INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

MANY DIFFERENT mathematical approaches have been used to study and quantify heart rate and heart period variability. Studies have featured spectral and nonlinear analyses (examples include Refs. 1-4, 9-11, 13-16, 19, 20, 22, 25). Because both of these techniques are typically global in application, wherein one number or set of numbers represents an entire sequence, their results are often interpreted in terms of putative long-term deterministic structures such as physiological oscillators or chaotic attractors. However, recent analyses of frequency transformations, nonlinear predictability, correlation dimension, and information scaling have demonstrated that resting heart period variability is not characterized by long-term deterministic control (7, 10, 13, 14, 19, 20). If long-term structures do not constitute heart period variability, then what kinds of structure or structures do constitute normal resting heart period variability?

This question has been addressed indirectly by nonlinear analyses that compared results obtained from the analysis of original heart period sequences with results obtained from sets of Fourier phase-randomized surrogate sequences. These surrogate sequences have the same power spectrum as the original yet lack any phase-dependent features that may be present in the original sequence. Both Kanters et al. (9, 10) and Roach and Sheldon (20) showed that original heart period sequences from resting subjects were more predictable than their surrogates and that this predictability lasted for only 4-30 beats. Because predictability is a result of the recurrence of similar subsequences, we proposed that the original heart period sequences contain recurring and similarly shaped subsequences (20) and that heart period sequences are organized somewhat akin to sentences. That is, there is a lexicon of recurrent, similarly shaped transient structures, analogous to words, in which each word has a characteristic physiological basis. We use the term "lexon" to denote meaningful, transient structures in heart period sequences. For lexons to be meaningful, we propose that they fulfill four criteria: 1) they should be present in heart period sequences of most or all members of a healthy population; 2) their morphological parameters should have central statistical tendencies; 3) they should be nonrandom structures; and 4) they should be associated with a characteristic physiology.

In examining heart period sequences from healthy humans and rabbits, we noted abrupt, large-magnitude, transient bradycardias (LMTBs) that quickly recovered to baseline (Fig. 1). We hypothesized that they might represent a lexon. To test this hypothesis we determined whether these transient bradycardias fulfill all four criteria for a lexon in a healthy rabbit population.

View larger version (23K): [in this window] [in a new window]   Fig. 1.   Heart period recordings for healthy human subject walking at 1.7 km/h on a treadmill (A) and for resting female rabbit (B). No ectopy occurred in either sequence. , Location of large-magnitude, transient bradycardias (LMTBs).

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Data acquisition. Twelve adult female New Zealand White rabbits were studied. The rabbits were acclimatized to the laboratory and then gently restrained and instrumented with an intra-arterial cannula in one ear and an intravenous cannula in the contralateral ear. Four surface electrocardiogram (ECG) leads were applied to regions of the abdomen and thorax. The room was darkened, movement of laboratory personnel was curtailed, and passage in and out of the room was discouraged. The room was not soundproofed, and extraneous sounds could not be prevented completely. After a 30-min rest period, we recorded continuous ECG and blood pressure signals for ~15 min. To ensure tranquil recordings, runs were aborted if the rabbit stirred significantly or tried to leave its restraining box. At least two recordings were obtained from each rabbit. Blood pressure was acquired with a Gould transducer, and both ECG and blood pressure signals were passed through a preamplifier and antialiasing filter. The signals were digitized at 1 kHz, stored, and delineated in a personal computer with the program CVSoft (Odessa Software, Calgary, Canada); then they were transferred into MATLAB (The Mathworks, Natick, MA) for further analysis. As a convention, we used the time of the second R-wave of each heart period interval as the time of that beat's heart period value. The blood pressure measurement at this time was recorded as the beat's diastolic pressure, and the subsequent systolic pressure was recorded as the beat's systolic blood pressure. Mean arterial pressure (MAP) values for each beat were calculated as MAP = (systolic pressure)/3 + 2 × (diastolic pressure)/3. The resulting heart period, diastolic, systolic, and MAP sequences were stored in MATLAB.

Finding nonrandom transient bradycardic events. A transient bradycardia is defined as a heart period subsequence bordered on either side by a local minimum of heart period. By definition, this subsequence contains one local maximum of heart period, situated somewhere between the start and end local minima (Fig. 2A). Because we were interested in detecting transient, reversible bradycardias, we also stipulated that the heart period must recover to within ±30% of the baseline heart period. The "bradycardic magnitude" of a transient bradycardia is defined as the difference between the enclosed local heart period maximum and the starting heart period local minimum.

