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Journal of Electrocardiology 47 (2014) 236–239www.jecgonline.com

Editorial

QT/RR hysteresis

In this issue of the Journal, Jacquemet et al. [1] report onQTc assessment in patients with atrial flutter. Not surpris-ingly, in such patients, heart rate correction of measured QTinterval may be substantially complicated by abrupt changesin ventricular rate which produces erratic relationshipbetween simultaneously measured QT and RR intervals.Jacquemet et al. need to be commended for their suggestionof a universal technology for dealing with the so-calledQT/RR hysteresis.

The implications of QT/RR hysteresis span well beyondthe RR interval irregularities during atrial flutter. The sameproblem of QT interval correction exists in every situationwhen the RR intervals are not truly regular. It seemstherefore appropriate to accompany the study by Jacquemetet al. by a general consideration of what is known aboutQT/RR hysteresis and, perhaps more importantly, what is notknown and what further studies of the phenomenon shouldaim at solving.

Phenomenon of QT/RR hysteresis

The relationship between the QT interval and theunderlying heart rate (usually expressed by the correspond-ing RR interval) is governed by two processes, the QT/RRdependency, that is by how much the QT interval changeswhen the underlying heart rate alters, and by the QT/RRhysteresis, that is how fast the QT interval adapts in responseto the changes of the underlying heart rate. In some previousstudies, these two processes have occasionally been lumpedtogether but more detailed investigation seems to prove thatQT/RR dependency and QT/RR hysteresis represent differ-ent physiologic mechanisms [2]. Healthy subjects who havefairly similar profiles of QT/RR dependency may havedifferent profiles of QT/RR hysteresis and vice versa. Inseminal studies, QT/RR hysteresis has been measured inartificially paced hearts in situ [3] and the observations werein close agreement with similar measurements of the speedwith which the duration of monophasic action potentials ofmyocytes adjusts following an abrupt change of thestimulation rate [4]. These observations suggested thatfollowing abrupt heart rate change, approximately 2 minutesare needed under normal physiologic conditions to reach95% of the equilibrium between the QT interval duration andthe new level of heart rate.

0022-0736/$ – see front matter © 2014 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.jelectrocard.2014.01.002

QT/RR hysteresis needs to be considered in all situationswhen the underlying heart rate is not stable or when the RRintervals representing the underlying heart rate are not constant.This includes fully physiologic conditions such as respiratorysinus arrhythmia during which the QT interval durationremains stable in spite of beat-to-beat RR interval variations[5,6]. Therefore, even in fully normal recordings, it is notappropriate to correct the QT interval for the preceding RRinterval. More stable expressions of underlying heart rate areneeded. In resting physiologic recordings during which theunderlying heart rate does not change, averaging RR intervalsover a period of time (possibly as short as the standard 10-second duration of the standard bedside electrocardiogram) issufficient to control for the effects of QT/RR hysteresis. Oncethe underlying heart rate is more erratic, such as in casesreported by Jacquemet et al. [1], more sophisticated approachesto the expression of the underlying heart rate are needed.

Presently available studies seem to suggest that QT/RRhysteresis is driven by the autonomic nervous system [7].Among others, the speed of QT/RR hysteresis appears todecline with increasing age [8] and a decreased speed ofhysteresis is observed in survivors of myocardial infarctionin whom the prolonged hysteresis is associated with anincreased risk of an early death [9], well in line with otherexpressions of autonomic reactions and reflexes.

Models of QT/RR hysteresis and correctionfor hysteresis

Studies of QT/RR hysteresis require tools suitable for thedescription of the phenomenon. Some authors used themeasurement of the area of the loop created by thesimultaneously measured QT and RR intervals while heartrate increases and decreases during physical exercise andrecovery. While such an approach might be suitable foroverall characterization of individual patients [10], simpleconsiderations show that it is inappropriate to characterizethe QT/RR hysteresis because the area of the loop largelydepends on the speed of heart rate changes.

The attempts to describe the profile of QT/RR moreobjectively may be broadly divided into two categories.Some, perhaps more technically minded researchers considerthe QT/RR hysteresis as a question of an autoregressive filterof the sequence of RR intervals preceding the QT intervalmeasurement. Application of such a filter provides the value

Fig. 1. The bold red (panel A) and bold blue (panel B) lines showthe conversion of the autoregressive filter proposed by Jacquemet et al. [1]into the weights of the RR intervals preceding the QT measurement.For different order of RR intervals k (horizontal axis), the bold blue lineshows the individual values of ωk, while the bold red line shows the valuesof ∑i=0

k ωi. Note that the bold blue and bold red lines are superimposed bydotted black lines. These show the individual weights and their sums for theexponential decay model with λ = 7.7159. Note that the autoregressivemodel and the exponential decay model lead to practically the same resultsalthough mathematically, their values are not equal to each other. Theoverlay panel in panel B shows the differences of weights of ωk

corresponding to the exponential decay and the filter models (i.e. thedifference between the black dotted and bold blue lines in panel B). Thedotted and dashed red (panel A) and blue (panel B) lines show the weights ofthe autoregressive filters with 50% and 200% of the constant proposed byJacquemet et al. [1] (i.e. with ϑ = 0.01263 and ϑ = 0.05052 for the dashedand dotted lines). Note that the modeled speed of the adaptation isapproximately linearly dependent on the coefficient ϑ (while the red solidline reaches 95% adaptation after approximately 120 cycles, the dotted anddashed lines reach 95% after approximately 60 and 240 cycles). Colorillustration online.

