Abstract
To study spontaneous cardiac baroreflex at different timescales, a new method has been developed that identifies such episodes. Mean arterial pressure (MAP) and heart rate (HR) were recorded beat to beat over 1 h in freely moving control (n = 10) and acutely (1 day before study, n = 7) and chronically (2 wk before study, n = 10) sinoaorticdenervated (SAD) 12 to 14wkold male SpragueDawley rats. These beattobeat time series were successively lowpass filtered seven times and resampled at different time intervals from 0.1 to 6.4 s, allowing different timescales to be scanned. With the use of theZ coefficient, the statistical relationship was estimated for the associations of inverse MAP and HR variations when these inverse MAP and HR variations occurred simultaneously or were time shifted. In control rats and for timescales ≥0.4 s, the highest Zcoefficient(0.38) was obtained when MAP variations preceded inverse HR variations by one sampling interval. The baroreflex origin of this link was demonstrated by its disappearance after acute SAD. In conclusion, this method enabled spontaneous baroreflex episodes to be identified for unusually long timescales without limiting the study to fast, linear, stationary, or oscillating phenomena.
 statistical dependence
 cardiovascular
 blood pressure
 heart rate
many studies of the baroreflex have been reported using pharmacological or mechanical methods to stimulate the baroreceptors. These studies enable pulse interval or heart rate (HR) to be correlated to blood pressure during changes induced by administration of vasoactive drugs (7, 12, 19) or by stimulation of the carotid baroreceptors by neck suction (14, 15). Although validated, these methods assess nonspontaneous phenomena that are slow compared with HR. Consequently, they must be insufficient to appraise the regulatory functions under normal conditions.
These limitations led to the development of other methods to assess baroreflex in spontaneous conditions, such as crossspectral analysis (8, 18) or sequence method (2, 10, 16). However, these methods are limited to shortterm oscillatory phenomena that occur in the socalled high and lowfrequency ranges (6) and for which oscillatory functions are difficult to understand at the present time.
The aim of this work was to develop a tool allowing phenomena of much longer duration to be analyzed. For that purpose, we used the previously developed Zcoefficient method (5, 9) with a major improvement, a method of lowpass filtering to study the relationships between mean arterial pressure (MAP) and HR variations at different timescales instead of being restricted to beattobeat analysis. Indeed, the previousZcoefficient method using beattobeat analysis did not show dynamic functioning of the baroreflex. In addition, the study of time series at different timescales may disclose different physiological phenomena related to the baroreflex that may act with different time responses. To identify the baroreflex origin of observed relationships, the current method was applied to blood pressure recordings obtained under basal conditions in freely moving control or sinoaorticdenervated (SAD) rats.
METHODS
Animals and Experimental Protocol
For this study, twentyseven 12 to 14wkold male SpragueDawley rats were used. The initial mean weight of these rats was 331 g. They were separated into three groups: one control group (n = 10) and two groups submitted to SAD according to the method of Krieger (13). Acute SAD rats (n = 7) were studied 1 day after SAD, and chronic SAD rats (n = 10) were studied 14 days after SAD.
All rats were maintained on a 12:12h lightdark cycle and were housed in controlled conditions (21 ± 1°C). They received a standard rat chow and tap water ad libitum. After a 5h period of habituation to the recording environment, blood pressure was continuously recorded for 1 h.
Pharmacological Estimation of Baroreflex Sensitivity
The extent of denervation was evaluated in each rat at the time of the study by measuring the changes in MAP and pulse interval in response to two intravenous bolus injections of phenylephrine (3 μg/kg) in a volume of 250 μl/kg. In these conditions, cardiac baroreflex sensitivity was given by the average ratio of the peak changes in pulse interval to MAP.
Blood Pressure Recording
Polyethylene catheters made of a piece of heatstretched PE10 fused to a PE50 extension were inserted under halothane anesthesia via the femoral artery and vein into the lower abdominal aorta and inferior vena cava for blood pressure recording and intravenous injection, respectively. The femoral catheter was sutured to the vessels, filled with heparinized saline (50 IU/ml), and led subcutaneously to emerge between the scapulae. Blood pressure was continuously measured in freely moving rats by connecting the femoral catheter to a precalibrated pressure transducer (Statham P23ID, Gould, Cleveland, OH) coupled to an amplifier recorder (model 8802, Gould). Analog outputs of pulsatile blood pressure were then digitalized at 500 Hz and processed by our previously described technique (11) on a computer (Motorola MVME SYS 147, Motorola, Tempe, AZ). Cardiac cycles were first recognized, and then MAP and HR were computed for each beat.
