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Brain. 2009 August; 132(8): 2139–2150.
Published online 2009 April 15. doi:  10.1093/brain/awp079
PMCID: PMC2714058

Resonance in subthalamo-cortical circuits in Parkinson's disease

Abstract

Neuronal activity within and across the cortex and basal ganglia is pathologically synchronized, particularly at ~ 20 Hz in patients with Parkinson's disease. Defining how activities in spatially distributed brain regions overtly synchronize in narrow frequency bands is critical for understanding disease processes like Parkinson's disease. To address this, we studied cortical responses to electrical stimulation of the subthalamic nucleus (STN) at various frequencies between 5 and 30 Hz in two cohorts of eight patients with Parkinson's disease from two different surgical centres. We found that evoked activity consisted of a series of diminishing waves with a peak latency of 21 ms for the first wave in the series. The cortical evoked potentials (cEPs) averaged in each group were well fitted by a damped oscillator function (r ≥0.9, P < 0.00001). Fits suggested that the natural frequency of the subthalamo-cortical circuit was around 20 Hz. When the system was forced at this frequency by stimulation of the STN at 20 Hz, the undamped amplitude of the modelled cortical response increased relative to that with 5 Hz stimulation in both groups (P  0.005), consistent with resonance. Restoration of dopaminergic input by treatment with levodopa increased the damping of oscillatory activity (as measured by the modelled damping factor) in both patient groups (P ≤0.001). The increased damping would tend to limit resonance, as confirmed in simulations. Our results show that the basal ganglia–cortical network involving the STN has a tendency to resonate at ~ 20 Hz in Parkinsonian patients. This resonance phenomenon may underlie the propagation and amplification of activities synchronized around this frequency. Crucially, dopamine acts to increase damping and thereby limit resonance in this basal ganglia–cortical network.

Keywords: synchronization, basal ganglia, resonance, Parkinson's disease, deep brain stimulation

Introduction

Electrophysiological recordings in patients with Parkinson's disease and animal models of this disorder demonstrate an exaggerated and oscillatory synchronization of neuronal activity in the basal ganglia at frequencies below about 30 Hz (Rivlin-Etzion et al., 2006; Uhlhaas and Singer, 2006; Hammond et al., 2007). Such prominent synchronization is not seen in healthy animals and is suppressed by treatment with the dopamine prodrug, levodopa, and by dopamine agonists, in tandem with an improvement in symptomatology. This has lead to the suggestion that pathological synchrony at low frequency is mechanistically linked to phenotypic features of Parkinson's disease, such as tremor, slowness of movement and stiffness, although this remains to be established (Rivlin-Etzion et al., 2006; Uhlhaas and Singer, 2006; Hammond et al., 2007).

In patients with Parkinson's disease, in whom most data comes from surgical implantation of the subthalamic nucleus (STN) or globus pallidus, pathological synchrony tends to occur at ~ 20 Hz (Brown et al., 2001; Cassidy et al., 2002; Williams et al., 2002; Priori et al., 2004; Alegre et al., 2005; Foffani et al., 2005; Kuhn et al., 2005; Alonso-Frech et al., 2006; Devos et al., 2006; Fogelson et al., 2006; Weinberger et al., 2006; Lalo et al., 2008; Steigerwald et al., 2008; Bronte-Stewart et al., 2009). More recently, it has become clear that excessive synchrony is a feature of the entire basal ganglia–cortical network in Parkinson's disease, with populations of neurons not only synchronizing their activity locally, but also across levels. Thus, there is coherent rhythmic activity both between nuclei in the basal ganglia (Brown et al., 2001; Cassidy et al., 2002; Goldberg et al., 2004; Foffani et al., 2005), and between these and cortical areas (Marsden et al., 2001; Williams et al., 2002; Sharott et al., 2005; Fogelson et al., 2006; Lalo et al., 2008). In particular, in patients with Parkinson's disease, there is strong coherence between activity in STN and the cortex centred around 20 Hz (Marsden et al., 2001; Williams et al., 2002; Fogelson et al., 2006; Lalo et al., 2008). Such synchronization at ~ 20 Hz has been associated with slowness of movement in both correlative (Brown and Williams, 2005; Kuhn et al., 2006b, 2008, 2009; Weinberger et al., 2006; Ray et al., 2008) and interventional (Fogelson et al., 2005a; Chen et al., 2007; Eusebio et al., 2008) studies. Even though a causal rather than epiphenomenal link between this pathological synchronization and motor impairment is by no means proven, synchronization at ~ 20 Hz therefore appears worthy of further investigation as it may provide insight into the pathophysiology of parkinsonism.

Here, we explore the mechanism of the strong coupling of oscillations at ~ 20 Hz across basal ganglia–thalamo–cortical circuits, and propose and test the hypothesis that dopaminergic hypoactivity in Parkinson's disease exposes a network resonance at ~ 20 Hz that favours the propagation of activity at this pathological frequency around basal ganglia–cortical loops in patients with Parkinson's disease. To this end, we studied the cortical response to STN stimulation in Parkinson's disease patients receiving therapeutic high frequency deep brain stimulation (DBS) through electrodes implanted in the STN.

