An analysis of the time relationships within the cardiac cycle in electrocardiograms of normal men

The optimal QTc selection in patients of acute myocardial infarction with poor perioperative prognosis

BACKGROUND

The predictive utility of QTc values, calculated through various correction formulas for the incidence of postoperative major adverse cardiovascular and cerebrovascular events (MACCE) in patients experiencing acute myocardial infarction (AMI), warrants further exploration. This study endeavors to ascertain the predictive accuracy of disparate QTc values for MACCE occurrences in patients with perioperative AMI.

METHODS

A retrospective cohort of three hundred fourteen AMI patients, comprising 81 instances of in-hospital MACCE and 233 controls, was assembled, with comprehensive collection of baseline demographic and clinical data. QTc values were derived employing the correction formulas of Bazett, Fridericia, Hodges, Ashman, Framingham, Schlamowitz, Dmitrienko, Rautaharju, and Sarma. Analytical methods encompassed comparative statistics, Spearman correlation analysis, binary logistic regression models, receiver operating characteristic (ROC) curves, and decision curve analysis (DCA).

RESULTS

QTc values were significantly elevated in the MACCE cohort compared to controls (P < 0.05). Spearman's correlation analysis between heart rate and QTc revealed a modest positive correlation for the Sarma formula (QTcBaz) (ρ = 0.46, P < 0.001). Within the multifactorial binary logistic regression, each QTc variant emerged as an independent risk factor for MACCE, with the Sarma formula-derived QTc (QTcSar) presenting the highest hazard ratio (OR = 1.025). ROC curve analysis identified QTcSar with a threshold of 446 ms as yielding the superior predictive capacity (AUC = 0.734), demonstrating a sensitivity of 60.5% and a specificity of 82.8%. DCA indicated positive net benefits for QTcSar at high-risk thresholds ranging from 0 to 0.66 and 0.71-0.96, with QTcBaz, prevalent in clinical settings, showing positive net benefits at thresholds extending to 0-0.99.

CONCLUSION

For perioperative AMI patients, QTcSar proves more advantageous in monitoring QTc intervals compared to alternative QT correction formulas, offering enhanced predictive prowess for subsequent MACCE incidents.

Influence of heart rate correction formulas on QTc interval stability

Monitoring of QTc interval is mandated in different clinical conditions. Nevertheless, intra-subject variability of QTc intervals reduces the clinical utility of QTc monitoring strategies. Since this variability is partly related to QT heart rate correction, 10 different heart rate corrections (Bazett, Fridericia, Dmitrienko, Framingham, Schlamowitz, Hodges, Ashman, Rautaharju, Sarma, and Rabkin) were applied to 452,440 ECG measurements made in 539 healthy volunteers (259 females, mean age 33.3 ± 8.4 years). For each correction formula, the short term (5-min time-points) and long-term (day-time hours) variability of rate corrected QT values (QTc) was investigated together with the comparisons of the QTc values with individually corrected QTcI values obtained by subject-specific modelling of the QT/RR relationship and hysteresis. The results showed that (a) both in terms of short-term and long-term QTc variability, Bazett correction led to QTc values that were more variable than the results of other corrections (p < 0.00001 for all), (b) the QTc variability by Fridericia and Framingham corrections were not systematically different from each other but were lower than the results of other corrections (p-value between 0.033 and < 0.00001), and (c) on average, Bazett QTc values departed from QTcI intervals more than the QTc values of other corrections. The study concludes that (a) previous suggestions that Bazett correction should no longer be used in clinical practice are fully justified, (b) replacing Bazett correction with Fridericia and/or Framingham corrections would improve clinical QTc monitoring, (c) heart rate stability is needed for valid QTc assessment, and (d) development of further QTc corrections for day-to-day use is not warranted.

Heart Rate Correction of the J-to-Tpeak Interval

Drug-induced changes of the J to T peak (JTp) and J to the median of area under the T wave (JT50) were reported to differentiate QT prolonging drugs that are predominant blockers of the delayed potassium rectifier current from those with multiple ion channel effects. Studies of drug-induced JTp/JT50 interval changes might therefore facilitate cardiac safety evaluation of new pharmaceuticals. It is not known whether formulas for QT heart rate correction are applicable to JTp and JT50 intervals. QT/RR, JTp/RR, and JT50/RR profiles were studied in 523 healthy subjects aged 33.5 ± 8.4 years (254 females). In individual subjects, 1,256 ± 220 electrocardiographic measurements of QT, JTp, and JT50 intervals were available including a 5-minute history of RR intervals preceding each measurement. Curvilinear, linear and log-linear regression models were used to characterize individual QT/RR, JTp/RR, and JT50/RR profiles both without and with correction for heart rate hysteresis. JTp/RR and JT50/RR hysteresis correction needs to be included but the generic universal correction for QT/RR hysteresis is also applicable to JTp/RR and JT50/RR profiles. Once this is incorporated, median regression coefficients of the investigated population suggest linear correction formulas JTpc = JTp + 0.150(1-RR) and JT50c = JT50 + 0.117(1-RR) where RR intervals of the underlying heart rate are hysteresis-corrected, and all measurements expressed in seconds. The established correction formulas can be proposed for future clinical pharmacology studies that show drug-induced heart rate changes of up to approximately 10 beats per minute.