OffLine Data Analysis Methods
The offline statistical algorithms ran on a SparcClassic SUN workstation (SUN Microsystems, Mountain View, CA) under Solaris 2.4.
Timescale and lowpass filtering.
To analyze time evolution of MAP and HR at different timescales, we developed a “pyramidal” technique of successive lowpass filters. Before filtering, MAP and HR beattobeat time series were equally resampled (sampling interval: ΔT _{1} = 0.1 s). These two equally sampled time series were then filtered a first time by a classical digital lowpass (null phased) filter at the cutoff frequency (CF_{1}) = 2.5 Hz (17).
A second, similar lowpass filter was then applied on these time series so that the current cutoff frequency (CF_{2}) = 1.25 Hz = CF_{1}/2, and filtered data were resampled at the sampling interval ΔT _{2} = 0.2 s = 2ΔT _{1}. Consequently, a new time series of MAP and HR was obtained at a new timescale in which the number of points was reduced by onehalf and the fluctuations of frequency >CF_{2}were eliminated. The same process was successively applied seven times to obtain seven MAP and HR time series at seven different timescales giving a large temporal point of view as described in Table1.
Figure 1 illustrates the result of this transformation on MAP and HR time series from the first (ΔT _{1} = 0.1 s and CF_{1} = 2.5 Hz) to the third (ΔT _{3} = 0.4 s and CF_{3} = 0.63 Hz) timescale. The fluctuations caused by respiration (frequency > 0.63 Hz) are visible on the timescale for ΔT _{1} (0.1 s) for HR. They completely disappear on the timescale for ΔT _{3} (0.4 s), revealing lowfrequency fluctuations (0.25–0.75 Hz in rats; Ref.6) that are partially masked in the first timescale.
Definition of statistical events and event associations.
With the Zcoefficient method, events that would allow characterization of baroreflex episodes had to be defined. For that purpose, for each MAP and HR time series, variations between two successive points were computed and defined as positive or negative variations according to variation thresholds that were fixed at 1 mmHg for MAP and 3 beats/min for HR at any sampling interval (2). Three possible events could be distinguished for each parameter: increase (↑), decrease (↓), or stability. Because cardiac baroreflex was the object of the study, the associations of MAP and HR inverse variations were examined for all sampling intervals.
We focused on shortterm time shifts, i.e., simultaneous MAP and HR variations or those shifted by one sampling interval. In the latter case, two possibilities were considered, MAP variation preceding HR variation or the reverse.
Estimation of Z coefficient for association of events.
As previously described (9), the Zcoefficient computed for two events gives the strength of their statistical relationship. Briefly, Zis defined from probabilities of each event and their association. It varies from zero in the case of total independence to unity for total dependence. It is negative in the case of exclusion. In practice, the probability of events was estimated by their observed frequency.
To test the significance of Z values estimated for each group of animals, theZ sampling fluctuation was simulated by the Monte Carlo approach under the null hypothesisZ = 0 (20). This simulation was performed for each sampling interval with its statistical constraints (number of data, observed frequency of events). The confidence interval of Z mean under the null hypothesis was built at the risk P = 0.05.
Data are expressed as means ± SE. Nonparametric variance analysis (KruskalWallis) was performed to study the influence of the time shift between MAP and HR variations and to compare control and SAD rats. A Wilcoxon rank test was performed to compare two data groups.P < 0.05 was considered as statistically significant.
RESULTS
Influence of Sampling Interval on Z Values in Control Rats
Figure 2 gives theZ value in control rats as a function of sampling interval in the case of MAP↑ and HR↓ being either simultaneous or time shifted by one sampling interval. In all cases, Z values were outside the confidence interval of Z mean under the null hypothesis, showing their significance. The highestZ values (>0.25) were obtained when MAP↑ preceded HR↓ and for sampling intervals between 0.4 and 6.4 s. Z values were also positive when MAP↑ and HR↓ appeared simultaneously, but they were much lower. On the other hand, when HR↓ preceded MAP↑,Z values were negative for sampling intervals >0.4 s, suggesting an exclusion.
