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Published in final edited form as: J Neurosci Methods. 2019 Oct 22;330:108467. doi: 10.1016/j.jneumeth.2019.108467

An impedance matching algorithm for common-mode interference removal in vagus nerve recordings

Todd J Levy a,*, Umair Ahmed a, Tea Tsaava a, Yao-Chuan Chang a, Peter J Lorraine b, Jacquelyn N Tomaio a, Marina Cracchiolo a,c, Maria Lopez a, Loren Rieth a, Kevin J Tracey a, Stavros Zanos a, Theodoros P Zanos a,d,*
PMCID: PMC8323500  NIHMSID: NIHMS1724549  PMID: 31654663

Abstract

Background:

The peripheral nervous system is involved in a multitude of physiological functions. Recording neural signals provides information that can be used by diagnostic bioelectronic medicine devices, closed-loop neuromodulation therapies and other neuroprosthetic applications. The ability to accurately record these signals is challenging, due to the presence of various biological and instrument-related interference sources.

New method:

We developed a common-mode interference rejection algorithm based on an impedance matching approach for bipolar cuff electrodes. Two unipolar channels were recorded from the two electrode contacts of a bipolar cuff. The impedance mismatch was estimated and used to correct one of the two channels.

Results:

When applied to electrocardiographic (ECG) artifacts collected from three mice using CorTec electrodes, the algorithm reduced the interference to noise ratio (INR) over simple subtraction by 12 dB on average. The algorithm also reduced the INR of stimulation artifacts in recordings from three rats collected using flexible electrodes by an additional 2.4 dB. In the same experiments evoked electromyographic (EMG) interference was suppressed by 1.3 dB.

Comparison with existing methods:

Simple subtraction is the common approach for reducing common-mode interference in bipolar recordings, however impedance mismatches that exist or emerge compromise its efficiency.

Conclusions:

The algorithm significantly reduced the common-mode interference from ECG artifacts, stimulation artifacts, and evoked EMG interference, while retaining neural signals, in two animal models and two recording setups. This approach can be used in a variety of different neurophysiological setups to remove common-mode interference from a variety of sources.

Keywords: Vagus nerve, Common-mode interference, Impedance, Cuff electrode, Noise suppression, Neuromodulation, Bioelectronic medicine, Nerve recordings, Compound action potentials

1. Introduction

The nervous system maintains physiological homeostasis through a multitude of reflexes. The main conduits of the neural signals that govern the function of these reflexes, both efferent and afferent, are peripheral nerves. Interfacing with these nerves and recording the activity that propagates through them is essential for developing diagnostic bioelectronic medicine devices, as well as neural-based closed-loop neuromodulation therapies. The ability to accurately monitor these neural signals depends on the quality of the neural interfaces, surgical techniques, and data-processing framework needed to record and analyze them (Zanos, 2019). From a signal processing standpoint, most challenges involved with detecting neural signals from peripheral nerve recordings stem from the fact that, in most cases, the raw electroneurogram (ENG) recordings are prone to various sources of noise, both physiological (cardiac, respiratory, muscle-related etc.) as well as instrumentation related. To detect and isolate this neural activity from these noise sources, various signal-processing strategies need to be deployed.

One of the challenges of peripheral nerve recordings is the fact that the amplitude of action potentials falls off rapidly, as a function of distance from their source (Bharucha et al., 2014). Penetrating electrodes (Kashkoush et al., 2019; Wendelken et al., 2017) minimize this distance, but less invasive cuff electrodes measure neuronal signals at the surface of the nerve so a subset of the neural fibers will be in close proximity to the electrode contacts. This diminishes the signal power for most of the neuronal signals (Kashkoush et al., 2019). The sensitivity of an electrode can still be improved by increasing the surface area of the contacts (González-González et al., 2018), however all these approaches are still subject to common-mode noise sources. ENG signals measured with cuff electrodes are typically not much larger than the noise floor (Chu et al., 2012), and low noise amplifiers require often at least 40 dB mid-band gain in order to discern the signals from the input-referred noise (Ruiz-Amaya et al., 2010). Moreover, various sources of interference, such as line noise, electromyographic activity (EMG) and electrocardiographic (ECG) activity are usually present. Completely removing the interference results in a higher signal to interference plus noise ratio (SINR) that helps avoid confounding analysis results to extraneural sources and improves performance of neural decoding algorithms.

