Phase-amplitude coupling, an indication of bursting in parkinsonism, is masked by periodic pulses

Abstract

Interactions between neural oscillations in the brain have been observed in many structures including the hippocampus, amygdala, motor cortex, and basal ganglia. In this study, one popular approach for quantifying oscillation interactions was considered: phase-amplitude coupling. The goals of the study were to use simulations to examine potential causes of elevated phase-amplitude coupling in parkinsonism, to compare simulated parkinsonian signals with recorded local field potentials from animal models of parkinsonism, to investigate possible relationships between increased bursting in parkinsonian single cells and elevated phase-amplitude coupling, and to uncover potential noise and artifact effects. First, a cell model that integrates incremental input currents and fires at realistic voltage thresholds was modified to allow control of stochastic parameters related to firing and burst rates. Next, the input currents and distribution of integration times were set to reproduce firing patterns consistent with those from parkinsonian subthalamic nucleus cells. Then, local field potentials were synthesized from the output of multiple simulated cells with varying degrees of synchronization and compared with subthalamic nucleus recordings from animal models of parkinsonism. The results showed that phase-amplitude coupling can provide important information about underlying neural activity. In particular, signals synthesized from synchronized bursting neurons showed increased oscillatory interactions similar to those observed in parkinsonian animals. Additionally, changes in bursting parameters such as the intraburst rate, the mean interburst period, and the amount of synchronization between neurons influenced the phase-amplitude coupling in predictable ways. Finally, simulation results revealed that small periodic signals can have a surprisingly large masking effect on phase-amplitude coupling.

since the early 1900s, rhythmic oscillations have been observed in EEGs (Berger 1931). The oscillations were lumped into different frequency bands, and each band was characterized by the type of behavior that coincided with the brain rhythms in that band (Pfurtscheller and Aranibar 1977). Eventually looking at the power in each band became common practice for classifying segments of steady-state brain activity such as depth of anesthesia, sleep stages, and stress levels (Lewis et al. 2012; Weiss et al. 2011; Wolf et al. 1988).

Measures of power in frequency bands provide some limited and widely accepted information about brain activity and health. However, measures that quantify nonstationary oscillations and multiple interacting oscillations (Cannon et al. 2014) may reveal greater information, although they are not currently well understood.

Phase-amplitude coupling (PAC) belongs to the class of cross-spectral measures along with the bispectrum (Gajraj et al. 1998), spectral cross-correlation, and cross-covariance. These measures enable analysis of interactions between oscillations in neural recordings. One implementation, referred to here as the PAC map, is computed with a phase-amplitude histogram, quantified with a modulation index (MI) (Tort et al. 2010), and then displayed in a comodulation heat map. This approach is becoming increasingly popular, perhaps because it is straightforward to calculate and is available in several spectral analysis packages.

Recently, PAC measures have been shown to correlate with certain types of brain activities and pathologies (Igarashi et al. 2014; Sanders et al. 2013b; Tort et al. 2009). For example, in patients with Parkinson's disease, coupling between beta phase (13–30 Hz) and higher frequency (50–200 Hz) amplitude has been observed in subdural electrocorticography recordings from the primary motor cortex (M1) (de Hemptinne et al. 2013) and in bipolar deep brain stimulation (DBS) electrode recordings from the subthalamic nucleus (STN) (Lopez-Azcarate et al. 2010). In further work by de Hemptinne et al. (2015), STN DBS in 23 patients (stimulation frequencies ranging from 130 to 213 Hz) was reported to reduce PAC in M1. However, as with other cross-spectral measures, the interpretation of the neural basis for PAC is often not well understood. The following analyses used PAC mapping as an example method to shed light on what cross-spectral measures can imply about interacting oscillations, as well as to reveal some of the common pitfalls in interpreting these results in biological signals. Since PAC has recently been suggested as a potential feedback signal for closed-loop brain stimulation (DBS) in Parkinson's disease (Gunduz et al. 2015), particular attention was given to the neuronal firing changes that may lead to elevated PAC in parkinsonism and the dramatic PAC signal reduction (masking) induced by artifacts from periodic pulses similar to those used for clinically therapeutic DBS.

