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INNOVATIVE METHODOLOGY
1Autonomic Dysfunction Center, Division of Clinical Pharmacology, Department of Medicine, Vanderbilt University School of Medicine, and 2Department of Biomedical Engineering, Vanderbilt University, Nashville, Tennessee
Submitted 15 June 2006 ; accepted in final form 22 September 2006
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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) = 5.625 ± 0.15 s]. The HF components of spike rate (HFspike rate) and SBP (HFSBP) were not significantly correlated. Conversely, HFResp and HFSBP were highly correlated (r = –0.79 ± 0.04), whereas LFResp and LFSBP were significantly less correlated (r = 0.45 ± 0.08). The mean correlation coefficients between the measured and model-predicted LFSBP (r = 0.74 ± 0.03) in the supine position did not change significantly during tilt. The mean correlation between the measured and model-predicted HFSBP was 0.89 ± 0.02 in the supine position. R2 values for the regression analysis of the model-predicted and measured LF and HF powers indicate that 78 and 91% of the variability in power can be explained by the linear relation of LFspike rate to LFSBP and HFResp to HFSBP. We report a simple two-component model using neural sympathetic and mechanical respiratory inputs that can explain the majority of blood pressure fluctuation at rest and during orthostatic stress in healthy subjects.
wavelet transform; blood pressure variability; Mayer waves; respiration; muscle sympathetic nerve activity
Several lines of indirect evidence have been used to associate the oscillations in BP with oscillations in these other physiological rhythms. For example, physiological maneuvers have identified changes in the oscillatory patterns of sympathetic nerve activity and respiration that correspond to those in BP during sympathetic activation (20). During head-up tilt (HUT), 1) LF oscillations are evident in the nerve activity and BP, 2) HF oscillations are expressed in each of the three signals, i.e., respiration, BP, and nerve activity, and 3) relative changes in the LF component of spike rate (LFspike rate) and the HF component of respiration (HFResp) are also reflected in the BP (Fig. 1). Coherence analysis has objectively shown that the frequency-domain relations between these signals are significant under normal physiological conditions (18, 20, 40).
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Although there is much indirect evidence, a mathematical model may provide a more direct description of the relation between the BP oscillations and fluctuations in other cardiovascular parameters. A number of models using heart rate (HR) and respiration (12, 29, 30, 47) have been developed to help explain the fluctuations in human BP. One limitation of most models is that they do not include sympathetic activity as a direct input parameter. Modeling of BP fluctuations from sympathetic activity in animals has been successfully applied using a system identification approach (5, 22, 24). Kamiya et al. (23) adapted a transfer function approach used in rabbits to explain the LF fluctuations in human BP and sympathetic activity during tilt but applied this model only to simulated data. In their explanation of human BP fluctuations, Myers et al. (31) used a linear model with integrated sympathetic activity as an input parameter, which yielded less accurate results than the transfer functions used in animals. However, the primary concern of this model was explanation of LFBP; it utilized integrated burst areas with arbitrary units to quantify sympathetic activity, rather than the spike rates typically found in animal models, and involved euglycemic clamping to enhance sympathetic activation, a procedure that induces vasodilation through increased insulin release and may alter the neurovascular coupling (11).
We propose a different mathematical model that combines subbands of the sympathetic spike rate and respiration to explain the LF and HF oscillations in human BP. A technique to detect action potentials in raw human sympathetic nerve recordings has been recently introduced and can be used to form a spike rate density series to quantify sympathetic activity (3, 14). Using the spike rate density along with measured respiratory patterns, we examine the accuracy of a two-component linear model that attempts to describe the LF-neurovascular interaction and the HF mechanical effects of respiration on the fluctuations in human BP.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Eight healthy subjects (6 male, 2 female; 23–47 yr old) were recruited from the Vanderbilt University General Clinical Research Center volunteer database. All subjects underwent extensive physical examination and had no signs of cardiovascular disease or history of syncope before the study. The subjects abstained from all drugs, including caffeine and nicotine, for 
72 h before testing. Their body mass index was 26 ± 1.7 kg/m2, resting HR was 61 ± 2 beats/min, and BP was 111 ± 2/65 ± 2 mmHg.
