Being able to map a particular set of cardiac ventricles to a generic topologically equivalent representation has many applications, including facilitating comparison of different hearts, as well as mapping quantities and structures of interest between them. We describe Universal Ventricular Coordinates (UVC) which can be used to describe position within any biventricular heart. UVC comprise four coordinates which we have chosen to be intuitive, well defined, and relevant for physiological description. We describe how to determine these coordinates for any volumetric mesh, primarily by setting appropriate boundary conditions and utilizing solutions to Laplace's equation.

Using UVC, we transferred scalar, vector, tensor, and structural data between four unstructured ventricular meshes from three different species. Performing the mappings was very fast, on the order of a few minutes, since model nodes were searched in a KDtree. Distance errors in mapping nodes back and forth between meshes were less than the size of an element. Analytically derived fiber directions were also mapped across meshes and compared, showing $<5$ degree difference over most of the ventricles. The ability to transfer gradients was also demonstrated.

Topologically variable structures, like papillary muscles, required further extending definitions outside of the UVC framework. In conclusion, UVC can aid in transferring many types of data between different b9ventricular geometries.