# Introduction

The morphology of the ECG waveform varies slightly from beat to beat. Quantification of these changes, in particular within the ST-T segment, has been receiving increasing interest, because electrocardiographic phenomena such as microvolt T wave alternans and augmented QT interval variability have been associated with malignant ventricular arrhythmia in clinical populations as well pro-arrhythmic risk in pharmacological safety testing studies. More recently, P wave variability has received attention by cardiologists due its potential link to atrial fibrillation propensity. Since all those ECG changes are typically very small, high precision as well as robustness of measurement algorithm is of utmost importance for obtaining reliable results.

By Martin Schmidt (Own work) [CC BY-SA 4.0], via Wikimedia Commons

The technique proposed in [1] provides a general framework for analysing beat-to-beat changes in ECG waveform and can be utilized for accurately tracking changes in common features of interest, e.g. the P, QRS or QT intervals or amplitude related information. The algorithm first generates a template beat based on ensemble averaging of relatively noise-free beats. Features of interest are annotated on the template in a semi-automated fashion. The template is then adapted to each incoming beat, exploiting a technique called Two-Dimensional Signal Warping (2DSW). In brief, a 2D mesh of warping points is superimposed on the template beat. These warping points are shifted in x- and y-directions, minimizing the Euclidean distance between segments of the template and the incoming beat. By advancing these technique to a generalized iterative template adaptation process, iterative two-dimensional signal warping (i2DSW) [2] yields a more flexible template and allows for better fitting of subtle variations of signal shapes. Moreover, the template segmentation is not dependent on signal morphology. From the optimally adapted template, changes in annotated features can be tracked from beat to beat, providing the foundation for studying ECG variability.

[1] M. Schmidt, M. Baumert, A. Porta, H. Malberg, and S. Zaunseder, “Two-Dimensional Warping for One-Dimensional Signals—Conceptual Framework and Application to ECG Processing,” IEEE Transactions on Signal Processing, vol. 62, iss. 21, p. 5577–5588, 2014.
[Bibtex]
@article{schmidt_two-dimensional_2014,
title = {Two-{{Dimensional Warping}} for {{One-Dimensional Signals}}\textemdash{{Conceptual Framework}} and {{Application}} to {{ECG Processing}}},
author = {Schmidt, M. and Baumert, M. and Porta, A. and Malberg, H. and Zaunseder, S.},
year = {2014},
month = nov,
journal = {IEEE Transactions on Signal Processing},
volume = {62},
number = {21},
pages = {5577--5588},
issn = {1053-587X},
doi = {10.1109/TSP.2014.2354313},
abstract = {We propose a novel method for evaluating the similarity between two 1d patterns. Our method, referred to as two-dimensional signal warping (2DSW), extends the basic ideas of known warping techniques such as dynamic time warping and correlation optimized warping. By employing two-dimensional piecewise stretching 2DSW is able to take into account inhomogeneous variations of shapes. We apply 2DSW to ECG recordings to extract beat-to-beat variability in QT intervals (QTV) that is indicative of ventricular repolarization lability and typically characterised by a low signal-to-noise ratio. Simulation studies show high robustness of our approach in presence of typical ECG artefacts. Comparison of short-term ECG recorded in normal subjects versus patients with myocardial infarction (MI) shows significantly increased QTV in patients (normal subject 2.36 ms {$\pm$} 1.05 ms vs. MI patients 5.94 ms {$\pm$} 5.23 ms (mean {$\pm$} std), ). Evaluation of a standard QT database shows that 2DSW allows highly accurate tracking of QRS-onset and T-end. In conclusion, the two-dimensional warping approach introduced here is able to detect subtle changes in noisy quasi-periodic biomedical signals such as ECG and may have diagnostic potential for measuring repolarization lability in MI patients. In more general terms, the proposed method provides a novel means for morphological characterization of 1d signals.},
keywords = {Correlation,Cost function,Dynamic time warping,ECG,Electrocardiography,Heuristic algorithms,Physiology,QT,QT interval,QT variability,signal processing,Signal processing algorithms,two-dimensional warping,Vectors,warping},
file = {C\:\\Users\\martin\\Zotero\\storage\\BYDNA77L\\6891378.html}
}
[2] M. Schmidt, M. Baumert, H. Malberg, and S. Zaunseder, “Iterative Two-Dimensional Signal Warping—Towards a Generalized Approach for Adaption of One-Dimensional Signals,” Biomedical Signal Processing and Control, vol. 43, p. 311–319, 2018.
[Bibtex]
@article{schmidt_iterative_2018,
title = {Iterative Two-Dimensional Signal Warping\textemdash{{Towards}} a Generalized Approach for Adaption of One-Dimensional Signals},
author = {Schmidt, Martin and Baumert, Mathias and Malberg, Hagen and Zaunseder, Sebastian},
year = {2018},
month = may,
journal = {Biomedical Signal Processing and Control},
volume = {43},
pages = {311--319},
issn = {1746-8094},
doi = {10.1016/j.bspc.2018.03.016},
abstract = {The assessment of subtle morphological changes in noisy signals is a common challenge in the field of biomedical signal processing. Concerning the electrocardiogram (ECG), it may yield novel risk factors for cardiac mortality. Here, we describe an iterative two-dimensional signal warping algorithm (i2DSW), which morphological analyses even in case of noise ratios. i2DSW adapts a generalized iterative template adaptation process that yields a more flexible template and allows for better fitting of subtle variations of signal shapes. Moreover, the template segmentation is not dependent on signal morphology. We test its performance, by measuring beat-to-beat repolarization variability in simulated and clinical ECG. Simulation studies show higher robustness of i2DSW in presence of typical ECG artefacts compared to previously proposed methods including the existing two-dimensional warping technique (26\% improvement). Comparison of short-term ECG recorded in normal subjects versus patients with myocardial infarction (MI) confirmed increased repolarization variability in MI patients (p\,\<\,0.0001). Results obtained with long-term ECG show improved waveform adaptation of i2DSW (overall 19\%, up to 33\%). The assessment of subtle morphological changes by i2DSW may yield novel and more robust risk factors for cardiac mortality. By avoiding a fixed template segmentation, the generalized design of i2DSW has the potential to be also powerful in the application to other quasi-periodic signals.},
keywords = {2DSW,ECG,i2DSW,QT interval,QT variability,Warping},
file = {C\:\\Users\\martin\\Zotero\\storage\\YEVSWUAU\\Schmidt et al. - 2018 - Iterative two-dimensional signal warping—Towards a.pdf;C\:\\Users\\martin\\Zotero\\storage\\FD9Q2M38\\S1746809418300740.html}
}