Protocol
Straps were used to secure the subjects to a tilt table. The subjects were instructed to remain relaxed and quiet throughout all studies and were monitored for any signs of presyncope during all tests (53). After 15 min of supine rest, the subjects were tilted by 15° increments every 5 min until an angle of 60° was reached. All studies were conducted at Vanderbilt University General Clinical Research Center, and all procedures were approved by the local Institutional Review Board.
Instrumentation
The following variables were measured: electrocardiogram (ECG), BP, respiration, and muscle sympathetic nerve activity (MSNA). The ECG of lead II was recorded with an ECG/Biotach amplifier (Gould Electronics, Cleveland, OH). The continuous finger BP waveform was measured by a photoplethysmograph-based volume-clamp method (39) with a finger cuff (Finapres, Ohmeda, Englewood, CO) on the middle finger of the nondominant hand and verified by brachial BP, which was obtained by an automated auscultometric device (Dinamap BP monitor, model 1846SX, Critikon, Tampa, FL) on the contralateral arm. The hand with the Finapres sensor was fixed at heart level. Respiration was measured by a pneumobelt (Pneumotrace II, UFI, Morro Bay, CA).
Microneurography. MSNA of the peroneal nerve was recorded randomly in either of the legs (51). A unipolar tungsten electrode with a 1- to 5-µm-diameter uninsulated tip and a 200-µm-diameter shaft (Frederick Haer, Bowdoinham, MA) was inserted into the muscle nerve fascicles of the peroneal nerve at the fibular head for multiunit recordings. Raw nerve activity was amplified with a total gain of 100,000, band-pass filtered from 0.7 to 2 kHz (662C-3 Nerve Traffic Analysis System, University of Iowa, Iowa City, IA). Satisfactory recordings of MSNA were defined by 1) heart pulse synchronicity, 2) facilitation during Valsalva straining and suppression during the hypertensive overshoot after release, 3) increases in response to breath holding, and 4) no change during tactile or auditory stimulation (13).
Data Preprocessing
Data were acquired at 5,000 Hz, 14-bit resolution using the Windaq data acquisition system (DI-720, DATAQ Instruments, Akron, OH) and analyzed off-line with custom software written in the PV Wave (Visual Numerics, Houston, TX) and MATLAB (Mathworks, Natick, MA) environments. QRS detection was performed using a modified Pan-Tompkins algorithm (38). Systolic and diastolic values in the continuous BP recordings were automatically identified as the maxima and minima for each cardiac cycle. All detections were visually verified.
A modified form of a technique described elsewhere (4, 14) was used to detect action potential spikes in raw MSNA recordings. A stationary wavelet transform with the Symlet 7 wavelet was used to decompose the MSNA into four bands of wavelet detail coefficients. Regions dominated by normally distributed noise in each band were identified as those with a kurtosis value <4. A kurtosis value of 3 indicates an ideal Gaussian distribution, and signal episodes with spike activity usually have higher kurtosis values. All coefficients with an absolute value less than four times the standard deviation of the identified noise regions were set to zero, and the denoised signal was reconstructed using the inverse stationary wavelet transform. Action potential spikes were then automatically detected from the denoised signal using a peak detector with a 3-ms time window.
We analyzed diastolic (DBP), systolic (SBP), and mean blood pressure (MBP) series, continuous respiration, and MSNA spikes detected over 200-s periods after 100 s of stabilization in the supine position and at 15°, 30°, 45°, and 60° HUT. DBP, SBP, and MBP variability series were formed by linear interpolation of the detected values onto regular 200-ms intervals (5 Hz). The detected MSNA spikes were used to form a spike rate series as previously described (3, 45). Briefly, a binary spike train was formed by insertion of delta functions into a 5-kHz sampled series at the detected spike times. The spike train was converted to a spike rate series by convolution with a Gaussian filter with a 3-Hz cutoff frequency (3). The spike rate signal was decimated by iterative convolution with an antialiasing Gaussian filter with a corner frequency of 0.4 times the current sample rate and downsampling by 2 until a sample rate of 4.88 Hz was reached. The resultant series was linearly interpolated at 5 Hz. The respiration signal was also decimated to 5 Hz after application of an eighth-order, antialiasing, Chebyshev type I low-pass filter with a corner frequency of 2 Hz. Each series was detrended by removal of the mean offset plus the VLF (0–0.04 Hz) components by filtering with a high-pass, finite-impulse response filter with a corner frequency of 0.04 Hz before any analysis or comparisons.