The early PAC papers focused on the interactions between two phase-locked oscillating signals in noise (Canolty et al. 2006; Jensen and Colgin 2007; Tort et al. 2009, 2010). The assumed underlying composite signal can be thought of as the modulation of the amplitude of the faster signal by the slower one, e.g.,

$$y\left(t\right)=\left\{\sin \left[2\pi t{\hspace{0.17em}x}_{\text{slow}}\left(t\right)\right]+1\right\}\cdot \sin \left[2\pi t{\hspace{0.17em}x}_{\text{fast}}\left(t\right)\right]+\sin \left[2\pi t{\hspace{0.17em}x}_{\text{slow}}\left(t\right)\right]+\text{noise}$$

(see Fig. 1 for x_slow at 10 Hz and x_fast at 80 Hz). The PAC map then shows a hot spot at the intersection of the “amplitude frequency” (fast signal) and “phase frequency” (slow signal). For this synthetic example, the two frequency components can easily be observed in the power spectral density of the composite signal. However, the relationship between the power and the PAC is not always this straightforward in actual neural recordings, leaving room for ambiguity in the interpretation of signal dynamics.

Fig. 1.

Classical phase-amplitude coupling (PAC) with x_slow at 10 Hz and x_fast at 80 Hz. Top and middle: sample local field potential (LFP). Bottom: power spectral density (left) and PAC map (right).

The PAC example above, with two phase-locked sinusoids, elevated power at the frequencies of the two sinusoids, and visible modulation of the amplitude of the faster sinusoid by the phase of the slower one, is considered the “classical” form of PAC. However, significant PAC may occur without significant peaks in the power spectral density or clear periodic modulations in the envelope of the signal. In these instances, interpretation of the signal interactions behind the PAC can be problematic. One such instance is the observed correlation between elevated PAC in local field potential (LFP) (and EEG) signals and parkinsonism (Connolly et al. 2015; de Hemptinne et al. 2013; Lopez-Azcarate et al. 2010; Sanders et al. 2013b).

MATERIALS AND METHODS

Since parkinsonism is associated with episodes of bursting in basal ganglia neurons (Bergman et al. 1994; Miller and DeLong 1987; Sanders et al. 2013a), and the bursting is hypothesized to be synchronized across multiple neurons (Gatev et al. 2006; Hammond et al. 2007), a simple bursting simulation with selectable synchronization was tested to see whether the synthetic bursting could be made to produce PAC patterns similar to those generated by LFPs recorded from parkinsonian mammals. The simulation generated normally distributed bursting patterns for individual neurons. The neuron firing for each burst cycle was calculated as shown below. A user-specified fixed incremental input current was injected into the model at 1-ms intervals for a burst duration (width) drawn from a normal distribution. The current injections were repeated after a burst cycle time period (referred to as the interburst period; also drawn from a normal distribution). The burst cycles were repeated until the desired epoch length was reached (>10 s). The means for the burst duration and interburst period were specified by the user.

The individual neuron bursting patterns were combined with a user-specified degree of synchronization to produce a composite signal (see below for synchronization calculation). The composite signals were low-pass filtered and sampled with the same filter (<500 Hz) and sampling rate (1,000 Hz) used for the analysis of the primate and rodent recordings.

Simulated neuron firing calculation.

The following neural firing equations with spike-rate adaptation (sra) from Dayan and Abbott's theoretical neuroscience text were used to calculate each neuron's membrane potential, current, and spike firing (Dayan and Abbott 2001):

$${\tau }_{\text{m}}\frac{\text{d}V}{\text{d}t}=E_{\text{L}}-V-r_{\text{m}}{g}_{\text{sra}}\left(V-E_{\text{K}}\right)+R_{\text{m}}{I}_{\text{in}}$$

$${\tau }_{\text{sra}}\frac{\text{d}{g}_{\text{sra}}}{\text{d}t}=-g_{\text{sra}}$$

$$I\left(t\right)=C_{\text{m}}\frac{\text{d}V\left(t\right)}{\text{d}t}$$

The equation parameters were leakage potential (E_L) = −65 mV; membrane time constant (τ_m) = 10 ms; membrane resistance (R_m) = 10 MΩ; potassium reversal potential (E_k) = −70 mV; spike-rate adaptation time constant (τ_sra) = 100 ms; spike-rate adaptation conductance (r_mΔg_sra) = 0.06; neuron threshold voltage (V_T) = −54 mV; post-action potential reset voltage (V_reset) = −80 mV; and capacitance (C_m) = τ_m/R_m.