Cardiac Conduction Model for Generating 12 Lead ECG Signals With Realistic Heart Rate Dynamics

We present an extended heterogeneous oscillator model of cardiac conduction system for generation of realistic 12 lead ECG waveforms. The model consists of main natural pacemakers represented by modified van der Pol equations, and atrial and ventricular muscles, in which the depolarization and repolarization processes are described by modified FitzHugh-Nagumo equations. We incorporate an artificial RR-tachogram with the specific statistics of a heart rate, the frequency-domain characteristics of heart rate variability produced by Mayer and respiratory sinus arrhythmia waves, normally distributed additive noise and a baseline wander that couple the respiratory frequency. The standard 12 lead ECG is calculated by means of a weighted linear combination of atria and ventricle signals and thus can be fitted to clinical ECG of real subject. The model is capable to simulate accurately realistic ECG characteristics including local pathological phenomena accounting for biophysical properties of the human heart. All these features provide significant advantages over existing nonlinear cardiac models. The proposed model constitutes a useful tool for medical education and for assessment and testing of ECG signal processing software and hardware systems.

Methodologies to characterize the QT/corrected QT interval in the presence of drug-induced heart rate changes or other autonomic effects

This White Paper, written collaboratively by members of the Cardiac Safety Research Consortium from academia, industry, and regulatory agencies, discusses different methods to characterize the QT effects for drugs that have a substantial direct or indirect effect on heart rate. Descriptions and applications are provided for individualized QT-R-R correction, Holter bin, dynamic QT beat-to-beat, pharmacokinetic-pharmacodynamic modeling, and QT assessment at constant heart rate. Most of these techniques are optimally performed using continuous electrocardiogram data obtained in clinical studies designed to characterize a drug's effect on the QT interval. An important study design element is the collection of drug-free data over a range of heart rates seen on treatment. The range of heart rates is increased at baseline by using ambulatory electrocardiogram recordings in addition to those collected under semisupine, resting conditions. Discussions in this study summarize areas of emerging consensus and other areas in which consensus remains elusive and provide suggestions for additional research to further increase our knowledge and understanding of this topic.

Estimation of the timing of carotid artery flow using peripheral pulse wave-gated MRI

PURPOSE

To investigate the relationship between peripheral pulse wave (PPW)-gating and the carotid systolic pulse wave in a large clinical patient cohort, and to establish a process for correct estimation of delay time from PPW-gating to foot (ie, beginning) or peak times of carotid systolic pulse waves.

MATERIALS AND METHODS

Subjects comprised 209 patients scanned using 3T magnetic resonance imaging (MRI) for PPW-gated phase contrast images at the common carotid artery. Stepwise multiple regression analysis was conducted for the relationship between foot or peak times and the following factors after excluding correlated factors with coefficients ≥0.5: pulse rate (PR); systolic blood pressure; diastolic blood pressure; height; body weight; body mass index; Brinkman index; diabetes mellitus; hypertension; and hyperlipidemia.

RESULTS

PR showed significant correlation with foot (r = -0.86, P < 0.001) and peak (r = -0.87, P < 0.001) times. The following equations were derived: foot time (msec) = -8.55 × PR + 993.1 and peak time (msec) = -9.21 × PR + 1142.3. No other factors showed significant correlations.

CONCLUSION

PR was the only factor showing significant relationships to foot and peak times of carotid artery flow. The derived equations will facilitate various kinds of noncontrast MR acquisition with simple PPW-gating.

Subject-specific profiles of QT/RR hysteresis

The time lag of the QT interval adaptation to heart rate changes (QT/RR hysteresis) was studied in 40 healthy subjects (18 females; mean age, 30.4+/-8.1 yr) with 3 separate daytime (>13 h) 12-lead electrocardiograms (ECG) in each subject. In each recording, 330 individual 10-s ECG segments were measured, including 100 segments preceded by 2 min of heart rate varying greater than +/-2 beats/min. Other segments were preceded by a stable heart rate. In segments preceded by variable rate, QT/RR hysteresis was characterized by lambda parameters of the exponential decay models. The intrasubject SDs of lambda values were compared with the intersubject SD of the individual means. The lambda values were also correlated to individually optimized parameters of heart rate correction. Intrasubject SDs of lambda were substantially smaller than the population SD of individual means (0.390+/-0.197 vs. 0.711, P<0.0001). The lambda values were unrelated to the QT/RR correction parameters. When compared with the corrected QT (QTc) for averaged RR intervals in 10-s ECGs and with the averaged RR intervals in 2-min history, QTc for QT/RR hysteresis led to a substantially smaller SD of QTc values (11.4+/-2.00, 6.33+/-1.31, and 4.66+/-0.85 ms, respectively, P<0.0001). Thus the speed with which the QT interval adapts to heart rate changes is highly individual with intrasubject stability and intersubject variability. QT/RR hysteresis is independent of the static QT/RR relationship and should be considered as a separate physiological process. The combination of individual heart rate correction with individual hysteresis correction of the QT interval is likely to lead to substantial improvements of cardiac repolarization studies.