Materials and Methods

Patients and surgery

Most recordings were performed in eight patients (eight males, mean age 58.0 years ± 3.0; mean disease duration 14.1 years ± 1.6) in London. Patients participated with written informed consent and the permission of the Joint Ethics Committee of the National Hospital for Neurology and Neurosurgery and the Institute of Neurology. However, we also repeated the main experiment in an independent population of eight similar Parkinson's disease patients (seven males, mean age 62.1 years ± 2.0; mean disease duration 12.8 years ± 1.5) recorded in Marseille. These patients participated with written informed consent and the permission of the local Ethics Committee (CPP Marseille 2). The clinical details of all patients are summarized in Supplementary Table 1. Implantation of bilateral STN DBS electrodes was performed in all subjects for treatment of Parkinson's disease at least 6 months prior to study (mean 29.9 months ± 3.6). The implanted pulse generator used was a Kinetra® (Medtronic Neurological Division, Minneapolis, USA). The DBS electrode used was model 3389 (Medtronic Neurological Division, Minneapolis, USA) with four platinum-iridium cylindrical surfaces (1.27 mm diameter and 1.5 mm length) and a centre-to-centre separation of 2 mm. Contact 0 was the most caudal and Contact 3 was the most rostral. The intended coordinates at the tip of Contact 0 were 10–12 mm from the midline, 0–2 mm behind the midcommissural point and 3–5 mm below the anterior commissural-posterior commissural line. For the patients operated in London, adjustments to the intended coordinates were made in accordance with the direct visualization of STN in individual stereotactic MRI (Hariz et al., 2003) and implantation performed under local anaesthesia. Correct placement of the DBS electrodes in the region of the STN was further supported by: (i) effective intra-operative macro-stimulation; (ii) immediate postoperative stereotactic T2-weighted MRI compatible with the placement of at least one electrode contact in the STN region; (iii) significant improvement in UPDRS motor score during chronic DBS off medication (14.9 ± 2.5) compared with UPDRS off medication with stimulator switched off (44.8 ± 4.5; P < 0.0001, paired t-test). The patients operated in Marseille were implanted under light general anaesthesia as previously described (Witjas et al., 2004). Intended coordinates were adjusted according to the direct visualization of STN in stereotactic MRI performed under general anaesthesia. Correct placement of the DBS electrodes in the region of the STN was further supported by: (i) intra-operative micro-recordings (five electrodes on each side); (ii) intra-operative macro-stimulation for the detection of capsular spread; (iii) intra-operative stereotactic telemetric radioscopy and immediate postoperative CT-scan providing final coordinates of each contact; (iv) significant improvement in UPDRS motor score during chronic DBS off medication (11.5 ± 3.0) compared with UPDRS off medication with stimulator switched off (32.8 ± 3.2; P < 0.0001, paired t-test).

Protocol

Our aim was to artificially synchronize activity in the STN area at different frequencies and to follow changes in its propagation characteristics, as indicated by the amplitude of the cortical evoked potentials (cEPs). Previous studies have shown that DBS applied in the vicinity of the STN reliably induces a cEP with a peak latency of 20–25 ms predominantly over the sensorimotor cortex of Parkinson's disease patients and likely to reflect orthodromic activation of basal ganglia projections to the cortex (Baker et al., 2002; MacKinnon et al., 2005). Earlier potentials (< 10 ms) occur, but may be more inconsistently observed, at least in part because of their obscuration by stimulation artefact. For example, MacKinnon et al. (2005) found these after stimulation of only 6 out of 14 electrodes. These early potentials may represent the effects of anti-dromic activation of the hyperdirect pathway (Ashby et al., 2001; Baker et al., 2002; MacKinnon et al., 2005). As we wanted to specifically test the transfer function of pathways originating in the STN or passing as close to this nucleus as possible, we choose to stimulate those DBS contacts affording the best clinical response, even though the highest amplitude cEPs may often be obtained with DBS applied through more dorsal contacts (MacKinnon et al., 2005).

All 16 patients were assessed after overnight withdrawal of anti-parkinsonian medication. Fifteen of the patients (those in whom a significant cEP was found; see below) were also recorded during another experimental session after administration, in a dispersible form, of their morning levodopa-equivalent dose of medication or 200 mg of levodopa, whichever was the higher. Experimental sessions on and off medication were performed on separate days due to time constraints. In London, the two experimental sessions were separated by a mean of 47 ± 7 days and the ON-drug session always followed the OFF-drug session. In Marseille, the two experimental sessions took place on two consecutive days and the OFF-drug session followed the ON-drug in two patients. In the OFF-drug state, the stimulator was switched off for at least 20 min and basal OFF-drug OFF-stim UPDRS III scoring was performed. About 75% of the UPDRS III score decrease occurs within this time frame following discontinuation of DBS (Temperli et al., 2003). All patients had maximal clinical effect using monopolar DBS (the implanted pulse generator being the anode). However, in this configuration, the stimulus artefact prevents any analysis of the evoked potentials (MacKinnon et al., 2005). Accordingly, the stimulator was turned back on using a bipolar configuration and the voltage increased to 130% of the monopolar voltage by way of compensation (MacKinnon et al., 2005). There was no evidence of capsular spread during DBS, as determined by clinical examination. The negative contact was the one used by the patient in a monopolar configuration. The positive contact was chosen next to the negative one. When the active contact was between two other contacts, the positive contact producing the best clinical effect was utilized. The pairs of contacts chosen for all patients are summarized in Supplementary Table 1. In addition, postoperative MRI or CT-scan was consistent with placement of at least one of these two contacts in the STN region. The clinical effect was assessed using the UPDRS III score after 20 min of DBS using the patients’ usual therapeutic stimulation frequency and pulse width. All patients improved their UPDRS III score by at least 30% (mean 50.6% ± 2.4 in London and 63.6% ± 6.6 in Marseille; P  0.0001 for both, paired t-tests), consistent with stimulation of the local STN area.