To produce periodic bursting, for each neuron a fixed I_in (from 3 to 14 pA) was applied at 1-ms intervals throughout the burst duration at the beginning of each burst cycle.

When membrane voltage V exceeded V_T, the neuron produced a spike, r_mg_sra was incremented by r_mΔg_sra, and the potential was reset to V_reset.

Synchronization calculation.

The synchronization parameter used to quantify the degree of cell firing alignment was calculated as follows. Currents were calculated for each neuron in the population using the specified input current and burst parameters. For this study, all neurons in a particular population had the same mean interburst rate, mean burst duration, and input current. Desynchronization was modeled by delaying subpopulations of the neurons by user-selected mean offsets (“synchronization offset”; must be < interburst rate). In this study, subpopulations within a population were delayed by multiples of a single synchronization offset. For example, if three subpopulations were to be modeled with a synchronization offset of 5 ms, the currents from the first subpopulation of neurons start with mean time t = −10 ms, the currents from the second at mean time t = −5 ms, and the currents from the third at mean time t = 0 ms. This allowed calculation of a “synchronization factor” for each subpopulation, defined as $1-\frac{\text{synchronization offset}}{\text{interburst rate}}$. The composite synchronization was then defined as the product of the subpopulation synchronization factors. See Table 1 for example synchronization factor calculations for a set of five neuron subpopulations. Note that, while the synchronization factor was useful for selecting modeling parameters in this study and generally correlated with increasing PAC (see Fig. 2K), the measure is not a precise calculation of synchronization. For large numbers of neurons with complex dynamics, coherence between neurons or other measures should be used to evaluate the degree of synchronization.

Table 1.

Synchronization factors for five subpopulations of neurons

	Interburst Period, ms
Synchronization Offset	40	60	80	100
0	1	1	1	1
3	0.426541	0.5814	0.671629	0.730169
5	0.205078	0.3819444	0.499878	0.5814
7	0.098536	0.2347704	0.360879	0.454926
9	0.013853	0.1309	0.250622	0.348625
Composite (1 of each offset)	0.185	0.3705	0.49268	0.599247

Fig. 2.

Simulated bursting and resulting PAC. A–D: effect of varying incremental input current. E–H: effect of varying interburst period. I–K: summary of effects of varying incremental input current, mean interburst period, and synchronization factor. A: spiking pattern for a single burst cycle with incremental input current of 5 pA (interburst period of 76 ms and SD of 10 ms). B: PAC map for single neuron with parameters specified in A. C: spiking pattern for a single burst cycle with incremental input current of 6 pA. D: PAC map for single neuron with parameters specified in C. E: 10-s output from a single cell with interburst period of 40 ms. F: PAC map for cell specified in E. G: 10-s output from a single cell with mean interburst period of 80 ms. H: PAC map for cell specified in G. I: mean firing rate as a function of incremental input current for a cell with mean interburst period of 60 ms. J: mean phase frequency at region of highest (peak) PAC. K: mean PAC magnitude as a function of synchronization factor for 100 cells phasically firing (bursting) with periods synchronized about 5 evenly spaced offsets (offset interval in ms shown in parentheses), all with mean interburst period of 60 ms and incremental input current of 10 pA. Red dashed lines indicate the simulation parameters that produced the best match to the parkinsonian primate LFPs and PAC map. Note: all standard deviations are 5 ms unless otherwise specified.

Forming the LFP.