Magnitude of error introduced by application of heart rate correction formulas to the canine QT interval

BACKGROUND

Accurate detection of drug-induced QT interval changes is often confounded by concurrent heart rate changes. Application of heart rate correction formulas has been the traditional approach to account for heart rate-induced QT interval changes, and thereby identify the direct effect of the test article on cardiac repolarization. Despite numerous recent studies identifying the imprecision of these formulas they continue to be applied.

METHODS

Using a chronic atrioventricular dissociated His-paced canine model, heart rate correction methods were evaluated for their ability to generate a corrected QT interval independent of original heart rate. Additionally, His bundle pacing at a heart rate of 60 beats/min allowed calculation of the magnitude of error introduced by application of heart rate correction formulas.

RESULTS

Of the fixed parameter heart rate correction formulas, only Van de Water was able to predict corrected QT values independent of the original heart rate. The magnitude of error discovered by application of heart rate correction formulas varied, but in many cases was very large. Bazett's formula was associated with a mean overcorrection of 67.9 ms; Fridericia's 28.7 ms. Van de Water was the best fixed parameter formula with a mean error of 10.8 ms. As expected, group and individual corrections derived from linear regression of the HR-QT data offered improvement over the traditional formulas. Both were able to predict QTc values independent of the heart rate. However, errors of the magnitude of 10 and 6 ms, respectively, were still introduced.

CONCLUSION

Van de Water and linear regression correction methods were superior to others in this study, but all methods generated QTc errors equal to or much greater than the magnitude of interest for drug safety evaluation.

Relation between QT and RR intervals is highly individual among healthy subjects: implications for heart rate correction of the QT interval

OBJECTIVE

To compare the QT/RR relation in healthy subjects in order to investigate the differences in optimum heart rate correction of the QT interval.

METHODS

50 healthy volunteers (25 women, mean age 33.6 (9.5) years, range 19-59 years) took part. Each subject underwent serial 12 lead electrocardiographic monitoring over 24 hours with a 10 second ECG obtained every two minutes. QT intervals and heart rates were measured automatically. In each subject, the QT/RR relation was modelled using six generic regressions, including a linear model (QT = beta + alpha x RR), a hyperbolic model (QT = beta + alpha/RR), and a parabolic model (QT = beta x RR(alpha)). For each model, the parallelism and identity of the regression lines in separate subjects were statistically tested.

RESULTS

The patterns of the QT/RR relation were very different among subjects. Regardless of the generic form of the regression model, highly significant differences were found not only between the regression lines but also between their slopes. For instance, with the linear model, the individual slope (parameter alpha) of any subject differed highly significantly (p < 0.000001) from the linear slope of no fewer than 21 (median 32) other subjects. The linear regression line of 20 subjects differed significantly (p < 0.000001) from the linear regression lines of each other subject. Conversion of the QT/RR regressions to QTc heart rate correction also showed substantial intersubject differences. Optimisation of the formula QTc = QT/RR(alpha) led to individual values of alpha ranging from 0.234 to 0.486.

CONCLUSION

The QT/RR relation exhibits a very substantial intersubject variability in healthy volunteers. The hypothesis underlying each prospective heart rate correction formula that a "physiological" QT/RR relation exists that can be mathematically described and applied to all people is incorrect. Any general heart rate correction formula can be used only for very approximate clinical assessment of the QTc interval over a narrow window of resting heart rates. For detailed precise studies of the QTc interval (for example, drug induced QT interval prolongation), the individual QT/RR relation has to be taken into account.

