Transfer matrices for deriving the vectorcardiogram: a consumer guide

Background In the literature, several different transfer matrices have been presented for deriving the vectorcardiogram (VCG) from the signals observed using a limited set of electrodes. Even when the electrode locations were identical, like 9 of the standard 12-lead ECG, the reported transfer matrices differed widely. We compared the quality of 18 published transfer matrices. Methods As in Frank's work, a homogeneous thorax model was used. Unit strength current dipoles were placed at the center of gravity of either the ventricular or the atrial myocardium. At each location, the orientations of the dipoles were set in the X, Y, or Z direction. For each orientation, a body surface potential map (BSPM) was computed and sampled at the locations of the respective electrode systems. Application of the transfer matrices to any of the 3 sets of potentials (say, BSPM generated by the X dipole) should then, ideally, signal a unit strength of the corresponding VCG component and zero strength in the remaining 2 (Y, Z). From the 3 BSPMs applied, this should ideally yield a (3 × 3) matrix having unit diagonal elements and all remaining elements zero. The quality of the matrices studied was quantified by Q values: Q = 1 − RD, with RD being the relative, root mean square-based values of observed differences with respect to the ideal situation (high Q value: high quality), as well as by Maxabs: the maximum absolute of observed differences (high Maxabs value: poor quality). The analysis was validated in 25 magnetic resonance imaging-derived, different thorax geometries in which individual heart positions were documented. Results As expected, the quality of a transfer matrix was higher if more electrodes were involved. For the matrices based on the 9 electrodes, the range of Q values for the ventricular location of the dipole was as follows: best, 0.74 and 0.23 for Q and Maxabs, respectively; and worst, 0.65 and 0.34, respectively. The figures for the much-used “inverse Dower” matrix were 0.69 and 0.29, and for Frank leads, 0.77 and 0.23. Where just 4 electrodes were involved (EASI leads), the quality was much poorer, the worst being 0.55 and 0.68. For the atrial location of the dipole, the corresponding values were as follows: best (9 electrodes), 0.74 and 0.23; worst (9 electrodes), 0.65 and 0.34; inverse Dower, (9 electrodes), 0.69 and 0.29; Frank leads, 0.77 and 0.23; and the worst of the EASI leads, 0.55 and 0.68. Conclusion The Maxabs error quantifies the crosstalk between the individual estimated dipole components. The high Maxabs errors found for limited lead systems questions their use when aiming at VCG surrogates.