The single-cell currents were summed to form the LFP with the point current source model (Bedard et al. 2004; Koch and Segev 1998).

$$V\left(r\right)=\frac{1}{4\pi \sigma }{\displaystyle \sum _j}\frac{I_j}{\left|r-r_j\right|}$$

where σ is the electrical conductivity of the extracellular medium, r is the location of the measured LFP, and r_j is the location of the jth single cell. For this study, the electrical conductivity was assumed to be a constant, non-frequency-dependent 0.35 S/m and each neuron was assumed to be located 500 μm from the recording electrode. The output of the model was low-pass filtered (<500 Hz), sampled at 1,000 Hz, and then input to the cross-frequency-coupling analysis software where the PAC was calculated as described in the next section.

Calculation of phase-amplitude coupling and power measures.

All signals were band-pass filtered between 3 Hz and 500 Hz and then downsampled to 1,000 Hz. Power spectral densities (psd) were calculated with the standard MATLAB Welch spectrogram. A 60-Hz FIRLS filter (MATLAB filtfilt) with a bandwidth of 4 was applied to the parkinsonian animal data to remove residual line noise before psd and PAC calculations.

PAC was calculated with EEGfilt subroutines with a Morlet wavelet and the MI measure proposed by Tort et al. (2010). Briefly, the LFPs were filtered into 2-Hz bands from which the amplitude and phase were extracted. The coupling between bands was then quantified by calculating the average of the amplitudes in each band from 50 to 300 Hz that co-occurred with the phase in each band from 3 to 50 Hz. The MI measure was used to assign a single value to the degree of coupling by comparing the phase-amplitude quantification curve to a uniform distribution (the expected distribution is uniform if no coupling is present).

Addition of symmetrical periodic artifact.

Four symmetrical periodic artifacts with 1-ms pulse widths were tested to evaluate the effects of periodic signals on the PAC map. In the first two experiments, a 20-μA, 143-Hz symmetrical pulsed current and a 20-μA, 125-Hz symmetrical pulsed current were added to simulated bursting currents. In the third experiment, a 250-Hz pulsed signal was added to an LFP recorded from a parkinsonian primate. The magnitude of the pulsed signal was set equal to 1 standard deviation of the magnitude distribution from the primate LFP (z score = 1). In the fourth experiment, a 100-Hz pulsed signal was added to an LFP recorded from a mouse with parkinsonism. The pulsed signal magnitude was set to one-fourth of the standard deviation of the mouse LFP magnitude distribution. To examine the feasibility of recovering the masked PAC by filtering out the stimulus frequency, notch filters were applied at the stimulus frequency (100 Hz) and its next higher harmonic (200 Hz) for the fourth example. The procedures used to record the experimental data are described below.

Experimental procedures.

All experimental procedures were conducted in accordance with the Guide for the Care and Use of Laboratory Animals (8th ed.), the PHS Policy on Humane Care and Use of Laboratory Animals, and the American Physiological Society's “Guiding Principles for the Care and Use of Vertebrate Animals in Research and Training” (updated 2014) and approved by the Emory Animal Care and Use Committee. Every effort was made to minimize the number of animals used and their discomfort.

The experimental data shown here were obtained from completed studies with the permission of the researchers who collected the data (see acknowledgments). No additional experiments were conducted to obtain the data shown. Detailed surgical and experimental procedures for the primates are available in previous publications (Devergnas et al. 2014; Sanders et al. 2013b).

Animals.

The rhesus monkeys (Macaca mulatta, 4–5 kg) that were used for these studies were housed under conditions of environmentally controlled protected contact housing, with free access to standard primate chow, water, and supplemental fruit and vegetables. Before the recording sessions, the animals were adapted to the laboratory environment and trained to sit in a primate chair and permit handling by the experimenter.

Male C57BL/6J mice (Jackson Labs) were housed with free access to chow and water in environmentally controlled conditions with a reversed 12:12-h light-dark cycle (lights on at 7 PM). Mice were handled daily for 1 wk before surgery and habituated to the arena used for freely moving recording in the study. Video was recorded for the purpose of baseline movement assessment.

Surgical procedures.

