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

Abstract

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