Direct evaluation of the electrocardiographic spatial QRS-T angle without the need for orthogonal transformation
File(s)
Published version
Author(s)
Type
Journal Article
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.
Date Issued
2026-02-04
Date Acceptance
2026-01-21
Citation
Scientific Reports, 2026, 16
ISSN
2045-2322
Publisher
Nature Portfolio
Journal / Book Title
Scientific Reports
Volume
16
Copyright Statement
© The Author(s) 2026. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
10.1038/s41598-026-37361-w
Subjects
Electrocardiogram
QRS-T angle
Orthogonal transformation
Direct computation
Stability
Reproducibility
Publication Status
Published
Article Number
7317
Date Publish Online
2026-02-04