Spike Detection of Human Sympathetic Nerve Activity Using Wavelet Transformation and Valsalva Maneuver Denoising

Abstract

Background

Sympathetic function is directly assessed by microneurography measuring muscle sympathetic nerve activity (MSNA). The recordings are typically corrupted with noise and require denoising. We aim to estimate microneurographic noise individually from physiologically suppressed MSNA during Valsalva phase 4 (VM4).

New method

We developed MSNA adaptive processing (MAP). MSNA recordings during Valsalva were transformed by stationary wavelet transformation. Level-specific noise thresholds were computed from 4SD of detail coefficients from VM4 and were implemented for denoising. The denoised signals were inverse transformed, then the MSNA spikes were detected.

We compared detection performance of the MAP with the current two-stage kurtosis method in simulated MSNA signals, and recordings from 17 healthy and 19 postural orthostatic tachycardia syndrome (POTS) female subjects performing Valsalva.

Results

The MAP had higher correct detections of MSNA spikes than the kurtosis method in simulated signals with high burst rate (50 burst/min) and low signal-to-noise ratio (SNR =2) (MAP vs kurtosis; 23.81±15.49% vs 16.98±12.75%, p<0.001). The improvement was confirmed by shorter error distance of the precision-recall plot (0.535±0.175 vs 0.542±0.177, p=0.011).

The MAP detected higher spike rate during VM phase 2 in healthy (24.11±9.85 vs 19.57±8.60 spike/s, p=0.049), but non-significant in POTS (24.19±13.70 vs 20.30±11.85 spike/s, p=0.101).

Comparison with existing methods

The detection performance of the MAP is superior to the current two-stage kurtosis method.

Conclusions

The proposed MAP method individually estimating noise from VM4 could improve MSNA spike detection, compared with the kurtosis method. The advantages are most prominent in high burst rate and low SNR MSNA recordings.

1. Introduction

Muscle sympathetic nerve activity (MSNA) plays a critical role in blood pressure regulation by controlling peripheral vascular resistance. It is a direct measurement of sympathetic neural activity innervating vessels that supply skeletal muscle. MSNA is a part of baroreflex that should be physiologically suppressed when there is high blood pressure, while activated when blood pressure is low. Incorporating MSNA measurement with autonomic function tests that perturb blood pressure such as Valsalva maneuver and tilt table test allows researchers to study sympathetic noradrenergic function. For instance, low MSNA during Valsalva phase 2 may suggest sympathetic dysfunction in neuropathic postural orthostatic tachycardia syndrome (POTS)^[1].

Extracting neural activity from background noise is a major challenge of microneurography. Conventionally, raw MSNA is filtered then discriminated from noise by thresholding. The discriminated signal is integrated by resistance-capacitance low pass filter to generate the averaged envelope curve – the integrated MSNA. The limitation of integrated MSNA is that amplitude depends on how close a needle tip is positioned in the nerve and noise. This makes direct inter-individual comparison impossible. Further, single action potential information is filtered out. Recently, we and other groups have proposed wavelet transformation algorithms that can extract single MSNA spikes to estimate sympathetic activity ^[2-4].

Transforming raw signal to wavelet coefficients by an appropriate mother wavelet can amplify the contrast between noise and action potential, leading to a more apparent thresholding. The point of interest here is how one estimates noise standard deviation and noise threshold. Salmanpour et al. estimated noise standard deviation by a robust estimator, dividing median absolute deviation of wavelet coefficients with a scaling factor specific for Gaussian distribution^[4]. Diedrich et al. calculated standard deviation of normally distributed noise by fitting a linear line to a quantile to quantile plot (Q-Q plot)^[2]. Recently, Brychta et al. introduced a two-stage kurtosis method taking advantage of the fact that any Gaussian distribution data will have kurtosis exactly equal to 3. They picked up noise from signals having kurtosis levels lower than their optimized kurtosis threshold, then used these identified noise to calculate noise standard deviation and threshold ^[3]. It is noticeable that previous works usually estimate noise based on mathematical properties e.g., Gaussian distribution. However, noise during microneurography depends on mechanical, environmental, and biological factors^[5] and may not always satisfy this statistical assumption.

