Electrocardiographic Imaging: A Comparison of Iterative Solvers

Area of Science:

• Biomedical Engineering
• Computational Cardiology
• Medical Imaging

Background:

• Cardiac disease is a major cause of death globally.
• Non-invasive diagnostic tools like electrocardiographic imaging (ECGI) are essential for patient risk identification and treatment guidance.
• Current ECGI accuracy is limited by the ill-posed nature of the inverse problem in reconstructing cardiac electrical activity.

Purpose of the Study:

• To enhance the accuracy and stability of the inverse problem solutions in ECGI.
• To evaluate the performance of novel inverse problem methods adapted for ECGI.
• To compare these methods against existing solutions for improved cardiac diagnostics.

Main Methods:

• Adapted and applied four inverse problem methods: Algebraic Reconstruction Technique (ART), random ART, ART Split Bregman (ART-SB), and Range Restricted Generalized Minimal Residual (RRGMRES) to ECGI.
• Utilized the Experimental Data and Geometric Analysis Repository (EDGAR) for testing and validation.
• Compared reconstructed epicardial potentials and activation maps against recorded data and a Generalized Minimal Residual (GMRES) solution.

Main Results:

• ART demonstrated the most stable solutions and provided the best reconstructions for certain datasets.
• ART and random ART showed negligible differences in solution accuracy.
• RRGMRES and ART-SB offered improved accuracy over GMRES, with RRGMRES showing dataset-dependent performance.
• GMRES yielded the least accurate reconstructions among the tested methods.

Conclusions:

• The investigated methods, particularly ART, random ART, and RRGMRES, significantly improve upon the standard GMRES solution for ECGI inverse problems.
• These advanced techniques offer more stable and accurate reconstructions, paving the way for better understanding and treatment of cardiac diseases.
• Further development and application of these methods hold promise for advancing non-invasive cardiac diagnostics and therapy guidance.