INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

DESCENDING AUTONOMIC ACTIVITIES of higher cerebral origin are necessary and, in some cases, sufficient to evoke lethal cardiac arrhythmogenesis (3, 5, 9, 30, 33, 39, 46, 49) and myopathy (4, 8, 16, 18, 26). Indexes of heart rate variability (HRV) are currently thought to reflect this deleterious neural activity (42), and such indexes have shown promise as predictors of mortality in high-risk cohorts (17, 22, 25, 48). There is a problem, however, in trying to deal with the descending neural activities in a quantitative manner, because they are complexly regulated by the higher cerebral centers in parallel with the simpler homeostatic regulation by the brain stem. The higher neural centers, especially those involved in perception and defensive behaviors, can produce uncontrolled nonstationary effects in the heartbeat data.

The HRV indexes are based on stochastic models, each of which presumes that the variation of the heartbeats is randomly distributed around a mean (i.e., is noisy) and remains stationary throughout the interval of data collection. The potential for nonstationary neural regulation of the heartbeats plus the recent observations of their nonrandom variations suggest that the HRV measures based on the presumption of underlying stochastic dynamics may be inappropriate.

Nonlinear deterministic measures of the heartbeats have recently been shown to be more sensitive than the stochastic indexes in detecting the autonomic changes related to mortality (13, 19-21, 31, 33, 40, 41, 47). The primary explanation for the greater sensitivity is that the nonlinear measures are based on deterministic models, each of which presumes that the variation may be caused by a low-dimensional mechanism, not a high-dimensional stochastic process, and thus is a more appropriate measure (32, 38, 41, 47). Furthermore, some of the time-dependent nonlinear measures can treat the severe problem of data nonstationarity (32, 38, 41, 47).

What the time-dependent nonlinear algorithms show as indicators of cardiac vulnerability to lethal arrhythmias are transient nonstationary shifts of dimension of the heartbeat dynamics to a low value. This has been demonstrated in controlled data from conscious pigs undergoing experimental heart attack (32), in retrospective clinical data from patients with nonsustained ventricular tachycardia (NSVT) (38, 47), and in prospective clinical data from patients with chest pain and high-diagnostic risk (34). The significance of these low-dimensional excursions remains to be explained.

We previously studied dimensional reductions in a simple system model, the intrinsic cardiac nervous system of the isolated rabbit heart (40). We provided evidence that the system variables (inotropy and chronotropy) are measured by the subintervals of the electrocardiogram (ECG) (1/Q-T, 1/R-R-Q-T) and that they continue to undergo systematic nonlinear changes during stimulation by anoxia/ischemia. It was found that the system variables dissociate 2 min after the block of coronary flow but then reassociate, within 1 min, and manifest a new system attractor (an attractor is the geometric structure formed by the plot of the system variables).

We now report on a new model, one with a little more autonomic superstructure intact and one in which the perturbation of the cardiovascular system can be extended in time. Ketamine is known to block the N-methyl-D-aspartate (NMDA) receptors in the higher centers of the rat cerebrum (cortex, striatum, and hippocampus) (2), with only a small, stereospecific, cholinergic, inhibitory effect exerted directly on the heart (10). The rat is the animal of choice because of the large body of specific knowledge about its neurochemical centers and their stereotaxic accessibility. Specifically, we used this new model to test the hypothesis that the evoked nonlinear dynamics of the R-R intervals and of the Q-T and R-R-Q-T subintervals will be more complex in the ketamine-anesthetized rat than in the intrinsic cardiac nervous system.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Data

Each rat was stabilized for 15 min after the surgery. After the recording of a 2.5-min control period, blood was then removed from the right femoral artery at a constant rate of 2 ml/min. The animals were bled to a mean arterial pressure between 30 and 35 mmHg for 15 min. The experiment was discontinued at 15 min, and the animal was euthanized by a barbiturate overdose (70 mg/kg).

Specific Analytic Algorithms

R-R interval determinations. The R-R intervals were determined algorithmically by a running 3-point convexity operator that has >95% correspondence to the nearest millisecond for visually determined intervals (29). The Q-T interval (Q peak to T end) used the maximum negative derivative in a forward-looking T window. T end was the first subsequent slope 40% greater than that of the maximum.

Correlation dimension. The three-dimensional algorithms all make similar correlation integrals (6, 35). They differ only in how the vector-difference lengths that form the integrals are added together [e.g., all of the vector differences, to increase signal-to-noise ratio, as in the classical correlation dimension (D2)] or in how the linear scaling region is determined [e.g., restricted in length, as in the point correlation dimension (PD2i)].