Steady-state versus non-steady-state QT-RR relationships in 24-hour Holter recordings

The aim of the present study was to investigate the QT-RR interval relationship in ambulatory ECG recordings with special emphasis on the physiological circumstances under which the QT-RR intervals follow a linear relation. Continuous ECG recordings make it possible to automatically measure QT duration in individual subjects under various physiological circumstances. However, identification of QT prolongation in Holter recordings is hampered by the rate dependence of QT duration. Comparison of QT duration and QT interval rate dependence between different individuals implies that the nature of the QT-RR relationship is defined in ambulatory ECG. Holter recordings were performed in healthy volunteers at baseline and after administration of dofetilide, a Class III antiarrhythmic drug. After dofetilide, beat-to-beat automated QT measurements on Holter tapes were compared with manually measured QT intervals on standard ECGs matched by time. The QT-RR relationship was analyzed at baseline in individual and group data during three different periods: 24-hour, daytime, and nighttime. Data were collected under steady-state or non-steady-state conditions of cycle length and fitted with various correction formulae. Our study demonstrated an excellent agreement between manually and automated measurements. The classic Bazett correction formula did not fit the QT-RR data points in individual or group data. When heart beats were selected for a steady rhythm during the preceding minute, QT-RR intervals fit a linear relationship during the day and night periods, but not during the 24-hour period in both individual and group data. In contrast, in the absence of beat selection, data fit a more complex curvilinear relationship irrespective of the period. Our study provides the basis for comparison of QT interval durations and QT-RR relationships between individuals and between groups of subjects.

Human atrial repolarization: effects of sinus rate, pacing and drugs on the surface electrocardiogram

OBJECTIVES

We studied the effects of rate and some cardioactive drugs on the atrial surface electrocardiogram (ECG).

BACKGROUND

In atrioventricular block, atrial surface ECG is unmasked. The effect of rate alone permits detection of the effect of other exogenous stimulations such as drugs in the presence of rate alterations.

METHODS

High fidelity, high gain ECG leads I, II and III were recorded from 51 patients with heart block. Durations of P and Ta waves and the total PTa interval were measured from nonconducted atrial events.

RESULTS

No relationship was found between sinus cycle length and PTa, P or Ta in 31 patients. In 20 patients, progressively decreasing the atrial pacing cycle length from 853 ms to 381 ms resulted in a linear reduction of the PTa interval from 444 to 291 ms (rho = 0.76, slope = 0.24). This was largely due to shortening of Ta. A linear rate correction formula was derived: corrected PTa = PTa - 0.24 (PP - 1000). Atropine (0.02 mg/kg) shortened the PP interval (p < 0.001) and the PTa interval (p < 0.01). Propranolol (0.1 mg/kg) prolonged the PP interval (p < 0.001) but did not alter the PTa interval. Neither disopyramide (2.0 mg/kg) nor flecainide acetate (2.0 mg/kg) altered the PP interval, but both prolonged the PTa interval (p < 0.001). This was largely due to P wave lengthening after flecainide (p < 0.001) and to Ta prolongation after disopyramide (p < 0.001).

CONCLUSIONS

In heart block, PTa, P and Ta waves can be measured reliably. The effects of pacing and some antiarrhythmic drugs on the atrial myocardium are similar to those known at the ventricular level.

QT corrected for heart rate and relation between QT and RR intervals in beagle dogs

The beagle dog has been widely used in cardiovascular research, but the adequacy of QT prediction formulas in dogs over a wide range of RR intervals has not been evaluated sufficiently. We investigated the QT-RR relation in beagles by analysis of the QT and preceding RR intervals obtained from 24-h ambulatory electrocardiograms. The acceptability of 14 QT prediction formulas was evaluated by use of 100-150 selected pairs of QT-RR points per animal in seven male and seven female beagles. The accuracy of fit with the measured data was assessed according to the minimum Akaike information criterion. The best fit was given by the logarithmic and inverse Kovács' formulas among one- and two-parameter linear regression equations, respectively. Exponential formulas produced a better fit than did the linear regression formulas, but are impractical because of the complicated interpretation of parameters due to the nonlinearity. In addition, the results obtained under physiological conditions were also confirmed by those of the pharmacological intervention study with disopyramide. Consequently, we propose a one-parameter logarithmic formula (QTc= log600 x QT/logRR) for correcting the QT interval for a heart rate of 100 bpm and the inverse Kovács' formula for evaluating a reverse-use-dependency of QT prolongation.

Dynamics of the QT interval in patients with exercise-induced ventricular tachycardia in normal and abnormal hearts

