Session S63.2

Individually Improved VCG Synthesis

S Man*, EW van Zwet, AC Maan, MJ Schalij, CA Swenne

Leiden University Medical Center
Leiden, Netherlands

Background: Vectorcardiographic variables (spatial ventricular gradient, QRS-T angle, T-vector loop complexity) bear important prognostic information. Since usually 12-lead ECGs are recorded, the vectorcardiogram (VCG) must be mathematically synthesized. Usually, this is done by multiplying the first 8 independent leads I, II, V1-V6 by a 3x8 matrix M: VCG=M*ECG. Often, M is the inverse of an 8x3 matrix L; this matrix was originally published by Dower to construct ECGs from VCGs: ECG=L*VCG. As L is not square and has no inverse, the pseudoinverse least-square solution M=inv (L'*L)*L' is taken instead. Hence, there is always a difference between the original ECG and a reconstruction ECGr=L*M*ECG. In some individuals this difference can be large because L (and, hence, M) is a fixed matrix, optimized for a population. An individual matrix would be better to account for individual anatomical differences. An individual pseudo-VCG that contains most of the information in the ECG can be generated by taking the first three principal components. This has, however, several drawbacks: possible incorporation of non-dipole ECG activity, orthogonality in signal space rather than in physical space, undefined scaling. Here, we propose a method to individualize the ECG-to-VCG transformation matrix that reduces the ECGr-ECG difference, while keeping the advantages of the Dower transformation (orientation in physical space, calibration).
Methods: We use the Errors-In-Variables model (Adcock, 1877; Golub & Van Loan, 1980) that accepts changes in the transformation matrix in addition to a difference between ECG and ECGr. We may choose how much we are willing to deviate from either the ECG or the original Dower transformation matrix. When we choose that the individual transformation matrix Li (and, hence, the individual inverse transformation matrix Mi) deviates as little as possible from L, Mi*ECG synthesizes the least squares VCG. Alternatively, when we choose that ECGr=Li*Mi*ECG deviates as little as possible from ECG, Mi*ECG synthesizes a linear transformation of the first three principal components of ECG, providing the best possible three dimensional (in signal space) approximation to the ECG. Any compromise between these two extremes is also possible. We tested this procedure in 180 subjects (101/79 men/women, age 54±17(19-87) yrs, body mass index 26±4(17-39) kg/m2, body surface area 1.94±0.22(1.37-2.60) m2, with 80/100 normal/ pathological ECGs.
Results: When the individual tolerated percentual deviation between the VCG synthesized by use of the original matrix M or by use of the individually adapted matrix Mi was increased from 0 to 10%, the percentual error of reconstructed ECGr with respect to the original ECG decreased from 6.1±4.5 (max 28.6) to 0.8±0.7 (max 4.4).
Conclusions: The Errors-in-Variables algorithm facilitates individual optimization of VCG synthesis while remaining close to the group-based inverse Dower transform.

(Abstract Control Number: 52)