Dopamine-dependent non-linear correlation between subthalamic rhythms in Parkinson's disease
1 Dipartimento di Scienze Neurologiche, Università di Milano, Fondazione IRCCS Ospedale Maggiore Policlinico, Milano, Italy
2 School of Biomedical Engineering, Science and Health Systems, Drexel University, Philadelphia, PA, USA
3 Fundación del Hospital Nacional de Parapléjicos para la Investigación y la Integración, SESCAM, Toledo, Spain
4 Dipartimento di Bioingegneria, Politecnico di Milano, Milano, Italy
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5 Dipartimento di Neurologia Clinica, Ospedale San Paolo, Milano, Italy
Abstract
The basic information architecture in the basal ganglia circuit is under debate. Whereas anatomical studies quantify extensive convergence/divergence patterns in the circuit, suggesting an information sharing scheme, neurophysiological studies report an absence of linear correlation between single neurones in normal animals, suggesting a segregated parallel processing scheme. In 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP)-treated monkeys and in parkinsonian patients single neurones become linearly correlated, thus leading to a loss of segregation between neurones. Here we propose a possible integrative solution to this debate, by extending the concept of functional segregation from the cellular level to the network level. To this end, we recorded local field potentials (LFPs) from electrodes implanted for deep brain stimulation (DBS) in the subthalamic nucleus (STN) of parkinsonian patients. By applying bispectral analysis, we found that in the absence of dopamine stimulation STN LFP rhythms became non-linearly correlated, thus leading to a loss of segregation between rhythms. Non-linear correlation was particularly consistent between the low-beta rhythm (13–20 Hz) and the high-beta rhythm (20–35 Hz). Levodopa administration significantly decreased these non-linear correlations, therefore increasing segregation between rhythms. These results suggest that the extensive convergence/divergence in the basal ganglia circuit is physiologically necessary to sustain LFP rhythms distributed in large ensembles of neurones, but is not sufficient to induce correlated firing between neurone pairs. Conversely, loss of dopamine generates pathological linear correlation between neurone pairs, alters the patterns within LFP rhythms, and induces non-linear correlation between LFP rhythms operating at different frequencies. The pathophysiology of information processing in the human basal ganglia therefore involves not only activities of individual rhythms, but also interactions between rhythms.
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Introduction
In the classic view of basal ganglia processing, single neurones represent the elementary channels of thalamo-cortico-basal ganglia communication (Albin et al. 1995; Wichmann & Delong, 1996; Wichmann & Delong, 2003). Under physiological conditions in animals, the firing activity between nearby neurones is virtually independent, suggesting that these channels are functionally segregated (Hoover & Strick, 1993; Nini et al. 1995; Bar-Gad et al. 2003) to maximize information transmission (Bar-Gad & Bergman, 2001). In 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) treated monkeys (Bergman et al. 1994; Nini et al. 1995; Raz et al. 2000, 2001; Heimer et al. 2002) and in parkinsonian patients (Levy et al. 2000, 2002a), the firing activity between neurones becomes linearly correlated, suggesting that the lack of dopamine results in a loss of segregation between communication channels (Bergman et al. 1998).
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Recent studies with local field potential (LFP) recordings from electrodes implanted for deep brain stimulation (DBS) in patients with Parkinson's disease are providing a new complementary scenario of information processing in the human basal ganglia (Brown & Williams, 2005). In this scenario, the elementary channels of thalamo-cortico-basal ganglia communication are defined at the network level by LFP rhythms operating at various frequencies (Brown et al. 2001; Marsden et al. 2001; Levy et al. 2002b; Priori et al. 2002, 2004; Cassidy et al. 2002; Williams et al. 2002, 2003, 2005; Silberstein et al. 2003; Kühn et al. 2004, 2005; Foffani et al. 2003, 2004, 2005a,b,c,d; Doyle et al. 2005; Alegre et al. 2005; Fogelson et al. 2005, 2006). LFPs reflect the synchronous presynaptic and postsynaptic activity of large neuronal populations and can detect focal network rhythms that are not necessarily observable in single neurones or neurone pairs (Creutzfeldt et al. 1966; Frost, 1968; Murthy & Fetz, 1992, 1996a,b; Baker et al. 1997; Donoghue et al. 1998; Magill et al. 2004; Goldberg et al. 2004). The presence of multiple LFP rhythms suggests ‘the existence at the network level of multiple functionally independent – but not necessarily spatially separated – subsystems operating at different frequencies’ (Priori et al. 2004). Hence ‘tuning to distinct frequencies may provide a means of marking and segregating related processing, over and above any anatomical segregation of processing streams’ (Fogelson et al. 2006). Little information is available on the segregation between LFP rhythms at different frequencies. This issue is critical for clarifying whether the segregation concept is pathophysiologically relevant for human basal ganglia information processing at the network level.