237Editorial / Journal of Electrocardiology 47 (2014) 236–239

of RR interval that needs to be used in the correction of theQT interval measurement. The suggestion by Jacquemetet al. [1] belongs to this category. The use a simple auto-regressive filter in the form RRi ¼ #RRi þ 1−#ð ÞRRiþ1

with the initial condition RRn ¼ RRn , where {RRi}i = 0n is

the sequence of RR intervals preceding the QT intervalmeasurement (RR0 being the closest and RRn being the mostdistant in the past) and RR0 is the RR interval value forwhich the measured QT interval should be corrected (notethat Jacquemet et al. number the RR intervals preceding theQT interval measurement in the opposite order but the

meaning of the proposed filter is exactly the same). This isthe same autoregressive filter approach as used previously byothers [11] while somewhat more complicated autoregres-sive filters have also been proposed [12].

Others, possibly driven more by physiologic consider-ations, understand the QT/RR hysteresis as QT intervalbeing influenced by the RR intervals in the history of themeasurement and thus describe the hysteresis as a sequenceof weights {ωi}i=0

n representing the contributions ofpreceding RR intervals. This leads to the suggestion thatthe QT interval should be corrected for ∑i=0

n ωiRRi, on thecondition that ∑i=0

n ωi=1. There are different ways ofconstructing the sequence of weights {ωi}i=0

n ranging fromtheir individual estimates based on fairly long sequences ofbeat-to-beat QT and RR measurements [9] to using moresimple mathematical forms that allow more direct compar-ison between different subjects [2]. Simple exponentialdecay [2] has been reported which gives the weights as∑k

i¼0ωi ¼ 1−eλkþ1nþ1

� �= 1−eλ� �

, where k = 0, …, n.Superficially, these “technical” and “physiological” ap-

proaches may seem to be mutually incompatible. However, itis not difficult to show that the autoregressive filter is aspecial case of the weights approach since in the autore-gressive formula described above, ωi = ϑ(1 − ϑ) i for alli b n, while ωn = (1 − ϑ)n. It is trivial to show that thecondition ∑i=0

n ωi = 1 is valid in this case. Moreover,although this form of the autoregressive filter is not mathemat-ically equivalent to the weights of the exponential decaysequence, it is also not difficult to show that for everymeaningful coefficient ϑ, a coefficient λ can be found (andvice versa) that the exponential decay and the describedautoregressive filter produce practically the same results (Fig. 1).

The initial “technical” suggestions of expressing theQT/RR hysteresis by an autoregressive filter of RR intervalsequence might have been contributed also by the consid-erations of computational efficacy. The filter is easy toimplement even if using low performance computer pro-cessors which used to be the case in older models ofelectrocardiographic equipment. This no longer applies andthus the technical and physiological approaches differ onlyconceptually in the mechanistic comprehension of thephenomenon. As shown in Fig. 1, there is little if anydifference between the approaches for the measurement ofthe phenomenon. Likewise, the two approaches offerpractically the same advantages when the correction forQT/RR hysteresis needs to be incorporated into the QTccalculation as in the report by Jacquemet et al. [1]. Thephysiological approaches of constructing more complexsequences of weights {ωi}i=0

n might be seen as more flexible[9] but, as already mentioned, more complex autoregressivefilters offering more flexibility are also possible [12].

Using the exponential decay approach, it has beenpreviously shown that similar to QT/RR dependency profile,QT/RR hysteresis profiles are subject-specific with largedifferences between different individuals and close intra-subject reproducibility [2]. That has also been confirmed bythe previous, more technically oriented study by Jacquemetet al. [13] since by using different value of the coefficient ϑ,different hysteresis profiles are obtained.

238 Editorial / Journal of Electrocardiology 47 (2014) 236–239

The established individuality of the QT/RR hysteresisprofiles does not invalidate the proposal of universal cor-rection. While QT/RR dependency profiles are also knownto be individual, universal heart rate corrections, such as theFridericia formula, are still very useful unless there is theneed to compare QT interval measured at markedly differentheart rates [14]. Likewise, universal QT/RR hysteresiscorrection is also likely to prove useful unless dealing withsituations in which the heart rate is changing verydramatically and rapidly. It might be plausible to speculatethat some cases of abrupt change in atrioventricular blockratio during atrial flutter might produce dramatic and rapidchanges in the ventricular rate. While it is true that in suchcases, the patient-specific hysteresis correction might lead tomore accurate results, the proposed universal hysteresiscorrection will surely be more appropriate than any correc-tion for simultaneously measured RR intervals.

