Lanczos bidiagonalization-based inverse solution methods applied to electrical imaging of the heart by using reduced lead-sets: A simulation study

Serinağaoğlu Doğrusöz, Yeşim
In inverse problem of electrocardiography (ECG), electrical activity of the heart is estimated from body surface potential measurements. This electrical activity provides useful information about the state of the heart, thus it may help clinicians diagnose and treat heart diseases before they cause serious health problems. For practical application of the method, having fewer number of electrodes for data acquisition is an advantage. Additionally, inverse problem of ECG is ill-posed due to attenuation and smoothing within the body. Therefore, the solution of ECG inverse problem has to be regularized. In this study, we constrain ourselves to two Lanczos-bidiagonalization-based inverse solution methods, namely, Lanczos least-squares QR (L-LSQR) factorization and Lanczos truncated total least-squares (L-TTLS). Tikhonov regularization is also implemented as a base for comparison for these methods. We use body surface measurements simulated using epicardial potentials measured from the surface of canine hearts. In these experiments, the hearts are stimulated from the ventricles at various sites, mimicking ectopic beats. Torso potentials are obtained from these epicardial measurements by multiplying them with the forward transfer matrix and adding Gaussian distributed noise. We solve the inverse problem using different number of leads on the body surface (771, 192, 64, and 32 leads), and assess the performances of these regularization methods for the reduced lead-sets. These reduced lead-sets are selected from the primary 771-lead configuration by using two main approaches. The first approach is manually selecting appropriate leads, and the second one uses the inverse problem approach to select leads sequentially. The results show that the L-TTLS method is more successful in reconstructing epicardial potentials than the L-LSQR method. The L-TTLS method is faster than the Tikhonov regularization, since it benefits from bidiagonal form of the forward matrix. Reducing the number of electrodes to 64 has a small effect on the solutions, but with 32 leads, inverse solutions get less precise, and the difference between the results of Tikhonov regularization and L-TTLS method becomes less significant.