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In the same way as a loss of segregation at the cellular level induces linear correlation between neurones (i.e. linearly correlates neural signals oscillating at the same frequency), a loss of segregation at the network level presumably induces non-linear synchronization between LFP rhythms (i.e. non-linearly correlates neural signals oscillating at different frequencies). We therefore hypothesized that Parkinson's disease produces non-linear correlations between subthalamic LFP rhythms oscillating at different frequencies and that these non-linear correlations are reversed by dopaminergic medication. A useful approach for studying non-linear correlations is bispectral analysis, a procedure widely used in scalp EEG studies (Dumermuth et al. 1971; Barnett et al. 1971; Kearse et al. 1994a,b, 1998; Sebel et al. 1995, 1997; Glass et al. 1997; Pfurtsheller et al. 1997; Pfurtsheller & Lopes da Silva, 1999; Bannister et al. 2001) and already applied to investigate non-linear cortico-cortical correlations between LFP rhythms in mammals (Schanze & Eckhorn, 1997; Villa et al. 2000). We therefore tested our hypothesis by applying bispectral analysis to LFPs recorded from DBS electrodes implanted in the STN of patients with Parkinson's disease, searching for non-linear correlation between subthalamic rhythms before and after administration of levodopa.
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Methods
Patients and surgical procedure
The study sample consisted of nine patients (four men, five women) with idiopathic Parkinson's disease admitted to the Department of Neurological Science, IRCCS Ospedale Maggiore di Milano and fulfilling the specific inclusion criteria for DBS treatment (L.I.P.E., 2003). All of them were studied after informed consent and local ethical committee approval, and the study conformed with the Declaration of Helsinki. The average age was 55 years (range 44–69 years), years of disease history 12.3 (7–20 years), levodopa equivalent therapy presurgery 1535 mg day–1 (800–2800 mg day–1), after surgery 335 mg day–1 (75–800 mg day–1), Unified Parkinson's Disease Rating Scale (UPDRS) III (motor part) presurgery off therapy 43.7 (27–72.5), on therapy 5.2 (1–23.5), UPDRS III 12 months postsurgery off therapy on stimulation 9.0 (1.5–20), UPDRS IV (complications, A + B) presurgery 10.1 (5–14), and UPDRS IV 12 months postsurgery 2.3 (0–6). Patients were predominantly rigid-akinetic, with severe motor fluctuations not responsive to pharmacological treatment. No patient was on long-acting agonists at the time of surgery. One of the main inclusion criteria was a good response to levodopa, as measured by the UDPRS III.
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All patients were bilaterally implanted in the STN with macroelectrodes for DBS (model 3389 Medtronic, Minneapolis, MN, USA). The STN was targeted by direct visualization through a CT-MRI fusion-based technique before surgery, as extensively reported elsewhere (Egidi et al. 2002; Rampini et al. 2003). The STN position was estimated by matching the CT-MRI fused images with a digitized stereotactic atlas. During surgery, the implant position was assessed by microrecordings from explorative microelectrodes (Priori et al. 2003) and by clinical assessment of the effects induced by stimulation through the implanted macroelectrodes. The implanted 3389 Medtronic electrode has four cylindrical contacts (1.27 mm in diameter, 1.5 mm in length, placed 2 mm apart, centre-to-centre) denominated 0–1–2–3, beginning from the more caudal contact. According to neuroimaging and intraoperative clinical and neurophysiological tests, for all nuclei studied the position of contact 1 was consistent with placement within the STN. Four subjects were studied bilaterally, five only unilaterally, for a total of 13 nuclei.
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Local field potential (LFP) recordings
The LFP recording procedure is described in detail elsewhere (Priori et al. 2004). In brief, LFPs were recorded from the implanted electrodes 2 or 3 days after surgery, before the subcutaneous high-frequency stimulators were connected. LFPs were recorded at rest (60–80 s), 8–12 h after withdrawal of dopaminergic treatment both before (‘off’ therapy condition) and after (‘on’ therapy condition) patients received dopaminergic medication (100–200 mg of oral fast-acting levodopa – Madopar Dispersibile; Roche, Monza, Italy).
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After-medication LFPs were recorded at least 20 min after drug administration, when the patient showed clinical changes, as evaluated by self-scoring and by an experienced neurologist. In order to monitor the temporal dynamics of the dopaminergic effects, in three nuclei from three of the above patients, LFPs were recorded at rest (60–80 s) every 2–5 min from the off-state until the on-state, 33–50 min after levodopa administration.
LFPs were bipolarly captured from the 3389 electrode using the closely spaced pair of contacts 1–2, then preamplified, differentially amplified (100 000x) and filtered (band pass 2–1000 Hz) with an analogical amplifier (Signal Conditioner Cambridge 1902, Cambridge Electronic Design, Cambridge, UK). The output signal was digitized (Cambridge Micro 1402, Cambridge Electronic Design), with sampling rate 2500 Hz and 12 bit quantization with 5 V range. All further analysis was conducted off-line with Matlab software (version 6.5, The Mathworks, Natik, MA, USA). As a preprocessing step, each LFP recording was normalized by subtracting the mean and dividing by the standard deviation of the 600–1000 Hz band-pass filtered signal, which is supposed to contain only background noise. This procedure therefore imposes the same background noise on all recordings, thus reducing the variability between subjects and between pharmacological conditions (Foffani et al. 2003, 2005d; Priori et al. 2004).