Previous studies have tried to tackle interference removal using specific electrode architectures and bipolar re-referencing schemes (Silverman et al., 2018; Steinberg et al., 2016; Yoshida, 2015; Zanos, 2019). The common basis of these approaches is that the recorded signals resulting from neural impulses propagate longitudinally within the nerve bundle (Yoshida, 2015) at slower speeds than extraneural interference. Thus, electrode contacts that are oriented longitudinally along the nerve, sense similar electric potentials delayed with respect to each other by the amount of time it takes for the neural activity to propagate the distance between them. In contrast, interfering signals should be identical in all electrode contacts, since the field propagates via electrical conduction through the tissue from a relatively distant source. While bipolar re-referencing usually removes much of the common-mode interference, it could potentially remove part of the neural activity as well. Fast-propagating neural signals would also appear nearly identical at neighboring electrode contacts, however, this issue could be mitigated by increasing the distance between the contacts or decreasing the speed of propagation (Sahin and Durand, 1998) or by using an indifferent unipolar electrode configuration (Yoshida, 2015). Another possible issue with bipolar re-referencing would emerge when the total impedance of each of the two contacts is not matched. This results in only partial cancellation of the interference.

Alternate approaches to address this problem used variations of tri-polar configurations, such as true tripolar (Demosthenous et al., 2004; Pflaum et al., 1996) or quasi-tripolar (Chu et al., 2012; Pflaum et al., 1996; Rahal et al., 2000). The hypothesis behind the quasi-tripolar re-referencing scheme is that extraneural sources will generate a nearly linear voltage gradient through the insulated cuff and the external interference is supposedly completely suppressed at the electrical center of the cuff. However, quasi-tripolar schemes do not preserve information related to the propagation direction (Sabetian et al., 2017). Moreover, due to non-uniform tissue impedances, imprecise manufacturing tolerances, and asymmetrical edge effects from local interference sources, it is difficult to completely suppress the common-mode interference in practice (Chu et al., 2012; Triantis et al., 2005). Approaches such as the adaptive true tripolar configuration (Demosthenous et al., 2004) try to overcome these practical limitations, at the expense of increased circuit complexity and higher power consumption (Chu et al., 2012).

In this study, we propose an approach to remove interference using unipolar recordings and an algorithm that adaptively matches total complex impedances. The proposed methodology estimates the frequency-dependent ratio of the impedances at each contact using spectrotemporal decomposition techniques. We showcase the efficacy of this algorithm in two different experimental setups used to record vagus nerve activity, in rats and mice, during spontaneous and electrically evoked activity, using two different electrodes and neural signal acquisition systems. The algorithm successfully accounts for impedance mismatches when present and removes ECG, EMG and stimulation artifacts.