We propose to estimate noise directly from Valsalva phase 4 where blood pressure overshoot will physiologically suppress MSNA, leaving a pure noise recording. Then, noise threshold from Valsalva phase 4 will be used to detect MSNA action potential spike elsewhere, for instance, during Valsalva phase 2. We hypothesize that using noise from individual Valsalva phase 4 will give more accurate MSNA estimations than the current two-stage kurtosis method. We tested this proposed method and compared it to the kurtosis method on simulated MSNA neurograms and real signals recorded from healthy subjects and patients with postural orthostatic tachycardia syndrome (POTS).

2. Materials and methods

2.1. Data

Our experimental data consists of two parts 1.) Simulations, and 2.) Human MSNA recordings during Valsalva maneuver. Human data were recorded as a part of the registered clinical trials (NCT04050410). The protocol was approved by the Vanderbilt University Institutional Review Board in Human Research. All participants have given written consent.

1. Simulations

We simulated MSNA neurograms by inserting action potential templates into noise in burst fashion as described in detail in Brychta et al., 2007^[3]. Briefly, action potential templates were extracted from MSNA recordings having high signal to noise ratio of 8 healthy subjects during head up tilt. The recording sampling frequency was 5 kHz. Noise portions were obtained from the healthy subjects’ recordings during Valsalva phase 4. Autoregressive model by Burg method was used to extend noise signal length to 60 seconds^[6]. Within each burst, action potential templates were inserted to get spike rate at 60 spike/s, while the burst duration varied with an average of 0.8 seconds. Burst locations and spike location within each burst were set by random numbers from Poisson distribution. The inserted spikes were assured not to be overlapped.

We generated simulated neurogram covering low, medium, and high burst rates at 5, 25, and 50 burst/min, respectively. Signal to noise ratio (SNR) was defined as an absolute peak amplitude of signal over noise standard deviation^[7]. The maximum action potential amplitude was set at 1. The noise of each simulation was scaled to have signal to noise ratio from 1 to 6, with 0.25 increment. In essence, there were 8 simulations of each specific 3 different burst rates and 21 different SNRs.

2. Human MSNA recording during Valsalva maneuver

We recruited 17 healthy females and 19 POTS females to perform the Valsalva maneuver. Raw MSNA were recorded by microneurography at 20 kHz sampling frequency (662C-3 Nerve Traffic Analysis System, University of Iowa, Iowa City, USA). A unipolar tungsten electrode with uninsulated tip diameter 1-5 μm and shaft diameter 200 μm (Frederick Haer and Co, Bowdoinham, MA, USA) was inserted into the muscle nerve fascicles of left peroneal nerve near fibular head. Continuous finger blood pressure (Finapres, Ohmeda, Englewood, CO) and electrocardiogram (ECG) were recorded simultaneously. Valsalva maneuver was performed in supine position at 30 mmHg for 15 seconds. We ensured a 30-mmHg intrathoracic pressure, not intraoral pressure, by letting subjects blow into a syringe with a tiny leak hole. Baseline was recorded from 45^th to 15^th seconds prior to the Valsalva, while recovery period was recorded for 1 minute after stop straining.

Data were processed on customized software written in MATLAB (Physiowave^©, A. Diedrich, Vanderbilt University Medical Center, TN, USA). MSNA recordings were divided into 4 phases of Valsalva based on blood pressure changes and straining time. Phase 2 is an interval from maximum systolic blood pressure (SBP) during straining until the end of straining. Phase 4 starts from the lowest SBP after releasing the strain, followed by blood pressure overshoot then return to baseline^[8]. We cut MSNA signal during baseline, phase 2, and phase 4 of each subject for further analyses.

2.2. MSNA Adaptive Processing (MAP)

MSNA adaptive processing (MAP) algorithm was developed in MATLAB (The MathWorks, Inc., Natick, MA, USA). MSNA recordings were separated into a signal section and a pure noise section. For simulations, the signal section was noise inserted by bursts of action potential templates, while noise section was simply the extracted noise. For human MSNA recordings, signal sections were parts of interest e.g., baseline and Valsalva phase 2. We assumed that Valsalva phase 4 was a pure noise section since there was baroreflex MSNA suppression due to SBP overshoot.