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Bispectral analysis
Previous studies defined the LFP rhythms in the human basal ganglia by means of power spectral analysis. The power spectrum transforms second-order statistics (i.e. the variance) from the temporal to the frequency domain, assuming that spectral rhythms at different frequencies are statistically independent (i.e. not correlated). Non-linear correlation between spectral rhythms can be detected by means of bispectral analysis (Kim & Powers, 1979; Nikias & Mendel, 1993). The bispectrum (third-order spectrum) transforms third-order statistics (i.e. the skewness) from the temporal to the frequency domain, representing non-linear correlations between spectral components in a two-dimensional (2-D) frequency map, according to the following equation:
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(1)
where f1 and f2 are the frequencies of the spectral components, R(m, n) is the third-order cumulant as a function of the corresponding time lags m and n, and X(t) is the signal, i.e. a zero-mean stationary random process. Non-linear correlation between three spectral rhythms at frequencies f1, f2 and f1+f2 produces a peak in the bispectral frequency map at the intersection between f1 and f2 (Nikias & Raghuveer, 1988) (Fig. 1A). Non-linear correlation between two harmonically related spectral rhythms at frequencies f and 2f produces a peak in the bispectral frequency map at the intersection between f and itself, namely, on the diagonal (Fig. 1B). The bispectrum, similarly to the cross-spectrum in the second-order statistic, can be normalized. The normalized bispectrum is called bicoherence and combines the information from the bispectrum and the power spectrum. The following is a mathematical definition of the bicoherence:
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(2)
where B(f1, f2) is the bispectrum at frequencies (f1, f2) and P(fi) is the power spectrum at frequency fi (Mendel, 1991).
A, bispectral analysis of a simulated signal x characterized by 3 rhythms given by the following formula: x= cos(2F1t+1) + cos(2F2t+2) + cos(2F3t+3) + e(t), where F1= 10 Hz, F2= 25 Hz, F3= 10 + 25 = 35 Hz, t is time, the phases 1 and 2 are independently uniformly distributed between 0 and , 3=1+2 and e(t) is a non-gaussian random noise (Raghuveer & Nikias, 1985; Mendel, 1991). The central 2-D plot shows the bicoherence of the signal as a function of frequencies f1 (x-axis, in Hz) and f2 (y-axis, in Hz). The power spectrum of the signal is shown in the left plot and in the lower plot corresponding to the two frequency axes. The diagonal in the central plot defines the two regions of symmetry of the bicoherence: the peak below the diagonal is exactly the same as the peak above the diagonal. This example illustrates the presence of non-linear correlation between three rhythms at 10 Hz, 25 Hz (dashed arrows) and 35 Hz (continuous arrow). Accordingly, the bicoherence of the signal shows a peak at [10 Hz, 25 Hz] and, symmetrically, at [25 Hz, 10 Hz]. The value of the bicoherence peak is 0.2905. B, bispectral analysis of a simulated signal x characterized by 2 rhythms given by the following formula: x= cos(2F1t+1) + cos(2F2t+2) + e(t), where F1= 15 Hz, F2= 2F1= 15 + 15 = 30 Hz, t is time, the phase 1 is uniformly distributed between 0 and , 2= 21 and e(t) is a non-gaussian random noise (Raghuveer & Nikias, 1985; Mendel, 1991). This example illustrates the presence of harmonic non-linear correlation between two rhythms at 15 Hz (dashed arrows) and at 30 Hz (continuous arrow). Accordingly, the bicoherence of the signal shows a peak on the diagonal at [15 Hz, 15 Hz]. The value of the bicoherence peak is 0.80086. C, regions of interest (ROIs) in the bispectral plane. The diagonal represents a symmetry axis: ROIs in the lower part of the plane (squares with continuous border) are the same as ROIs in the upper part of the plane (squares with dotted border). ROIs on the diagonal are symmetrical, too. ROI 1 =[2–7 Hz, 2–7 Hz]; ROI 2 =[8–12 Hz, 8–12 Hz]; ROI 3 =[13–20 Hz, 13–20 Hz]; ROI 4 =[2–7 Hz, 8–12 Hz]; ROI 5 =[2–7 Hz, 13–20 Hz]; ROI 6 =[8–12 Hz, 13–20 Hz].
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Both the power spectrum P(f) and the bispectrum B(f1, f2) can be directly estimated from the Discrete Fourier Transform coefficients evaluated from the data, according to the following equations:
(3)
where X(k) is the discrete signal, Y(f) values are the Discrete Fourier Transform coefficients, N is the total number of samples and indicates the complex conjugate.