2. Results

2.1. Impedance adjustment followed by channel subtraction suppresses ECG interference

The first application of the impedance adjustment algorithm was to remove ECG interference from vagus nerve recordings. We recorded two unipolar channels from the surface of the left cervical vagus nerve in three anesthetized mice using a CorTec Micro Cuff Sling electrode and Plexon neural acquisition system. ECG interference was present in the recordings, as evident by the large periodic spikes (Fig. 2A). By calculating the difference of the unipolar channels, a large part (11.8 dB) of the common mode ECG interference was removed (Fig. 2B blue trace) for a specific example. However, some ECG interference persisted (Fig. 2B blue trace), due to the fact that coupling impedances of each contact on the electrode were not matched. Applying our impedance adjustment algorithm using a window of 15 ms centered on the ECG artifacts further suppressed (12.0 dB) the ECG interference (Fig. 2B red trace) on this specific example. In the time-frequency domain, ECG interference in channel 1 was characterized by a fundamental frequency of about 9 Hz with high-power harmonics that began to taper off past 600 Hz (Fig. 2C left panel). The spectral content of the ECG interference across time masked neural information that occurred concurrently with the ECG artifacts. Subtracting channel 1 from channel 2 suppressed the ECG interference across all of the relevant harmonics but the ECG spectrum was still visible and partially obscured the neural information. While simple subtraction removed much of the spectrotemporal footprint of the interference, a portion of it remained (Fig. 2C, middle panel). The impedance adjustment algorithm further suppressed the ECG interference (Fig. 2C, right panel). Across all ECG artifacts (N = 120,578) in three different animals and experiments, subtracting channel 1 from channel 2 resulted in a significant average 14.4 dB decrease (Fig. 3, Table 1, one-sided Wilcoxon sign rank test, p < 0.01) in mean ECG interference to noise ratio (INR) at each ECG artifact. Using our impedance adjustment algorithm, ECG artifacts were significantly suppressed relative to the simple subtraction method (Fig. 3, Table 1, one-sided Wilcoxon sign rank test, p < 0.01) by an additional 9.2 dB on average. As evident in Fig. 3, the aforementioned differences in suppression of ECG power translated to shifts in the distributions of the ECG INR between the mean unipolar recording, simple subtraction channel, and subtracted channels after applying the impedance adjustment algorithm. These results show that surface vagus nerve recordings of spontaneous nerve activity can contain ECG interference. This interference is not completely removed using a simple bipolar re-referencing scheme when the two channel impedances do not match. Moreover, our impedance adjustment algorithm can correct for impedance mismatches and completely remove the ECG interference.

Fig. 2.

Fig. 2.

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ECG Suppression. (A) Five ECG artifacts are shown in a segment of an ENG collected using a Plexon neural acquisition system and a CorTec cuff electrode. There was a discrepancy between channel 1 (gold) and channel 2 (purple) as seen on the right panel resulting from an impedance mismatch. The ECG artifact had a 23.2 dB INR (B) Simple subtraction of channel 1 from channel 2 (blue) reduced the magnitude of the ECG INR to 11.4 dB, and applying the impedance adjustment algorithm (red) further suppressed the ECG INR to −0.6 dB. (C left) The spectrogram of channel 1 is cluttered with ECG interference that has a fundamental frequency of about 9 Hz and high-power harmonics that persist until about 600 Hz. (C middle) Simple subtraction of channel 1 from channel 2 reduced the ECG INR but it was still visible on the spectrogram. (C right) Applying the impedance adjustment algorithm almost completely suppressed the ECG interference while preserving the underlying neural signals.

Fig. 3.

Fig. 3.

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ECG INR Distributions. The ECG INR distributions were calculated as the ratio of the average interference power at each ECG artifact and the average noise power around each ECG artifact for the mean unipolar (purple), simple subtraction (blue), and impedance adjusted subtraction channels (red). The average interference power was measured by squaring and averaging the ENG signal in 15 ms windows centered on each ECG artifact, and the average noise power was measured by squaring and averaging the ENG signal between the previous and current ECG artifact windows and the subsequent and current ECG artifact windows. There were a total of N = 120,578 ECG artifacts over three Plexon mouse recordings. Simple subtraction yielded a significantly smaller INR than the mean unipolar INR (one-sided Wilcoxon sign rank test, p < 0.01), and the impedance adjustment algorithm yielded a significantly smaller INR than the simple subtraction INR (one-sided Wilcoxon sign rank test, p < 0.01).

Table 1.

Cumulative Results.

Artifact Type Electrode / Recording Device Animal models Number of artifacts Simple Subtraction Attenuation (over unipolar) (dB) Impedance Matching Attenuation (over simple subtraction) (dB) Window Length (ms)
ECG Cortec cuff / Plexon 3 mice 120,578 14.4 9.2 15
Stimulation Flexible cuff / Intan 3 rats 3330 5.5 2.5 1.3
EMG 810 1.3 0 1.3
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2.2. Impedance adjustment for suppressing stimulation artifacts

