Real‐time reconstruction of endocardial potential maps in non‐contact cardiac mapping

The purpose of this paper is to describe a numerical inversion technology developed to reconstruct endocardial electric potential maps on the internal surface of heart chambers utilizing intracavitary multi‐electrode catheter measurements. The objective is to perform the reconstruction real time with high accuracy, thereby allowing the incorporation of the technology into medical imaging systems.

Electrode potential points from several beats are merged in order to maximize the information extracted from the catheter measurements. To solve the ill‐posed inverse problem fast, numerically stable solution algorithms based on generalized Tikhonov regularization and bidiagonalization are developed. The latter algorithm also provides an efficient framework for choosing the regularization parameter optimally.

Results of three examples are presented to thoroughly illustrate the performance of the algorithm: one with synthetic data generated in a computational electromagnetics (virtual lab) environment, thereby allowing exact error analysis; another with measured data from a phantom‐bench human heart model where the effect of measurement errors can be investigated in a controlled environment; and a third example that illustrates how the algorithm performs when the catheter data are collected in vivo in a swine heart.

The speed and accuracy in the three examples successfully prove that the inversion technology can be a key component of medical imaging systems.

While some elements of these computational models and techniques presented have been used for decades, the authors achieve speed and accuracy that have not been reported before by combining multi‐beat catheter measurements, the generalized Tikhonov regularization technique, a bidiagonalization algorithm and other top‐notch linear algebra techniques.