The bicoherence can be estimated by applying eqn (2) with the spectrum and bispectrum estimated with eqn (3). Two main quantitative measures were used in our study: the modulus of the bispectrum, |B(f1, f2)|, and the squared modulus of the bicoherence, |Bic(f1, f2)|2, which throughout this paper will be consistently called bispectrum and bicoherence for simplicity. The bicoherence has three important properties: (i) if the generating process is Gaussian, then the bicoherence is constant, which makes it a useful detector for the gaussianity of a given signal (Godfrey, 1965; Hinich, 1982); (ii) because the bicoherence is normalized by the power spectrum, it provides a measure of non-linear correlation between rhythms that is independent of the peaks in the power spectrum (Godfrey, 1965); (iii) because the asymptotic distribution of the estimated bicoherence is known, its statistical significance is easy to evaluate on a single signal. However, the estimate of the bicoherence is highly dependent on the number of samples per segment and on the total number of samples used in the analysis. We therefore used the bicoherence for quantifying the significance of the results at the single-nucleus level, and used the bispectrum to confirm the results at the population level.
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Parameter extraction and statistical analysis
The data were analysed in the classic EEG range of frequencies (2–40 Hz), consistent with our previous work (Priori et al. 2004). Signals were digitally low-pass filtered (cutoff at 40 Hz) and down-sampled at 125 Hz. To facilitate statistical analyses within and between nuclei, frequencies below 40 Hz were divided into four bands, as previously described (Priori et al. 2004): very-low frequencies (2–7 Hz), alpha (8–12 Hz), low-beta (13–20 Hz) and high-beta (20–35 Hz). Accordingly, we defined six regions of interest (ROIs) in the bicoherence/bispectrum frequency map that represent all the possible intersections of the spectral bands (Fig. 1C): ROI 1 =[2–7 Hz, 2–7 Hz], ROI 2 =[8–12 Hz, 8–12 Hz], ROI 3 =[13–20 Hz, 13–20 Hz], ROI 4 =[2–7 Hz, 8–12 Hz], ROI 5 =[2–7 Hz, 13–20 Hz], and ROI 6 =[8–12 Hz, 13–20 Hz]. Intersections corresponding to the high-beta band were not considered, because the generated harmonics would be within the range of the line noise (50 Hz). The direct non-parametric method (eqn (3)) was applied to estimate both spectra and bispectra, to be consistent with the methodology used in previous studies (Priori et al. 2004). For each nucleus, the LFP signal was divided into segments of 128 samples with no overlap and no tapering; each segment was detrended (i.e. the mean was subtracted); the spectrum and bispectrum were estimated in each segment and then averaged to obtain the spectrum and bispectrum of the whole signal (Nikias & Raghuveer, 1987; Mendel, 1991; Nikias & Mendel, 1993). The frequency resolution is 0.98 Hz.
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Data were analysed statistically at two levels, as previously introduced: at the single-nucleus level using the bicoherence, and at the population level using the bispectrum. At the single nucleus level, significant non-linear correlations between LFP rhythms were identified by the presence of significant bicoherence within the aforementioned ROIs. The bicoherence estimate has an asymptotical chi-squared distribution with 1/2 degrees of freedom, where , N0 is the number of samples per segment (i.e. 128), fs is the sampling frequency (i.e. 125 Hz), N is the total number of samples (about 60–80 s with 125 Hz of sampling frequency), when no tapering or overlapping procedures are applied to the data (Brillinger, 1965; Brillinger & Rosenblatt, 1967; Huber et al. 1971; Kim & Powers, 1979; Elgar & Guza, 1988; Nikias & Mendel, 1993). We therefore used the 95% confidence interval of the chi-squared distribution as the threshold level for the significance of the bicoherence (Huber et al. 1971; Kim & Powers, 1979; Elgar & Guza, 1988; Nikias & Mendel, 1993), given by:
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(4)
The significant threshold used was calculated from eqn (4) applied to our data for each recording, namely 0.12 ± 0.05 for STN LFPs recorded before levodopa and 0.10 ± 0.03 for STN LFPs recorded after levodopa. At the population level, the effect of levodopa on the non-linear synchronizations between LFP rhythms was quantified by submitting the maximum value of the bispectrum (in arbitrary units, AU) in each ROI and each clinical condition to a two-way repeated measures analysis of variance (ANOVA). Each nucleus was considered as a different sample and logarithmic transformation was applied to reduce the variance. The first main factor of the ANOVA was therefore the ROI, with six levels: ROIs 1–6. The second main factor was the clinical condition, with two levels: off (i.e. before levodopa) and on (i.e. after levodopa). Tukey's honestly significant difference test was used for post hoc comparisons. Results were considered significant at P < 0.05. Throughout the text values are means ± standard deviation.