Inhomogeneity of ventricular repolarization reflected in prolongation of the QT interval of the surface electrocardiogram can predispose patients to ventricular arrhythmia. This study examines whether an abnormality of QT adaptation to changes in heart rate is likely to be of importance in the pathogenesis of ventricular tachycardia (VT) in patients with and without underlying structural heart disease. The QT-R-R relationship during exercise was studied in 52 patients. Forty-two patients had VT associated with a "clinically normal" heart (idiopathic VT), of which 23 had no VT on exercise and 19 had exercise-induced VT. These patients were compared to 10 subjects with exercise-induced VT related to ischemic heart disease. The QT interval was measured manually from computer-averaged QRS complexes recorded at 1- to 3-minute intervals during treadmill exercise tests. An approximately linear association existed between the QT and R-R intervals within the range of heart rates observed. The slope of the QT-R-R relation was lower in patients with structural heart disease (0.23 +/- 0.06) than in patients with normal hearts with (0.29 +/- 0.12) and without (0.29 +/- 0.12) exercise-induced VT (p < 0.05). The intercept of the regression line was higher in patients with structurally abnormal hearts (209.2 +/- 55.3 msec) than in patients with idiopathic VT with (155.6 +/- 49.7 msec) and without (157.7 +/- 69.0 msec) exercise-induced VT (p < 0.02). The corrected QT (Bazett's formula) was similar all three groups at rest, but was higher in patients with structurally abnormal hearts at peak exercise, 449.6 +/- 28.0 versus 425.8 +/- 27.4 msec (idiopathic VT, exercise induced) versus 427.3 +/- 26.6 msec (idiopathic VT, not exercise induced) (p < 0.05).(ABSTRACT TRUNCATED AT 250 WORDS)

Atrial fibrillation: new management strategies

The main goal of therapy in atrial fibrillation is to restore sinus rhythm, if this is possible, to avoid adverse hemodynamic, electrical, and embolic consequences. The restoration of sinus rhythm is urgent if the patient is unstable. In a stable patient, if the duration is shorter than 48 hours and an atrial thrombus is unlikely, then sinus rhythm can be restored after initial rate control. If the duration of atrial fibrillation is more than 48 hours, the embolic risk may be significant, and anticoagulation will be required for 2 to 4 weeks before an attempt at cardioversion. In patients in whom sinus rhythm cannot be restored or maintained, the goal of therapy is rate control and reduction of embolic risk unless the risk of anticoagulation outweighs its benefit. In difficult cases, rate control may be accomplished with AV nodal ablation and pacemaker implantation or with one of the surgical procedures described above with varying degrees of normalization of the physiology. Although not included in this flow chart, we do not advocate episodic intermittent therapy for patients with infrequent episodes of atrial fibrillation because this could be potentially dangerous and may place the patient at a higher risk for developing proarrhythmia.

Mode of QT correction for heart rate: implications for the detection of inhomogeneous repolarization after myocardial infarction

In 22 conscious, chronically instrumented dogs, the relationship between R-R interval and QT interval was better explained by linear regression than by nonlinear regression according to Bazett's formula. The correction formula QTL = QT-0.1*(RR-1000), which is based on the assumption of a linear relationship between QT and R-R interval, was then compared with Bazett's formula regarding its capability to detect inhomogeneous repolarization 5 to 7 days after temporary occlusion of the left anterior descending coronary artery. This comparison was performed only in those dogs exhibiting changes in QRS duration of less than 5 msec in response to myocardial infarction (n = 12). In these animals, myocardial infarction resulted in a significant dispersion of repolarization between the left ventricular normal zone and the infarct zone and a shift to the right of strength-interval curves of the infarct zone with respect to the normal zone, indicating local dispersion of refractoriness. As opposed to QTc (Bazett's formula), QTL was significantly (p = 0.04) prolonged after occlusion. Hence the adequacy of QT correction contributes significantly to the detection of inhomogeneous ventricular recovery after acute myocardial infarction.

Estimation of QT prolongation. A persistent, avoidable error in computer electrocardiography

A pooled community-based population sample of 17,139 North American children, adolescents, and adults aged from birth to 75 years was used to evaluate a variety of one-, two-, and three-parameter formulas for correction of the QT interval for heart rate throughout a wide range of heart rates in sinus rhythm. QT measurements were made by a computer program from simultaneously sampled standard 12-lead or orthogonal XYZ leads, and all QT measurements were visually verified using a high-resolution display terminal. A random subsample of 1,920 was drawn 3 times by allocating 20 subjects to each heart rate subinterval of 1 beat/min, and the performance of a set of 13 QT prediction formulas was compared by ranking them according to the Akaike Information Criterion. The traditional Bazett's square root formula failed at low heart rates and the cube root formula of Fridericia at high rates. None of the linear two-parameter functions of R-R interval or heart rate performed with adequate accuracy. The best one-parameter formula for predicted QT(QTp) was obtained by regressing the inverse of QT on heart rate, with the expression QTp(ms) = 656/(1 + 0.01 H R), and by adding the term 0.4 x Age - 25 for age-related trend correction in males 15-50 years old. Percentile population distributions for the QT index (QTI = (QT/QTp) x 100) produced a convenient and stable 98 percentile normal QT range spanning 10% above and below the population median QTI = 100 in all major subgroups by age, sex, and race.(ABSTRACT TRUNCATED AT 250 WORDS)