PD2i parameters. If one records from a sine-wave generator that is suddenly replaced by, e.g., a Lorenz chaotic generator, then a nonstationarity will occur in the data stream. Formally, the statistical properties of the data will be different the moment after the replacement. Our laboratory developed the PD2i algorithm to address data nonstationarity, because this problem invariably arises in long epochs of biological data when the system uncontrollably changes state (e.g., when shifting from sleeping to waking, or from quiescence to alerting). The first insight that led to our algorithm was that in nonstationary data, the vectors made from "points" of data that are stationary with respect to the "point" the reference vector is in (a "point" is a small strip of data, m ×  data points long) will contribute uncontaminated vector-difference lengths only to the small log  R part of the scaling region.

Surrogate controls. Any nonlinear algorithm suffers from its sensitivity to stochastic noise. R-R data contain discretization errors (0.2% for 1,000 Hz digitization of the ECG) and amplifier noise (~2 mV, RMS). Each R-R interval was therefore expressed as 0.5 integer/ms, because this enables a small amount of noise in the R-R data to be tolerated by the PD2i algorithm (35).

Statistics

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Each rat was bled to a final mean arterial pressure between 30 and 35 mmHg, accomplished within a period of 15 min. The blood pressure drop during the first few minutes was not as great as that during the last few minutes (i.e., it was nonlinear). Although all animals remained in the anesthetized state, it was noticed that some were more reactive to a tail pinch than others, but this was not studied systematically. None of the rats appeared to suffer labored breathing or respiratory distress during this 15-min period.

Figure 1 shows the effects on the rat ECG of 5 min of blood loss (2 ml/min, 500 g). Note that although the experimental shock results in a reduction of the R wave and an increase in the T wave, there is still ample amplitude for discrimination of the two peaks.

View larger version (23K): [in this window] [in a new window]   Fig. 1.   Electrocardiogram (ECG) recorded from the ketamine-anesthetized rat before (A) and after (B) 5 min of blood loss at 2 ml/min in a 500-g rat. The first derivative (DV/DT) is also shown below each ECG. , Position of the 3-point convexity operator at its maximum output; slope lines indicate maximum negative DV/DT in T window and its subsequent increase by 40% (T end).

Figure 2, top, shows the effects of slow, continuous hemorrhage (downward arrow, 2 ml/min blood loss) on the R-R, Q-T, and R-R-QT intervals in the ketamine-anesthetized rat. The infrequent abnormal beats on the Q-T trace are due to small movement artifacts. Such inaccuracies always lead to rejection of the PD2i at these locations in the data stream. The rejection occurs because the presence of the artifact as a coordinate in the reference vector leads to failure of one or more of the scaling criteria.

View larger version (33K): [in this window] [in a new window]   Fig. 2.   Interval series (INTERVAL, in ms), time-dependent dimensions (point correlation dimensions; PD2i), and attractors (QT vs. RR-QT, in ms) in the ketamine-anesthetized rat during experimental hemorrhagic shock (arrow, 2-ml/min blood loss). Subepochs indicated in the PD2i trace are shown for attractors A, B, and C separately (third row) and all of them together, sequentially (fourth row). Heartbeats shown (2,800) consumed 14.0 min of time. See RESULTS for more information.

The PD2i of the R-R intervals is shown in Fig. 2 immediately below the R-R and subinterval traces (middle). The mean value for the light-anesthesia control period (A) is ~3.1 dimensions (i.e., degrees of freedom). During the 2.0-min period after the hemorrhage was initiated (B), there was an immediate and relatively stable reduction in the dimension of the R-R interval series to a mean of 0.8 (1.01 grand mean for all rats, P < 0.01, binomial probability, paired t-test). This subepoch was also associated with a marked reduction in the standard deviation of the R-R intervals, as can be seen graphically in Fig. 2, top, just after the downward arrow. At 2.2 min after the hemorrhage was initiated, there was an abrupt rise in dimension followed by what appeared to be a series of "dimensional oscillations" for the next 2.3 min (C). These fluctuations, 4.5 min after the initiation of hemorrhage, abruptly rose in dimension for a prolonged period and then decreased to a rather steady level of 1.6 dimensions for a while. At 8.5 min there began a rather wild series of dimensional fluctuations that slowly rose to a mean of 4.0 by 15 min (3.22 grand mean for all rats, P < 0.01, paired t-test).

