Abstract
Coronary artery disease (CAD) is among the leading causes of death worldwide. Initial studies require an electrocardiogram stress test often followed by cardiac imaging procedures. However, conventional indices still show insufficient diagnostic performance. We propose quaternion methods to evaluate abnormal alterations during ventricular depolarization and repolarization. Assessment was conducted during a Bruce protocol treadmill stress test and after the end of the exercise. We developed an algorithm to automatically determine the beginning and end of exercise and then, computed the angular and linear velocities. Statistical analysis for feature selection and classification between ischaemic and non-ischaemic patients was used. The most significant markers were maximum linear velocity during ventricular depolarization (p < 5E-9) and maximum angular velocity during the second half of the repolarization loop (p < 5E-16). The latter reached sensitivity / specificity pair of 78 / 92 (AUC 0.89). A linear classifier showed a trend of reduction in cardiac vector velocity in at-risk patients after the end of exercise. The sensitivity / specificity pair reached was 86 / 100. Trajectory deviations of depolarization / repolarization loops that result from ischaemia effects, could be responsible for the observed reduction in dynamic changes during exercise. Further studies could provide non-invasive complementary tools to detect CAD risk.

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Acknowledgements
We appreciate the contribution of Dr. Ingallina, F.J. of the Institute of Medical Research “Dr. Alfredo Lanari”, UBA, Buenos Aires, Argentina, for his collaboration in the revision and correction of the current methods for diagnosing coronary disease described in the introduction.
Funding
This work was supported by CONICET, under project PIP #112-20130100552CO and Agencia MINCYT, under project PICT 2145-2016, Argentina. Moreover, the authors acknowledge the financial support from UTN BA (ICUTIBA0006564TC).
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Cruces, P.D., Soria, M.L. & Arini, P.D. Velocity tracking of cardiac vector loops to identify signs of stress-induced ischaemia. Med Biol Eng Comput 60, 1313–1321 (2022). https://doi.org/10.1007/s11517-022-02503-5
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DOI: https://doi.org/10.1007/s11517-022-02503-5