Both signal and noise sections were separately transformed by stationary wavelet transformation (SWT) using a mother wavelet “Symlet 7”. Standard deviation of noise wavelet coefficients was computed directly for each decomposition level. The threshold was set at 4 times of the noise standard deviation of the corresponding level. Absolute values of detail coefficients of signal section less than the level-specific threshold were hard thresholding^[2,9]. The denoised neurogram signal was reconstructed by inverse wavelet transformation of the selected levels. We chose level 2 and 3 detail coefficients for the 5 kHz simulated signal^[3] and level 3, 4, and 5 detail coefficients for the 20 kHz human MSNA recordings to cover the physiological frequency ranges of MSNA (Figure 1).

Figure 1.

MSNA adaptive processing (MAP) algorithm using Valsalva Maneuver (VM). Noise is estimated from VM phase 4 (green patch) where blood pressure (blue) overshoot suppresses MSNA (orange). Estimated noise threshold will be applied at each wavelet decomposition level for VM phase 2 (red patch) where blood pressure fall engages MNSA. Inverse Wavelet Transform reconstructs the denoised MSNA signal. Simple peak detection will be performed to estimate MSNA activity.

MSNA action potential spikes were counted by a simple peak detection on the denoised signal. We kept only peaks that have more than 1% of total signal energy to avoid tiny insignificant local maxima and minima. Interpeak interval must be at least 0.003 s since it was the maximum duration of a MSNA spike^[3].

2.3. Two-stage kurtosis method

We compared MSNA spike estimation between the MSNA adaptive processing method and the two-stage kurtosis method. The SWT two-stage kurtosis method was described in detail by Brychta et al, 2007^[3]. Briefly, they distinguished noise and MSNA burst using kurtosis window on the stationary wavelet transformed neurogram. Areas having kurtosis less than a predefined kurtosis threshold were identified as noise. Median absolute deviation of noise coefficients, divided by 0.6745 correction factor, were used to estimate noise standard deviation (Eq 1)^[3,9]. Then, hard thresholding was performed on signal by a threshold calculated from the estimated noise standard deviation. In the present study, we used kurtosis window length (N_k) = 961, and kurtosis threshold (T_k) = 3.7 as have been optimized by Brychta et al.^[3]. Level-specific threshold was set to be 4 times of noise standard deviation.

$${\sigma }_{\mathrm{j}}=\frac{\text{median}(\mid {\mathrm{d}}_{\mathrm{j}}-{\overline{\mathrm{d}}}_{\mathrm{j}}\mid )}{0.6745};$$ Eq 1

${\sigma }_{\mathrm{j}}$ = standard deviation of level $\mathrm{j}$

${\mathrm{d}}_{\mathrm{j}}$ = noise detail coefficient level $\mathrm{j}$

${\overline{\mathrm{d}}}_{\mathrm{j}}$ = average of noise detail coefficient level $\mathrm{j}$

2.4. Detection performance evaluation

Simulated signals were evaluated by percentage of correct detection ($\text{PCD}$, Eq 2) and percentage of false alarm ($\text{PFA}$, Eq 3). Correct detection means the detected spikes are at the same location where we have inserted the action potential templates. False alarm means the detected spikes are outside the inserted area.

$$\text{PCD}(\%)=\frac{\text{number of correct detections}}{\text{number of inserted action potentials}}\times 100;$$ Eq 2

where $\text{PCD}$, percentage of correct detection

$$\text{PFA}(\%)=\frac{\text{number of false alarms}}{\text{number of detected spikes}}\times 100;$$ Eq 3

where $\text{PFA}$, percentage of false alarm

Furthermore, we compared the MAP and kurtosis models by the precision-recall curve. We selected simulation properties that provide the greatest differences of PCD between the two methods to calculate precisions (Eq 4) and recalls (Eq 5) from different thresholds ranging from 1-5 times of noise standard deviation. We preferred the precision-recall curve over the receiver operating characteristic (ROC) curve because MSNA detection was an imbalance dataset with high number of negative outcomes^[10]. Error distance was the minimum Euclidean distance from the curve to the perfect classifier point (1,1) (Eq 6). Area under the curve was estimated by trapezoidal numerical integration.

