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Correction of the QT interval in the ECG for changes in heart rate (RR interval) is needed to compare groups of patients and assess the risk of sudden cardiac death. The QTc represents the QT interval at 60 bpm, although most patients typically have a faster heart rate, thus requiring extrapolation of the QT-RR relationship. Objective: This paper investigates the ability of QT-RR models with increasing number of parameters to fit beat-to-beat variations in the QT interval and provide a reliable estimate of the QTc. Approach: One-, two- and three-parameter functions generalising the Bazett and Fridericia formulas were used in combination with hysteresis reduction (memory) obtained by time-averaging the history of RR intervals with exponentially-decaying weights. In normal men and women datasets of Holter recordings in normal subjects (24 h monitoring), two measures were computed for each model: the root mean square error (RMSE) of fitting and the difference between the estimated QTc and a reference QTc obtained by collecting data points around RR  =  1000 ms. Main results: The two- and three-parameter functions all gave similar low RMSE with uncorrelated residues. An optimal memory parameter was found that still minimized the RMSE and could be used for all functions and subjects. This reduction in RMSE resulted from changes in the parameters linked to the increased steepness of the QT-RR relation after hysteresis reduction. At optimal memory, the two and three-parameter models provided poorer prediction of the QTc as compared to the Fridericia’s model in subjects with fast heart rates, since accurate representation of the steeper QT-RR relation worsened the extrapolation that was then needed to determine the QTc. Significance: As a result, among all models investigated, the Fridericia formulation offered the best trade-off for QTc prediction robust to memory and fast heart rates. [ABSTRACT FROM AUTHOR]

The QT interval in the electrocardiogram (ECG) is a measure of total duration of depolarization and repolarization. Correction for heart rate is necessary to provide a single intrinsic physiological value that can be compared between subjects and within the same subject under different conditions. Standard formulas for the corrected QT (QTc) do not fully reproduce the complexity of the dependence in the preceding interbeat intervals (RR) and inter-subject variability. In this paper, a subject-specific, nonlinear, transfer function-based correction method is formulated to compute the QTc from Holter ECG recordings. The model includes five parameters: three describing the static QT-RR relationship and two representing memory/hysteresis effects that intervene in the calculation of effective RR values. The parameter identification procedure is designed to minimize QTc fluctuations and enforce zero correlation between QTc and effective RR. Weighted regression is used to better handle unbalanced or skewed RR distributions. The proposed optimization approach provides a general mathematical framework for further extensions of the model. Validation, robustness evaluation and comparison with existing QT correction formulas is performed on ECG signals recorded during sinus rhythm, atrial pacing, tilt-table tests, stress tests and atrial flutter (29 subjects in total). The resulting average modeling error on the QTc is 4.9 +- 1.1 ms with a sampling interval of 2 ms, which outperforms correction formulas currently used. The results demonstrate the benefits of subject-specific rate correction and hysteresis reduction. [ABSTRACT FROM AUTHOR]

Objective: In the electrocardiogram, adaptation of the QT interval to variations in heart rate is not instantaneous. Quantification of this hysteresis phenomenon relies on mathematical models describing the relation between the RR and QT time series. These models reproduce hysteresis through an effective RR interval computed as a linear combination of the history of past RR intervals. This filter depends on a time constant parameter that may be used as a biomarker. Approach: The most common hysteresis model is based on an autoregressive filter with an impulse response that decreases exponentially with the beat number (lag-based model). Recognizing that the QT time series is unevenly spaced, we propose two exponential moving average filters (time-based models) to define the effective RR interval: one with an impulse response that decreases exponentially with time in seconds, and one with a step response that relaxes exponentially with time in seconds. These two filters are neither linear nor time-invariant. Recurrence formulas are derived to enable efficient implementation. Main results: Application to clinical signals recorded during tilt table test, exercise and 24 h Holter demonstrates that the three models perform similarly in terms of goodness-of-fit. When comparing the hysteresis time constant in two conditions with different heart rates, however, the time-based models are shown to reduce the bias on the hysteresis time constant caused by heart rate acceleration and deceleration. Significance: Time-based models should be considered when intergroup differences in both heart rate and QT hysteresis are expected. [ABSTRACT FROM AUTHOR]