The Kinetra® stimulator stimulates alternately both sides, producing an artefact at twice the frequency actually used. Therefore, to avoid this and any interaction of evoked potentials elicited at different times from the two hemispheres, only the side with the best clinical benefit of DBS (assessed by the UPDRS III score) was stimulated (nine right sides). The same side was stimulated in the OFF- and ON-drug conditions using the same DBS parameters. In both conditions, the stimulator was turned off for the other side. Efficacy of the levodopa administration in the ON-drug state was assessed using the UPDRS III score about 30 min after ingestion of levodopa with the stimulator ON with the usual therapeutic parameters in order to diminish the discomfort of the patients (ON-DBS ON-drug state). All patients felt at “best ON” and improved their UPDRS III score by at least 25% compared with the ON-DBS OFF-drug state (mean 52.3% ± 5.9 in London and 60.4% ± 8.4 in Marseille; P  0.005 for both, paired t-tests) before the start of the recording in the ON-drug state. Moreover, eleven of them experienced peak-dose dyskinesias throughout the recording in the ON-drug state. The four patients who did not have dyskinesias were not usually prone to this kind of abnormal movement in the ON-drug state. The duration of the experiment (~ 90 min) was consistent with the duration of efficacy of the medication. On three occasions, however, an additional dose of 200 mg levodopa was administered to the patient as they subjectively felt the effect of the first dose of levodopa was wearing off, even though no significant deterioration of the UPDRS III score was noticed. We then waited 30 min before resuming the experiment.

A baseline recording without stimulation was performed first and then STN stimulated at 5, 10, 15, 20 and 30 Hz in London, and 5 and 20 Hz in Marseille. Stimulation frequencies were assessed in pseudo-randomized order across patients and patients were not informed of the stimulation frequency. The stimulation settings (i.e. contacts and parameters) used during the experiments are summarized in Supplementary Table 1. In order to diminish the duration of the experiments, we waited 5 min after changing between frequencies before recording since it has been previously shown that this short duration is sufficient to produce a practical steady state in Parkinsonian motor symptoms (Moro et al., 2002).

EEG recordings

Patients were comfortably seated in a chair during the whole experiment. In London, scalp EEG was recorded through 19 Ag/AgCl electrodes covering the scalp according to the 10:20 international system and referenced to linked ear electrodes. One additional electrode was used to record the stimulus artefact and was located either along the wire ipsilateral to the stimulated STN (close to the burr-hole or to the mastoid) or in the vicinity of the stimulator case, whichever produced the highest amplitude artefact. Signals were amplified and filtered (band-pass filter: 0.25–300 Hz) and sampled at 1500 Hz using a Brain Dynamics Analyzer® amplification system (St Petersburg, Russia) and custom-written software (developed by A.P.). In addition, the signal from the electrode recording the stimulus artefact was amplified and filtered (band-pass filter: 530–30 000 Hz) using a Digitimer®160 amplifier (Digitimer Ltd, Hertfordshire, UK) and processed through an amplitude discriminator (custom-made Schmitt trigger) that produced a timing pulse coincident with the peak of the artefact, so that both analogue and digital representations of the stimulus timing (artefact) were recorded. In Marseille, scalp EEG was recorded using 11 Ag/AgCl electrodes covering the sensorimotor cortex (Fp1, Fp2, F3, F4, Fz, C3, C4, Cz, P3, P4, Pz) referenced to linked ear electrodes. Signals were amplified and filtered (band-pass filter: 0.25–300 Hz) and sampled at 2048 Hz using a Porti® amplification system (TMS International, Oldenzaal, The Netherlands) and custom-written software (developed by A.P.). All recordings were performed at rest during 120 s after waiting 5 min between each frequency change.

Signal analysis

Recordings were edited using custom-made software (EditEEG©, developed by A.P.). Sections with artefacts from eye movements or scalp muscle activation were deleted. Recordings were then imported into Spike® version 2.06 (Cambridge Electronic Design, Cambridge, UK) using a custom-made script. The mean durations of the recordings in the OFF and ON conditions were 114.4 s ± 2.2 and 103.7 s ± 2.4 for 5 Hz, 115.0 s ± 2.3 and 99.6 s ± 3.2 for 10 Hz, 114.4 s ± 2.2 and 104.0 s ± 3.2 for 15 Hz, 113.8 s ± 3.0 and 107.2 s ± 3.4 for 20 Hz, 115.2 s ± 2.6 and 99.8 s ± 4.4 for 30 Hz for the patients from London (Group 1), and 80.4 s ± 3.6 and 86.0 s ± 8.1 for 5 Hz and 82.6 s ± 6.8 and 75.6 s ± 4.4 for 20 Hz for the patients from Marseille (Group 2). For each recording, channels were averaged around each artefact (trial width 0.4 s; offset 0.2 s) using Spike® version 2.06. The mean number of sweeps averaged in the OFF and ON conditions were 578 ± 12 and 528 ± 13 for 5 Hz, 1123 ± 23 and 977 ± 32 for 10 Hz, 1697 ± 41 and 1553 ± 43 for 15 Hz, 2275 ± 60 and 2144 ± 69 for 20 Hz, 3428 ± 87 and 2993 ± 131 for 30 Hz for the patients from London (Group 1) and 402 ± 18 and 430 ± 41 for 5 Hz and 1652 ± 135 and 1512 ± 88 for 20 Hz for the patients from Marseille (Group 2). The recording lengths were slightly shorter in the ON-state compared with the OFF-state in the London group due to the presence of muscular artefacts caused by levodopa-induced dyskinesias, resulting in the deletion of larger sections of the recordings. Analysis of the averaged trials in the OFF-drug state showed that DBS consistently induced a significant cEP at 5 Hz with a peak latency of 18–25 ms in all but one patient (Case No. 8 in Supplementary Table 1), who was excluded from further analysis. The peak was considered significant when its amplitude exceeded 2 SD of the amplitude of the baseline trace (95% confidence limit) in at least one electrode over the sensorimotor cortex. The baseline trace was obtained by averaging the EEG recording in the OFF-drug state around fictitious events created in Spike® at 5 Hz when the stimulator was turned off (mean number of sweeps: 564 ± 13, not significantly different from the number of sweeps during genuine 5 Hz stimulation). The SD was measured for the 200 ms between each fictitious event. Short (3–8 ms) latency cEPs were not consistently seen, at least partly because of stimulation artefact. Cortical maps of the cEP amplitude averaged between 15 and 30 ms for all electrodes were created in Matlab® version 7.0.1 (The Mathworks Inc., Lowell, MA, USA) for the London patients and revealed maximum amplitudes over the sensorimotor, premotor and mesial cortices (Fig. 1). This was confirmed in an ANOVA of the cEP amplitude averaged between 15 and 30 ms for the ipsilateral, contralateral and mesial pairs of electrodes across the five different frequencies in both drug-states (3 levels × 5 levels × 2 levels). We found a significant effect of the pair of electrodes [F(2,12) = 10.493, P = 0.002] and within-subject contrasts revealed that the amplitude of the evoked potential was significantly higher for both mesial and ipsilateral electrodes compared with the contralateral electrodes across frequencies [F(1,6) = 30.798, P = 0.001 and F(1,6) = 11.011, P = 0.016, respectively; see Supplementary Fig. 1]. We thus analysed the cEPs in the corresponding electrodes (e.g. F3/F4, C3/C4, Fz, Cz) and decided accordingly to reduce the number of EEG electrodes in the Marseille patients. The peak latency of the first consistent cEP wave was measured for each patient (one side per patient) and at each stimulation frequency as the peak latency of the cEP averaged across these six electrodes between 15 and 30 ms. The cEPs were then averaged for each patient across the four electrodes covering the ipsilateral and mesial sensorimotor cortex obtained at different stimulation frequencies for further analyses. Similar cEPs were obtained with a fixed number of sweeps across stimulation frequencies instead of a fixed recording length (see Supplementary Fig. 2 and supplementary Table 2). We did not attempt a thorough source localization due to the relatively small number of electrodes used and the presence of burr holes.