$$\text{Precision}=\frac{\text{true positive}}{\text{true positive}+\text{false positive}};$$ Eq 4

where Precision, positive predictive value

$$\text{Recall}=\frac{\text{true positive}}{\text{true positive}+\text{false negative}};$$ Eq 5

where Recall, true positive rate

$$\text{Error distance}=\text{min}{\left\{\sqrt{{({\mathrm{x}}_{\mathrm{i}}-1)}^2+{({\mathrm{y}}_{\mathrm{i}}-1)}^2}\right\}}_{\mathrm{i}=1}^{\mathrm{n}};$$ Eq 6

We compared the MSNA spike rate of human MSNA recording between the MAP and the kurtosis method. Spike rate was defined as number of MSNA spikes per second. We compare spike rate, instead of number of spikes, to standardize for variation in Valsalva straining duration. We calculated spike rate of Valsalva phase 2 (VM2), as well as the spike rate difference between phase 2 and baseline (Δbaseline).

2.5. Statistical analysis

We compared MSNA estimations from MAP and the kurtosis method for both simulations and real human MSNA recordings from healthy and POTS subjects. We performed paired t-test using MATLAB software (The MathWorks, Inc., Natick, MA, USA) for the statistical comparison. Statistical significance was considered when p-value ≤ 0.05.

3. Results

Simulations

The MAP method generally had higher percentages of correct detection (PCD) than the kurtosis method. The MAP could improve PCD as high as 6.83% in simulation with burst rate = 50 burst/min and SNR = 2 (PCD: MAP = 23.81±15.49%, kurtosis = 16.98±12.75%, p<0.001). In simulations with 50 burst/min, MAP significantly increased PCD, compared with the kurtosis method, when SNR was lower than 3 (Figure 2).

Figure 2.

Percentage of correct detection (PCD) comparison between the MSNA adaptive processing (MAP) and the kurtosis method in different burst rate and signal to noise ratio simulated signals. *p≤0.05.

Although percentages of false alarm (PFA) were occasionally higher in MAP, most of the differences were non-significant. Both methods could provide lower than 1% PFA when there were high SNR as shown in 50 burst/min with SNR = 6 simulation (Figure 3).

Figure 3.

Percentage of false alarm (PFA) comparison between the MSNA adaptive processing (MAP) and the kurtosis method in different burst rate and signal to noise ratio simulated signals. *p≤0.05.

Computed level-specific thresholds were generally higher from the kurtosis than the MAP method. The kurtosis had higher average threshold in 50 burst/min with 2 SNR simulations than the MAP in both decomposition level 2 (kurtosis vs MAP; 2.539±0.058 vs 2.440±0.068, p<0.001) and level 3 (1.543±0.186 vs 1.445±0.182, p<0.001). In contrast, there were no differences of thresholds in low burst rate (e.g., 5 burst/min) with high SNR (e.g., SNR = 6) simulation in both levels (Table 1).

Table 1.

Level-specific threshold in selected simulations with 5 kHz sampling frequency.

burst rate (burst/min)	snr	d2			d3
		MAP	kurtosis	p	MAP	kurtosis	p
5	2	2.436±0.071	2.446±0.072	<0.001	1.444±0.185	1.449±0.189	0.079
	4	1.218±0.036	1.217±0.036	0.475	0.721±0.093	0.720±0.096	0.179
	6	0.812±0.023	0.811±0.022	0.422	0.481±0.061	0.481±0.060	0.368
25	2	2.437±0.071	2.480±0.069	<0.001	1.446±0.185	1.479±0.202	0.003
	4	1.219±0.035	1.221±0.037	0.398	0.722±0.092	0.720±0.091	0.457
	6	0.811±0.023	0.810±0.022	0.467	0.481±0.063	0.479±0.064	0.020
50	2	2.440±0.068	2.539±0.058	<0.001	1.445±0.182	1.543±0.186	<0.001
	4	1.218±0.035	1.225±0.040	0.170	0.724±0.092	0.725±0.099	0.795
	6	0.813±0.024	0.811±0.024	0.826	0.481±0.060	0.488±0.063	0.044

Data shown in mean ± SD. d2, detail coefficients level 2; d3, detail coefficients level 3; snr, signal to noise ratio; MAP, MSNA adaptive processing.