Figure 2, bottom, shows the joint plot of the Q-T versus R-R-Q-T subintervals for each heartbeat during the whole experiment. The points A, B, and C are shown in the three smaller panels above it. Because Q-T versus R-R-Q-T is a plot of the 1/inotropy versus 1/chronotropy variables that regulate the heart, it is a way to show the system attractor (an attractor is a multidimensional plot of the system variables that specifies its dynamics over all time). During the control period (subepoch A), when the PD2i is around 3, the Q-T versus R-R-Q-T points fluctuate around the center of mass and form a "fuzzy ball" (i.e., the dots are space filling in 3 dimensions). During the subepoch B period, when the dimension is around 1, the points move up and down negative-sloped lines, each of which has similar slopes (see Fig. 3). During the subepoch C interval, when the oscillations between 1 and 2 dimensions began, there is a change in the negative sloped lines (1-dimensional) to those of a "zigzag" pattern (i.e., space filling in 2 dimensions).

View larger version (28K): [in this window] [in a new window]   Fig. 3.   Expanded time base for R-R intervals and corresponding PD2i values of the subepoch C shown in Fig. 1. In the PD2i trace, A-D indicate four halves of the first two cycles of the "dimensional oscillations." The attractors (Q-T vs. R-R-Q-T) for each half cycle are shown in the bottom row. R-R values are in milliseconds, and PD2i values are in dimension. See RESULTS for more information.

This zigzag pattern is seen in more detail on the expanded time base of Fig. 3. The same R-R and PD2i series are shown for the subepoch C as in Fig. 2, but now the "dimensional oscillations" are more easily seen as systematic changes from higher to lower values. Four parts of the first two cycles are indicated (A-D). The Q-T versus R-R-Q-T plots (attractors) are shown in Fig. 3, bottom, for each of the A-D periods. During the first half cycle, when the dimension is around 1 (A), the plot of Q-T versus R-R-Q-T is a thin negative-sloped line. During the second half cycle (B), when the dimension is closer to 2, the plot becomes space filling in two orthogonal directions. That is, a zigzag pattern is observed when the dots are interconnected, as in the letter Z. This same pattern is observed during the next cycle (C, D), and so on.

Figure 4 shows the PD2i of the R-R data series (top) and each of the concomitant subinterval series, Q-T (bottom) and R-R-Q-T (middle). During the subepoch B (dark underline), all three series have approximately the same lower dimension, around 1. During subepoch C, especially during the dimensional oscillations seen in the R-R series (thin underline), there is a dissociation of the mean PD2i values. The mean for the Q-T series is considerably higher (most PD2i values > 2.0) than that for the R-R-Q-T series (most PD2i values < 2.0).

View larger version (31K): [in this window] [in a new window]   Fig. 4.   Time-dependent dimensions (PD2i values) for the R-R intervals and their corresponding Q-T and R-R-Q-T subintervals during blood loss. Ordinates are 0 to 5 dimensions. Dark line is subepoch B, and thin line is subepoch C (see RESULTS).

Table 1 shows the composite results for the 16 rats during hemorrhagic shock. Three of the rats (indicated by rats 6, 9, and 10) did not show any dimensional variation during the bleeding; one of these (rat 6) showed relatively high ventricular ectopy during the control condition. We have no explanation for the lack of variation. Of the remaining 13 rats, none showed any ectopy, but some did show twitch movement artifacts. In these 13 rats, each manifested a lower dimension during the first few minutes after the start of the bleeding than it did during the previous control period observed during light anesthesia (P < 0.01, binomial probability test, paired t-test). Many of these rats, however, did not manifest the normal unanesthetized PD2i level of ~3.0 during the control period, but rather showed reduced dimensional levels.

The dimensional reduction within 2 min after the start of bleeding was to a level of ~1.0 (grand mean equals 1.0). As seen in both Table 1 and Fig. 5, as the hemorrhage progressed, there is a systematic rise in dimension to larger values by the end of the 15-min experiment (grand mean equals 3.4, P < 0.01). Most animals showed at least one "dimensional oscillation" during the interval between 2.0 and 4.5 min after the start of the bleeding (designated by Y). In some, however, the PD2i values during this interval either linearly elevated (e.g., Fig. 5, rat 5) or stayed constant, without any characteristic cycling or wandering behavior. Of those that did show the cycling, there often occurred a large initial dimensional increase, as seen in Fig. 2 (middle panel, between the subepochs B and C) and in Fig. 5 (after the B interval, rat 7). This large cycle was then followed by one or more smaller-amplitude dimensional oscillations.