Physiologic relation between cardiac cycle and QT duration in healthy volunteers

To determine the relation between QT duration and RR interval on the electrocardiogram, 2 studies were undertaken in 23 young healthy volunteers (mean age 24 years). In study 1, the electrocardiogram (paper speed at 50 mm/s, 800 measurements/subject) was recorded in 11 subjects (5 men, 6 women) at rest, during dynamic exercise and after rapid intravenous injections of isoproterenol (0.2 to 12.8 micrograms), before and after intravenous atropine (2 mg). In study 2, the QT-RR relation was studied at rest and during exercise in 12 subjects (6 men, 6 women) before and after oral propranolol (80 mg). The results confirmed a monoexponential individual relation of the QT and RR intervals during rest and exercise: QT = A-B.Exp (-k.RR). By pooling the RR-QT plots from the 11 subjects in study 1, we found that the measured QT interval = 425-676.Exp (-3.7.10(-3) RR. During isoproterenol-induced tachycardia, QT either did not change or increased and this may indicate an increase in temporal dispersion of ventricular repolarization. Atropine-induced tachycardia produced changes similar to those resulting from exercise testing. Propranolol did not change the QT-RR relation despite a lengthening in RR intervals. These results suggest that physiologic QT-RR adaptation is mainly under parasympathetic control.

The QT interval in atrial fibrillation

The electrocardiogram was recorded for 100 seconds in 50 patients with atrial fibrillation to determine the relations between QT intervals and both the mean and instantaneous ventricular rates. The mean ventricular rate was 94 beats per minute with a mean QT interval of 357 ms. The mean QTc, corrected beat by beat with Bazett's formula, was 444 ms--longer than reported for sinus rhythm. Between subjects, the mean QT interval was linearly related to the mean RR interval, with a slope of +21%. Within all 50 recordings there was a statistically significant correlation between QT intervals and immediately preceding RR intervals, with an average slope of +7%. This within subject QT/RR interval slope was greater at faster mean ventricular rates. In atrial fibrillation, as in sinus rhythm, the QT interval is a function of both the mean ventricular rate and the instantaneous ventricular rate, with the mean ventricular rate predominating; a simple correction of QT intervals for heart rate is therefore inadequate. Comparison of uncorrected QT intervals with those of earlier published series of people in sinus rhythm, however, suggested that atrial fibrillation is associated with prolongation of the mean QT interval.

Evaluation of 10 QT prediction formulas in 881 middle-aged men from the seven countries study: emphasis on the cubic root Fridericia's equation

In 881 middle-aged men from one Italian cohort of the Seven Countries Study, QT and RR intervals were measured in lead 2 from resting ECGs (25 mm/sec) and fitted separately with 10 mathematically different QT prediction formulas. The relative accuracy of fit to data was assessed from the minimum mean-squared residual and the minimum Akaike Information Criterion values. Using the Minnesota code, 588 men had normal (group 1) and 293 had abnormal (group 2) ECGs. A better fit to QT-RR data by all formulas was observed in group 1, compared with group 2. Among one-parameter equations in both groups, the cubic root Fridericia's formula is better suited to fit the data than the Bazett's square root or other formulas. The former compares favorably with multiparameter equations or with the inverse relation and gives the best fit in group 2. Thus the cubic root equation might be more accurate than the square root or several complex formulas for correcting measured QT intervals for cardiac cycle length in middle-aged men.

The QT and QS2 intervals in patients with mitral leaflet prolapse

The QT interval was plotted against the R-R interval in 92 patients with mitral prolapse and 92 age- and sex-matched control subjects. Ten patients (11%) lay above the upper 95% confidence limit for the control group, and analysis of variance confirmed a small group effect (p less than 0.05). Despite this, the mean QT intervals in the two groups differed by only 7 msec and a t test showed no significant difference between the groups. The prevalence of QT prolongation was exaggerated by Bazett's rate correction formula (62%) or historical control groups published by Simonson (58%) or Ashman (70%). Simultaneous QT and QS2 intervals were measured in 67 patients with mitral prolapse. Inversion of the normal QT:QS2 relationship occurred in nine patients (13%) and was more common in the presence of severe mitral regurgitation. It was not associated with an increased prevalence of absolute QT prolongation and was therefore thought to be caused by relative shortening of the QS2 interval. In conclusion, the prevalence of QT prolongation in mitral prolapse is low (11%). The QT:QS2 ratio is unlikely to be a reliable indicator of QT prolongation in these patients.

The QT-sensitive cybernetic pacemaker: a new role for an old parameter?

A critical review of the available data on QT interval is presented to delineate techniques useful to the development of a QT-sensitive cybernetic pacemaker. The reason for the development of this unit stems from the ability of QT prolongation to predict the onset of life-threatening ventricular arrhythmias in some clinical situations; the QT interval is physiologically related to the cardiac cycle length, therefore providing adequate information to drive both ventricular and atrioventricular sequential rate-responsive pacemakers. This unit might also monitor cardiac rhythm and detect the pathophysiologic precursors of advanced grades of ventricular arrhythmias. A therapeutic role, both pharmacologic and electrical, may also be possible in the future. Integration of these concepts and cooperation between interested physicians, technicians and manufactors will be necessary to produce such a unit at a low cost-benefit ratio. The potential clinical application of this pacemaker deserves attention for the prophylaxis and treatment of sudden arrhythmic death.