Figure 1
Shape and distribution of the cortical evoked potentials. (A) Example of cEP in Case 1 from Group 1 (see Supplementary Table 1) OFF-drug during 5 Hz stimulation. The time period over which cEP amplitude was averaged in B and C is indicated ...

Oscillation modelling

A free natural oscillation is damped if there is an external damping force to resist its changing and this was the model we choose to describe the cortical cEP (Pain, 2005; Rao, 1995). The damping oscillation can be described by a two-order differential equation as

equation image
(1)

where x(t) is the damped oscillation, An external file that holds a picture, illustration, etc.
Object name is awp079i1.jpg and An external file that holds a picture, illustration, etc.
Object name is awp079i2.jpg are first- and second-order differentiation of x(t). Parameters m and k are the mass and elasticity constant. Parameter c is a damping constant, which is related to the level of damping force. Damping force is directly proportional to the changing of oscillation x(t) as An external file that holds a picture, illustration, etc.
Object name is awp079i3.jpg. If we define

equation image

where An external file that holds a picture, illustration, etc.
Object name is awp079i4.jpg is the natural frequency in radians of the undamped natural oscillation. An external file that holds a picture, illustration, etc.
Object name is awp079i5.jpg is a damping factor.

Then the damped oscillation x(t) is expressed in the following function as the solution of Equation (1)

equation image
(2)

An external file that holds a picture, illustration, etc.
Object name is awp079i6.jpg is the initial phase angle of the oscillation. X0 is the amplitude of the natural oscillation.

When An external file that holds a picture, illustration, etc.
Object name is awp079i7.jpg is zero, the oscillation is a free natural oscillation without damping. When An external file that holds a picture, illustration, etc.
Object name is awp079i8.jpg is 1, the oscillation is critically damped and the solution of the Equation (1) becomes

equation image
(3)

where An external file that holds a picture, illustration, etc.
Object name is awp079i9.jpg is a constant of the initial value of An external file that holds a picture, illustration, etc.
Object name is awp079i10.jpg.

As the recorded physiological signal usually has a floating baseline, we adjusted Equations (2) and (3) as

equation image
(4)

equation image
(5)

where At + D represents the linear or constant floating baseline.

The parameters X0, An external file that holds a picture, illustration, etc.
Object name is awp079i11.jpg, An external file that holds a picture, illustration, etc.
Object name is awp079i12.jpg and An external file that holds a picture, illustration, etc.
Object name is awp079i13.jpg were estimated from the average evoked cortical potentials at 5, 10, 15, 20 and 30 Hz stimulation in Matlab® version 7.0.1 (The Mathworks Inc., Lowell, MA, USA). The stimulation artefacts were deleted from the ERP, to avoid the influences of artefacts on parameter estimation (See Supplementary Fig. 3). The processed ERP was then fitted with the waveform generated by Equation (3) according to the least mean square principle. The optimized parameters were iteratively computed till the mean square of the residual between the average ERP and fitting waveforms was minimal.

We only analysed data between stimulus artefacts over a single averaged stimulation cycle. This meant that stimulation artefact was not analysed but fewer data points were analysed for higher stimulation frequencies. However, qualitatively similar results were derived when several stimulation cycles of stimulation at 15–30 Hz were considered with the artefact deleted, so that similar numbers of data points were analysed across frequencies (data not shown). We first fitted the traces averaged across subjects for each stimulation frequency and both OFF- and ON-drug states. Wavelet transform filters were used to clean the average ERP as they provided reliable decomposition according to the waveform of short data segment. The data were low-pass filtered to remove EMG activity (London: 80–90 Hz for all stimulation frequencies, except for 30 Hz where a low pass of 135 Hz was used; Marseille: 110–120 Hz for both 5 and 20 Hz). In addition, a linear floating baseline for 5 Hz (constant baseline for all other frequencies) was incorporated in the model so as to correct for DC offsets.

Both cEPs averaged across groups (London and Marseille) and within patients were fitted using the above procedures. When analysing data from individual patients, the last 60 ms of the 200 ms cEP trace was deleted from one case from London and the last 90 ms was deleted in three cases from Marseille due to muscular artefacts. One case from London showed a natural frequency of 48 Hz, with a ~ 20 Hz component being identified in the residual to this fit. It was the results from the latter fit that were considered further as this lower frequency component appeared homologous to that seen in the remaining individual subjects in whom the predominant natural frequency was around 20 Hz. Note that harmonically related components may not merely reflect irregularities in waveform shape but can also be accompanied by multi-unit activity in resonant brain systems (Rager and Singer, 1998).