We chose simulations of 50 burst/min and 2 SNR to compare performance between MAP and the kurtosis methods using precision-recall curve. The average precision-recall plot was shifted upward and to the right in MAP, compared with kurtosis (Figure 4). Error distance was significantly shorter in MAP (MAP vs kurtosis; 0.535±0.175 vs 0.542±0.177, p=0.011). The area under the curve was not different between the two methods (0.600±0.113 vs 0.618±0.132, p=0.070).

Figure 4.

A) Average precision-recall curves of MSNA detection of simulated signals with burst rate at 50 burst/min and signal to noise ratio at 2 by MSNA adaptive processing (MAP) method and kurtosis method. B) The precision-recall curves plotted with Euclidean error distance from the perfect classifier point (1,1).

Human MSNA recording during Valsalva maneuver

The MAP method estimated higher MSNA spike rate in Valsalva phase 2 in healthy subjects (MAP vs kurtosis; 24.11±9.85 vs 19.57±8.60 spike/s, p=0.049). There was a similar higher detection trend in POTS, but not significant (24.19±13.70 vs 20.30±11.85 spike/s, p=0.101). As expected, MSNA spike rates in Valsalva phase 2 were greater than baseline. When computing the responses of spike rate increase during phase 2 from baseline, MAP revealed a higher delta spike rate than the kurtosis method for both healthy and POTS subjects (MAP vs kurtosis in POTS: 16.02±11.26 vs 9.51±7.60 spike/s, p=0.008, in Healthy: 15.75±8.94 vs 9.19±4.31 spike/s, p=0.002, Figure 5).

Figure 5.

MSNA action potential spike rate computed from kurtosis method and MSNA adaptive processing method in healthy (top) and POTS (bottom) during Valsalva phase 2 (left) and the difference between phase 2 and baseline (right). VM2, Valsalva phase 2; POTS, postural orthostatic tachycardia syndrome; MAP, MSNA adaptive processing.

4. Discussion

The proposed MSNA Adaptive Processing (MAP) specialized for Valsalva maneuver showed higher accuracy than the current two-stage kurtosis method. The key difference of MAP is that it individually estimates noise from each Valsalva phase 4 without using pre-optimized kurtosis threshold and Gaussian distribution assumption. Valsalva phase 4 is characterized by blood pressure overshoot due to a recovery of venous return filling a vasoconstricted vascular bed ^[11]. Phase 4 begins when blood pressure starts increasing from its nadir after release of straining. The increased blood pressure would suppress MSNA due to a baroreflex depressor response. Previous studies have shown that time delay of the feedback response of MSNA was 0.375s immediately after blood pressure changes^[12]. The immediate response was hypothesized to be related to blood pressure changes rather than blood pressure values^[12,13]. Thus, it is reasonable to collect noise interval at the beginning of Valsalva phase 4, rather than at the top of blood pressure overshoot.

MSNA background noise depends on distinct lab environments, recording devices, and subjects themselves^[14]. The difference between postmortem noise and noise after phenylephrine stimulation in microneurographic animal study suggested that in addition to electrical noise, there were biological noise from other organs not under baroreflex influence confounded the MSNA signals^[5]. Perfect noise estimation from one specific experiment may not be optimal for other settings. Assuming Gaussian distribution for random noise is a sensible way to generalize the denoising method^[2,4,7,15]. However, we cannot be certain that it will be applicable for every recording. In fact, the reported optimized kurtosis threshold at 3.7 hinted that MSNA noise is not perfectly Gaussian, since the kurtosis of normal distribution data would be 3^[3]. Thus, MAP method that determines noise specifically from each Valsalva recording should be more precise in noise estimation. It also allows us to skip the computational expensive steps of local kurtosis calculation. The individualized noise estimation would be robust, independent of various ambient factors. We chose to use raw MSNA signals, instead of bandpass filtered signal, because applying multiresolution wavelet analysis is a filter by itself^[16]. Further prefiltering would distort the actual action potential shape of the MSNA recordings. The concept of customized MSNA processing has also been presented in the development of matched mother wavelet. Salmanpour and colleagues showed that using a mother wavelet matched with mean action potential improved the MSNA detection performance^[4,17].