The proposed setting of the universal autoregressive filterwith ϑ = 0.02526 [1] also appear reasonable since, as shownin Fig. 1, this particular coefficient leads (with sufficientlylong {RRi}i=0

n sequences) to 95% of QT-heart rate equilib-rium after 120 cardiac cycles, which, at 60 beats per minute,

Fig. 2. Hypothetical profiles of QT/RR hysteresis (panel A shows thecumulative sums of weights, panel B the individual weights) that all reach95% of the QT/RR equilibrium after 120 seconds but differ in theircharacteristics. The bold red line in the middle is the exponential decaymodel. Note that while Fig. 1 shows QT/RR hysteresis profile related tocardiac cycles, the profiles shown here consider hysteresis driven by the timebefore the QT interval measurement. The colors of the both panelscorrespond to each other. Color illustration online.

corresponds to the previously observed QT/RR hysteresis95% lag of 2 minutes.

Limits of present knowledge

Our understanding of the processes of QT/RR depen-dency is surely not complete with a number of openquestions. Nevertheless, our present knowledge of thedetails of QT/RR hysteresis processes is far more limited.Thus, to stimulate further research of the topic, it might bebeneficial to list the questions that need to be answeredbefore the field advances further.

While we have good reasons to believe that QT/RRhysteresis is driven by autonomic control [7,8], we knowpractically no details of such regulation reflexes. This is notsurprising since changes in cardiovascular autonomic status,whether drug-induced or caused by specific provocations,lead to marked heart rate changes. Only pacing can produceheart rate changes independent of prior autonomic changes.However, it is not obvious whether dramatic changes in thepacing rate can be made free of secondary autonomicalterations. Still, well controlled studies are needed, perhapscombining both pacing and gradual autonomic blockades, togain insight into the autonomic control of QT/RR hysteresis(and perhaps also QT/RR dependency).

The autoregressive filtering models of QT/RR hysteresisassume that the gradual changes of the QT interval duration aregoverned by the number of cardiac cycles rather than by timewhile the RR interval weightmodels can easily bemodified [2]to model a process in which certain time is needed for the QT/RR equilibrium to be restored after a heart rate change. It is notknown which of these possibilities is physiologically valid.Borderline observations have been made preferring the time-based rather than cycle-based hysteresis. If the process is trulydependent on the autonomic regulation, it seems indeedunlikely that the QT/RR equilibrium would be reached twiceas fast if changing heart rate from 100 to 120 beats per minutethan when changing it from 40 to 60 beats per minute.Nevertheless, no solid data are available to make thisdistinction with confidence.

We also do not know whether the QT/RR hysteresisprofile is the same following heart rate acceleration and heartrate deceleration. Autonomic processes involved in acceler-ating and slowing heart rate are clearly different and hence, itis not unreasonable to ask whether the corresponding QT/RRhysteresis is also different. Pacing experiments might bemisleading to make this distinction because of the brokenlink between the heart rate changes and autonomic control.Very well controlled studies of specific autonomic provoca-tions are likely needed.

It seems that if different physiologic processes (e.g. mentalchallenges, physical provocation, meal intake, etc.) changeheart rate, the QT/RR dependency profile is either the same oronly little influenced [8]. Nothing is known on the differencethat such processes might have on QT/RR hysteresis.

Our approaches to the mathematical description of theQT/RR profile have also been rather limited so far. Asalready shown in Fig. 1, the existing experience mostly

239Editorial / Journal of Electrocardiology 47 (2014) 236–239

utilized the exponential decay models or their closeequivalents. These are not the only possible profiles thatmight need to be considered (Fig. 2). It is even plausible thatdifferent processes that have just been discussed lead todifferent hysteresis profiles.

Finally, it is not known whether QT/RR hysteresis (andsimilarly QT/RR dependency) is a single uniform process ofwhether it is a combination of different regulation mecha-nisms. It is well plausible that different and mutuallyindependent regulatory processes maintain the stability ofQT interval duration during physiologic respiratory arrhyth-mia and during the abrupt and substantial heart rate changessuch as those associated with fast vagal withdrawal, e.g. atthe beginning of substantial physical or mental provocation.If this is the case, the characteristics of the different processesmight lead to different profiles. As a consequence, anaccurate description of QT/RR hysteresis might need toconsider combinations of different profiles, possibly differ-ent than those shown in Fig. 2.

Marek Malik, PhD, MDSt. Paul’s Cardiac Electrophysiology

University of London, and Imperial College, LondonE-mail address: marek.malik@btinternet.com

References

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[3] Lau CP, Freeman AR, Fleming SJ, Malik M, Camm AJ, Ward DE.Hysteresis of the ventricular paced QT interval in response to abruptchanges in pacing rate. Cardiovasc Res 1988;22:67–72.

[4] Franz MR, Swerdlow CD, Liem LB, Schaefer J. Cycle lengthdependence of human action potential duration in vivo. Effects of singleextrastimuli, sudden sustained rate acceleration and deceleration, anddifferent steady-state frequencies. J Clin Invest 1988;82:972–9.

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