The second application of our algorithm was to remove electrical stimulation artifacts from the right vagus nerve recordings in rats, where one tripolar electrode stimulated the nerve 5–6 mm rostral to one bipolar electrode that recorded the evoked compound action potentials (CAPs). We recorded two unipolar channels in three anesthetized rats using a flexible cuff electrode and an Intan neural acquisition system. In one specific case where 5 repeats of the same stimulation pulse were delivered, the median of the five evoked responses was computed. The stimulation artifact was observed at the time of stimulation followed by A, B and C-fiber neural responses, as well as some EMG activity (Fig. 4A). While present in both channels, the stimulation artifact did not have the same amplitude (Fig. 4A inset, gold and purple traces) and simple subtraction of the two channels did not completely remove (2.5 dB difference) the artifact (Fig. 4B & inset, blue trace). Applying our impedance adjustment algorithm using a window of 1.3 ms centered on the stimulation artifacts (2.2 dB additional difference from simple subtraction) reduced the mean INR of the stimulation artifacts (Fig. 4B red trace). Across all stimulation artifacts (N = 3330) in three different animals and experiments (Fig. 5), simple subtraction of the two channels resulted in a significant (One-sided Wilcoxon sign rank test, p < 0.01) suppression of the stimulation artifact by an average of 5.5 dB (Fig. 5 blue trace, Table 1). Applying the impedance adjustment algorithm further significantly (One-sided Wilcoxon sign rank test, p < 0.01) suppressed the stimulation artifacts (Fig. 5 red trace, Table 1) on average by an additional 2.4 dB.

Fig. 4.

Fig. 4.

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Stimulation Artifact Suppression. (A) The median over five stimulation artifacts in an ENG followed by the median evoked response is shown. The data was collected using an Intan neural acquisition system and a flex cuff electrode. There was a discrepancy between channel 1 (gold) and channel 2 (purple) around the stimulation artifact at time t = 0 as seen in the inset. The INR of the average of the unipolar channels was 15.3 dB (B) Simple subtraction (blue) reduces yielded an INR of 12.8 dB. The impedance adjustment algorithm (red) yielded an INR of 10.6 dB.

Fig. 5.

Fig. 5.

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Stimulation Artifact INR Distributions. The stimulation artifact INR distributions were calculated as the ratio of the average interference power at each stimulation artifact and the average noise power around each stimulation artifact for the mean unipolar (purple), simple subtraction (blue), and impedance adjusted channels (red). The average interference power was measured by squaring and averaging the ENG signal in 0.1–1.1 ms windows, based on the stimulation pulse width, centered on each stimulation artifact. The average noise power was measured by squaring and averaging the ENG signal between the previous evoked response and the current stimulation artifact and the subsequent stimulation artifact and the current evoked response. We allowed 67 ms for an evoked response and also buffered the time before the next stimulation by 17 ms. There were a total of N = 2430 stimulation artifacts over three Intan rat recordings. Simple subtraction yielded a significantly smaller INR than the mean unipolar INR (one-sided Wilcoxon sign rank test, p < 0.01), and the impedance adjustment algorithm yielded a significantly smaller INR than the simple subtraction INR (one-sided Wilcoxon sign rank test, p < 0.01).

2.3. Impedance adjustment for suppressing evoked EMG responses

In the stimulation evoked CAPs, on top of the electrical stimulation artifact, stimulation evoked EMG activity was also recorded. Using the same setup as in the previous section (rat vagus nerve, flex cuff electrode and Intan recording system), we calculated the median over the evoked unipolar responses from stimulation pulses for two experimental conditions: before and during vecuronium (Chang et al., 2019), a neuro-muscular junction blocker (Blobner et al., 1999). EMG activity was temporally synchronous on both recording channels, as evident in a specific case (Fig. 6A, gray regions). These EMG activity traces, present between 2.5–8 ms post stimulation, completely disappeared due to vecuronium administration (Fig. 6A, gray regions). These gray regions of EMG activity were estimated on a per recording basis as the regions in channel 1 that were statistically different before and during vecuronium (one-way ANOVA, p < 10−5) and were not significantly different between channel 1 and channel 2 before vecuronium (one-way ANOVA, p > 10−5). We wanted to test whether our impedance adjustment algorithm can efficiently remove EMG activity along with the electrical stimulation artifact, akin to vecuronium administration. Contrary to EMG activation, neural responses, due to activation of different fiber types, were evident by the different time lags they occur on the two channels. For instance, C-fiber activation was identified between 8 and 13 ms (Fig. 6A and B). Applying the impedance matching algorithm by centering a 1.3 ms window on the stimulation artifact to estimate the impedance adjustment scaling factors just as before yielded an 8.7 dB reduction in power over the EMG region (One-sided Wilcoxon sign rank test, p < 0.01). While the EMG activity was successfully removed akin to the traces recorded during vecuronium administration, the neural responses were retained (Fig. 6B). We applied our impedance adjustment algorithm across all stimulations (N = 810) and three different animals, in experiments before and after vecuronium administration (Fig. 7). The distribution of the EMG INR after the algorithm was shifted left by an average of 1.3 dB and was significantly lower (One-sided Wilcoxon sign rank test, p < 0.01) with respect to the distribution of the unipolar EMG INR (Fig. 7, Table 1). Thus, using the impedance matching algorithm to remove stimulation artifacts also removed EMG activity and spared neural evoked activity. There was no difference between the EMG suppression using simple subtraction and using the impedance matching algorithm.