Monkeys underwent aseptic surgery under isoflurane anesthesia (1–3%) during which they were implanted with EEG recording electrodes above M1 and two stainless steel recording chambers above the STN as described in detail in Devergnas et al. (2014).

Mice were anesthetized with isoflurane (3% for initial sedation, then 1.5–2.0% delivered via nose cone throughout surgery), administered subcutaneous buprenorphine (0.1 mg/kg), and placed in a stereotaxic frame. Ophthalmic ointment was applied to prevent corneal dehydration, and a heating pad was used to maintain body temperature at 37°C. Anesthesia levels were adjusted as needed to ensure ongoing deep anesthesia (assessed by visual monitoring and toe pinches). An incision was made to allow 0.9-mm-diameter craniotomies above the medial forebrain bundle, M1, and STN. One microliter of 6-hydroxydopamine (6-OHDA) was injected in the medial forebrain bundle (−1.2 AP, −1.2 ML, −4.75 DV) with the procedure described in Cenci and Lundblad (2007). Four 50-μm tungsten microwires were inserted; one pair was inserted in M1 (2.0 AP, −1.56 ML, −1.0 DV) and one pair in STN (−1.76 AP, −1.56 ML, −4.2 DV). An additional wire was attached to a skull screw above the cerebellum to serve as an instrument ground. All wires were then attached to a Neuralynx EIB-16 with gold pins and affixed to the skull with dental cement. Immediately after surgery, Bacitracin ointment with pramoxine was applied to the region around the incision to prevent infection and alleviate pain. Mice were weighed twice daily and assessed for overall health and comfort for 1 wk after surgery. Subcutaneous buprenorphine injections (0.1 mg/kg) were administered (up to twice daily) if the animal showed discomfort.

Recordings.

The primate data were recorded acutely with tungsten microelectrodes (0.5–1.0 MΩ at 1 kHz) inserted through the chambers into the STN of head-fixed monkeys during awake periods. The monkeys were made progressively parkinsonian with weekly 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) injections (0.2–0.6 mg/kg im) as described in Sanders et al. (2013b) and Devergnas et al. (2014). Data were collected from each monkey before MPTP treatment, thus allowing each monkey to serve as its own control. Awake periods were assessed by visual analysis of videos and EEG recordings.

Mouse recordings were made with two 1-MΩ tungsten electrodes chronically implanted in the left STN and two 0.5- to 1.0-MΩ electrodes in left M1 (20 kHz sample rate). Examples from one control mouse and one mouse injected with 6-OHDA in the left medial forebrain bundle 5 wk prior to recording are shown for comparison purposes. Both mouse recordings were made while the mice were awake but stationary during freely moving recording sessions.

Parkinsonism was confirmed behaviorally in both the 6-OHDA-injected mouse and the MPTP-treated monkeys. The degree of parkinsonism in the mouse was assessed by calculating the distance traveled and net number of rotations (in the direction ipsilateral to the lesioned side) during biweekly video recording sessions. Monkey motor signs such as bradykinesia, tremor, and freezing were assessed biweekly and assigned component and overall motor scores reflecting the degree of observed parkinsonism as described in detail in Devergnas et al. (2014).

Limitations of the methods.

As with any synthetic or simulated data, differences may exist between experimental recordings and the data output by the model. In particular, the use of fixed regular current application times and Gaussian burst parameters will not produce all possible (and likely) bursting patterns. Gamma or other distributions may provide more realistic results depending on the type and state of neurons to be simulated. The use of a single incremental input current rather than separate Na⁺, K⁺, Ca²⁺, and other currents limits the shaping of the burst and may result in nonphysiological bursting.

RESULTS

The results show that synchronized single-cell bursting can cause PAC and that certain characteristics of the resulting PAC can be calculated from the burst parameters. To evaluate the effects of varying burst and synchronization parameters, fixed incremental input currents from 3 to 14 pA and mean burst periods from 40 to 120 ms were tested. Standard deviations of 5–10 ms for each burst period and for each burst width were also examined. Composite signals from five neuron populations with synchronization factors from 0.1 to 1.0 were simulated.