Finally, we simulated the response of an oscillating system with a natural frequency of 20 Hz and variable damping factors (0.05–0.6) when the system was driven by impulse input at frequencies from 1 to 60 Hz. The initial undamped amplitude was set as one and the peak amplitude relative to the initial value was extracted from the model for various stimulation frequencies and damping factors (Fig. 3).

Figure 3
Simulation of response of an oscillating system with a natural frequency of 20 Hz showing dependency of resonance phenomena on damping factor. Changes in damping factor of the same degree as seen with the shift from the OFF- to ON-drug state, ...

Transfer function

The transfer function was estimated by fitting a convolution kernel which best predicted the EEG signal using the stimulus train. Specifically, we fit the following model:

equation image
(6)

where y(t) is the EEG signal, h(k) is the convolution kernel, and s(t  k) is the stimulus train and η is a Gaussian random variable. The convolution kernel was then estimated by minimizing the sum of the squared error (SSE) of the estimate of y

equation image
(7)

using linear regression techniques. The frequency domain representation was then found by taking the Fourier transform of the convolution kernel, h(k), with respect to k.

The transfer function, unlike the oscillation model, which operates on the average stimulus triggered cEP, controls for the fact that some stimuli arrive before the effects of the previous stimuli have gone to zero. More specifically, the transfer function controls for autocorrelation in the input stimulus. This is because the transfer function estimate, h, is equal to the cEP premultiplied by the inverse of the autocorrelation matrix of the stimulus. To see this, if we put the raw cEP data into a vector, y and the lagged stimulus values into a matrix S, we can write the solution of the vector of the convolution kernel as

equation image
(8)

These are the normal equations from regression, i.e. they are the equations used to find the solution to the coefficients in multivariate regression (Draper and Smith, 1998). The matrix STS is equivalent to the autocorrelation matrix of the stimulus train, and the vector STy is equivalent to the average evoked potential. Thus, pre-multiplying by the inverse of STS deconvolves the transfer function estimate. If the input stimulus were truly a delta function, or if it were white noise, this step would not be necessary. If the stimulus were white noise, the matrix STS is a scaled identity matrix, and therefore it would only scale the estimate of h, it would not change its frequency content.

Statistics

cEP amplitudes, latencies, fitted oscillator parameters (undamped amplitude, damping coefficient and natural frequency) and transfer function derived amplitudes were normally distributed (One-sample Kolmogorov Smirnov tests P > 0.05). Repeated measures ANOVAs with repeated within-subjects contrasts were performed to compare the effects of drug-state and different frequencies of stimulation on cEP latencies and predominant cortical distribution. Mauchly's test was used to determine the sphericity of the data entered in the ANOVAs, and where data were non-spherical Greenhouse-Geisser corrections applied. Oscillator parameters were compared using two-tailed, paired Student's t-test (using step-wise correction for multiple comparisons). Means ± SEM are presented throughout the text. All statistical analyses were performed in SPSS (SPSS for Windows version 12, SSPS Inc., Chicago, Illinois, USA).

Results

We stimulated the STN with trains of delta functions (pulses) at lower frequencies than used clinically in two groups of eight Parkinson's disease patients from different surgical centres, and contrasted the amplitudes of the potentials evoked in cortex (cEPs). We stimulated the STN only on the most severely affected side demonstrating the best clinical benefit to therapeutic stimulation.

Patient Group 1 (from London)

The natural frequency of the modelled STN-cortical circuit is about 20 Hz

A significant cEP (Fig. 1A) was observed in seven patients from this group during STN stimulation at 5 Hz. The peak latency of the first consistent wave of the cortical response was 21.2 ± 1.3 ms. Scalp mapping of the ~ 21 ms component during 5 Hz stimulation indicated that cEP amplitude was maximal ipsilateral to the stimulated STN and over mesial cortical areas (see box in Fig. 1 where hemispheres have been reversed for right-sided stimulation prior to averaging, and Supplementary Fig. 1). Accordingly, we focused on the cEPs recorded through the four electrodes covering the ipsilateral and mesial sensorimotor cortex, averaging the cEPs at these sites in each patient. Averaged cEPs to STN stimulation at 5 Hz consisted of a series of diminishing waves with periods of around 50 ms (see box in Fig. 2A), consistent with the response of an impulse forced damped oscillator with a natural frequency of about 20 Hz. To test this, we fitted a damped oscillator function to the grand average of STN stimulation at 5 Hz according to the least mean squares principle. The fit was excellent (r = 0.9, P < 0.00001, box in Fig. 2A). The natural frequency of the damped oscillator fitting the cEP was 19.8 ± 0.1 Hz, the undamped amplitude (e.g. the theoretical amplitude of the response of the undamped system) 1.7 ± 0.1 µV and the damping factor 0.14 ± 0.01.

Figure 2
Fittings and parameters of the oscillator OFF- and ON-drugs. (A) Fitting of cEP traces averaged across seven patients in Group 1 in OFF- and ON-drug states for each stimulation frequency by the function for an impulse forced damped oscillator. Both the ...

Oscillatory responses are damped by dopaminergic therapy

We then recorded cEPs to 5 Hz STN stimulation in the same patients from Group 1 after treatment with levodopa was recommenced (hereafter referred to as ON-drug state). This drug helps restore dopaminergic tone in Parkinson's disease, and, as is usually the case, the motor state of our patients improved in the ON-drug state (see Materials and methods section). The pattern of the cEP was similar to that OFF-drug, with the exception that successive waves reduced in amplitude faster in the ON-drug state. The ON-drug state grand average cEP was again well fitted by a damped oscillator function (r = 0.9, P < 0.00001, box in Fig. 2A). The undamped amplitude was the same (1.7 ± 0.1 µV) and the natural frequency of the damped oscillator fitting the cEP slightly lower (18.1 ± 0.1 Hz) than that in the OFF-drug state. Importantly, however, and consistent with the observation that successive cEP waves reduced in amplitude faster after levodopa, the damping factor was ~ 30% higher in the ON-drug state (0.18 ± 0.01, P = 0.001).