LF and HF time series were formed using a set of band-pass filters based on the Meyer wavelet, a modulated sinusoid with compact support (10), with approximate respective pass bands of 0.04–0.15 Hz (LF) and 0.15–0.5 Hz (HF) (see Ref. 49 for details of wavelet filtering).
Data Analysis
For study of the relation between each BP series (SBP, DBP, and MBP) and the MSNA spike rate and respiration, time-based cross-correlations were performed. In general, during the cross-correlation procedure, one time series, x, was delayed between the time constants start and end (in seconds) while the other series, y, remained stationary. After each delay, correlation between the two series was determined. First, the LF components of each series were compared, with LFspike rate and LFResp as x and LFSBP, LFDBP, and LFMBP as y. The procedure was repeated using the HF components of each series. For the HFspike rate and respiratory series, the maximum absolute correlation was recorded for time delays between start = 10 s and end = 0 s, meaning that our only interest was the relation in which changes in respiration and HFspike rate preceded changes in the BP. For the LFspike rate and LF components of the BP series, two relations were investigated. The minimum negative cross-correlation value, termed the baroreflex-feedback relation, was studied between start = 2 s and end = –2 s. In this case, a negative time delay (e.g., = –2 s) would indicate that the spike rate is advanced in time. The positive maximum cross-correlation value, termed the feedforward relation, was studied between start = 10 s and end = 0 s.
Before the BP fluctuations were modeled, LFspike rate was delayed by an amount equal to the feedforward delay and HFResp was delayed by an amount equal to the time shift that produced the maximum absolute correlation to HFBP.
Data Predictive Modeling
The LF oscillations in sympathetic nerve activity and the HF fluctuations in respiration were used in a two-component, MA linear model to predict the fluctuations in BP. First, the LF model predicts the current value of LFBP with use of the MA model, in which the output is a linear combination of p previous values of the LF components of the spike rate series (LFspike rate). The term wspike rate is added to indicate the presence of randomly distributed noise in the measurement of sympathetic spike rate
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Similarly, the HF model predicts the current value of the HF BP series (HFBP) with use of a linear combination of k previous values from the HF respiration series (HFResp). The term wResp is added to indicate the presence of random noise in the recording of respiration
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The proposed total model (Fig. 2) is a summation of the outputs of the LF and HF models and predicts the current value of the detrended BP series.
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is the mean squared error between the model and true output, n is the total number of points in the signal, and p is the current model order. This modeling technique was applied to components of the signals recorded during a baseline period and over increasing orthostatic load during graded HUT. The values predicted by each model were compared with the corresponding measured values by point-by-point linear regression analysis and by comparison of their power spectral density (PSD) in specific frequency ranges. PSD
The Welch periodogram method (54) is used to compare the estimated PSD of the measured BP series with that of the BP series predicted by the total model. The 200-s signals, which were recorded and predicted during each angle of tilt, were divided into 60-s segments that overlapped by 50%. Each segment was detrended, multiplied by a Hamming window, and zero padded to the next power of 2. The power in the LF (0.04–0.15 Hz) and HF (0.15–0.5 Hz) ranges was estimated as the area under the PSD curve.
Statistics
Regression analysis was performed using a linear least squares fit, and the Pearson correlation coefficient (r) or the coefficient of determination (R2) was used to quantify the goodness of fit. Wilcoxon's signed ranks test was used to test for significant differences in the correlation between the components of three different BP series (SBP, DBP, and MBP) and the components of the sympathetic spike rate and respiration. This test was also used to determine whether significant differences existed between measured and model-predicted BP values at different degrees of HUT. P = 0.05 was defined as the significance level. Unless otherwise noted, values are means ± SE.