As expected, larger input currents increased the intraburst rate (Fig. 2, A–D and I). The on/off burst periods generated a slow oscillation at a frequency equal to the inverse of the burst period. Thus the mean phase frequency for the resulting slow oscillation (and the region of elevated PAC) was determined by the simulated interburst rate. Increasing the burst period from 40 ms to 100 ms resulted in mean phase frequencies from 25 Hz down to 10 Hz (1/burst period) and shifted the PAC region to the left (Fig. 2, E–H and J) accordingly. Increased synchronization of the simulated neurons resulted in increased PAC magnitude (Fig. 2K).

Matching experimental data from parkinsonian animals.

The 10-pA input current for the simulated example in Fig. 3 resulted in a mean intraburst rate of 124 Hz, a rate that agrees with previous results showing an increased intraburst firing rate (>100 Hz) in STN cells in parkinsonian primates (Sanders et al. 2013a).

Fig. 3.

PAC maps, voltage traces, power spectral densities (psds), and interspike interval (ISI) histograms from normal and parkinsonian sources. Top row: PAC map, LFP, and psd from the subthalamic nucleus (STN) of a normal mouse. Second row: PAC map, LFP, and psd from the STN on the lesioned side of a unilateral 6-hydroxydopamine (6-OHDA) mouse [lesion histologically confirmed and behavior measured at net 10 ipsilateral rotations/min; note the irregular broadband gamma frequencies (150–300 Hz) in the psd]. Third row: PAC map from LFP recorded from a monkey with mild parkinsonism, corresponding LFP voltage trace, and ISI histogram (inset shows histogram for a normal monkey). Bottom row: elevated PAC in simulated synchronized bursting, simulated LFP, and ISI histogram for LFP data (bimodal histogram with large peak for ISIs < 20 ms indicates bursting). Simulation parameters: 60-ms burst period, 10-pA incremental input current, 100 neurons with 5 primary offsets, synchronization factor of 0.23.

The recorded parkinsonian animal LFPs and the simulated bursting LFPs were unremarkable, with the main distinguishing feature being irregular high gamma (150–300 Hz) power (Fig. 3). The composite simulated signal from five populations of bursting neurons with a sample rate of 1,000 Hz, a burst period of 60 ms, an incremental input current of 10 pA, and an across-population synchronization factor of 0.23 produced LFPs with characteristics similar to the LFPs recorded from the monkeys with moderate parkinsonism. The PAC patterns from the simulated LFPs, while not identical to the patterns from the recorded primate data (Fig. 3), clearly showed burst-driven PAC with similar magnitude centered at the same amplitude and phase frequencies. The LFPs and PAC maps from the parkinsonian mice, with their slower phase frequency and visible oscillatory characteristics (possibly indicating more synchronization), were simulated with burst firing having a period of 120 ms, an incremental input current of 8 pA, and a synchronization factor of 0.3.

Effect of adding symmetrical periodic signals.

As described in materials and methods, four examples were explored to evaluate the effect of adding small symmetrical pulsed signals to LFPs. The first example added a 20-μA, 143-Hz symmetrical pulsed current to currents from five bursting cells, each with a 14-pA incremental input current and an interburst period of 80 ms, with a synchronization factor of 0.2. The second example added a 20-μA, 125-Hz symmetrical pulsed current to currents from five bursting cells, each with a 14-pA incremental input current and an interburst period of 80 ms, with a synchronization factor of 0.36. The 20-μA current was simulated as a point source located 127 mm from the electrode, while the bursting cells were point sources located 500 μm from the electrode. The currents were summed with the conductivity value and the equations specified in materials and methods. This small symmetrical pulsed current masked the previously visible PAC at the primary frequencies and their harmonics (Fig. 4).

Fig. 4.

