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

Steffen Schuler, Nicolas Pilia+2 more|arXiv (Cornell University)|Feb 4, 2021

Cardiovascular Function and Risk Factors34 references33 citations

TL;DR

Cobiveco is a symmetric, consistent, and intuitive biventricular coordinate system that improves upon existing methods by using normalized distances along bijective trajectories between anatomical boundaries to define coordinates, reducing transfer and linearity errors by over 4-fold compared to UVC. It enables precise, continuous, and normalized position description across both ventricles with MATLAB code available under an open-source license.

ABSTRACT

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.

Motivation & Objective

• To develop a biventricular coordinate system that ensures symmetry, continuity, and consistency across the left and right ventricles.
• To address limitations in existing methods like UVC, including discontinuities at the LV-RV junction and inconsistent coordinate values across different heart geometries.
• To improve the accuracy of data transfer between patient-specific heart models, especially for applications like electrocardiographic imaging (ECGI) and machine learning-based excitation localization.
• To introduce a novel one-way transfer error metric to objectively assess coordinate consistency across geometries.
• To provide a robust, open-source MATLAB implementation for widespread use in cardiac image analysis and modeling.

Proposed method

• Defines coordinate directions symmetrically by placing the transventricular boundary at the center of the septum, ensuring consistent parameterization in both ventricles.
• Uses normalized distances along bijective trajectories between anatomical boundaries (e.g., endocardium to epicardium) as the basis for coordinate values, computed via linear PDEs.
• Applies implicit domain remeshing to ensure accurate internal boundaries and avoid errors from imprecise geometry.
• Employs Laplace’s equation with Neumann boundary conditions for certain coordinates, while using distance-based normalization for improved linearity and consistency.
• Applies sine and cosine transformations to rotational coordinates to ensure continuity at singularities and avoid discontinuities.
• Introduces a novel one-way transfer error metric to quantify coordinate consistency when mapping data between different heart geometries.

Experimental results

Research questions

• RQ1 Can a biventricular coordinate system be designed with symmetric, continuous, and normalized coordinates across both ventricles, even at the septal junction?
• RQ2 Does using normalized distance along bijective trajectories between boundaries yield more linear and consistent coordinate values than solutions to Laplace’s equation?
• RQ3 How does the proposed coordinate system compare to UVC in terms of transfer and linearity errors across diverse patient geometries?
• RQ4 Can the new coordinate system reduce localization errors in ECGI and machine learning applications by improving coordinate consistency?
• RQ5 To what extent does the one-way transfer error metric effectively capture inconsistencies in coordinate mapping between different heart models?

Key findings

• Cobiveco reduces the mean one-way transfer error from 7.1 mm (UVC) to 1.5 mm, representing a more than 4-fold improvement.
• The 99th percentile of one-way transfer error is reduced from 24 mm (UVC) to 6 mm, indicating significantly improved consistency across diverse geometries.
• Linearity errors are substantially reduced, with spatially uniform coordinate changes proportional to coordinate increments, enhancing reliability for data interpolation.
• The coordinate system achieves full continuity across the LV-RV junction by redefining the transventricular boundary at the septal center, eliminating discontinuities present in UVC.
• Evaluation on 36 patient geometries confirms that trajectory-based normalization outperforms Laplace-based solutions in terms of both transfer and linearity errors.
• The open-source MATLAB implementation enables reproducible and accessible use in cardiac image analysis, modeling, and machine learning applications.