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Results
Off condition
In the off clinical state, after overnight withdrawal of dopaminergic therapy, the power spectrum evidenced activity in the four frequency bands previously described (Priori et al. 2004), namely very-low frequencies (2–7 Hz), alpha band (8–12 Hz), low-beta band (13–20 Hz) and high-beta band (20–35 Hz) (Fig. 2A and Fig. 3A, left and lower plots). In the analysis seeking non-linear correlations between LFP rhythms, all nuclei and ROIs displayed significant bicoherence (ROI 1 =[2–7 Hz, 2–7 Hz]; ROI 2 =[8–12 Hz, 8–12 Hz]; ROI 3 =[13–20 Hz, 13–20 Hz]; ROI 4 =[2–7 Hz, 8–12 Hz]; ROI 5 =[2–7 Hz, 13–20 Hz]; ROI 6 =[8–12 Hz, 13–20 Hz]; Fig. 1C), suggesting that the off condition led to numerous non-linear correlations between LFP rhythms. More specifically, 11 nuclei (of 13) displayed significant bicoherence in ROI 1 (max bicoherence = 0.26 ± 0.17 at [3.46 ± 0.8 Hz, 3.46 ± 0.8 Hz]), five nuclei in ROI 2 (0.31 ± 0.23 at [9.2 ± 1.3 Hz, 9.2 ± 1.3 Hz]), 12 nuclei in ROI 3 (0.36 ± 0.19 at [14.9 ± 2.0 Hz, 14.9 ± 2.0 Hz]), two nuclei in ROI 4 (0.23 at [6.8 Hz, 10.7 Hz] and 0.31 at [4.9 Hz, 8.8 Hz]), two nuclei in ROI 5 (0.12 at [5.8 Hz, 17.6 Hz] and 0.28 at [5.8 Hz, 14.6 Hz]) and three nuclei in ROI 6 (0.11 ± 0.01 at [10.4 ± 1.1 Hz, 15.6 ± 1.7 Hz]). Of 13 nuclei, 11 displayed significant bicoherence in more than one ROI, and seven nuclei in three or more ROIs (see Fig. 2 for a representative example). Despite the frequency variability between nuclei, the mean bispectrum clearly showed the most consistent peaks of non-linear correlation (i.e. in ROIs 1, 2, 3) thus indicating exactly how bicoherence behaved in the population as a whole (Fig. 3A). The mean bispectral peak in ROI 1 suggests that the broad peak in the low-frequency band (2–7 Hz) of the power spectrum reflects complex activity resulting from non-linear correlations within this frequency band. The mean bispectral peak in ROI 2 suggests that alpha LFP rhythms (8–12 Hz) can produce harmonic non-linear correlation with the low-beta range (13–20 Hz) or even with the high-beta range (20–35 Hz). The mean bispectral peak in ROI 3 was remarkably consistent, suggesting that in the off state the LFP activity in the high-beta range (20–35 Hz) is, partially, a harmonic of the LFP activity in the low-beta range (13–20 Hz).
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The figure is organized as in Fig. 1A and B and shows a representative example of bicoherence in one nucleus in the off condition. The central 2-D plot shows the bicoherence of the LPF signal as a function of frequencies f1 (x-axis, in Hz) and f2 (y-axis, in Hz). The level-lines in the plot represent bicoherence values colour coded as indicated in the colour-bar on the right. Only bicoherence values greater than the threshold for significance (see methods) are shown. The power spectrum of the signal is presented in the left plot and in the lower plot corresponding to the two frequency axes. The diagonal in the central plot defines the two regions of symmetry of the bicoherence. The arrows indicate the harmonic non-linear correlation between the LFP rhythm in the low-beta range (13–20 Hz, dashed lines) and the LFP rhythm in the high-beta range (20–35 Hz, continuous line). This non-linear correlation is evidenced by the bicoherence peak in ROI 3 [13–20 Hz, 13–20 Hz]. In this nucleus significant bicoherence can also be observed in other ROIs. Most notably, a marked bicoherence peak is present in ROI 2 [8–12 Hz, 8–12 Hz], indicating a non-linear correlation between the LFP rhythm in the alpha range and its harmonic around 20 Hz.
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Mean bispectrum in 13 nuclei before (A) and after (B) levodopa administration. Each panel is organized similarly to Figs 1A and B and 2. The central 2-D plot shows the mean bispectrum of the LFP signals as a function of frequencies f1 (x-axis, in Hz) and f2 (y-axis, in Hz). The level lines in the plot represent bispectrum values colour coded as indicated in the colour bar on the right (log transform of the average bispectrum, expressed in log arbitrary units, log AU). The mean power spectrum is presented in the left plot and in the lower plot corresponding to the two frequency axes. The diagonal in the central plot defines the two regions of symmetry of the bispectrum. A, before levodopa administration, the arrows indicate the harmonic non-linear correlation between the LFP rhythm in the low-beta range (13–20 Hz, dashed lines) and the LFP rhythm in the high-beta range (20–35 Hz, continuous line). This non-linear correlation is evidenced by the bispectral peak in ROI 3 [13–20 Hz, 13–20 Hz]. Note that this bispectral peak appears broad due to the frequency variability between nuclei. Bispectral peaks are also present in other ROIs, most notably ROI 1 [2–7 Hz, 2–7 Hz], ROI 2 [8–12 Hz, 8–12 Hz] and ROI 4 [2–7 Hz, 8–12 Hz], suggesting the presence of non-linear correlations between different LFP rhythms in the off parkinsonian state. B, after levodopa administration, the mean bispectrum in ROI 1 is increased but no peaks appear in the other ROIs. The mean spectral peak that is evident in the high-beta range is therefore independent of activity at lower frequencies.
