Prolonged ventricular repolarisation is the best-studied measurable predictor of malignant arrhythmias in childhood. Its measurement, however, rests on a method that is systematically unreliable in children. We present an approach in which the end of repolarisation is not determined geometrically but estimated as a parameter of a physical model — with quantified uncertainty and with an explicit ability to reject an unmeasurable recording.
Abstract
Background. A prolonged QT interval and increased spatio-temporal dispersion of repolarisation are recognised predictors of ventricular tachyarrhythmias of the torsade de pointes type and of sudden cardiac death. In the paediatric population their measurement is burdened by a combination of high and variable heart rate, low T-wave amplitude and a low signal-to-noise ratio, which gives rise to false positive and false negative findings at the same time.
Objective. To design a measurement chain for the 1–15 years population that, instead of a single point value, provides an estimate with a confidence interval, and that explicitly distinguishes a measurement that is valid from a recording that does not qualify for measurement.
Approach. We do not determine the end of repolarisation by a geometric construction on the curve, but by inverting a generative physical model of the T wave: the model describes the wave as the aggregate manifestation of the distribution of recovery times of ventricular myocardial cells, the sought output being not a point on the curve but a parameter of that distribution. Estimation proceeds without training on annotated examples. The classical geometric method runs alongside as an independent check, and disagreement between the two is evaluated rather than ignored.
Contribution. Besides the duration of repolarisation, the procedure also yields a measure of its temporal dispersion — a quantity that geometric delineation cannot provide in principle. It makes the uncertainty of an individual measurement quantifiable, and it provides a formal mechanism of abstention (an “unmeasurable” output) instead of a confident but erroneous number.
Keywords: ventricular repolarisation, QT interval, paediatric electrocardiography, inverse problem, uncertainty quantification, selective prediction, explainable artificial intelligence, federated evaluation.
1. Clinical background
Congenital long QT syndrome occurs with a prevalence on the order of 1 : 2000 [1] and ranks among the principal identifiable causes of sudden cardiac death in otherwise healthy children and adolescents. A substantial proportion of carriers remain free of symptoms until their first event. Acquired prolongation of repolarisation — in drug interactions, disturbances of the internal environment or during oncological treatment — raises the risk further and is potentially reversible.
The clinical value of the measurement therefore does not lie in a one-off finding, but in the availability of repeated, sufficiently accurate and interpretable measurement: screening of families at risk, a check when risk-bearing treatment is initiated, following the trend in a patient under long-term care. A method that is expensive or uninterpretable will not be used in this regime.
2. The metrological problem of paediatric measurement
Current practice rests on two pillars, neither of which is satisfactory for the paediatric population.
(a) Geometric delineation. The end of the T wave is determined as the intersection of the tangent to the descending limb with the isoelectric line. The method is simple and auditable, but its sensitivity to noise grows in inverse proportion to the steepness of the descent. In the low-amplitude, broad waves typical of small children, a deviation of a few microvolts translates into tens of milliseconds. Crucially, the error is not random but systematic: a broad, flat wave leads to an intersection located before the true end of repolarisation.
(b) Heart-rate correction. Converting the measured interval into a value comparable between patients relies on empirical formulae [2–4]. At the heart rates at which the paediatric population commonly finds itself, the formulae diverge from one another by tens of milliseconds, and the most widespread of them systematically overestimates the value. A finding of “prolonged QTc” may therefore be an artefact of the choice of formula rather than a property of the heart. Using adult reference limits instead of age-specific percentiles [5] compounds the error further.
The consequence is the simultaneous occurrence of both types of error: false positive findings (a healthy child with a fast pulse) and false negative findings (a low-amplitude T wave with a prematurely determined end).
3. The approach: estimation instead of construction
The proposed procedure changes the formulation of the task. Instead of asking “where on the curve does the wave end?”, it solves an inverse problem: which values of the physical parameters best explain the observed course?
The model is generative and physically motivated — it describes the T wave as the aggregate manifestation of the distribution of recovery times of individual regions of the ventricular myocardium. The sought quantity is therefore not a point but the parameters of that distribution; the end of repolarisation follows from them as its quantile. This change has three consequences:
- The estimate is stable even where the geometric construction is unstable, because it relies on the entire shape of the wave and not on the neighbourhood of a single point.
- Alongside duration, a measure of the temporal dispersion of repolarisation arises, a quantity with an electrophysiological meaning of its own that the geometric method does not provide.
- The model is not trained on annotated examples — it has no weights learned from data and does not require the extensive expert-labelled paediatric corpora that are not available in practice. This also removes an entire class of failures associated with domain shift between the training and the target population.
Implementation details — the specific form of the model, the method of parameter estimation, the calibration relations and the setting of decision thresholds — are the subject of our development and are not stated in this text.
4. Overview of the innovations
I1 · Repolarisation as an estimated physical quantity. A shift from geometric construction to parametric inversion. The output has a physical interpretation and is not an artefact of the choice of tangent.
I2 · Dispersion of repolarisation as a direct output of the measurement. The measure of how far repolarisation is spread out in time is obtained together with its duration, from one and the same estimate — not as a difference between leads, which is metrologically problematic.