View larger version (21K): [in this window] [in a new window]   Fig. 2.   A: illustration of measured heart period features describing LMTB structure. , Heart period values constituting bradycardic structure; , values used in calculating skewness and kurtosis. Larger circles are minima and maximum that define bradycardic structure. B: measured features of concomitant mean arterial blood pressure (MAP) subsequence. , MAP subsequence having greatest negative correlation with bradycardic event. In this case, lag = 2 beats. C: linear regression of lagged MAP subsequence (from B) as a function of bradycardic event heart period values (from A).

Despite the seemingly self-evident distinctiveness of these LMTBs, we needed an objective way to distinguish these putative LMTBs from other transient bradycardias in each of the original heart period sequences. We chose their large bradycardic magnitude as the distinguishing feature. To do this, we first produced phase-randomized surrogate sequences for each original sequence. These surrogate sequences have the same linear temporal correlation as their original sequences, but they lack any phase-dependent (or deterministic) structures that may be present in the original sequences. Because LMTBs were defined using a beat basis, (i.e., subsequences of beat-by-beat heart period values, rather than nonuniformly sampled time series values), we also used a beat basis to construct the surrogate heart period sequences. Thus to construct the surrogate sequences (10, 18), we made fast Fourier transformations (FFTs) of the original heart period sequences and replaced the phases of the Fourier coefficients with values drawn randomly from a uniform distribution between 0 and 2. We then applied the inverse FFT and finally quantized the resulting sequence to the 1-ms precision of the original sequences (equivalent to RR-interval delineation of a 1-kHz sampling of ECGs). For each original heart period sequence, we produced surrogate sequences until we acquired 10,000 randomly derived transient bradycardias. Because each original heart period sequence contained ~3,000 intervals, the maximum number of reversible bradycardias longer than 1 beat is ~1,000. This was estimated with the assumption that the minimum requirements for a transient bradycardia are 3 beats: two shorter intervals surrounding a longer interval. The bradycardic magnitudes for each of these phase-randomized transient bradycardic events were measured, and the 99.9% value was chosen as the threshold value of bradycardic magnitude. In other words, for each original recording, we determined the expected value of the largest bradycardic magnitude that could be obtained from 1,000 randomly derived transient bradycardias. We then used this threshold value of bradycardic magnitude to locate those transient bradycardias in the original heart period sequences whose magnitudes would be improbably large if this original sequence were just another phase-randomized realization. This set of transient bradycardias, whose large magnitudes and occurrence rates make it unlikely that they are random structures, was the set of local structures defined as the putative LMTB lexon.

Control events. Two types of controls were used (Fig. 3). The first control was the set of improbably large, transient bradycardias that might arise given enough phase-randomized surrogate sequences. For each of the original heart period sequences, we made phase-randomized surrogate sequences and collected the randomly derived bradycardias that had bradycardic magnitudes exceeding the calculated 99.9%. For every LMTB structure detected in an original heart period sequence, we collected five randomly derived, equally improbable structures from surrogate sequences derived from the original sequence. This allowed us to compare the putative LMTB lexons with the randomly derived heart period structures of similarly improbable bradycardic magnitude.

View larger version (18K): [in this window] [in a new window]   Fig. 3.   Example of original heart period sequence (A), its phase-randomized surrogate (B), and its beat-randomized surrogate (C). Note loss of originally shaped transient bradycardic events in surrogate sequences.

The second set of controls was obtained from beat-randomized surrogates. For each original heart period sequence, we produced a random permutation of the heart period values. These surrogates have heart period value distributions identical to the originals, but their order in the sequence is randomized.

Measuring the putative LMTB lexon. Figure 2A demonstrates the parameters that were measured for each putative LMTB structure. The scale parameters are the number of beats and the time elapsed from the first beat to maximum bradycardia (i.e., onset time) and from maximum bradycardia to the final baseline beat (i.e., recovery time). The magnitude parameter is the bradycardic magnitude (see Finding nonrandom transient bradycardic events). The shape parameters are the skewness and kurtosis of the transient bradycardic structures about the maximum bradycardic heart period value. Skewness measures the asymmetry of a sequence, and kurtosis measures the peakedness of a sequence. Both are independent of scale and magnitude. They were calculated on a beat basis, using a maximum number of beats while maintaining equal number of beats on both sides of the maximum bradycardic beat.

MAP sequences. The delineation of MAP sequences is illustrated in Fig. 2B. To assess whether the putative LMTBs might have physiological meaning, we correlated the heart period values of the LMTBs with their associated blood pressures. Moreover, we measured this correlation using variable MAP lags of 3 to 3 beats (Fig. 2C). For each LMTB we recorded the maximum correlation coefficient and the MAP lag at which it occurred. As well, we recorded the coefficients obtained for linearly regressing heart period values as a function of the lagged MAP values. For control sequences, we made both phase- and time-randomized surrogates for the MAP sequences.