The above findings were corroborated in individual subjects (Fig. 2C). A damped oscillator function was fitted to the average cEPs to STN stimulation at 5 Hz OFF- and ON-drug from each subject. Fits in all cases were good (mean r = 0.78 ± 0.03, range 0.51–0.95, P < 0.00001). As above, the undamped amplitude did not differ between drug-states (2.1 ± 0.7 and 2.2 ± 0.8 µV ON and OFF-drugs, respectively; P = 0.733), and the natural frequency of the damped oscillator fitting the cEP was slightly lower ON- than OFF-drugs (20.7 ± 4.9 and 22.9 ± 4.4 Hz, respectively; P = 0.048). The damping factor was 64% higher ON-drugs (0.18 ± 0.05) than OFF-drugs (0.11 ± 0.04; P = 0.001).

Stimulation at 20 Hz provokes resonance and this resonant response is attenuated by dopaminergic therapy

The finding that the natural frequency of the modelled system underlying the cEP was ~ 20 Hz encouraged us to seek evidence of resonance when this system was forced by stimulating the STN at 20 Hz. To this end, we stimulated STN at several additional frequencies in the patients from London (10, 15, 20 and 30 Hz), having first confirmed that the output current and waveform of the chronically implanted pattern generator used to stimulate patients remained constant across the different stimulation frequencies (See Supplementary Fig. 4). As before, we fitted damped oscillator functions to each grand average from stimulation at a given frequency for each drug state. Fits were very good (r > 0.94, P  0.00001, Fig. 2A), confirming that the potentials evoked in cortex by STN stimulation were well described as the response of an impulse forced damped oscillator at all the frequencies of STN stimulation tested. Critically, the undamped amplitude of cEPs was clearly greatest during stimulation at 20 Hz (3.1 ± 0.7 µV at 20 Hz OFF versus 1.7 ± 0.1 µV at 5 Hz OFF, P = 0.0053 corrected for multiple comparisons; Fig. 2B). There was no difference in the undamped amplitudes between drug states during 20 Hz stimulation (3.1 ± 0.7 µV, both ON- and OFF-drug).

Simulation of the response of an oscillating system with a natural frequency of 20 Hz suggested that the changes in damping factors identified between drug states in patients were sufficient to make a major difference to resonance phenomena (Fig. 3). Another relevant factor in this regard was the slight drop in natural frequency of the damped oscillator fitting the cEP with drug treatment noted above. This too would contribute to the reduction in observed resonance during driving at 20 Hz, although under natural conditions pure driving at 20 Hz is rather unlikely, as suggested by the breadth of activity in the beta frequency band in power spectra of STN local field potentials (Brown and Williams, 2005; Bronte-Stewart et al., 2008), so the effect of the drop in natural frequency upon resonance phenomena may not be as important as the increase in damping upon treatment. Note that the response to STN stimulation at 30 Hz did not merely recover after the resonance at 20 Hz, but was actually diminished relative to stimulation at 5 Hz, regardless of drug state (Figs. 1B and C; C;2A2A and B). This suggested an additional low-pass filtering effect of the system underlying the cEP although proof of this would require stimulation at even higher frequencies.

In the above analysis, we assumed in our modelling that the responses of the impulse forced oscillator were unaffected by linear summation of the early evoked components to one pulse with the later evoked components of earlier pulses. This was not a factor when modelling the response to 5 Hz as Fig. 2A shows that the response had died off before the next stimulus. However, this may have been a factor with stimulation at 20 Hz, particularly in the OFF-drug state where the damping of successive oscillations was reduced. To investigate this point further we used an alternative approach involving the transfer function that modelled the effect of the most recent stimulus having allowed for the effect of earlier stimuli on the evoked activity in each subject. An ANOVA of FREQUENCY (5 levels: 5, 10, 15, 20 and 30 Hz) in the OFF-drug state confirmed an effect of frequency [F(4,24) = 4.681, P = 0.006] and within-subjects contrasts indicated that the response to 20 Hz stimulation was greater than that to 5 Hz stimulation [F(1,6) = 7.308, P = 0.035]. Thus, irrespective of any effect of linear summation, the response to an input at 20 Hz was bigger than that to an input at 5 Hz (See Supplementary Fig. 5).

The properties of the network change with dopamine and stimulation frequency but the network itself remains the same

Our core results suggested that basal ganglia−cortical circuits may have a natural oscillation frequency of about 20 Hz, that the amplitude of the cortical response to STN stimulation increases when the system is driven at or near its natural frequency and that this resonance phenomenon is predominantly limited by damping which is under the strong influence of dopaminergic input. This physiological interpretation assumes that the cortical response to STN stimulation at different frequencies and in different drug states has essentially the same mechanism. This assumption is supported by three observations. First, the same damped oscillator model fitted the grand average data well across stimulation conditions. Second, the latency of the initial wave in the cEP remained similar across conditions. Thus there was no significant effect of stimulation frequency, drug-state nor interaction between these two factors on the latencies of this wave as revealed by an ANOVA of latencies with factors FREQUENCY (5 levels: 5, 10, 15, 20 and 30 Hz) and STATE (two levels: OFF-drug and ON-drug). Third, the relative scalp topography (but not amplitude; Fig. 1B and C) of the cEP remained similar across conditions.