Fig. 6.

Fig. 6.

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EMG Suppression. (A) The median over 270 stimulation artifacts and corresponding evoked responses in one ENG is shown for the data channels corresponding to channels 1 (gold) and 2 (purple). This was repeated for two different experimental conditions: before vecuronium (solid) and during vecuronium (dotted). The data was collected using an Intan neural acquisition system and a flex cuff electrode. The gray overlays correspond to regions of EMG activity defined as regions in channel 1 that are statistically different before and during vecuronium (one-way ANOVA p < 10−5) and are not significantly different between channel 1 and channel 2 before vecuronium (one-way ANOVA p > 10−5). The median INR over the EMG region was 6.6 dB (B) The median of the impedance adjusted channels before and during vecuronium are shown here with the same regions overlaid. The median INR over the EMG region after applying the impedance adjustment algorithm was −2.1 dB. The noise power was computed exactly the same as for the stimulation artifact INR calculation.

Fig. 7.

Fig. 7.

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EMG INR Distributions. The EMG INR distributions were calculated as the ratio of the average EMG interference power, and the average noise power around each stimulation artifact for the mean unipolar (purple), and impedance adjusted channels (red). The average interference power was measured by squaring and averaging the ENG signal in the EMG region during each evoked response. The average noise power was computed in the same way as for the stimulation artifacts. There were a total of N = 1620 evoked EMG regions without vecuronium over three Intan rat recordings. Simple subtraction yielded a significantly smaller INR than the mean unipolar INR (one-sided Wilcoxon sign rank test, p < 0.01), and the impedance adjustment algorithm did not yield a smaller INR than the simple subtraction INR (one-sided Wilcoxon sign rank test, p = 1).

3. Discussion

In this study we found that estimating and compensating for the impedance mismatch between the channels of a two-contact, bipolar cuff electrode significantly reduced the common-mode interference from ECG artifacts, stimulation artifacts, and evoked EMG interference, while retaining neural signals. Previous studies report improvements in common-mode interference rejection using tri-polar (Demosthenous et al., 2004; Pflaum et al., 1996) or quasi-tripolar (Chu et al., 2012; Pflaum et al., 1996; Rahal et al., 2000) electrode configurations. Tri-polar electrodes require a longer electrode length for the same contact spacing as compared to bipolar electrodes. For space-limited applications such as ENG recordings from the cervical vagus nerves in mice, bipolar electrodes might be easier to implant and reduce nerve damage.

The proposed method assumed that the electrical potential originating from interference sources was equivalent in amplitude and occurred at the same time (with negligible temporal shift) at both recording electrode contacts. This assumption was based on the fact that confounding ECG signals, electrical stimulation artifacts, and EMG interference can be considered to be conducted through tissue via standard electromagnetic propagation. The propagation speed of electromagnetic waves through a medium is a function of the frequency dependent relative permeability and permittivity of the medium compared to a vacuum. Given that tissue is not a lossless medium, the conductivity must also be taken into account resulting in complex permittivity and attenuation of the signal. The resultant propagation velocity is still comparable to the speed of light (Dove, 2014). In contrast, propagation of action potential impulses along nerve fibers is much slower. Even in the case of saltatory conduction along the nodes of Ranvier in large myelinated nerve fibers, action potentials propagate at up to 120 m/sec (Lodish et al., 2000). The fastest conducting fibers do, however, restrict the window length around the stimulation artifacts. The algorithm performance degrades when the common-mode only assumption is violated. To our knowledge, common-mode interference suppression via impedance matching has not been applied to peripheral nerve recordings before.