Masking effect of symmetrical periodic artifacts. Top: simulated effect of adding a 143-Hz pulsed-current stimulus from a 20-μA source located 127 mm away from the electrode. Left: PAC map from LFP simulated with 100 neurons bursting with periods synchronized relative to 5 primary offsets, 14-pA incremental input current, interburst period of 80 ms, and a synchronization factor of 0.2. Center: 143-Hz pulsed signal with 1-ms pulse width. Right: PAC map for summed currents from bursting signal and pulsed stimulus. Note how a wide section of the PAC is masked at the primary frequency (143 Hz) as well as at the harmonics above and below (286 Hz and 71.5 Hz). Middle: simulated effect of 125-Hz pulsed-current stimulus. Left: PAC map from simulated LFP with 14-pA incremental input current, interburst period of 80 ms, and a synchronization factor of 0.36. Center: 125-Hz pulsed signal with 1-ms pulse width. Right: PAC map for summed currents from LFP and pulsed stimulus. Bottom: parkinsonian primate data recorded from STN. Left to right: LFP, corresponding PAC map, masking effect in PAC map due to addition of a 250-Hz pulsed signal with magnitude equal to 1 standard deviation of the LFP, and LFP with pulsed signal added.

In the third example, a 250-Hz symmetrical pulsed signal was added to a 10-s-epoch LFP collected from the STN of a parkinsonian primate. For this experimental data case, since the input currents were unknown, the magnitude of the pulsed signal was set equal to 1 standard deviation of the primate LFP distribution (z score of 1). The small 250-Hz pulsed signal masked the previously visible PAC in a large band about 250 Hz in the parkinsonian primate LFP.

The fourth example shows the effect of adding a 100-Hz pulsed signal to a 10-s-epoch LFP collected from the STN of a 6-OHDA mouse (Fig. 5). The small 100-Hz signal masked the previously visible PAC at 100 Hz and also at the 200 Hz harmonic frequency. These examples show that the addition of a symmetrical periodic signal can reduce the total PAC at and near the stimulus frequency and also at its harmonic frequencies, obscuring PAC that would otherwise be present.

Fig. 5.

Masking effect of periodic pulsed signal added to mouse LFP and attempted recovery of PAC using filters at the artifact and harmonic frequencies. Top, left to right: PAC from parkinsonian mouse data recorded from STN, masking effect due to addition of a 100-Hz pulsed signal with magnitude 1/4σ of the LFP. Note that notch filtering at 100 Hz and 200 Hz allowed partial retrieval of the PAC but altered its pattern (the PAC phase frequency is no longer distinct from 0° phase). Bottom: LFPs corresponding to PAC maps at top. Left to right: original STN LFP from parkinsonian mouse, LFP with simulated stimulus added, and LFP after notch filtering. Note that the PAC maps vary significantly despite minimal changes in the LFP.

Application of notch filters at the stimulus frequency (100 Hz) and its next higher harmonic (200 Hz) for the fourth example allowed partial recovery of the PAC signal. However, the resulting PAC pattern changed and was no longer clearly recognizable as true PAC because of distortion across the phase axis (Fig. 5).

DISCUSSION

The simulation results in this report are the first to show that synchronized single-cell bursting can cause PAC and that measurable characteristics of the resulting PAC are directly related to the burst parameters. This suggests that population bursting characteristics may be estimated from PAC, an important finding since PAC is calculated from LFPs, which are generally more straightforward to record than single-cell firing patterns.

These results are also the first to show that the presence of a periodic stimulus occurring at common therapeutic stimulation frequencies and voltages/currents may reduce the apparent PAC without inducing any physiological changes. This is a significant finding since PAC has become an important clinical measure for Parkinson's disease and has been proposed as a feedback signal for closed-loop DBS (Gunduz et al. 2015). If the DBS stimulus artifact causes the PAC signature to be reduced without any therapeutic effect, it may not be a useful measure for patients undergoing DBS treatments, much less an appropriate closed-loop feedback signal.

However, apart from its use during stimulation, PAC may be a particularly effective analysis tool for understanding neural signals because of the nature and structure of neural activity. The oscillatory tendency of neural firing, the modulation of interconnected cells by their afferents, and the tendency for bursting to be associated with peaks or troughs of oscillating potentials in the brain are all factors that result in field potentials composed of superimposed and interacting oscillations.