Patient Group 2 (from Marseille)

A natural frequency of about 20 Hz and increased damping with dopamine are consistent features

In order to determine the reproducibility of our core findings in patient Group 1 we repeated the experiment in an independent population of eight Parkinson's disease patients (Group 2) from a different surgical centre (Marseille). The cEPs were recorded during 5 Hz STN stimulation both in OFF- and ON-drug states. As before, the cEPs averaged over the ipsilateral and mesial sensorimotor cortex, consisted of a series of diminishing waves with a peak latency of 21.6 ± 0.6 ms for the first consistent wave. The fitted grand average cEP (r = 0.9 OFF and 0.95 ON, P < 0.00001, for both) had a natural frequency of 21.8 ± 0.1 Hz OFF and 20.8 ± 0.1 Hz ON (P < 0.00001) and a damping factor of 0.13 ± 0.01 OFF drugs increasing by 85% to 0.24 ± 0.01 ON-drugs (P < 0.00001; Fig. 4). As before the undamped amplitude of cEPs was greater during stimulation at 20 Hz (3.9 ± 0.3 µV at 20 Hz) than during 5 Hz stimulation OFF (P = 0.002; Fig. 4). The only major difference between this cohort of Parkinson's disease patients and those reported above was a higher undamped amplitude OFF (2.8 ± 0.1 µV; P < 0.00001 OFF Group 1 versus Group 2) that increased even further ON-drugs during 5 Hz stimulation (4.4 ± 0.2 µV; P < 0.00001 Group 2 OFF versus ON).

Figure 4
Fittings and parameters of the oscillator OFF- and ON-drugs in an independent Parkinson's disease patient group. Fitting of cEP traces averaged across eight patients in Group 2 in OFF- and ON-drug states for 5 and 20 Hz stimulation by the function ...

The above findings were corroborated in individual subjects. A damped oscillator function was fitted to the average cEPs to STN stimulation at 5 Hz OFF- and ON-drug from each subject. Fits in all cases were good (mean r = 0.85 ± 0.03, range 0.66–0.95, P < 0.00001). As above, the damping factor significantly increased by 53% ON-drugs (0.26 ± 0.04) compared with OFF-drugs (0.17 ± 0.04; P < 0.05). The modelled natural frequency (20.2 ± 1.2 and 22.0 ± 1.1 ON- and OFF-drugs, respectively; P = 0.19) nor the modelled undamped amplitude (4.8 ± 0.7 µV and 3.5 ± 0.6 µV ON- and OFF-drugs, respectively; P = 0.16) were significantly different between drug-states. In summary, the natural frequency of about 20 Hz and the increased damping of the modelled oscillatory response after levodopa were consistent findings within and across the two patient groups.

Discussion

Our findings are compatible with a scheme in which, at the systems level, basal ganglia−cortical circuits can act as an oscillator, with a tendency to resonate at around 20 Hz. Ordinarily, dopaminergic input to the basal ganglia cortical system effectively increases the damping of oscillations, thereby limiting resonance phenomena in these circuits. However, in the relative absence of dopaminergic input in the untreated Parkinson's disease patient the system becomes less damped and thus, resonance is more marked, contributing to the relatively preferential propagation and amplification of activities synchronized around 20 Hz. Our study focused on the dynamic response of basal ganglia–cortical circuits over five to 30 Hz, in line with the evidence for exaggerated and distributed oscillation at similar frequencies in the basal ganglia–cortical system of patients with Parkinson's Disease demonstrated by multiple groups (Brown et al., 2001; Cassidy et al., 2002; Williams et al., 2002; Priori et al., 2004; Alegre et al., 2005; Foffani et al., 2005; Kuhn et al., 2005; Alonso-Frech et al., 2006; Devos et al., 2006; Fogelson et al., 2006; Weinberger et al., 2006; Lalo et al., 2008; Steigerwald et al., 2008; Bronte-Stewart et al., 2009). However, as such we cannot exclude additional resonances at other frequencies, such as that reported in the cerebral cortex at frequencies around or above 100 Hz during DBS (Li et al., 2007; Montgomery and Gale, 2008).

The above interpretation of our findings makes no assumption regarding the site or sites within the circuit responsible for the oscillatory response. Although evident in the cEP, the resonance at ~ 20 Hz could have been partially or entirely generated at a subcortical relay and activity then propagated to the cortex. However, independent estimates of the preferred frequency response of circuits involving frontal and sensorimotor cortical areas generally also implicate frequencies of about 20 Hz. Thus, the natural frequency of the damped oscillator fitting the evoked responses corresponds closely to the frequency of steady state sensorimotor cortical responses to peripheral vibration (Tobimatsu et al., 1999), the predominant frequency of cortico-muscular coherence (Gilbertson et al., 2005) and the predilection of cortical myoclonus to occur at around 20 Hz (Ugawa et al., 2003).

A related issue is the nature of the pathway activated by STN stimulation that eventually modulates cortical activity. Previous reports suggest that the initial cEP wave peaking at ~ 21 ms is the product of activity in the subthalamo–pallidal–thalamo–cortical pathway (MacKinnon et al., 2005; Tisch et al., 2008), in line with recent animal work suggesting that regular trains of inhibitory pallidal discharges can drive phase-locked thalamocortical output, and hence produce a cEP (Person and Perkel, 2005). Furthermore, there is no evidence to indicate that later evoked waves might have a different origin in a system that is known to be characterized by rhythmic activity at ~ 20 Hz (Brown et al., 2001; Rivlin-Etzion et al., 2006). Recent data, however, suggest the existence of direct subthalamo–cortical projections (Degos et al., 2008) and a fast orthodromic transmission followed by recruitment of cortico-cortical or cortico–subcortico–cortical loops cannot be excluded. Similarly, anti-dromic stimulation of the cortex via the hyperdirect pathway is possible, although this is generally believed to lead to initial activation of the cortex at latencies of under 10 ms (Ashby et al., 2001; Baker et al et al., 2002; MacKinnon et al., 2005), rather than 21 ms as in our recordings.