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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A representative temporal relation between SBP and MSNA spike rate is shown in Fig. 3. The sample-to-sample correlation between the unfiltered SBP and spike rate does not reveal an inherent linear relation between the two series (r = –0.37; Fig. 3A, bottom). However, their LF components appear to have two distinct relations. A shift in the LFspike rate series back in time by 0.4 s results in a strong negative correlation to LFSBP (r = –0.87; Fig. 3B, bottom), which indicates the strength of the baroreflex-mediated feedback (high spike rates during low BP). A shift in the LFspike rate series back in time by 5.2 s yields a strong positive correlation to LFSBP (r = 0.70; Fig. 3C, bottom), which suggests a feedforward relation between the two series, meaning that an increase in LFspike rate will produce a corresponding increase in LFBP.
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= 5.625 ± 0.15 s, increases in spike rate lead to increases in BP) was used in favor of the feedback time delay ( = 0.375 ± 0.10 s, spike rate decreases with increase in BP) in the predictive model, because the intention of this model is to predict LF changes in BP from the LF changes in spike rate. HFspike rate and HFSBP are not significantly correlated (r = –0.22 ± 0.04; Fig. 5, top right). Conversely, HFResp and HFSBP are highly correlated (r = –0.79 ± 0.04; Fig. 5, bottom right), whereas LFResp and LFSBP have a significantly lower and less consistent correlation across subjects (r = 0.45 ± 0.08; Fig. 5, bottom left).
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= 5.625 ± 0.15 s), LFDBP (r = 0.62 ± 0.05, = 5.1 ± 0.14 s), and LFMBP (r = 0.62 ± 0.04, = 4.8 ± 0.17 s) also had statistically similar feedforward correlations to LFspike rate. However, the correlations between HFResp and HFDBP and HFMBP were significantly less than the correlation between HFResp and HFSBP (P < 0.01 in both cases). Consequently, LFSBP and HFSBP will serve as the output of the predictive model. Predictive Modeling at Rest in the Supine Position
The LF model (Fig. 2) used previously determined values of LFspike rate to predict the current values of LFSBP. The results of this model at baseline are displayed in Fig. 6A. The oscillations in the predicted LFSBP follow those in the measured LFSBP (Fig. 6A, top), and the two series have a strong linear correlation (r = 0.80; Fig. 6B, top). The HF model (Fig. 2) used previously determined values of the HFResp time series to predict the current values of the HFSBP series. This model also demonstrates an ability to follow the measured HFSBP (Fig. 6A, middle), and the measured and predicted sequences show a high positive correlation (r = 0.94; Fig. 6B, middle). When the outputs of the LF and HF models were summed, the resultant series was able to predict the total fluctuations in SBP (Fig. 6A, bottom). The sum of the LF and HF models produces a greater correlation to the measured SBP (r = 0.78; Fig. 6C, bottom) than either the individual LF (r = 0.70; Fig. 6C, top) or HF (r = 0.37; Fig. 6C, middle) models. (Statistical analyses for the supine model are discussed in the following section.)
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The LF, HF, and total models were also tested over increasing degrees of orthostatic stress during HUT. Two methods were used to predict the BP fluctuations during HUT: 1) the unmodified model coefficients computed at baseline were applied to the spike rate and respiratory sequences during HUT, and 2) the optimal coefficients were recomputed for each degree of HUT. Method 2 achieved significantly higher correlation coefficients than method 1 (P < 0.01 in all cases). Consequently, optimal model coefficients were computed separately during each degree of HUT.
The model is effective in predicting the total oscillations in the SBP components (Fig. 7, left), and the correlation between measured and predicted SBP fluctuations remains strong during increasing orthostatic load (Fig. 7, right).
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When a simple slope model (model order = 0, 1 coefficient) was used to predict the components of the SBP from the components of the spike rate and respiration, the correlation between the measured and predicted values still indicated a strong linear relation (mean r = 0.60 for total model), but the correlations were significantly less than those computed using the optimal model order defined by the minimum FPE (P < 0.01).
