The standard approach described above may be inaccurate when there are errors in the measurement of QRS and T-wave onset and offset. In our proposed approach we implement improvements, based on the results of sensitivity analyses carried out to assess the impact of VCG marker inaccuracies on the QRS-Ta in this study (as described in results section 3.1). Critical sources of QRS-Ta estimation errror include: inaccuracy in the positioning of the loops origin, delay in the onset of the QRS loop, anticipation in the onset of T-wave loop and impact of noise on low-amplitude T-waves. Our proposed algorithm (Fig. 1) implements the following amendments to minimize the impact of these issues:

The origin of both loops is taken as the median value of vt over a short interval preceding QRSon:

This is to identify in a robust manner an interval when there is limited electrophysiological activity, which does not significantly influence the amplitude of the QRS loop and subsequently the estimation of the QRS-Ta. In this study, τ0 = 25 ms. This short window (QRSONτ0 : QRSON) was chosen to avoid encroachment into either the P-wave or the QRS complex, with the latter being particularly problematic and a vulnerability when using the standard approach. If either the end of the P wave or the beginning of the QRS complex are within this window, taking the median amplitude as the time point for the vector origin will reduce the risk of these regions influencing its location.

The onset and end of the QRS loop are modified such that:

These time points before QRS onset and after QRS end contribute very little to the formation of the loop and the calculation of its peak and mean amplitudes, and therefore can be used as a ‘buffer’ in case of inaccurate marker placement. A value of τQRSON=τQRSEND= 15 ms was chosen based on the results from this study investigating the impact of marker placement on QRS-Ta calculation, that show that QRS-Ta estimates can be severely affected when error in marker placement results in longer QRSon and shorter QRSend (see results section 3.2 and Fig. 2).

Effect of systematically moving manually annotated reference VCG markers within ± 20 ms, on the estimation error of peak (A) and mean (B) QRS-Ta using the standard approach. Markers and bars represent the mean and standard deviation of the absolute error. From left to right, changes were made to QRSon, QRSend or Tend only.

The beginning of the T wave loop is delayed:

This is to ensure no part of the QRS loop is included in the construction of the T wave loop should, for example, QRS end be delayed by inaccurate marker placement. The value τTWON= 40 ms was chosen following review of a random sample of VCG signals and their constructed QRS and T-wave loops, for example as shown in Fig. 1. The core information forming the T wave loop is centred around the T-wave peak (see results section 3.1), which is retained using this window.

No attempt to measure QRS-Ta is made if:

In our analysis, we observed that T waves showing extreme low amplitudes require manual revision as automated marker placement is significantly more likely to be inaccurate. Although this condition is rarely verified, it has an impact on accurate identification of abnormal QRS-Ta.

QRS-T angle measurement using our proposed approach. A: X, Y and Z leads showing the QRS and T-wave in orange and blue, respectively. The solid grey block prior QRS complex represents the interval for the calculation of the vectors’ origin. B: VCG loops in the XYZ space. The red dot represents the vectors’ origin and the dashed lines the peak QRS and T-wave vectors.

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