Statistics. Normally distributed values are reported as means ± SD, and nonparametric distributions are reported as 25%, 50%, and 75% quartile values. Comparisons of normal distributions are made using a t-test, and nonparametric distributions are compared by means of the Mann-Whitney U test. Distributions were tested for normalcy by visually examining their histograms, comparing their modes, medians, and means, and comparing them with an ideal normal distribution with the Mann-Whitney U test. The significance of correlation between heart period and blood pressure subsequences was determined using Fisher's r to z method. The significance of the probability of the association of hypotension with bradycardia as a function of the duration of the LMTB was calculated using ² analysis. To have equal spacing between columns yet also have all expected values >1 and at least 20% of expected values >5, columns were collapsed in sets of three contiguous columns for analysis.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Universality of putative LMTBs. Table 1 shows that 11 of the 12 rabbits had transient bradycardic events whose bradycardic magnitudes were improbably large, such that they were highly unlikely to have been produced at the observed occurrence rates by phase-randomized noise. In 10 of these 11 rabbits, the probability that these inherent large-scale bradycardic events were a result of random realizations was <0.0001. Thus most rabbits experience nonrandom, large magnitude, transient bradycardic events.

Morphological features of the putative LMTBs. Table 2 and Fig. 4 summarize some of the features of these LMTBs. The events are 8.4 beats (2.64 ± 0.87 s) in duration. Maximum bradycardia occurs in 3.4 ± 1.7 beats (1.09 ± 0.49 s), and subsequent recovery takes 5.0 ± 1.9 beats (1.56 ± 0.61 s). The mean bradycardic magnitude is 77 ± 49 ms from a mean baseline of 290 ± 28 ms. The mean skewness was 0.84 ± 0.96. Of the 12 rabbits, nine had a significantly positive skewness and one had significantly negative skewness. The remaining two rabbits had only one and two putative LMTBs, respectively. Therefore, the onset of the LMTB generally is more abrupt than is its recovery.

View larger version (27K): [in this window] [in a new window]   Fig. 4.   Histograms of distributions of 6 morphologic parameters that define LMTB events. Parameters are defined in Fig. 2, and their statistical properties are described in Table 2.

The mean kurtosis was 3.01 ± 0.83, and 10 of 12 rabbits had a kurtosis significantly >2.40. (The kurtosis of a linear peak, which is a linear increase followed by a linear decrease, is 2.40.) The remaining two rabbits had only one and two LMTBs, respectively. Thus the onset and offset of the LMTBs occur faster than can be described by simple linearly increasing and decreasing sequences.

All the scale, magnitude, and shape features were normally distributed according to the Mann-Whitney U test (Table 2 and Fig. 4). Therefore, all the parameters that described the morphology of the bradycardic events had centrally distributed values.

Nonrandomness of the putative LMTBs. Although the detected events were highly improbable, we needed to demonstrate that their morphology was nonrandom. To assess this we compared the morphological features of the putative LMTBs with those detected from both phase- and beat-randomized surrogate sequences. Table 2 shows that all of the measured features of the LMTBs significantly differed from their surrogate control sequences. Therefore, the LMTBs are nonrandom structures.

Associated MAP features. Table 3 summarizes the relationship between the LMTBs and their accompanying MAP sequences. Of the 162 putative LMTBs, 123 (76%) showed a significant correlation with their accompanying MAP subsequences. These bradycardic-hypotensive events had MAP sequences that optimally lagged 2 beats behind the heart period sequence; that is, the bradycardic structures systematically preceded the hypotensive structures. The hypotensive magnitude was 6.1 ± 3.9 mmHg, and linear regression analyses (example in Fig. 2) showed an increase in heart period of 10.5 ± 4.1 ms/mmHg decrease. The probability of significant hypotension rose with the number of beats in the LMTB (Fig. 5). This was significant by ² (P = 0.0011), and there was a significant linear trend across the durations of the LMTBs (P = 0.043). Thus a characteristic relationship exists between the LMTBs and their accompanying MAP subsequences.

View larger version (17K): [in this window] [in a new window]   Fig. 5.   Probability of significant hypotension occurring during LMTB as a function of length (in beats) of LMTB. This was significance at P = 0.043.

We also used the surrogacy technique to test whether these might be accidental associations. To test this hypothesis, the original MAP sequences were beat and phase randomized. Table 3 shows the lack of a relationship between the LMTBs and the accompanying surrogate MAP subsequences. The maximum correlation coefficients and the number of bradycardic events with significantly correlated hypotension are significantly reduced, the lag values are not consistently positive, and there is a much wider range of regression values.

Finally, Fig. 6 is a composite diagram that shows the mean values for LMTBs and their associated blood pressure changes. This figure is drawn from the data of all LMTBs. Note that the composite LMTB has a rapid onset of bradycardia, a slower recovery to baseline, and a total duration of about 7 beats. The MAP subsequence lags about 1 beat behind the heart period subsequence.

