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

J 2026

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

ŘEHOŘ, Jan; Katerina HNATKOVA; David POSPÍŠIL; Kateřina HELÁNOVÁ; Peter SMETANA et al.

Základní údaje

Originální název

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

Autoři

ŘEHOŘ, Jan; Katerina HNATKOVA; David POSPÍŠIL ; Kateřina HELÁNOVÁ; Peter SMETANA; Georg SCHMIDT; Irena ANDRŠOVÁ a Marek MALÍK

Vydání

Scientific Reports, Berlin, NATURE RESEARCH, 2026, 2045-2322

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

30201 Cardiac and Cardiovascular systems

Stát vydavatele

Německo

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 3.900 v roce 2024

Označené pro přenos do RIV

Ano

Organizační jednotka

Lékařská fakulta

Klíčová slova anglicky

Electrocardiogram; QRS-T angle; Orthogonal transformation; Direct computation; Stability; Reproducibility

Štítky

14110211, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 7. 4. 2026 14:25, Mgr. Tereza Miškechová

Anotace

V originále

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.

Citovat

ŘEHOŘ, Jan; Katerina HNATKOVA; David POSPÍŠIL; Kateřina HELÁNOVÁ; Peter SMETANA; Georg SCHMIDT; Irena ANDRŠOVÁ a Marek MALÍK. Direct evaluation of the electrocardiographic spatial QRS-T angle without the need for orthogonal transformation. Scientific Reports. Berlin: NATURE RESEARCH, 2026, roč. 16, č. 1, s. 1-15. ISSN 2045-2322. Dostupné z: https://doi.org/10.1038/s41598-026-37361-w.

@article{2565366,
   author = {Řehoř, Jan and Hnatkova, Katerina and Pospíšil, David and Helánová, Kateřina and Smetana, Peter and Schmidt, Georg and Andršová, Irena and Malík, Marek},
   article_location = {Berlin},
   article_number = {1},
   doi = {https://doi.org/10.1038/s41598-026-37361-w},
   keywords = {Electrocardiogram; QRS-T angle; Orthogonal transformation; Direct computation; Stability; Reproducibility},
   language = {eng},
   issn = {2045-2322},
   journal = {Scientific Reports},
   title = {Direct evaluation of the electrocardiographic spatial QRS-T angle without the need for orthogonal transformation},
   url = {https://www.nature.com/articles/s41598-026-37361-w},
   volume = {16},
   year = {2026}
}

TY  - JOUR
ID  - 2565366
AU  - Řehoř, Jan - Hnatkova, Katerina - Pospíšil, David - Helánová, Kateřina - Smetana, Peter - Schmidt, Georg - Andršová, Irena - Malík, Marek
PY  - 2026
TI  - Direct evaluation of the electrocardiographic spatial QRS-T angle without the need for orthogonal transformation
JF  - Scientific Reports
VL  - 16
IS  - 1
SP  - 1-15
EP  - 1-15
PB  - NATURE RESEARCH
SN  - 20452322
KW  - Electrocardiogram
KW  - QRS-T angle
KW  - Orthogonal transformation
KW  - Direct computation
KW  - Stability
KW  - Reproducibility
UR  - https://www.nature.com/articles/s41598-026-37361-w
N2  - 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.
ER  -

ŘEHOŘ, Jan; Katerina HNATKOVA; David POSPÍŠIL; Kateřina HELÁNOVÁ; Peter SMETANA; Georg SCHMIDT; Irena ANDRŠOVÁ a Marek MALÍK. Direct evaluation of the electrocardiographic spatial QRS-T angle without the need for orthogonal transformation. \textit{Scientific Reports}. Berlin: NATURE RESEARCH, 2026, roč.~16, č.~1, s.~1-15. ISSN~2045-2322. Dostupné z: https://doi.org/10.1038/s41598-026-37361-w.

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