Similar results were obtained in the reverse case, i.e., with MAP↓ and HR↑. Z values remained >0.2 when MAP↓ preceded HR↑ for sampling intervals >0.4 s.
Figure 3 shows how isolation of different baroreceptor episodes with different durations can be seen. Different areas of baroreflex activity are selected at these two successive timescales. Only three episodes with a duration of 0.4 s are included with the seven episodes with a duration of 0.8 s.
Influence of Sampling Interval on Z Values in SAD Animals
Table 2 indicates the characteristics of the animals after acute and chronic SAD. SAD induced hypertension and tachycardia that were more noticeable 1 day after surgery than they were 2 wk after surgery. SAD significantly enhanced MAP variability. The cardiac baroreflex sensitivity measured using a pharmacological method was unmeasurable after acute SAD and was significantly decreased after chronic SAD.
According to the data obtained in control rats, the analysis ofZ was restricted to the condition in which it reached its highest values, i.e., MAP↑ precedes HR↓ by one sampling interval.
Figure 4 shows thatZ values at sampling intervals of 0.4 and 0.8 s were close to 0 after acute SAD. At the other sampling intervals Z values were negative, suggesting an exclusion. In chronic SAD rats weak, significant positiveZ values reappeared when the sampling interval was >1.6 s, but they remained lower than in control rats. Similar results were obtained in the case of MAP↓ and HR↑.
DISCUSSION
The present work shows that the method we developed allowed activity caused by cardiac baroreflex to be identified at different timescales in spontaneous conditions by direct computation of the statistical relationship between associations of inverse MAP and HR variations. Although the physiological mechanisms underlying increases in MAP followed by decreases in HR and decreases in MAP followed by increases in HR are different, the statistical link obtained for these two cases was in close resemblance, allowing us to simply consider inverse MAP and HR variations together. Interestingly, spontaneous cardiac baroreflex seems to be active at unusual timescales up to 6.4 s.
Methodological Aspects
Three kinds of methods were used in this study:1) a filtering method that took into account a large range of timescales,2) a reduction of data to simple and relevant events, and 3) a direct analysis of the statistical relationship between two events.
Choice of filtering.
It was interesting to apply the filtering method for study of spontaneous cardiac baroreflex to separate the different temporal components of this regulation. In all time series, slow fluctuations are always masked by faster ones, and filtering is the most powerful method of isolating different temporal aspects of dynamic responses of a system. A lowpass band filter was chosen because cardiac baroreflex might be sensitive to the level of blood pressure, and it was important to select a filter that allowed the absolute values of parameters to be preserved. Therefore, a lowpass, nullphased filter that conserved the general shape of the curves and the continuous component was used (17).
Choice of events.
To characterize baroreflex episodes, simple events made up of inverse variations of parameters were chosen. This simplification was necessary to validate our method, which combined filtering and statistical events analysis. In the previously developedZcoefficient method (5), the chosen events were absolute beattobeat MAP and HR values. Such events allowed the relationship between MAP and HR levels to be studied without taking into account their chronological evolution.
Statistical analysis.
The use of a coefficient that evaluates the statistical link for discrete events is not usual in the study of relationships between the values of a time series. Intercorrelation methods are generally used, but stationarity must be assumed. TheZ coefficient enables us to evaluate the strength of the determinism that links two events without any hypothesis of linearity or stationarity. The efficiency of this statistical approach has already been demonstrated (5, 9).
It can be noted that Z mean fluctuation obtained with the Monte Carlo method remained weak for any sampling interval. It increased with sampling interval. This is mainly explained by the fact that the sampling fluctuation increases when the number of data decreases. With pyramidal filtering the number of data was reduced by onehalf from one sampling interval to the next. To avoid this problem, it would have been possible to increase sampling time, but this solution was not used because it would have increased the fluctuations of the physiological states of the animals.
When MAP↑ preceded HR↓ by a time shift outside the range of baroreflex regulation (1–10 min),Z values were not significantly different from 0 (data not shown). This allows us to conclude that no artifact and no artificial link were introduced by the numerical processing.
The methods based on crossspectral analysis detected lowfrequency oscillations related to the baroreflex (4, 8). These methods are well adapted to the study of the oscillatory effect of the baroreflex, but, on the other hand, they may miss isolated nonoscillating episodes also due to the baroreflex that can be slow.
