Space-time shape uncertainties in the forward and inverse problem of electrocardiography

Area of Science:

• Computational electrophysiology
• Biomedical engineering
• Mathematical modeling

Background:

• The electrocardiography (ECG) inverse problem aims to reconstruct cardiac electrical activity from body surface measurements.
• Anatomical uncertainties, arising from noisy and low-resolution imaging, significantly impact the accuracy of ECG inverse solutions.
• Understanding the influence of these uncertainties is crucial for reliable clinical applications.

Purpose of the Study:

• To investigate the impact of anatomical shape uncertainty on both the forward and inverse problems in electrocardiography.
• To develop and validate computational methods for quantifying uncertainty propagation in ECG modeling.
• To assess the performance of different regularization techniques in the presence of shape uncertainty.

Main Methods:

• The study reformulates the ECG problem using a boundary integral formulation and discretizes it with a collocation method.
• Shape uncertainty is modeled using a random deformation field and approximated with low-rank techniques for efficient sampling.
• Space-time uncertainty in potentials is evaluated using anisotropic sparse quadrature and validated with quasi-Monte Carlo methods.

Main Results:

• The proposed sparse quadrature approach is highly effective for the forward problem.
• Both sparse quadrature and quasi-Monte Carlo methods perform well for the inverse problem, though total variation regularization shows limitations.
• An L2 regularization method, derived from the boundary integral formulation, is investigated and compared to traditional methods.

Conclusions:

• Anatomical shape uncertainty significantly affects ECG inverse problem reconstruction.
• The developed computational framework effectively quantifies this uncertainty.
• The study highlights the importance of considering anatomical variability and proposes effective regularization strategies for improved ECG inverse solutions.