Ventricular Cycle Length Characteristics Estimative of Prolonged RR Interval during Atrial Fibrillation

Abstract

Background

When atrial fibrillation (AF) is incessant, imaging during a prolonged ventricular RR interval may improve image quality. It was hypothesized that long RR intervals could be predicted from preceding RR values.

Methods

From the PhysioNet database, electrocardiogram RR intervals were obtained from 74 persistent AF patients. An RR interval lengthened by at least 250 ms beyond the immediately preceding RR interval (termed T0 and T1, respectively) was considered prolonged. A two-parameter scatterplot was used to predict the occurrence of a prolonged interval T0. The scatterplot parameters were: (1) RR variability (RRv) estimated as the average second derivative from 10 previous pairs of RR differences, T13–T2, and (2) Tm–T1, the difference between Tm, the mean from T13 to T2, and T1. For each patient, scatterplots were constructed using preliminary data from the first hour. The ranges of parameters 1 and 2 were adjusted to maximize the proportion of prolonged RR intervals within range. These constraints were used for prediction of prolonged RR in test data collected during the second hour.

Results

The mean prolonged event was 1.0 seconds in duration. Actual prolonged events were identified with a mean positive predictive value (PPV) of 80% in the test set. PPV was >80% in 36 of 74 patients. An average of 10.8 prolonged RR intervals per 60 minutes was correctly identified.

Conclusions

A method was developed to predict prolonged RR intervals using two parameters and prior statistical sampling for each patient. This or similar methodology may help improve cardiac imaging in many longstanding persistent AF patients.

Background

Many patients with longstanding persistent atrial fibrillation (AF) undergo computed tomography (CT)¹ as part of their cardiovascular evaluation. When durable sinus or atrial-paced rhythm cannot be achieved, as is common for patients with persistent AF, then imaging may be performed during AF, which poses greater challenges for image interpretability. Image quality may be improved when image acquisition occurs during a prolonged RR interval, in which the duration of diastole is increased, resulting in minimization of coronary motion. This is particularly the case for scanners enabling single heart beat imaging. We hypothesized that prediction of such long RR intervals could be done by analyzing ventricular cycle length patterns during persistent AF over long periods. We used the electrocardiograms from the PhysioNet Long-Term AF Database to test this hypothesis.²

Methods

Clinical Data and the Electrophysiology Procedure

Electrocardiograms recorded during persistent AF were obtained from PhysioBank’s Automated Teller Machine—called PhysioBank ATM (http://www.physionet.org/cgi-bin/atm/ATM²). The PhysioNet “Long-Term AF Database,” subcategory “Show RR intervals as text” was used, and consisted of a set of records from 82 longstanding persistent AF patients. Each patient record is composed of two low-noise electrocardiogram waveforms, the waveform RR intervals in text format, and annotations. Most of the records were approximately 24 hours long. We used the RR intervals provided in a textual form for our analysis. These were extracted by displaying the text on a computer screen, highlighting the record from time 1.0 hour to 3.0 hours, pasting it into a separate text file, and removing extraneous information such as the time stamp. The RR intervals were predetermined by PhysioNet as the difference in time of a tallest peak deflection that followed a prior tallest peak deflection by at least 200 ms. The period from 0.0 hour to 1.0 hour in each file was excluded from analysis because in some of the records there was an interval for initialization before a low-noise electrocardiogram was recorded and could be measured. Extraction of the record from hours 1.0 to 3.0 was repeated for all 82 AF patients’ data. In records of eight patients, segments were present in which the RR interval was indeterminate (pauses of many seconds or minutes between RR intervals), and these were not used in the subsequent analysis. Thus, 74 AF patients records were used in this study.