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The effect of levodopa
As previously described (Priori et al. 2004), after patients received levodopa the frequency patterns in the power spectrum changed (Fig. 3B, left and lower plots): the spectral power at very-low frequencies dramatically increased, while the spectral power in the low-beta band decreased; oscillations in the alpha range remained almost unchanged; spectral power in the high-beta range tended to decrease, but a low-amplitude peak persisted. Bispectral analysis showed that levodopa administration also altered the non-linear correlation between rhythms: significant bicoherence remained in ROI 1 (11 of 13 nuclei; max bicoherence = 0.53 ± 0.50 at [4.7 ± 1.0 Hz, 4.7 ± 1.0 Hz]) and in ROI 2 (6 nuclei; 0.16 ± 0.08 at [11.1 ± 1.2 Hz, 11.1 ± 1.2 Hz]), but only few nuclei exhibited significant bicoherence in ROI 3 (2 nuclei; 0.46 at [17.6 Hz, 17.6 Hz] and 0.36 at [17.6, 17.6]) and in ROI 4 (1 nucleus; 0.20 at [3.9 Hz, 8.8 Hz]) and no significant bicoherence was found in ROI 5 and 6. These dopamine-dependent changes were clearly detectable in the mean bispectrum (Fig. 3B). The two-way ANOVA (Fig. 4) showed a significant interaction factor (P < 0.000001), between ROIs (6 levels: 1, 2, 3, 4, 5, 6) and the clinical condition (2 levels: off, on). The post hoc test (Tukey's HSD) revealed that after levodopa administration the max bispectrum significantly increased in ROI 1 (2–7 Hz, 2–7 Hz; P= 0.0114) and significantly decreased in ROI 3 (13–20 Hz, 13–20 Hz; P= 0.0001) and in ROI 6 (8–12 Hz, 13–20 Hz; P= 0.0003). The results obtained with the analysis at the population level using the bispectrum therefore confirmed the results obtained with the analysis at the single-nucleus level using the bicoherence. In three nuclei from three patients, we also studied the temporal dynamics of the dopaminergic effects. The non-linear correlation between the low-beta rhythm and the high-beta rhythm was very stable in the off state and it abruptly disappeared with the on state (Fig. 5), paralleling the abrupt changes observed in the power spectrum (Priori et al. 2004). In synthesis, levodopa increased non-linear correlations within the low-frequency band and decreased (or left unchanged) all the other non-linear correlations, thereby increasing segregation between LFP rhythms operating at different frequencies.
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Results of the two-way repeated measures ANOVA, illustrating the interaction factor between region of interest (ROI) and the clinical condition. The average max bispectrum, calculated after logarithmic transformation (y-axis, in log arbitrary units, AU) is reported for each ROI (x-axis, 1–6), separating the data recorded before levodopa administration (circles, continuous line) from the data recorded after levodopa administration (squares, dotted line). Error bars correspond to 95% confidence intervals. The single star indicates significant difference at P < 0.05, the double stars indicate significant difference at P < 0.001 (Tukey's honestly significant difference test, comparing before versus after levodopa; n= 13 nuclei).
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Both panels show the temporal evolution of the bicoherence (higher plots) and of the corresponding power spectrum (middle plots) from the off clinical state before levodopa administration to the on clinical state after levodopa administration. Each plot represents 60–80 s of LFP signal recorded at the time instants indicated on the time arrow (lower plot). Time 0 represents the instant of levodopa administration. The bicoherence 2-D plots are organized as in Figure 2. The red arrows indicate the consistent bicoherence peak corresponding to the non-linear correlation between the low-beta rhythm and the high-beta rhythm (ROI3), which abruptly disappeared when the two patients transitioned from the off state to the on state, respectively 26 min (A) and 39 min (B) after levodopa administration.
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Discussion
Our main finding is that Parkinson's disease produces non-linear correlations between subthalamic LFP rhythms oscillating at different frequencies. After levodopa administration these non-linear correlations decrease. The most marked non-linear correlation was found between the low-beta rhythm (13–20 Hz) and the high-beta rhythm (20–35 Hz). More precisely, we provide evidence that in the off state the high-beta rhythm is distorted by a harmonic of the low-beta rhythm and that this distortion is virtually eliminated by levodopa administration. When patients were in the off state, non-linear correlations were also observed between the low-beta rhythm and other rhythms at very-low frequencies (2–7 Hz) or in the alpha range (8–12 Hz). After levodopa administration non-linear correlation within very-low frequencies increased, but non-linear correlations between rhythms all decreased or remained unchanged. These results support the hypothesis that the lack of dopamine determines a loss of segregation between rhythms operating at different frequencies in the basal ganglia circuit in patients with Parkinson's disease. This dopamine-dependent segregation between STN rhythms opens a new level of pathophysiological information processing in the human basal ganglia.
