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Representation of Collective Electrical Behavior of Cardiac Cell Sheets

Seth Weinberg ^*, Shahriar Iravanian  and Leslie Tung ^*

^* Department of Biomedical Engineering, The Johns Hopkins University, Baltimore, Maryland; and Division of Cardiology, Emory University, Atlanta, Georgia

Correspondence: Address reprint requests to Dr. Leslie Tung, E-mail: ltung{at}jhu.edu.

The electrocardiogram (ECG) is a measure of the collective electrical behavior of the heart based on body surface measurements. With computational models or tissue preparations, various methods have been used to compute the pseudo-ECG (pECG) of bipolar and unipolar leads that can be given clinical interpretation. When spatial maps of transmembrane potential (V_m) are available, pECG can be derived from a weighted sum of the spatial gradients of V_m. The concept of a lead field can be used to define sensitivity curves for different bipolar and unipolar leads and to determine an effective operating height for the bipolar lead position for a two-dimensional sheet of heart cells. The pseudo-vectorcardiogram (pVCG) is computed from orthogonal bipolar lead voltages, which are derived in this study from optical voltage maps of cultured monolayers of cardiac cells. Rate and propagation direction for paced activity, rotation frequency for reentrant activity, direction of the common pathway for figure-eight reentry, and transitions from paced activity to reentry can all be distinguished using the pVCG. In contrast, the unipolar pECG does not clearly distinguish among many of the different types of electrical activity. We also show that pECG can be rapidly computed by two geometrically weighted sums of V_m, one that is summed over the area of the cell sheet and the other over the perimeter of the cell sheet. Our results are compared with those of an ad hoc difference method used in the past that consists of a simple difference of the sum of transmembrane potentials on one side of a tissue sheet and that of the other.