Quantitative Measurement

The data were analyzed using software developed by the authors and compiled in Fortran for implementation on a PC-type computer (Intel Visual Fortran Compiler 9.0, 2005, Intel Corp., Santa Clara, CA, USA). This software is not proprietary and can be duplicated by following the protocol described in these methods. The standard deviation in cycle length for each of the 74 analyzed Holter data records was found to be approximately 250 ms. On the basis of this value, an RR interval lengthened by >250 ms beyond the prior RR interval was considered to be an actual prolonged interval. For clarity, we refer to each prolonged RR interval and prior RR intervals using the following notation:

$$\begin{array}{l}\mathrm{T}0=\text{the}\text{prolonged}\text{RR}\text{interval}\\ \mathrm{T}1=\text{the}\text{RR}\text{interval}\text{just}\text{previous}\text{in}\text{time}\text{to}\text{the}\text{prolonged}\text{interval}\mathrm{...}\\ \text{Tx}=\text{the}\text{RR}\text{interval}\mathrm{x}\text{ventricular}\text{cycles}\text{prior}\text{in}\text{time}\text{to}\text{the}\text{prolonged}\text{interval}.\end{array}$$ (1)

We sought to develop parameters for prediction using the characteristics of the prior RR intervals. For simplicity, two parameters with high efficacy for cardiac electrophysiologic assessment were incorporated into our methodology. The first parameter is the second derivative of the RR interval, which was utilized previously to separate physiologic components from noise in the heart rate variability signal.³ The second parameter is the difference of a specific RR interval from the mean RR interval value preceding the prolonged RR, which was utilized previously to assess cardiac vagal tone.⁴

The period from hour 1.0 to hour 3.0 was divided into two equal sections. The data from the first section, from the first to the second hour, referred to as the preliminary or baseline data period, were used to define candidate parameters for estimating the limits of predictability. These parameters were then applied to the AF data observed in the second period, from the second to the third hour, to test their predictive values. Use of 1 hour measurement segments for development of parameters has been utilized previously to assess cardiac interbeat interval dynamics⁵ and was adopted for our study. The mathematical details of the parameters as implemented in this study are as follows.

Parameter 1

The prior RR variability (RRv) was measured as the average second derivative for 10 previous pairs of RR differences, that is, from T13 to T2. The average of the second derivative is given by:

$$\text{RRv}=1/10\sum _{\mathrm{j}}\text{abs}[({\mathrm{T}}_{\mathrm{j}+3}-{\mathrm{T}}_{\mathrm{j}+2})-({\mathrm{T}}_{\mathrm{j}+2}-{\mathrm{T}}_{\mathrm{j}+1})]\text{for}\mathrm{j}=10\text{to}1$$ (2)

where abs is the absolute value function.

Parameter 2

We determined that mean value T* selected from T13 to T2 that was most significantly different from T1 from the mean preliminary data of all patients. The difference T* – T1, where T* is the most significantly different value, was then used as parameter 2. We would expect this difference to provide the best discrimination of prolonged events (large difference in T* – T1) from nonprolonged events (smaller difference in T* – T1). To determine T*, mean values of each prolonged RR interval (T0) and the preceding RR intervals to T13 were tabulated for all incidences of a prolonged RR during hour 1–2 of each patient record. As an alternative parameter 2, the average difference Tm – T1 was also calculated, where Tm is the mean RR interval from T13 to T2.

For analysis, an RR interval longer by >250 ms from the previous RR, but within 13 cycles of a prior prolonged RR, was excluded and, therefore, not counted as a distinct prolonged event.

A scatterplot of parameter 1 versus parameter 2 was then constructed for each patient using all RR intervals from hour 1 to hour 2 (preliminary or baseline data). An automated algorithm determined the range of these two parameters (rectangular surface area in scatterplot) in which the proportion of RR intervals that were prolonged was ≥95% for a minimum of five prolonged RR intervals. If such an area did not exist, the rectangular box was adjusted to contain five prolonged intervals with a minimum number of nonprolonged intervals. The threshold of five was set so that over the course of 60 minutes, on average an event would be correctly detected every 60/5 = 12 minutes. The maximum average wait time would therefore be 12/2 = 6 minutes, considered to be a reasonable delay were the algorithm to be implemented for patient atrial imaging studies.

The constraints on parameters 1 and 2 identified by the rectangular surface were then used for prediction of prolonged RR using a 60-minute test interval from hour 2 to hour 3 of each patient record. As for the preliminary data, RRv was plotted versus Tm – T1 in the test set. A rectangular box of the same dimension was overlaid on the test scatterplot at the same location. The constrained rectangular area of the scatterplot for each patient consisted of points that were either true positives (correctly predicting that a prolonged event would occur) or false positives (incorrectly predicting the occurrence of a prolonged event). The positive predictive value (PPV) is defined as the number of true positives divided by all positives, times 100%. Measurement values were tabulated separately for each of the 74 patients.