Another method usually chosen for the study of the spontaneous baroreflex consists of the selection of sequences made up of several consecutive beats with progressively increasing or decreasing systolic blood pressure and pulse interval (2, 16). An indirect analysis must be performed to verify that these sequences were not due to chance, because no direct statistical link between the systolic blood pressure and pulse interval changes was computed. The observed frequencies of the sequences obtained in control conditions were compared with those obtained in other animals without baroreflex (2). Surrogate data analysis enabled us to verify that the sequence method did not only extract chance events (3). This method was applied to beattobeat data without any filtering and selected sequences over 3–5 beats, i.e., lasting <1 s on average in rats. Therefore, it was limited to fast and linear sequences selected principally from respiratory fluctuations, contrary to our method, which allows statistical links to be disclosed between slow variations at different sampling intervals up to 6.4 s.
Physiological Aspects
Because the statistical link between inverse MAP and HR variations disappeared after acute SAD, it can reasonably be postulated that it was related to baroreflex. In the same way, the disappearance of this link or even the occurrence of negativeZ values when HR variation preceded MAP variation by one sampling interval suggested that MAP variation caused HR variation, which is in accordance with the baroreflex function.
After chronic SAD and for long sampling intervals (3.2 and 6.4 s), slight but significant Z values were observed. This is in good agreement with the unexplained but usually observed reappearance of a slight cardiac baroreflex activity as measured after phenylephrine injection. Therefore, it can be postulated that a long time after SAD, compensatory mechanisms enabled the recovery of part of the reflex regulation, suggesting a possible role of the cardiopulmonary receptor reflex (1).
The maximum Z values for the baroreflex episodes were detected at sampling intervals of 0.4 and 0.8 s. Therefore, they may be partly related to lowfrequency fluctuations that are centered at 0.4 Hz in rats (4). Moreover, baroreflex episodes could still be identified at sampling intervals >1.6 s in conditions that exclude lowfrequency fluctuations because of lowpass filtering. The existence of these slow “nonoscillating” spontaneous cardiac baroreflex episodes is an unexpected finding that is compatible with the time response of the inhibition of sympathetic activity observed during phenylephrine infusion (7).
These slow episodes appeared on chronograms in a nonoscillating way, and 70% of these episodes that were identified at a given timescale were not selected at the same time at the previous timescale. This indicates that the different timescales disclose in great part baroreflex episodes that have different durations.
Finally, this method combined a technique of successive lowpass filtering and resampling, which allowed different timescales from 0.1 to 6.4 s to be scanned, with theZcoefficient method, which allowed the strength of the statistical link between two chosen events to be estimated. Focusing on cardiac baroreflex, we elected to calculate the statistical relationship between two events defined as inverse MAP and HR variations in spontaneous conditions. We demonstrated that the variations that were linked because of their high positiveZ value were related to baroreflex. These baroreflex episodes appeared at different timescales from 0.4 to 6.4 s. Local slow spontaneous cardiac baroreflex episodes (from 1.6 to 6.4 s) seemed to exist in addition to those already known in the range of lowfrequency oscillations (0.25–0.75 Hz in rats). This heuristic method enabled us to extract baroreflex episodes without limiting the study to fast, linear, stationary, or oscillating phenomena and therefore appeared more direct and general than classical methods.
Perspectives
This work appeared to confirm the necessity of improving tools that allow the identification of spontaneous baroreflex. First, to improve spontaneous cardiac baroreflex episode description, these episodes could be more precisely separated according to their different durations with filtering techniques. Different ways of computation could then be tested to define a set of reliable and relevant parameters of description such as gain, difference in phase, coherence, and the strength of their links. Second, these parameters could be evaluated in different physiological situations to provide new observations more directly applicable to research in physiology.
Acknowledgments
We are grateful to Prof. Jean Sassard for help in the review of the manuscript.
Footnotes

Address for reprint requests: M.P. Gustin, Dépt. de Physiologie et de Pharmacologie Clinique, CNRS ESA 5014, Faculté de Pharmacie, 8 Ave. Rockefeller, 69373 Lyon Cedex 08, France.

This research was supported by grants from Centre National de la Recherche Scientifique and Institut National de la Santé et de la Recherche Médicale (Contrat de Recherche Externe 93–0402).
 Copyright © 1998 the American Physiological Society