Once the signals are digitized, the scale factors can be determined as the ratio of the discrete Fourier transforms (DFT) over the windows containing the interference on each unipolar channel. The implicit assumption when calculating the scale factors is that the ratio of the power spectra isn’t ill-conditioned for frequencies that contain significant power in the neural signal. For instance, the DFTs over a narrow-band artifact would result in a ratio of noise powers at frequencies outside of the artifact bandwidth, and the ratio could fluctuate drastically with very small changes to the artifact signal. This situation would result in a frequency-dependent distortion of the neural signal. In these cases, a model-based approach may be required to extrapolate the ratio outside of a specific frequency range. We found that a 15 ms window was sufficient for estimating the ratio of the power spectra for ECG artifacts in mice. The stimulation pulses in our experiment varied between 0.1 ms and 1.1 ms, so we used a 1.3 ms window for estimating the ratio of the power spectra across the stimulation artifacts in rats. Morevoer, the algorithm was applied to a 4272 s long data set with two unipolar channels sampled at 40 kHz, with a runtime of 922 s on a Lenovo ThinkPad P50 Signature Edition (Intel Xeon CPU E3-1505 M v5 @ 2.80 GHz (4 cores) and 64.0 GB RAM) in the Matlab 2018b environment. While our algorithm was run offline for this analysis, it is computationally efficient enough to run in real-time in a commercially available desktop computer.

The duration of the window determines the frequency resolution for the power spectra. If the window is too short, the frequency resolution will be too coarse, and if the window is too long, the power spectra could become contaminated with power from sources other than common-mode interference. The first bin in the DFT represents the DC offset, or mean value, of the windowed signal. Adjusting one of the channels by a scaling factor that altered the DC offset would have the effect of adding a bias to the channel. Frequencies between zero and the frequency of the next bin are affected by time aliasing (Allen and Rabiner, 1977), so our algorithm ignores this bin by setting the ratio to one. Moreover, once several scale factors have been determined, they can be averaged over time to smooth over outliers resulting from poor scale factor estimates. As the number of estimates used to compute the average increases, the ability of the system to respond to abrupt changes in impedance will also be decreased. We averaged over nine scale factor estimates, which is approximately one second when suppressing ECG artifacts in mice.

Our algorithm relies on adjusting one of two unipolar recording channels to compensate for the impedance mismatch before deriving the bipolar channel. This is unlike a traditional bipolar recording setup that makes use of a differential amplifier. Because the unipolar signals, and not the differential signal, need to be digitized, the first requirement is to ensure that neither of the unipolar signals saturate the amplifier. Ignoring this would lead to nonlinear distortions in the acquired signals, corrupting the signal and making the algorithm ineffective. One also needs to ensure that the dynamic range is sufficient to digitize the neural components from the signals so that the quantization noise remains low. The interfering signals can be several orders of magnitude larger in amplitude than the neural signals (Yoshida, 2015) so the analog to digital converters on the amplifiers must have sufficient resolution to accurately record both the neural signals and the interfering signals. Recording unipolar channels has the additional advantage of higher signal to noise ratios prior to channel subtraction, and contains the unaltered neural signal amplitudes and, potentially, velocity information. While our algorithm requires subtraction of the two impedance matched electrode recordings to remove the interference, future efforts will be focused on methods to reconstruct common-mode interference-free unipolar recordings by decomposing the unipolar signals into neural and common-mode components. Parallel efforts will focus on creating electrodes that will feature a variant of the indifferent unipolar electrode configuration (Yoshida, 2015), where one or more electrode contacts will be deliberately placed off the nerve and will record all extraneural interference. Using our algorithm, these indifferent electrodes can be used as impedance-matched references to acquire interference-free unipolar recordings.