As a further test we determined whether, for each patient data set, the same rectangular window denoting the range of RRv and Tm – T1 could be used to correctly predict prolonged events during hour 10–11. This measurement was used to determine whether influences such as temporal drift and/or diurnal variations are present that can affect best prediction parameters.

For comparison with the methodology used for prediction of prolonged events, mean statistics were also compiled from T26 to T0, to determine whether any patterns were evident further back in time from each prolonged event. As a second comparison, mean statistics were also compiled using a threshold level for T1 – T0 of 50 ms and a threshold level of 500 ms to define a prolonged event. In a third comparison, rather than using T1 – T0, the difference Tmn – T0 was used to detect a prolonged event, where Tmn is the mean of prior intervals. Finally, average statistics were also compiled for all long-short-long (LSL) events, which were defined as any series of three RR intervals with the first and third RR being longer than the second RR interval, and previous RR from T13 to T1. Prolonged events are a subset of all LSL events.

Significances were determined using the unpaired t-test, with P < 0.05, indicating significance (SigmaPlot 2004 version 9.01, Systat Software, Chicago, IL, USA). The t-statistic was calculated as the ratio of the difference between an estimated and a known parameter value, divided by the standard error of the estimate (MedCalc 2011 version 9.5, MedCalc Software, Mariakerke, Belgium). Correlative relationships were determined using the Spearman Rank Order method (SigmaPlot 2004 version 9.01, Systat Software).

Results

From the pooled data of all patients, during the first (preliminary) period from hour 1.0 to 2.0, 348,210 RR intervals occurred. There were 11,882 nonoverlapping sequences ending in a prolonged interval. Thus, on average, there were 11,882/74 = 160.6 prolonged interval events (T13–T0) during hour 1–2, per patient record.

In Figure 1(A), means are shown for prolonged events (black) and LSL events (gray). Prolonged events had a shorter RR interval at T1 (mean 550.6 ± 198.4 ms), a much longer T0 of 996.0 ± 406.5 ms, and an intermediate average T13–T2 of 718.7 ± 306.8 ms (P < 0.001). LSL events had a shorter RR interval at T1, and on average, T0 was approximately the same as T13–T2. Panel B shows the prolonged and LSL traces from panel A when T1 and T0 are left out of the graph so that the ordinate axis scale can be expanded to show detail. Thus, panel B depicts the same event as in panel A, except that only the interval from T13 to T2 is shown in panel B. Using this higher resolution in ordinate axis scale (panel B), an alternans pattern is evident in the mean RR values from T13 to T4 for all patients. On average there is a downward trend from T4 to T2 in the prolonged events (black trace) and an upward trend from T4 to T2 for all LSL events (gray trace). These observations, however, reflect only what happens in mean data, not in individual prolonged RR events. It should be emphasized that individual events can have patterns completely different from those observed in Figure 1. In fact for all data, the average PPV was only 9% to predict a prolonged event from the sequence T4>T3>T2>T1. Therefore, these patterns cannot be used to predict prolonged events in individual patients. There is a consistent alternans pattern in the average values from T13 to T0, except for T2, for prolonged events (black trace in Fig. 1).

Figure 1.

Average values of RR series of length 14, all patients. (A) T13–T0 are shown. Black—prolonged events, gray—long-short-long (LSL) events. (B) T13–T2 are shown for greater resolution along the ordinate axis. On average for all data, an event with prolonged RR from T1 to T0 paradoxically has increasingly shortened RR from T4 to T1 (black traces). On average for all data, the RR interval of LSL events increases from T5 to T2 (gray traces). For both prolonged and all LSL events, on average there is long-short alternans on even-odd T’s from T13 to T4 (panel B).

Prolonged events from T26 to T0 and all LSL events of the same length are depicted in Figure 2, with the panels having the same ordinate scales as those in Figure 1. The traces are similar to Figure 1, with prolonged events having short T1 and long T0, while LSL events have a short T1 but T0 is only slightly above the level from T26 to T2. Showing the ordinate axis detail in Figure 2(B) by excluding T1 and T0 from the graph, it is again evident that for these mean values for all events, there is a tendency in the average values for alternans to occur prior to T1, with peaks on even T’s and valleys on odd T’s, similar to the pattern observed in Figure 1. For both prolonged and LSL events, the pattern breaks down for T’s earlier than T22. As in Figure 1, there is a downward trend from T4 to T2 in the prolonged events and an upward trend from T4 to T2 for LSL events. Again, these observations reflect only what happens on average. Individual events can have completely different patterns as compared with Figure 2.