The two-stage kurtosis method overestimated noise in high burst rate/low SNR signals (Table 1). The kurtosis threshold could not distinguish low amplitude action potential from noise. Consequently, some action potentials were included in the calculation of noise threshold. The high detail coefficients of action potentials then raise the computed noise standard deviation and noise threshold, respectively. The overestimation was less prominent in low burst rate signal since there was less action potential to be falsely included. The kurtosis threshold could also differentiate high amplitude spike from noise. Therefore, we found almost identical detection performance between MAP and kurtosis method in low burst rate, high SNR simulations e.g., 5 burst/min with SNR = 6 (Figure 2 and 3). Valsalva phase 2 normally has high MSNA due to a compensatory sympathetic baroreflex^[18]. Our MAP method that improves detection in high burst rate simulations particularly benefits the MSNA processing during Valsalva maneuver.

It is true that one could improve true positive detection at a cost of higher false positive rate by just lowering the detection threshold. Our precision-recall plot showing the curve was shifted upward and to the right when using the MAP confirmed the more precise noise estimation and model improvement. The perfect classifier would give values of recall and precision both equal to 1, meaning that it can detect all true positive without getting any false positive detection. We chose error distance rather than area under the curve as a performance parameter in our model evaluation. Error distance was defined as the deviation from the perfect classifier point with maximal accuracy and lowest false detection. The lower error distance in MAP was less dependent on disturbances at the curve ends of the precision-recall plot (Figure 4).

MSNA estimation of the healthy MSNA recordings during Valsalva showed a similar trend of higher detection in MAP, over the kurtosis method. Simulation results assured validity of the higher spike rates. In real data, kurtosis possibly further overestimate noise due to the presence of asynchronous action potential that occurs between bursts^[19]. The inter-burst action potential may be included in noise threshold calculation leading to higher threshold. Although the average Valsalva phase 2 MSNA spike rate in POTS also increased when switching detection method from kurtosis to MAP, it was not statistically significant. But the response calculated as the difference between VM phase 2 and baseline was higher in MAP (Figure 5). Some autonomic dysfunctions having an impaired baroreflex depressor response may invalidate our method which relies on Valsalva phase 4. The pathophysiology of POTS is beyond the scope of this article. However, the similar trend of detection differences, compared with healthy subjects’, suggested that the proposed MAP method should be applicable in people living with autonomic disorders such as POTS.

5. Limitations

The proposed MAP method using Valsalva relies on the presence of an intact baroreflex; In rare cases of afferent baroreflex failure, MSNA will not be suppressed from high blood pressure^[20]. These patients probably have high MSNA in Valsalva phase 4 either from impaired negative feedback or simply no blood pressure overshoot. Noise estimation from the MAP method may have also suffered from the asynchronous MSNA that were not suppressed by baroreflex during the Valsalva phase 4^[19]. We suspected that the drawback would be non-significant due to the low numbers and small size of the asynchronous action potential. Lastly, the MAP method requires at least one Valsalva maneuver to estimate noise. In our opinion, this step should not add much burden since Valsalva is one of the measures to confirm MSNA recording quality^[21].

6. Conclusion

We proposed a new MSNA adaptive processing method by estimating noise for each wavelet decomposition level using individual MSNA recordings from Valsalva phase 4. This new individualized method detected MSNA spike rates more precisely than the current two-stage kurtosis method, which overestimated noise in high burst rate low SNR simulations. The model improvement was confirmed by a precision-recall curve shifted upward and to the right. The new method estimated higher MSNA responses calculated as differences between activity during Valsalva phase 2 and baseline in both healthy and POTS subjects. However, the higher detection of action potentials during Valsalva phase 2 from MAP was found in healthy subjects, but not in POTS. This discrepancy could be due to different firing engagement in POTS, which has to be studied further.

Highlights.

• We propose the novel MSNA adaptive processing (MAP) which denoises MSNA using optimized individual noise estimation from Valsalva phase 4.

• The MAP improves MSNA spike detection in high burst rate low signal-to-noise ratio signals, compared with the two-stage kurtosis method.

• MAP detects higher Valsalva MSNA responses than the kurtosis in healthy and POTS, compared with the kurtosis method.