Combination of the LSQR method and a genetic algorithm for solving the electrocardiography inverse problem

Area of Science:

• Biomedical Engineering
• Computational Electrophysiology
• Medical Imaging

Background:

• The electrocardiography (ECG) inverse problem, computing epicardial potentials from body surface potentials, is ill-posed.
• Tikhonov regularization and truncated singular-value decomposition (TSVD) are common but impractical for large matrices.
• Iterative regularization methods offer potential advantages for solving complex inverse problems.

Purpose of the Study:

• To investigate the regularization properties of the least-squares QR (LSQR) method for the ECG inverse problem.
• To evaluate the performance of LSQR against established methods like Tikhonov and TSVD.
• To explore the potential of combining LSQR with genetic algorithms (GA) for improved accuracy.

Main Methods:

• Applied the Krylov subspace iterative method, LSQR, to the ECG inverse problem.
• Utilized the L-curve method to determine the optimal stopping iteration number due to LSQR's semi-convergence.
• Evaluated LSQR performance using a realistic heart-torso model simulation.

Main Results:

• LSQR demonstrated superior accuracy in recovering inverse solutions compared to Tikhonov and TSVD methods.
• The L-curve method effectively managed the semi-convergence property of LSQR.
• Combining LSQR with GA further improved the accuracy of the computed epicardial potentials.

Conclusions:

• The LSQR method is a numerically reliable and accurate approach for the ECG inverse problem.
• The combination of LSQR and GA presents a promising scheme for enhancing ECG inverse solution accuracy.
• LSQR offers a practical alternative to direct regularization methods for large-scale ECG inverse problems.