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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LFSBP-LFspike rate Relation
A great deal of indirect evidence supports the hypothesis that LF changes in MSNA contribute to the LF changes in BP. For example, LFSBP has been shown to increase during sympathetic activation, including orthostatic stress, such as lower body negative pressure (7, 41, 52) and upright tilt (9, 20), infusion of vasoactive drugs such as nitroprusside (41), and hypovolemia (26). Similarly, LFSBP power has been shown to decrease significantly during ganglionic blockade in normal subjects (15, 32, 56) and in patients with essential hypertension and multiple system atrophy (15), indicating that it is largely mediated by the sympathetic nervous system. Finally, LFSBP and LFMSNA power exhibited similar increases and decreases during pharmacological infusions of sodium nitroprusside and phenylephrine, respectively (36), and coherence analysis has quantifiably demonstrated that patterns in LFSBP and LFMSNA are correlated at baseline (18, 20) and during HUT in humans (20), whereas HFSBP and HFMSNA are not highly correlated (18).
Conversely, a model of human BP by Myers et al. (31) showed that the sympathetic activity contributes little to the LF oscillations in BP. In the present work, however, we have demonstrated a strong temporal forward and feedback correlation between the LF fluctuations in SBP and the LF changes in MSNA spike rate in healthy humans at rest. The relation also improves when past values of LFspike rate are incorporated to predict the present value of LFSBP (Fig. 6, top) and is unaffected by increased orthostatic load.
The discrepancy in these results may be explained by several differences in protocol. 1) The previous model used normalized arbitrary units of integrated sympathetic burst area to form a sympathetic activity series, whereas our process involved detected sympathetic action potentials. The action potential detection is not based on arbitrary units and is less sensitive to the pass-band noise and artifacts that influence the burst area. 2) We used a physiological maneuver (HUT), rather than vasoactive or metabolic drugs, to induce an increased sympathetic state. These pharmacological agents may block or reduce the ability of the vasculature to accept modulatory sympathetic input, particularly at high doses when operating on the nonlinear portion of the baroreflex curve. 3) For the LF range, Myers et al. (31) elected to use 0.05–0.20 Hz, which is broader than the range recommended by the Autonomic Task Force (0.04–0.15 Hz) (46), although breathing was controlled at a higher frequency (0.25 Hz).
In the present work, we have identified two distinct time constants between LFBP and LFMSNA. The strongest linear relation between LFSBP and LFspike rate occurred near 0 s (average = –0.375 s), which results in a highly negative correlation between the two (MSNA is high at low BP, and vice versa). We have termed this the baroreflex "feedback" relation, although the change in LFMSNA often precedes or occurs concurrently with changes in LFSBP. Although several authors have computed the transfer function between sympathetic activity and BP in humans, the phase relation between these components is rarely reported (18, 20). Interestingly, Myers et al. (31) also identified the strongest linear relation between LFSBP and LFMSNA near 0 s and also reported a negative correlation. This finding is also consistent with the 180° neural arc phase relation reported in closed- and open-loop identification of the MSNA-BP relation in animals (22, 25). We hypothesize that this could be a sympathetic response to the change in BP (first deviation), rather than the absolute BP itself (17). This is supported by animal studies that have shown a strong response of baroreceptor afferents to changes in pressure (28).
In this previous model of LFSBP using LFMSNA, Myers et al. (31) chose to use this inverse, feedback relation as the input to their model, which necessitated the use of a negative model coefficient. Instead, we have elected to use the feedforward relation, defined as the maximum positive cross-correlation between LFspike rate and LFSBP (high values of MSNA ultimately leading to high values in BP). This relation is more closely related to the peripheral arc of the closed-loop model used in animal studies (25). The feedforward time delay was found to be 
5.6 s, meaning a peak in LFSBP occurred 5.6 s after a peak in LFspike rate. This finding supports the reported peripheral arc phase values for animals, which are generally near 180° in the LF range (a 5-s time shift in a 10-s cycle) (25). It has been suggested that this phase shift is the combined result of the fixed physiological processing and transmission times from the baroreflex pathways, along with the slow response of the vascular smooth muscle to increased sympathetic activity (21). However, use of the feedback relation as the input to the LF model results in significantly higher correlations between the measured and predicted LFSBP (r = 0.744 ± 0.03 vs. 0.81 ± 0.03, P < 0.025 for the mean feedforward and feedback time shifts).