The results in this study specifically show that PAC, in addition to indicating potential modulation of one sinusoid by another, can provide a measure of the amount and characteristics of bursting in a signal. For example, in the simulated bursting signal, increased PAC magnitude corresponded to increased synchronization as shown in Fig. 2K. Additionally, the mean PAC phase frequency for the simulated bursting was the inverse of the mean interburst period. These results suggest that PAC maps may be useful for detection and characterization of bursting synchrony in measured LFPs with unknown underlying signal dynamics. In future work, it will be of interest to see whether different types of physiological bursting such as T-type calcium channel bursts, hippocampal bursts, and pathological bursting in neurological diseases can be characterized and detected with PAC measures.

Of course, if single-unit spiking data from individual neurons are available, the type of bursting present in the neurons can be determined directly. However, in chronic electrode implants, single units can be difficult to record from reliably, so an additional measure of bursting from LFP signals would likely be beneficial. Additionally, since single-unit spike data may be recorded from only a few local units, these burst measures may not reflect the nature of the population bursting as well as bursting measures such as PAC that are calculated from LFPs.

The dramatic masking effects that may occur because of the addition of symmetrical periodic signals must be considered when interpreting electrophysiological effects of neuromodulation, such as DBS, since the presence of a small periodic stimulus artifact may reduce the apparent PAC without inducing any physiological changes. The shorter pulse width of typical DBS (<100 μs) may lessen the effect shown in the simulation (1-ms pulse width). However, it is feasible that the typical 4-V DBS signal could induce a 20-μA current, even with a very small pulse width. For this reason, PAC measures may not be practical for closed-loop neuromodulation unless complete isolation from the stimulus artifact can be ensured. Note that, since stimulus or other symmetrical periodic artifacts may be difficult to observe in PAC maps, inspection of the psd to assist in identifying potential problematic frequency artifacts and harmonics is recommended.

This study does not address other issues that may alter cross-spectral measures, such as the variability of spectral results between users caused by the wide variety of filtering and smoothing processes that may be applied to the raw signal. Clearly, these factors can have a large effect on the resulting power and PAC measures and can induce artifacts and falsely elevate or mask aspects of a signal. Because of the potential for false and variable results in PAC analysis, caution should be exercised in interpreting results and signal processing experts should be involved in the analysis and review of results. Also, continued conversations regarding best methods and data sharing will be important to ensure that PAC results in the literature are sound and can be replicated.

The simulation in this study provides evidence that observed PAC may be related to synchronized bursting in LFPs. The simulation does not give insight into the physiological factors that might be behind the synchronized bursting. However, the PAC measures related to the interburst and intraburst rates and the degree of synchronization in the bursting may provide a useful starting point for further exploration with more detailed models (e.g., Rubin and Terman 2004) that consider a full range of ionic currents, along with afferent and efferent projections, receptor densities, and other cellular and molecular properties.

Conclusions.

The simulation and experimental results in this report are the first to show that 1) synchronized single-cell bursting can cause physiologically realistic PAC and 2) the presence of a periodic stimulus occurring at common therapeutic stimulation settings may reduce apparent PAC without inducing any therapeutic benefits. Specifically, PAC patterns similar to those measured in recorded data from parkinsonian primates and mice were successfully simulated by summing currents from synchronized bursting neurons. Changes in the simulated intraburst and interburst rates and in the degree of synchronization were shown to predictably impact the PAC map, suggesting that, in some cases, underlying spiking activity may be characterized from LFP PAC maps. Finally, the results suggest that caution is advised when interpreting PAC maps for neuromodulation applications such as closed-loop DBS since a small symmetrical periodic pulse can create a wide null in the PAC heat map, potentially masking evidence of oscillatory interactions and thus giving the false impression that a physiological change has occurred.

GRANTS

This study was supported by National Institute of Neurological Disorders and Stroke Grant T32 NS-007480.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

Author contributions: T.H.S. conception and design of research; T.H.S. performed experiments; T.H.S. analyzed data; T.H.S. interpreted results of experiments; T.H.S. prepared figures; T.H.S. drafted manuscript; T.H.S. edited and revised manuscript; T.H.S. approved final version of manuscript.