# Direct evaluation of the electrocardiographic spatial QRS-T angle without the need for orthogonal transformation

## TL;DR

This paper introduces a new method to calculate the QRS-T angle from ECG data without needing complex transformations, making it more accurate and efficient.

## Contribution

The study demonstrates a direct computation method for the QRS-T angle that avoids orthogonal transformations and yields higher precision.

## Key findings

- The direct method's results were closer to SVD-based results with differences below 1 degree.
- The direct method showed significantly higher reproducibility and lower variability compared to traditional methods.

## Abstract

Increased electrocardiogram (ECG) spatial QRS-T wave angle is a recognised risk factor. Standard evaluation of the angle requires deriving orthogonal ECG leads, either by general transformation matrices into XYZ leads or by singular value decomposition (SVD). This study shows that the transformation is not needed, and that the spatial QRS-T angle can be calculated directly from the original ECG leads. The direct computation was tested using long-term 12-lead ECGs of 523 healthy volunteers (259 females). A total of 659,313 individual 10-second ECG samples were obtained providing 7,350,733 individual beats which were analysed both by the direct method using 8 algebraically independent leads and by the conventional XYZ and SVD transformations. On average, the results of the direct non-transformation method were closer to the SVD-based results (averaged differences below 1 degree) than to the XYZ-based results (averaged differences below 2 degrees). The subject-specific regressions to the underlying heart rate showed that the proposed direct method was significantly more reproducible (p < 0.0001) and that it showed more compact variability within individual ECG samples (p < 0.0001). Thus, the study shows not only that the QRS-T angle can be computed without any orthogonal transformation but that the results of the direct computation are also more precise.