The impedance mismatches described in this study are theoretical but supported by our results. We hypothesized that the residual artifacts after subtraction were caused by impedance mismatches and estimated appropriate correction factors based on this assumption. While calculating correlations between the corrections made by the proposed algorithm with ground truth impedance values could provide further support for our hypothesis, these impedance values were not measured in these studies, thus not available.

It is not always the case that the impedances at each electrode site will be significantly different. Correcting for the impedance mismatch of the CorTec electrode that we used in our mice experiments resulted in greatly reduced ECG artifacts. However, the impedance matching algorithm had a smaller, but still statiscially significant, effect on the stimulation artifacts and was an improvement over unipolar on EMG interference in our rat recordings that used internally developed polyimide flexible electrodes. This is due to the fact that the impedances in those channels remained roughly equivalent throughout the experiments. The saline impedances for these electrodes are 0.946 ± 0.481 kΩ @ 1 kHz, which increase to values of 3.764 ± 0.119 kΩ @ 1 kHz during acute use on the vagus nerve of rat models. Applying the impedance matching algorithm to electrodes with closely matched impedances would be roughly equivalent to simple subtraction. This represents a lower bound on performance. The impedance matching algorithm should reject the artifacts at least as well or better than simple subtraction without distorting the neural signal. In the EMG suppression results, the EMG was rejected using simple subtraction, and the bandwidth of the stimulation artifact didn’t provide any additional information that was useful for rejecting the EMG further. The impedance of electrodes with larger differences, or electrodes that develop large differences in impedance during acute, repeated acute, or chronic use (Downey et al., 2018; Gardner et al., 2018; Michelson et al., 2018) continue to benefit from the impedance matching algorithm to compensate for these mismatches without affecting recorded neural activity. Moreover, the algorithm could be used to alert the experimenter of these mismatches and guide better electrode development as well as reject common-mode interference on previously recorded data collected using older electrode technology.

4. Methods

4.1. Animals

All experimental protocols were approved by the Institutional Animal Care and Use Committee at the Feinstein Institute for Medical Research, Northwell Health, which follows National Institutes of Health guidelines for the ethical treatment of animals.

For the experiments that used mice, male BALB/c purchased from Charles River or Jackson Laboratory were used between the ages of 8–16 weeks of age. Mice were fasted for 3–4 h prior to each experiment. For the experiments that used rats, male Sprague Dawley rats were used between the ages of 3–5 months, weight 450–600 g. (Chang et al., 2019).

4.2. Recording procedure

Mice were induced with 2.5 % isoflurane, maintained at 2.0 % during surgery, and maintained at 1.75 % during recording. Mice were placed in the supine position, and a midline cervical incision was made. The cervical vagus nerve was isolated from the carotid bundle, desheathed, and placed on the CorTec cuff electrode. A ground electrode was placed near the right salivary gland. The recording was collected with a Plexon Omniplex Neural Data Acquisition system at 40 kilo-samples per second. Parafilm was used to prevent the nerve from desiccating. More details on the recording procedure of the mouse experiments can be found in our previous studies (Silverman et al., 2018; Steinberg et al., 2016; Zanos et al., 2018).

Rats were induced with 4 % isoflurane and maintained at 1–2%. The rats were intubated with an endotracheal tube and connected to a ventilator set to 41 breaths per minute 4 ml tidal volume. Body temperature was maintained between 37.0–37.5 °C. The right cervical vagus was exposed and a tripolar electrode was placed for stimulation. A bipolar recording electrode was placed at a site 5–6 mm caudally to the first site. The neural recording was acquired using an Intan Neural Data Acquisition system, with a sampling rate of 30 kHz. A ground electrode was inserted in the ipsilateral salivary gland. Electrical stimuli consisted of 100–1100 μs square, pre, or quasi-trapezoidal pulses at amplitudes between 1–10 times the neural threshold of 10–30 μA delivered with Multichannel Systems stimulator. Both polarities were used for stimulation, the pulses were not charge balanced, and pulses were delivered at a rate of 1 Hz. To minimize stimulation-elicited muscle contraction and EMG contamination of the nerve recordings, vecuronium bromide was used as a paralytic agent (Blobner et al., 1999). A bolus dose of 0.15 mg/kg was administered intravenously (IV), followed by continuous IV infusion at a rate of 0.15 mg/kg/min using an infusion pump (Gemini 88, KD Scientific Inc., Holliston, MA). More details on the recording procedure of the rat experiments can be found in our previous study (Chang et al., 2019).