On the other hand, the nature of the pathway or pathways involved in the generation of the cEP oscillation does not necessarily impact on the functional significance of our findings as, irrespective of the pathways involved, the net effect at the cortical level is the preferential propagation of activities at around 20 Hz in untreated Parkinson's disease. The precise mechanisms by which restoration of dopaminergic input can modify the damping of oscillations and attenuate expression of 20 Hz activity at the cortical level remain unclear. One possibility is that dopamine alters voltage-dependent conductances (Nicola et al., 2000) that may act to dampen oscillations (Gutfreund et al., 1995). Alternatively, dopamine may alter potential re-entrant mechanisms in the basal ganglia–thalamo–cortical loop (Montgomery and Gale, 2008).

It is interesting to note that the natural frequency of around 20 Hz identified here is paralleled by the pattern of STN-cortical coherence in previous studies (Williams et al., 2002; Fogelson et al., 2006; Lalo et al., 2008). This suggests that the network properties characterized here may be of functional relevance in the amplification and propagation of spontaneous pathological oscillations in Parkinson's disease patients. However, further studies are required in peri-operative patients to determine whether the modelled natural frequency in each subject corresponds to the peak frequency of their STN-cortical coherence. The latter would be preferable to comparison with the peak frequency of their motor cortical EEG activity in the beta band, which may reflect synchronization supported not only by the basal ganglia, but also by cortico–cortical interactions and cerebello–thalamo–cortical relays (Marsden et al., 2000).

Another feature of note was that the response to STN stimulation at 30 Hz did not merely recover after the resonance at 20 Hz, but was actually diminished relative to stimulation at 5 Hz, regardless of drug state. This might reflect low-pass filtering by the skull and scalp and/or an additional low-pass filtering effect of the system underlying the cEP, consistent with a polysynaptic subthalamo–pallidal–thalamo–cortical relay, as frequency following in polysynaptic circuits tends to fail at higher frequencies. This might help explain why coherence between basal ganglia sites and cortex at frequencies in the gamma band is unusual, even though local field potentials power in the STN often has a discrete gamma band peak in treated patients (Marsden et al., 2001; Williams et al., 2002; Alegre et al., 2005; Fogelson et al., 2005b; Alonso-Frech et al., 2006; Devos et al., 2006), contrasting with the stereotypical coherence between basal ganglia sites and cortex in the beta band in patients with Parkinson's disease (Marsden et al., 2001; Williams et al., 2002; Fogelson et al., 2006; Kuhn et al., 2006a).

Finally, it is interesting to note that the natural frequency of around 20 Hz measured in our patients corresponds to the frequency band associated with slowness of movement in both correlative (Brown and Williams, 2005; Kuhn et al., 2006b, 2008, 2009; Weinberger et al., 2006; Ray et al., 2008) and interventional (Fogelson et al., 2005a; Chen et al., 2007; Eusebio et al., 2008) studies of STN. In the latter case there is evidence for impairment in motor function during stimulation of STN at around 20 Hz, but not at 15 or 30 Hz, when stimulation is performed in Parkinson's disease patients withdrawn from medication (Fogelson et al., 2005; Chen et al., 2007; Eusebio et al., 2008). This parallels the pattern of modelled resonance shown here. Indeed, stimulation at 40 and at 60 Hz is believed to improve some aspects of parkinsonism (Moreau et al., 2008; Brozova et al., 2009), as well as of dystonia and chorea (Moro et al., 2004; Alterman et al., 2007; Guehl et al., 2007). Likewise, our study provided evidence of a smaller tendency to resonance in the evoked response to stimulation of the STN at 10 Hz, evident in both the scalp topography of the cortical response at about 20 ms and in our simulations. It may be relevant, therefore, that exacerbations of motor impairment may also be seen with 10 Hz stimulation of the STN (Timmermann et al., 2004), although the same group has highlighted that this effect may be reversed when some cognitive functions are considered (Wojtecki et al., 2006), and the above observations may not apply to all targets for DBS in movement disorders. Thus stimulation of the region of the pedunculopontine nucleus at about 20 Hz is therapeutic (Lim et al., 2007; Stefani et al., 2007). Taken together these observations suggest that there may be several basal ganglia–cortical networks subserving different aspects of impairment in Parkinson's disease and each with its own pattern of susceptibility to resonance phenomena (Fogelson et al., 2006). Of these, the motor circuit involving STN may be particularly susceptible to frequencies of around 20 Hz, at least when dopaminergic activity is low.

In summary, the data presented here help explain why excessive neuronal synchrony at around 20 Hz in patients with Parkinson's disease is so remarkably propagated around the basal ganglia–cortical circuit involving the STN, leading to coherent activity over multiple levels within this circuit. The results show that this basal ganglia–cortical network has a tendency to resonate at ~ 20 Hz, thereby both propagating and amplifying spontaneous pathological activities at this frequency. Critically, dopamine acts to increase damping and thereby limit resonance in this basal ganglia–cortical network.

Supplementary material

Supplementary material is available at Brain online.

Funding

Medical Research Council, Wellcome Trust, Parkinson Appeal (UK); Société Française de Neurologie—Journées de Neurologie de Langue Française (France).

Supplementary Material

[Supplementary Data]

Acknowledgements

We thank Peter Magill, Pierre Pollak, Peter Redgrave, Stephen Tisch and Paul Sauleau for helpful comments, Vladimir Litvak for help building scalp map plots, Jean-Claude Péragut and Jean Régis for operating on the Marseille patients and Marwan Hariz for operating on the London patients and proof-reading the manuscript.

Glossary

Abbreviations

cEP
cortical evoked potential
DBS
deep brain stimulation
MRI
magnetic resonance imaging
STN
subthalamic nucleus
UPDRS
Unified Parkinson's Disease Rating Scale

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