Cobiveco: Consistent biventricular coordinates for precise and intuitive description of position in the heart -- with MATLAB implementation

Ventricular coordinates are widely used as a versatile tool for various applications that benefit from a description of local position within the heart. However, the practical usefulness of ventricular coordinates is determined by their ability to meet application-specific requirements. For regression-based estimation of biventricular position, for example, a symmetric definition of coordinate directions in both ventricles is important. For the transfer of data between different hearts as another use case, the consistency of coordinate values across different geometries is particularly relevant. To meet these requirements, we compare different approaches to compute coordinates and present Cobiveco, a symmetric, consistent and intuitive biventricular coordinate system that builds upon existing coordinate systems, but overcomes some of their limitations. A novel one-way transfer error is introduced to assess the consistency of the coordinates. Normalized distances along bijective trajectories between two boundaries were found to be superior to solutions of Laplace's equation for defining coordinate values, as they show better linearity in space. Evaluation of transfer and linearity errors on 36 patient geometries revealed a more than 4-fold improvement compared to a state-of-the-art method. Finally, we show two application examples underlining the relevance for cardiac data processing. Cobiveco MATLAB code is available under a permissive open-source license.