between different hearts, which is of considerable interest for detailed cardiac computational models or shape atlases.