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Methodological considerations
The concept of non-linear correlation as used in this paper refers to non-linear phase coupling between LFP rhythms operating at different frequencies, as detected by applying higher-order spectral analysis – bicoherence and bispectrum – to single LFP signals. In parallel, we have employed the expression linear correlation to refer to the linear coupling between neural rhythms operating at the same frequency, frequently described in the literature by applying second-order spectral analysis – cross-correlation function and coherence – to pairs of neural signals. It is worth mentioning that the coupling between neural rhythms, either linear or non-linear, is often described in terms of synchronization (Varela et al. 2001; Gross et al. 2004; Schnitzler & Gross, 2005; Foffani et al. 2005b). However, the word synchronization is used in neuroscience literature with a variety of slightly different meanings (Salinas & Sejnowski, 2001). We have therefore preferred the term ‘correlation’, interpreted in its more rigorous and general sense, as absence of statistical independence between communication channels (Schneidman et al. 2003; Latham & Nirenberg, 2005; Narayanan et al. 2005).
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Patterns of non-linear correlation between LFP rhythms in our patients showed variability. Possible reasons for variability within and between studies using LFP recordings in humans include the time elapsed from electrode implant, the clinical features of the patients and possible biases in the localization of electrodes within the STN (Foffani et al. 2003, 2005c; Priori et al. 2004). In relation to the clinical conditions of the patients, even though the Parkinsonism substantially worsened after overnight withdrawal of levodopa and no patient was on long-acting agonists at the time of surgery, our experimental design leaves open the possibility that long-term drug effects influenced LFP activity. Nevertheless if they did we would probably have underestimated the non-linear correlations between LFP rhythms in the off state and the segregating effects of levodopa, variables that both yielded statistically significant results. More important, studies on polarity reversals, amplitude gradients between adjacent electrode contacts and topographical synchronization between LFP oscillations and single-neurone activity supported the hypothesis that LFP oscillations in the alpha and beta range originate in the subthalamic nucleus (Brown et al. 2001; Levy et al. 2002a; Kühn et al. 2004; Doyle et al. 2005; Fogelson et al. 2006), whereas the origin of LFP oscillations at very-low frequencies is still not well defined. The non-linear correlations we observed between the alpha, low-beta and high-beta LFP rhythms probably therefore reflect non-linear interactions within the subthalamic nucleus, whereas the strong correlations we observed at low frequencies might have been more broadly distributed in nearby brainstem regions. Another possibility we cannot exclude is that the correlation between LFP rhythms at least in part reflected the non-linear behaviour of a single oscillator. Nevertheless, the presence of non-linear correlation between LFP rhythms should be carefully considered to interpret correctly the results obtained with traditional spectral analysis. Finally, even though our results strongly suggest that independence between LFP rhythms is physiologically relevant, studies based on LFP recordings from DBS electrodes have been conducted exclusively in patients with movement disorders. Caution is therefore needed in extending these findings to physiological conditions.
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Multiple rhythms in the human subthalamic nucleus
In this study we show that in the parkinsonian off state the low-beta rhythm in the human STN harmonically distorts the high-beta rhythm; the distortion disappears after dopaminergic medication. This distortion is probably responsible for the small power decreases already observed in the high-beta rhythm after dopaminergic medication (Priori et al. 2004), for the correlation between the two beta rhythms in their dopamine-dependent power-changes (Priori et al. 2004) and for at least part of the subthalamo-pallido-cortical coherence overlapping from the low-beta band to the high-beta band (Brown et al. 2001; Williams et al. 2002; Foffani et al. 2005b; Fogelson et al. 2006). Previous studies of human subthalamic activity showed that LFP beta oscillations (frequency range 13–35 Hz) are tightly related to local single-unit activity (Levy et al. 2002a; Kühn et al. 2005), are coherent across multiple structures in the cortico-basal ganglia loop (Brown et al. 2001; Cassidy et al. 2002; Williams et al. 2002; Foffani et al. 2005b; Fogelson et al. 2006), and are typically decreased by dopaminergic medication (Brown et al. 2001; Levy et al. 2002a; Priori et al. 2004; Foffani et al. 2005a) and movement execution (Priori et al. 2002; Cassidy et al. 2002; Levy et al. 2002a; Foffani et al. 2002, 2004, 2005d; Kühn et al. 2004; Williams et al. 2005; Doyle et al. 2005). These observations implied that beta oscillations could be essentially ‘antikinetic’, directly contributing to the bradykinetic parkinsonian symptomatology (Brown, 2003). This pathological interpretation nevertheless seemingly contrasts with the widespread modulation of beta activity observed in the striatum of normal primates (Courtemanche et al. 2003), with the remarkably small differences observed in the movement-related amplitude modulation of beta activity in the human STN during the off and on states (Priori et al. 2002; Doyle et al. 2005; Foffani et al. 2005d; Alegre et al. 2005), and with the presence of (probably physiological) movement-related beta modulations in the external pallidum of patients with epilepsy (Sochurkova & Rektor, 2003). By separating the subthalamic beta activity into two rhythms – low-beta and high-beta (Priori et al. 2002, 2004; Foffani et al. 2004, 2005a,d; Fogelson et al. 2006) – our study may help to solve the discrepancy. Overall, our results suggest that the previously postulated pathological ‘antikinetic’ role of beta activity in the human STN (Brown, 2003) could be more specifically played by the low-beta rhythm, whereas the high-beta rhythm could be essentially physiological. The significant decrease in non-linear correlation between the high-beta rhythm and rhythms at lower frequencies in the on state supports the idea that under physiological conditions multiple rhythms operate independently in the human STN (Priori et al. 2004; Foffani et al. 2005d; Fogelson et al. 2006).