The duration of the QT interval as a function of heart rate: a derivation based on physical principles and a comparison to measured values

Several quantitatively and qualitatively disparate formulas for the duration of electrical systole (the QT interval) as a function of the R-R interval are reviewed. These are compared by the use of dimensional analysis, which permits rectification of previously published algebraic and dimensional inconsistencies. With one exception, prior developments of formulas have been empiric in nature, with results therefore not based on or necessarily mathematically consistent with basic physical or biologic principles. In order to resolve ambiguity and determine which (if any) of the many proposed formulas is consistent with elementary principles, we began with physical principles as they relate to the results of experiments and derived a mathematical expression for the QT interval as a function of the R-R interval. By making use of equations for the conservation of energy for the heart as a pump and the first law of thermodynamics, a formula of the form QT alpha K'1 + K'2/R-R was derived. This derivation, stemming from first principles and founded on experimental data, does not quantitatively specify the additive (K'1) or multiplicative constant (K'2), but constrains the algebraic relationship of QT as a function of R-R. The formula is comprised of the sum of two terms, a HR (R-R) independent additive constant (K'1) and a term alpha (R-R)-1. The derivation resolves previous qualitative disparaties in proposed formulas and yields a finite limit for QT in the limit of large R-R intervals.(ABSTRACT TRUNCATED AT 250 WORDS)

An exponential formula for heart rate dependence of QT interval during exercise and cardiac pacing in humans: reevaluation of Bazett's formula

A new exponential formula to characterize the human RR-QT relation was evaluated in comparison with Bazett's formula in 16 subjects: 10 healthy, normal men (ages 18 to 30 years) who exercised on a stationary bicycle, and 6 patients (ages 50 to 80 years; 2 women and 4 men) with rate-programmable VVI pacemakers whose rates were changed by an external programmer. The RR and QT intervals for heart rate in the range of 50 to 180 beats/min were measured from electrocardiographic tracings recorded at a paper speed of 100 mm/s. The data from each subject were fitted separately by 4 formulas by an appropriate regression analysis using a statistical package program: (F1) QT = A1 - B1*Exp(-k1*RR); (F2) QT = A2[1-Exp-(-k2*RR)]; (F3) QT = A3* square root (RR) + B3; and (F4) QT = A4* square root (RR), where all A, B, and k are regression parameters. The relative goodness of fit of data by the 4 formulas was assessed by the mean-squared residual and the Akaike Information Criterion using Wilcoxon signed-ranks tests. This analysis confirmed that F1 is the best model among the formulas tested and F4 (Bazett's formula) is the least acceptable for both exercised and paced groups. The deviations from Bazett's formula were more striking for the paced group than for the exercised group, as reflected by the mean-squared residual values for F4 (715 +/- 86 for the paced group vs 384 +/- 41 for the exercised group, p less than 0.005).(ABSTRACT TRUNCATED AT 250 WORDS)

The QT interval and cycle length: the influence of atropine, hyoscine and exercise

Twenty-seven healthy male subjects of mean age 24.3 +/- 4.0 years and mean weight 74.9 +/- 9.1 kg took part in an investigation to assess the most suitable correction for the QT interval as a function of cardiac cycle length. 547 sets of data points were generated. Atropine 0.6, 1.2 and 1.8 mg, and hyoscine 0.4 and 0.8 mg, and exercise on a bicycle ergometer at power levels of 50-250 watts together with post-exercise values were employed to obtain a range of heart rates. Simultaneous measurement of cardiac output and total peripheral resistance were made. It was found that the traditional square root formula gave an unsatisfactory correction for the QT for supine subjects following atropine and hyoscine. The formula K = QT/RRN was linearized and fitted to the data by the least squares method and gave a best fit correction with N = 0.35, which is close to the cube root correction of Fridericia (1920). Neither stroke volume nor total peripheral resistance were found to provide a further enhancement of the correction. The relationship between QT and cycle length following the exercise protocol was found to be best represented by Bazett's correction but the complex changes in the QT produced by exercise were noted. These findings support the suggestion that either the cube root correction or the best fit correction with N = 0.35 provides a better correction factor than the traditional square root correction for the QT interval in clinical pharmacology experiments for data generated in resting patients.