View larger version (25K): [in this window] [in a new window]   Fig. 6.   Composite depiction of mean heart period and MAP expressions of LMTBs. Subsequences were aligned on beat with maximum bradycardia. Values are means ± SE.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

This work documents the existence of a lexon: a characteristically shaped, transient heart period structure that imperfectly recurs in multiple individuals of an animal population.

LMTBs as heart period variability lexons. LMTBs were the largest distinct, transient structure seen on initial inspection of the heart period sequences. We proposed and tested four criteria for assessing whether they were lexons. The events occurred in 11 of 12 resting rabbits. The values of their morphological parameters had central statistical properties, indicating that they reflected a common entity. They were nonrandom structures and were usually associated with hypotension. Thus they are a distinct lexon of heart period variability.

Is there a characteristic physiological basis for LMTBs? Transient hypotension is significantly associated with the LMTBs, suggesting that they may be distinct physiological events. One possibility is that they are startle responses. Many mammals, including cats, rabbits, woodchuck, and deer fawn, have transient bradycardias associated with startle responses (5, 6, 17, 23, 24). These may be associated with hypotension (12). Published reports, usually using these as conditioned responses to paired tones and periorbital shocks, have pooled heart rate and blood pressure responses in groups of several beats, preventing close comparison with our data. However, the magnitude and duration of these responses appear to be generally similar to ours (8). These responses to abrupt stress are mediated by brain stem nuclei, including the nucleus of the solitary tract and the amygdaloid central nucleus. Although the arterial baroreceptor does not appear to be directly involved, it does blunt the magnitude of the bradycardia and likely mediates recovery to baseline values. Thus the LMTBs observed in conscious, nonsedated, and apparently comfortable rabbits might be a similar physiological response to stochastic influences, such as movement of laboratory personnel or equipment and uncontrolled noises within the laboratory. Whether they are related to the hypotension and bradycardia that may be associated with vasovagal syncope is a fascinating conjecture that is now under investigation.

The close correlation between the changes in heart period and blood pressure suggests that the two are mechanistically related. It might be that the decline in blood pressure simply is caused by transiently longer diastolic run-off. Alternatively, it might be that when a decision is made to initiate a transient bradycardic event, a second decision occurs as to whether or not to have a hypotensive arm. If so, then the degrees of bradycardia and hypotension are both continuous responses to a common command.

Surrogate analysis. Surrogate analysis is a method of introducing randomness and therefore a control for the null hypothesis in analyses of time series. Usually the statistical properties of the original process are preserved while mathematical shuffling removes deterministic features. The surrogate sequences are therefore the random controls for the null hypothesis. We used two types of surrogate sequences. The beat-randomized sequences contain all the original heart period intervals, but their orders are randomized. Thus the statistical properties of the original heart period sets are preserved, but any logic to their arrangement is removed. The phase-randomized sequences have the power spectrum of the original sequence, but any logic to their phase arrangement of the spectral components is removed, thereby removing the spectral logic of the original shapes. Using both techniques we determined that LMTBs are not random collections of heart period intervals, and therefore have an intrinsic logic.

Perspectives

Interestingly, predictability analysis demonstrated the presence of short sequences 4-30 beats long that occurred repeatedly, albeit imperfectly. This suggests that nonrandom local structures are a source of heart period variability. These nonrandom local structures would then appear in heart period sequences much like words in a sentence. We term this a lexical approach (13), and the individual structures lexons. In early work we have identified four lexons. These include the LMTBs reported here, a reversible and high-magnitude tachycardia induced by the initiation of exercise (18), a transient cluster of 10-s heart period fluctuations that respond to orthostatic stress (21), and the origin of the standard deviation of all the 5-min mean heart periods and the ultralow frequency band in frequency analysis of ambulatory ECGs (19). There are likely to be more. Heart period subsequences have similar properties over a wide range of subscales (7), and this could be explained by a library of lexons of various sizes, each the result of one or more causes.

Lexical analysis has important advantages over globally based analyses. It is easily coupled with behavioral or physiological changes, and only short sequences are required for analysis. It makes no assumptions about global characteristics and no requirements for uniform sampling intervals or stationarity. It describes the duration, magnitude, and shape of the local event and accurately localizes it in the sequence. This may be important in examining the temporal location of paroxysmal disorders such as arrhythmias and vasovagal syncope. Finally and importantly, it offers the possibility of studying, under controlled circumstances, the physiology of events that can be observed on ambulatory ECGs. Indeed, work is underway in our laboratory to assess the physiology and pharmacology of LMTBs in humans, rabbits, and transgenically modified mice.