Figure 2.

Average values of RR series of length 27, all patients. (A) T26–T0 are shown. Black—prolonged events, gray—long-short-long (LSL) events. (B) T26–T2 are shown for greater resolution along the ordinate axis. The patterns are similar to those of Figure 2. For both prolonged and all LSL events, on average there is long-short alternans on even-odd T’s from T22 to T4 (panel B). The alternans pattern breaks down for cycles prior to T22 in the averaged data.

Figure 3 shows, using the same scales, graphs when different threshold levels are used to mark the occurrence of a prolonged event. In panels AC, the threshold level was 50 ms, 250 ms, and 500 ms, respectively. Using a low threshold level (panel A), more prolonged events are detected, but the average prolonged event is only slightly longer than the prior RR intervals. As threshold level increases from panels A to C, the total number of prolonged events N decreases. Using a threshold level of 500 ms provides a much higher average value of T0, approximately 1.4 seconds (panel C). However, the number of prolonged events that were detected reduced to approximately one-third that for the 250 ms threshold (panel B), thus increasing the waiting time for a prolonged event by almost three times. The 250 ms threshold, which was actually used for prediction in this study, represents a compromise in terms of the frequency of occurrence of prolonged events and the magnitude of the prolonged interval.

Figure 3.

Comparison of the average T13 to T0 when threshold values 50 ms, 250 ms, and 500 ms are used to detect a prolonged event in panels (A)–(C), respectively.

Figure 4 shows a comparison when T1 – T0 versus Tmn – T1 was used to detect prolonged events. In Figure 4(A), T1 – T0 is used to define a prolonged event, as was done to predict prolonged events in this study (Fig. 4A is the same as Fig. 3B except for different ordinate scales). In panels B and C, Tmn – T0 is used to define a prolonged event, where Tm is calculated as described in these panels. To maintain the same order of magnitude of prolonged events as in panel A (N = 11,882), the threshold levels for panels B and C were adjusted accordingly. The value of T0 is approximately the same in each panel of Figure 4 (1 second). However, if the method of panel B or C were to be used for prediction, new prediction parameters 1 and 2 would need to be devised since parameter 1 (RRv) would depend not only on variability, but also on the slope from T13 to T1, and parameter 2 (T* – T1 or alternatively Tm – T1) would be of low magnitude.

Figure 4.

Comparison of the average T13–T0 when using T1 – T0 (panel A), and Tmn – T0, where Tmn is the average from T5 to T1 (panel B) and the average from T13 to T1 (panel C), to detect a prolonged event, with varying threshold levels.

An example of actual prolonged RR prediction for T* – T1, where T* was found to be T4, is shown in Figure 5. The scatterplot has the prediction parameter 1 (RRv) as the abscissa, and the prediction parameter 2, T4 – T1, as the ordinate, for a selected patient record. In panel A the preliminary set, collected from hour 1 to hour 2, is shown, and many of the prolonged values (black) are located where T4 – T1 is large and RRv is relatively small. Within the optimized selection window, the PPV is 54/56 = 96.4%. The test set scatterplot, collected from hour 2 to hour 3, is shown in panel B, with the selection window being the same size and at the same position as in panel A. In this case, the PPV for predicting prolonged intervals is 70/76 = 92.1%. Thus, for the test set, 76 RR intervals would be predicted as prolonged, whereas 70 of them would actually be prolonged. For the rectangular area, the average time between actual prolonged RR is 60 minutes/70 prolonged events = 51 seconds; thus, on average the wait time for a prolonged event would be 51/2 or 25.5 seconds. In a clinical setting, the imaging technician would, therefore, need to wait approximately half a minute for a prolonged interval to be successfully predicted for imaging in this patient. There would be a 92.1% chance of successful prediction.

Figure 5.