HFSBP-HFResp Relation
Oscillations in BP corresponding to respiratory rhythms have been well documented using spectral methods (2, 8, 16). The HF range of the BP variability contains the range of frequencies associated with normal breathing rhythms. Ganglionic blockade has little or no effect on HFBP, suggesting that these oscillations are unrelated to the sympathetic activity and primarily due to changes in intrathoracic pressure caused by the mechanical aspects of respiration (15, 32, 56).
Here we report similar findings. We show that the temporal correlation between HFSBP and HFspike rate is low (r = –0.22 ± 0.04), meaning that vessels act as a neural low-pass filter (55), blocking transmission of the HF oscillations in MSNA to the arterial pressure. On the other hand, respiration has a strong mechanical influence on BP, evidenced by the high temporal correlation (r = –0.79 ± 0.04) between HFSBP and HFResp at rest in the supine position.
The correlation of HFSBP to HFResp was significantly higher than the correlation of HFDBP or HFMBP to HFResp (r = –0.45 ± 0.06 and 0.56 ± 0.08, respectively) at rest. This is consistent with the model proposed by Saul et al. (40), which showed that the mechanical effects of breathing would have a larger impact on SBP than on DBP because of the increased capacitance of the ventricles during systole.
Predictive Model
We have described how the fluctuations in SBP can be predicted by summing an optimized linear combination of past LF spike rate values, which predict LFSBP, and past HFResp values, which predict HFSBP. Using this approach, we were able to generate predicted SBP fluctuation series with good correlations to the measured values at baseline and during graded HUT. The relation between the power of the predicted and measured SBP also indicated that the models were able to explain a large majority of the fluctuations.
The optimized models produced predicted values that were more strongly correlated to the measured SBP fluctuations than a simple slope model, suggesting that some past information from the respiration and sympathetic spike rate contributes to the fluctuations in the SBP. Also, when model coefficients computed at baseline were used to predict the SBP oscillations during varying degrees of HUT, the correlations between measured and predicted SBP values were reasonable but significantly less than those predicted with the optimal models for each recording. This indicates that the relation between BP, sympathetic activity, and respiration changes during orthostatic load and cannot completely be explained by models created during baseline conditions. Indeed, some evidence suggests that the properties of the cardiac baroreflex (HR-BP relation) change during upright tilt (1, 33), but limited information about the sympathetic branch of the baroreflex has been reported during tilt. The results of the current model should be interpreted with caution, however, since a model will always have greater predictive value when its coefficients are reoptimized during each condition, as is the case here.
Limitations
VLF (0.004–0.04 Hz) fluctuations were excluded from the present model mainly because the length of each segment analyzed was too short (200 s) for accurate calculation of the influence of oscillations at this frequency range on the SBP. In this study, all subjects maintained a spontaneous breathing rate above 0.15 Hz (in the HF range); however, respiratory frequencies below 0.15 Hz would cause additional respiratory input in the LF range, and an LF model based solely on LFspike rate could not accurately predict changes in LFSBP. The present model takes into account only open-loop properties of the baroreflex system and ignores its closed-loop properties, i.e., feedback from the baroreceptors, which may also contribute to changes in BP and spike rate fluctuations (24). It has also been suggested that CO contributes to mean sympathetic activity (6) and BP fluctuations (31, 50). HR, one of the determinants of CO, has been associated with Mayer wave fluctuations (31). It has also been shown that respiratory fluctuations in BP can largely be explained by respiratory variation in the stroke volume (the other determinant of CO), independent of the vagally mediated changes in HR (50). Therefore, the addition of CO as an input parameter may help explain the remaining variability in the BP oscillations.
In conclusion, we have shown that a simple two-component model of neural sympathetic and mechanical respiratory input can explain the majority of BP fluctuation at rest and during orthostatic stress in a healthy subject.
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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