The ventricular paced QT interval--the effects of rate and exercise

Changes in the QT and QTc intervals in 19 patients were studied at a ventricular paced rate difference of 50 beats/min. In all patients the measured QT interval shortened as the pacing rate was increased, from a mean value of 441 ms to 380 ms (p less than 0.001), but when corrected for heart rate the QTc lengthened from a mean value of 518 ms to 575 ms. In 11 patients the QT interval was measured at rest and immediately following exercise sufficient to increase the atrial rate by approximately 50 beats/min at identical ventricular paced rates. In all patients exercise-induced QT interval shortening from a mean value of 433 ms to 399 ms (p less than 0.001). These results show first that Bazett's formula is unsuitable for correction of QT interval induced by ventricular pacing, and second that heart rate and changes in sympathetic tone independently influence the duration of the QT interval. It is suggested that these results are relevant to the design of physiological pacemakers in which the duration of the QT interval influences the discharge frequency of the pacemaker and to the consideration of ventricular pacing for the treatment of abnormal repolarization syndromes.

Electrocardiographic evidence for a cardioprotective effect of nifedipine during experimental hypercalcemia

To investigate the effect of nifedipine on hypercalcemic electrocardiographical alterations, steadily increasing hypercalcemia was induced in guinea-pigs by continuous calcium gluconate infusion until cardiac arrest occurred. During the experimental time the electrocardiograms were continuously recorded and compared in animals with and without pretreatment by nifedipine (Adalat). The hypercalcemia-induced electrocardiographical alterations intensified during increasing serum calcium levels. Ascending serum potassium and magnesium levels indicated increasing cell damage with a leak of these mainly intracellular ions. Pretreatment by nifedipine did not significantly influence the hypercalcemia-induced bradycardia and augmentation of the P-Q interval except a small and transient effect during relatively low calcium levels. The drug, however, exerted a distinct normalizing effect on hypercalcemic reduction of the S-T segment and the Q-T interval despite of an unaltered development of hypercalcemia. Accordingly, the cellular potassium and magnesium leaks were markedly reduced and the survival time during calcium infusion was significantly prolonged after nifedipine pretreatment. These electrophysiological data are in agreement with our previous cytochemical studies, which showed a protective effect of nifedipine against hypercalcemia-induced overloading of the cellular calcium depots in myocardial cells. Whether this cardio-protective effect of nifedipine during hypercalcemia can be used therapeutically in hypercalcemic crisis, has to be examined in clinical studies.

QT interval measurement by a computer assisted program: a potentially useful clinical parameter

The duration of electrical systole (QT interval) was measured in 72 subjects (48 women and 24 men) who had normal coronary arteries and left ventricular function at cardiac catheterization (group 1). The same measurements were obtained in 100 patients with a normal ECG (from 40 women and 60 men referred to our institution and found normal on a noninvasive clinical basis) and compared to a double independent manual calculation (group 2). The computer assisted program was found reliable in QT interval measurements. In both study groups women showed longer QTc. No difference in QTc duration was seen in subjects taking beta-blockers prior to angiography. As compared to group 1, subjects of group 2 showed similar average QTc values. However, 9 out of 100 subjects of group 2 had abnormal QTc as compared with none of group 1 (p less than 0.05). QTc calculations may improve the usefulness of computer assisted programs in ECG interpretation. Present data can be used as reference values for normality. They stress in addition the necessity of introducing the heart rate correction for the interpretation of QT interval. This can help in stimulating prospective clinical studies to assess the value of QTc as an index of risk for cardiac dysrhythmias.

Effect of intravenous propranolol on QT interval. A new method of assessment

Changes in the QT and QTc intervals were studied in 16 patients by atrial pacing at rates of 100, 130, and 150 beats/minute. In all patients the measured QT shortened when the atrial paced rate was increased, but when corrected for heart rate the QTc lengthened. Intravenously administered propranolol produced a bradycardia and a lengthening of the QT interval in 15 of the 16 patients studied. When the QT interval was corrected for heart rate using Bazett's formula the QTc was shortened in 13 patients, unchanged in one, and lengthened in two. However, when the QT interval was measured at identical atrial paced rates the QT of the 15 patients studied was lengthened in 10 and unchanged in five. In none was the QT interval shortened. These results show firstly that Bazett's formula is unsuitable for correction of QT interval changes induced by atrial pacing, and secondly that, though intravenously administered propranolol usally produces a shortening of the QTc, when its effect is assessed directly by using an identical atrial paced rate the QT interval usually lengthens, or may remain unchanged, but never shortens. It is suggested that the formal assessment of drug induced QT interval changes should be made at identical atrial paced rates.

The Q-T Interval in Normal Infants and Children

Because of renewed clinical interest in the Q-T interval and because of a need of normal values for an accompanying investigation in rheumatic fever, the Q-T was studied in 517 normal infants and children from birth to 13 years of age. A mean K of 0.404 for Bazett's formula and of 0.378 for Ashman and Hull's formula was obtained. With Bazett's curve approximating the data more closely, a Bazett's scattergram of the normal Q-T at varying heart rates was constructed. Although no difference in K value was noted between the sexes, significant differences were observed in certain age groups.