Example of classification and prediction of prolonged RR events. The T4 – T1 difference is plotted versus RRv for the preliminary set (panel A) and test set (panel B). Prolonged events are denoted by black points and nonprolonged events are denoted by gray points. The sampling window, which is the constraint in the range of two parameters used to identify prolonged events, is shown (same for preliminary and test sets). The fraction of prolonged events versus all events in the sampling window is given in both panels.

Summary Statistics

For all 74 patients, mean PPV when using T4 –T1 versus RRv for prediction of prolonged RR was 73.7% for the test set. However, using Tm – T1 versus RRv for prediction resulted in a mean PPV of 79.7% for the test set, or approximately 80%. Thus, Tm – T1 was in fact a better predictive parameter as compared with T4 – T1. A histogram of the individual PPV for Tm – T1 versus RRv prediction parameters is provided in Figure 6. PPV was >80% in 36 of 74 patients and <50% in 15 of 74 patients. An average number of 10.8 prolonged RR intervals per 60 minutes was correctly identified. Thus, the average wait time for correct prediction was 0.5 × 60/10.8 minutes = 2.8 minutes. The mean value of Tm – T1 used for prediction for all patients was 365.7 ± 125.4 ms, and the mean value of RRv used for prediction for all patients was 125.4 ± 93.2 ms. The large standard deviation in both values suggests that it would not be feasible to use an average range to predict prolonged RR in all patients.

Figure 6.

Histogram of positive predictive value (PPV) for individual patients, when prediction is done using the parameters of RRv versus Tm – T1, where Tm is the mean RR from T13 to T2. The PPV is 100% for 21 of 74 of the patient records. The PPV is <50% for 15 of 74 patient records. Thus, the method provides excellent results in prediction of a prolonged RR event for many but not all patient records.

The mean PPV when using Tm – T1 versus RRv for prediction resulted in a mean PPV of 80.2% for the test set at time 10–11 hours, virtually the same as for the test set at time 2–3 hours. However, in 18 of 74 patients (24.3%), no values of Tm – T1 versus RRv resided in the range determined by using the exemplar set at time 1 to 2 hours (zero true positives and zero false positives). If these patients were counted as having a PPV of 0%, then the overall PPV decreased to 60.8%.

There was a positive correlation found between patient mean ventricular cycle length (mean RR interval) and the PPV of the test set for that patient (0.382, P ≤ 0.01). There was a negative (inverse) correlation found between patient standard deviation in cycle length and the PPV of the test set for that patient (0.328, P = 0.01). Thus, increased PPV was correlated to a longer mean ventricular cycle length and a lesser standard deviation in cycle length.

Discussion

Summary

The prediction of prolonged RR intervals prior to their occurrence may be useful for improving the quality of cardiac imaging during CT scanning. In this study, we investigated the limits of accurate prediction of prolonged RR intervals during persistent AF, by measuring the characteristics of prior RR intervals. The general idea was to create a statistical model using data collected over an hour of persistent AF, from many patients, and to use this model to predict the minimum wait time for encountering a prolonged RR interval during AF. We found that the average prolonged interval was 1.0 second in duration, which would likely be useful for imaging. Using as prediction parameters first the variability in RR interval, that is, RRv observed over 12 cycle lengths—a period stretching from T13 to T2—versus Tm – T1, in order to create a scatterplot, we found that the PPV of our method, based on data from 74 patients with persistent AF, was ~80%. Using RRv versus Tm – T1 time difference, a wait time of approximately 2.8 minutes would be expected to accurately predict a prolonged RR interval using this method. The use of a window to sample the statistics of RR series characteristics during the preliminary and application phases precludes calculation of sensitivity and specificity of the method—the rectangular area contains only true positives and false positives. However, only the PPV (i.e., the fraction of true positives among true positives and false positives), which was calculated in this study, is required to improve atrial image quality.

Our findings showed that averaged over many prolonged events from 74 patients with persistent AF, the RR intervals preceding a prolonged interval T0 had a particular pattern. There is an alternans pattern from T13 to T0, except for T2 (Fig. 1). Using a longer data series, there is also an alternans pattern from T22 to T0, except for T2 (Fig. 2). In general, these results are not surprising, because even the RRv patterns during normal sinus rhythm have deterministic signatures, meaning that any present state is dependent on previous states.⁶ Figures 2 and 3 suggest that there tends to be an alternans pattern leading to a prolonged event, although not all long-short RR pairs may be present in any particular sequence. Any relationship between the patterns observed in averaged RR intervals and the intrinsic electrophysiology underlying conduction through the atrioventricular (AV) junction is yet to be elucidated. Models using techniques from nonlinear dynamics and chaos theory may be useful to extract additional information with respect to the presence of determinism in these signals.