View larger version (27K): [in this window] [in a new window]   Fig. 5.   R-R intervals and corresponding PD2i values for 6 rats without cardiac arrhythmias or movement artifacts during hemorrhage. Each trace shows 2,800 R-R intervals. The total time intervals for traces are the following: rat 1 = 14.0 min, rat 7 = 11.3 min, rat 5 = 18.7 min, rat 8 = 9.8 min, rat 12 = 10.8 min, and rat 13 = 10.2 min. All calibrations are the same as indicated at top left (R-R in ms; PD2i in dimensions), except for rat 5, in which R-R is 200-500 ms. The horizontal lines indicate the selected stable PD2i subepochs selected for stochastic-measure analyses (see Table 2).

Figure 5 shows the R-R values and associated PD2i values for six rats that had very few cardiac arrhythmias and movement artifacts. These were selected because the application of stochastic HRV measures requires absolute data stationarity. To make comparisons between PD2i and other HRV measures, three intervals were selected for each animal during relatively stable (stationary) periods of their respective PD2i values (Fig. 5, B-D). The correlation coefficients between the PD2i and each of the other standard measures of HRV are shown in Table 2.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Significance of a Low-Dimensional Excursion

Our previous study (40) discovered that in the isolated heart, a simple way to examine the system variables (i.e., inotropy and chronotropy) was through the heartbeat subintervals. We first noted that the Q-T subinterval is shortened by stimulating single sympathetic nerve fibers projecting to the ventricles (15) and is inversely related to inotropy as measured by intramural pressure. The R-R interval (chronotropy) appears to be regulated independently by nerve fibers projecting to the atria (14). Because the R-R variation also contains that of the Q-T variation, we proposed that the R-R-Q-T subinterval (i.e., the diastolic interval) would best serve as the independent measure for chronotropy and thus be the variable necessary for exhibiting the system attractor.

We found in the intrinsic cardiac nervous system that a dimensional decrease in the heartbeat dynamics occurred when the afferent-efferent neural loops began to change such that the relationship of the system variables exhibited a new system attractor (40). The changed shape of the system attractor indicated a new physiological function, for example, a shift from cardiac output preservation to cardiac energy preservation (40). Each change in the attractor was announced by a transient dimensional increase-decrease (i.e., a single cycle), and it occurred about once every 2 min.

In this study we found evidence of more rapid cycles (i.e., dimensional oscillations) that can occur on the order of tens of seconds (40-50 heartbeats). The system attractors exhibited in the subinterval plots (Figs. 2 and 3) show a change back and forth from a function that preserves cardiac output (1-dimensional, negative-sloped line attractor) to one that both preserves cardiac output and preserves cardiac energy (2-dimensional, zigzag attractor). As seen in Fig. 5, there is a wide variation in both the number and magnitude of these dimensional cycles.

The wide variety of individual patterns of dimensional change observed among the ketamine-anesthetized rats was not observed among the isolated rabbit hearts. The latter more or less showed similar attractor changes over time (40). The rich pattern of individualized variation seen in the present study with the brain stem intact could explain why the PD2i of the heartbeats is not correlated with any stochastic measures in other studies (32, 34, 38). If, in the present study, we had not selected the stable PD2i intervals, then the correlations with the stochastic measures would not have been high. That is, the mean PD2i values could have been quite different, larger or smaller, because of the nonstationarities within them. The poorer correlations between PD2i and the power spectra were because of the brevity of the stationary data lengths (i.e., there were not enough samples to adequately resolve the lower frequency spectra).

The intrinsic cardiac neurons, many located in the "fat pads," provide afferent-efferent regulations similar to those observed with the neural superstructure intact (1, 14, 15, 27, 28), but certainly the brain stem autonomic centers are there for some evolutionary reason. Ketamine is thought to be an anesthetic that targets the NMDA receptors that are mainly located in the higher central nervous system (cortex, striatum, and hippocampus) (2), thus leaving the cardioregulatory centers in the brain stem relatively intact. This is not to say that ketamine has no other effects, for it does produce a small amount of stereospecific inhibition of cholinergic re-uptake in the isolated heart (10). But certainly, it would seem reasonable to say that the ketamine-anesthetized rodent has a larger autonomic structure attached to its heart compared with the intrinsic cardiac nervous system that remains when the heart is surgically isolated.

It is not surprising that the more complex neural superstructure is related to a more complex dimensional response, but it is surprising that it is associated with rapid oscillations of multiple cycles. It is also surprising that brain stem autonomic complexity underlies such a rich variety of individualized nonlinear response patterns (Fig. 5).