4.3. Impedance matching algorithm

The algorithm presented in this manuscript can be downloaded from https://github.com/tlevy-nds/impedanceAdjustment.git. Deviations in the measured voltages of common-mode interference at each contact on a bipolar cuff electrode can be compensated by estimating the impedance mismatches. The input impedances are a property of the electrode and amplifier, and should already be matched, but the coupling impedances are dependent upon the surrounding tissue which is variable (Fig. 1A). The mismatch in the coupling impedance is what our algorithm effectively estimates and compensates for. To accomplish this, the signals collected at each electrode contact need to be compared. For this reason, two unipolar channels are amplified and recorded rather than using a differential amplifier to record a single bipolar channel.

Fig. 1.

Fig. 1.

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Schematic of the Impedance Adjustment Algorithm. (A) Bipolar cuff electrodes consist of two contact sites; each with a potentially different coupling impedance and input impedance. (B) The schematic diagram implements an analysis and synthesis filter bank to compensate for impedance mismatches prior to deriving the bipolar channel thereby improving the common-mode rejection ratio. The DC term is preserved because of time aliasing.

Next, the regions of interference are identified. For this step, the interference component, such as ECG artifacts or stimulation artifacts, is considered the signal, and the neural component is considered the interference. A high SINR in this context provides the basis for estimating the impedance mismatch. Peak picking is performed to identify ECG artifacts, and ECG peaks must be detected in each unipolar channel to declare a detection. The locations of stimulation artifacts are known a priori.

A window is centered on an artifact and the power spectrum of each channel is estimated using discrete Fourier transforms at the window locations. The windows must be large enough to capture the power in the artifacts, but not too large that neural power contaminates the artifact power. We used a 15 ms window to estimate the power spectrum of the ECG artifacts (601 frequency bins) and a 1.3 ms window to estimate the power in the stimulation artifacts (41 frequency bins). The ratio of the power spectra excluding the first bin determines the frequency dependent scaling factor that adjusts the impedance of one channel relative to the other.

Once the scaling factors are estimated, they are applied to the appropriate channel in the time-frequency domain. An analysis filter bank decomposes the original time-series from the channel that is to be adjusted into band-pass sampled sub-bands (Zhivomirov, 2019,Zhivomirov, 2018). The scaling factor evaluated at the appropriate frequency is multiplied for each sub-band, and then a synthesis filter bank reconstructs the modified time-series. The bipolar derivation is then performed between the modified channel and the unmodified channel from the other electrode contact (Fig. 1B). The interference will be rejected and the neural signals will remain.

The impedances are time-varying, so the scaling factors need to be updated periodically. Generally, the impedances are slowly time-varying, but abrupt changes may occur if there is motion between the electrode and the nerve, or if the nerve becomes too dry. Updating the scaling factors at each detected instance of interference would address this, but there is also the possibility of a poor quality estimate that would distort the resulting signal for the duration of time that the bad estimate was applied. A rolling average of several estimated scaling factors provides a good trade-off. We used a rolling median over 9 artifacts.

Because the sysnthesis filter can achieve perfect reconstruction when the overlap-add constraint is satisfied (Eq 7, Zhivomirov, 2019), it is not necessary to compute the DFT at every sample position. A hop size is used to increase the filtering efficiency. The modified maximum hop size is determined from the windowing functions, and the windowing functions are appropriately selected based on the bandwidth of the signal being analyzed. A Blackman-Harris window was used for analysis, and a synergy complementary Hamming window was used for synthesis (Zhivomirov, 2019).

Acknowledgments

The authors would like to thank Dr. Theresa Faughnan for assistance with animal care, Dr. Nikunj Bhagat and Dr. Yousef Al-Abed for helpful discussions regarding this study. This study was partly supported by General Electric Company (T.P.Z.).

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