Application to Cardiac Imaging

Cardiac computed tomography (CT) scans are increasingly used to make definitive cardiac diagnoses. Large numbers of patients in these studies or undergoing these interventions have longstanding persistent AF, and in many of these patients, especially those with very longstanding AF and large left atria, early return of AF after direct current cardioversion precludes long enough periods of sinus or atrial-paced rhythm and thus these studies should be performed in the absence of a grossly irregular rhythm. When the tests are performed in ongoing AF, imaging during a long diastolic interval can improve image quality.

We defined a prolonged RR event as an RR value at least 250 ms greater than the prior RR interval, that is, greater than the standard deviation in RR (see “Methods”). This definition was found to be useful for detecting prolonged RR, which averaged approximately 1.0 second in length in this study (Figs. 1 and 2), as compared to the mean RR interval of ~700 ms from all series. This 1.0 second average prolonged interval is in accord with current guidelines in which a patient with heart rate of less than 65 heart beats per minute (≥1 cycle per second) is recommended to receive a satisfactory CT scan of the heart.⁷ The successful prediction of a prolonged ventricular RR interval may improve diagnostic accuracy and possibly decrease exposure to ionizing radiation in patients with longstanding, chronic AF undergoing cardiac CT scan. The very low PPV of 9% for the pattern T4>T3>T2>T1 in individual patients shows that algorithms based on average trends cannot be used to make successful predictions in individual cases. Linear predictive methods are likely not very useful to predict prolonged intervals, which are rare occurrences with associated statistical properties that vary greatly from one patient to another.

Further analysis, in large numbers of patients and possibly by incorporation of spectral parameters,⁸ will be needed to shorten wait time, before this methodology achieves clinical utility. The current strategies used to reduce presence of cardiac motion for high-quality imaging involve either slowing the heart rate or scanning faster than the diastolic interval.⁹ However, reducing the heart rate is contraindicated in many cardiac patients.⁹ More rapid scanning may not be sufficient for quality imaging of a randomly selected cardiac cycle having a very short RR interval, and represents a hit-or-miss approach. Our proposed method of prediction of prolonged RR intervals represents a third strategy for improved cardiac imaging, which does not cause patient morbidity and is based on optimization of prediction parameters rather than random chance.

The algorithm can readily be implemented on a PC-type computer. This computer would need access to the electrocardiogram or to a calculated RR interval. These data could be inputted to the PC via an analog-to-digital converter. Exemplar RR intervals would be analyzed to determine parameter values. Then the algorithm could be used in real time to predict prolonged RR. A signal would then be sent from PC to imager via a digital-to-analog converter to commence imaging at the onset of a prolonged interval.

Limitations

For confirmation of our results, data from a larger number of patients with persistent AF should be analyzed. Another limitation of this study is that the 2.8-minute average wait time may be problematic in clinical use. Needless to say, other reasonable candidate electrocardiographic parameters, including a few others previously reported,⁸ may be used for further sharpening and narrowing the limits of predictability using the basic paradigm outlined in this study. Because of the constraints imposed by the available PhysioNet data, it was not possible to determine whether analysis on a different day in the same patient would have any effect on the predictive ability of the algorithm.

Conclusions

Parameters derived from the electrocardiogram RR interval of patients in persistent AF are highly variable between patients. If, however, the statistics are sampled on a per patient basis, it is possible to predict a prolonged RR interval using measurements from prior RR intervals. The reasonable accuracy of the method suggests that there is sufficient temporal stability over a 1-hour period during which baseline data are collected. For application to patient imaging, however, shorter intervals to obtain baseline data should be used to reduce wait time. Depending on the temporal stability of the AV conduction pattern statistics, parameters developed for prediction of prolonged RR events using a particular baseline statistical sampling interval may or may not be applicable for prediction, many hours or days later. Therefore, baseline measurement should be done just prior to prediction of prolonged RR events.