The PD2i Algorithm and Data Nonstationarity

The unique feature of the PD2i is the restriction of the scaling region to a small log  R part of the correlation integral (see METHODS). It has been demonstrated in nonstationary concatenated data that PD2i has only a 4% error compared with D2 values made with corresponding samples of stationary data of long length (37). It is this treatment of the problem of nonstationarity that, in part, may explain why the PD2i algorithm is so much more sensitive in predicting mortality among high-risk patients than other linear and nonlinear algorithms (37, 38, 41).

What is Significant About Low-Dimensional Excursions Below 1.2?

This result, however, was later confirmed in retrospective data from patients with NSVT who either died of VF on the day of their recording or did not die within at least 3 years. In 100% of the VF subjects there was found to be a low-dimensional excursion to or below 1.2 at least once every 15 min throughout the period of their Holter recording (38, 47). In the NSVT subjects who did not die, none showed any low-dimensional excursions below 1.2.

Our studies of R-R interval dynamics in the human transplanted heart (23, 24) show that cardiac denervation leads to a heartbeat dynamic of almost precisely 1.0 dimension. That is, a single variable appears to regulate changes in heart rate. This dimensional level is to be distinguished from those fractional dimensional ones, observed in the present and other studies, which are associated with cardiovascular risk (e.g., myocardial ischemia, hemorrhagic shock). The transplant studies, however, do show that the higher dimensions require descending neural projections to the heart.

The low-dimensional excursions observed in our previous studies in pigs (32) and humans (34, 38, 47) are on the same order of magnitude as those seen in Figs. 2-5. These excursions often resemble the dimensional oscillations (seen in the present study). In all of these cases the dimensional response is rapid, occurring within seconds after the onset of the cardiovascular event. The effects of psychosocial stressors and other higher central perturbations (e.g., pathway blockade) are known to be quite rapid in reducing R-R interval dimension (3, 32-34), and thus descending projections from higher neural systems could be an explanation for the early and rapid low-dimensional responses.

We do not yet know what the mechanism is for the fractional low-dimensional excursions. Furthermore, we cannot yet interpret what the significance is of any dimensional level. Other physiological systems, however, may relate to these rapid fractional shifts observed in the heartbeats.

Response Cooperativity

If three independent persons are turning the crank together, a rather jittery sinusoid will result having three degrees of freedom (PD2i = 3), but if the crankers follow a leader (internal or external), then the output will systematically return to a smooth sinusoid having a dimension of 1. The dimension (degree of jitter in the data stream) is therefore related to the cooperativity that exists among the components of the generator mechanism (24, 35).

In the control of the heartbeats, the representation of the crank turners would seem to be the large number of afferent-efferent loops contained within the autonomic nervous system. The following representations show examples of such loops: 1) those intrinsic to the small neuropil located in the heart; 2) those that loop from the peripheral receptors through the brain stem and back to the periphery; and 3) those that loop through the frontal granular cortex and amygdala and are known to control myocardial vulnerability to lethal arrhythmias in conscious pigs. By analogy with the cerebral control of cooperativity, some self-organized mechanism for the global control of phase among these afferent-efferent loops of the autonomic nervous system could be the basis for the rapid low-dimensional phenomena exhibited in this and other studies.

What is important to realize about all of these new data is that a new genre of response is exhibited in the nonlinear activities. The response is neither an autonomic reflex (i.e., homeostasis) nor an autonomic reaction to support survival behavior (i.e., cerebral defense). What is evoked is a complex autonomic adaptation to a strong stimulus event that may involve the self orchestration of large numbers of afferent-efferent loops in the continuous systematic control of nonlinear behavior.

We call the response an adaptation because it requires, like a Darwinian system, experience with its environment. The adaptive mechanism for hemorrhagic shock may result from some learning-dependent mechanism similar to that involved in "cardiac preconditioning." In this latter example, recent experience with anoxia/ischemia results in a smaller sized infarction (i.e., when a coronary artery is tied off), because of inhibitory g protein-dependent downregulation of the adenosine receptor (12). Such self-adaptive changes in the underlying neurocardiac mechanism may explain the rich variety of nonlinear responses (Fig. 5) observed in the R-R intervals during hemorrhage.

In conclusion, we now believe that the low-dimensional excursions occur when the nonlinear dynamics within the autonomic nervous system self-organize to change a physiological function that will lead to survival. This adjustment is like a Darwinian adaptation, but on a small time scale. All subdivisions of the autonomic nervous system appear to be capable of undergoing this self-organization (e.g., those neurons intrinsic to the heart, as well as those that loop through the brain stem). The present study shows that the larger the neural superstructure attached to the heart, the more rapid and complex the adaptation. The complex nonlinear regulation constitutes a new genre of autonomic response, one clearly distinct from a hardwired reflex or a cerebrally programmed defensive reaction.