I3 · Dual evaluation with managed disagreement. The physical estimate and the classical geometric method run alongside each other. Their agreement is a positive argument; their disagreement is not concealed but classified — we distinguish the case in which the difference is an expected consequence of the shape of the wave from the case in which it indicates a failure of the estimate. In the latter case the confidence in the result is lowered.
I4 · Formal abstention. The chain contains explicit acceptance conditions for a measurement. If a recording does not meet them, the output is “unmeasurable” rather than a number. In a medical device, selective prediction is a safety property, not a shortfall in coverage.
I5 · Uncertainty as part of the result. Every value is accompanied by a confidence interval derived from simulating the influence of noise and signal variability. The interpretation of a borderline finding thus rests on resolvability rather than on the apparent precision of a decimal place.
I6 · Concurrent multiple correction with age percentiles. Instead of a single formula, several corrections are reported at once together with an age-specific reference; the divergence between them is information for the clinician, not a hidden assumption.
I7 · Explainability as a design condition. Every step of the chain is auditable and reconstructible. There is no node whose output could not be justified other than by reference to learned weights.
I8 · Evaluation at the place where the data arise. Computational demands are designed so that evaluation runs on ordinary hardware in real time, that is, directly at the clinical site — which is at the same time a prerequisite for the architecture described in section 6.
5. Validation strategy
We build validation on three independent pillars, so that a systematic error cannot hide behind agreement with our own assumption:
- Synthetic signals with a known ground truth — the only regime in which the measurement error is known exactly and in which the influence of noise, baseline wander and wave amplitude can be quantified.
- Publicly available annotated databases, including large paediatric collections, which make it possible to assess the behaviour of the method across age groups and in the presence of concomitant findings.
- Comparison with assessments by cardiologists on field recordings, with emphasis on inter-rater agreement and on the cases in which the method and the rater diverge.
Numerical results of the validation are not part of this text.
6. Validation architecture: computation travels to the data
Validating a measurement method requires access to sufficiently diverse recordings from several clinical sites. Gathering them in one place is disadvantageous both legally and in terms of security, and it conflicts with the principle of minimising the data processed.
We therefore propose the opposite arrangement: computation travels to the data. Evaluation takes place at the site where the recording arose; only the results of the measurement are transmitted beyond the site. The nodes of the network are equals, without a central element; the same task can be independently recomputed by another node, so that results are comparable and replicable rather than accepted on trust. Every operation leaves an audit trail in a form transferable to central security monitoring.
7. Regulatory and safety framework
We are developing the system as a medical device with a software measuring function: with a documented development process, risk management, a defined intended purpose and explicitly stated conditions under which the device will not provide a result. The measurement chain is designed with a view to conformity with the standards for diagnostic electrocardiographs [6], the software life cycle according to the relevant standard [7] and the security and operational requirements of the NIS2 Directive.
8. Limitations
This is a development project, not a certified product. The model assumes a certain class of wave shapes; recordings outside this class are deliberately rejected, which reduces coverage in exchange for safety. Age-specific reference values are drawn from published population collections and their transferability to a different population is subject to verification. The clinical benefit — that is, the effect on the detection of children at risk and on the outcomes of their follow-up — is a hypothesis that metrological validation alone does not demonstrate and that calls for prospective verification.
9. Conclusion
The predictive value of repolarisation indicators is well documented in cardiology; the limiting link is not knowledge but the quality and availability of the measurement itself in the paediatric population. The shift from geometric construction to the estimation of physical parameters, complemented by quantified uncertainty and by the right of the device to remain silent, moves the measurement from the position of “a number to be interpreted with reservations” to that of a quantity with a stated reliability.
The technical solution, the parameters of the model and the measured results are the know-how of the project and are not part of this publication.
References (selected)
- Schwartz PJ, Stramba-Badiale M, Crotti L, et al. Prevalence of the congenital long-QT syndrome. Circulation. 2009.
- Bazett HC. An analysis of the time-relations of electrocardiograms. Heart. 1920.
- Fridericia LS. Die Systolendauer im Elektrokardiogramm bei normalen Menschen und bei Herzkranken. Acta Medica Scandinavica. 1920.
- Sagie A, Larson MG, Goldberg RJ, et al. An improved method for adjusting the QT interval for heart rate (the Framingham Heart Study). The American Journal of Cardiology. 1992.
- Rijnbeek PR, Witsenburg M, Schrama E, et al. New normal limits for the paediatric electrocardiogram. European Heart Journal. 2001.
- IEC 60601-2-25 — Medical electrical equipment: particular requirements for the basic safety and essential performance of electrocardiographs.
- IEC 62304 — Medical device software: software life cycle processes.
© 2026 Branislav Anwarzai · Institute of Advanced Studies. All rights reserved. The text may be quoted with attribution of author and source; any further distribution or modification requires the author’s written consent. Rights to the technical solution described — the model, its parameters and the measured results — remain reserved; publication of this text grants no licence or other authorisation to use them.