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Pathophysiological implications
The presence of multiple physiological LFP rhythms is in agreement with the idea that LFP rhythms not only reflect pathological linear correlation between single neurone pairs but also represent independent physiological channels of information. This duality in the pathophysiological interpretation of LFP rhythms (i.e. pathological or physiological) could shed new light on an old debate about information processing in the basal ganglia circuit: information sharing versus segregated parallel processing (Alexander & Crutcher, 1990; Percheron & Filion, 1991; Parent & Hazrati, 1993; Joel & Weiner, 1994; Bergman et al. 1998). The information sharing view (i.e. great overlap in incoming information to different cells at the basal ganglia output) is supported by the bulk of anatomical studies describing the convergence/divergence from the input to the output of the basal ganglia (Yelnik et al. 1984; Percheron et al. 1984; Parent & Hazrati, 1993; Kita & Kitai, 1994). The segregated parallel processing view is supported by neurophysiological studies showing the absence of linear correlation between neurones at the basal ganglia output in normal animals (DeLong et al. 1985; Hoover & Strick, 1993; Yoshida et al. 1993; Bergman et al. 1994; Nini et al. 1995; Bar-Gad et al. 2003). How can our results reconcile these conflicting views The wide convergence/divergence in the basal ganglia anatomical pathways could be necessary to sustain ‘normal’ LFP rhythms distributed in large ensembles of neurones (e.g. the ‘physiological’ high-beta rhythm), but not sufficient to induce correlated firing between pairs of neurones. The loss of dopamine in Parkinson's disease alters this equilibrium, generating pathological linear correlation between pairs of neurones (Bergman et al. 1994; Nini et al. 1995; Levy et al. 2000, 2002a; Raz et al. 2000, 2001; Heimer et al. 2002), inducing important alterations in the patterns of LFP rhythms (e.g. the pathological increase in the low-beta rhythm) and provoking the appearance of non-linear correlations between different LFP rhythms (e.g. the harmonic distortion of the low-beta rhythm onto the high-beta rhythm). In other words, our results suggest that Parkinson's disease determines a loss of segregation not only between different neurones, but also between different LFP rhythms. The present study therefore confirms and extends to the LFP level the idea that ‘the normal dopaminergic system supports segregation of the functional subcircuits of the basal ganglia, and that a breakdown of this independent processing is a hallmark of Parkinson's disease’ (Bergman et al. 1998). Intriguingly, the disruption of non-linear correlations between different LFP rhythms in the human STN could be critical not only for improving the clinical efficacy of dopaminergic medication, but also for understanding the mechanisms responsible for the action of deep brain stimulation. In conclusion, the dopamine-dependent non-linear correlations between LFP rhythms in the human STN open a non-linear dimension for rhythm-based pathophysiological models of basal ganglia processing, pointing out the importance of interactions between rhythms.
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Footnotes
S. Marceglia and G. Foffani contributed equally to this work.
References
Albin RL, Young AB & Penney JB (1995). The functional anatomy of disorders of the basal ganglia. Trends Neurosci 18, 63–64.
Alegre M, Alonso-Frech F, Rodriguez-Oroz MC, Guridi J, Zamarbide I, Valencia M, Manrique M Obeso JA & Artieda J (2005). Movement-related changes in the oscillatory activity in the human subthalamic nucleus: ipsilateral vs. contralateral movements. Eur J Neurosci 22, 2315–2324.
, http://www.100md.com
Alexander GE & Crutcher MD (1990). Functional architecture of basal ganglia circuits: neural substrates of parallel processing. Trends Neurosci 13, 266–271.
Baker SN, Olivier E & Lemon RN (1997). Coherent oscillations in monkey motor cortex and hand muscle EMG show task-dependent modulation. J Physiol 501, 225–241.
Bannister CF, Brosius KK, Sigl JC, Meyer BJ & Sebel PS (2001). The effect of bispectral index monitoring on anesthetic use and recovery in children anesthetized with sevoflurane in nitrous oxide. Anesth Analg 92, 877–881.
, 百拇医药
Bar-Gad I & Bergman H (2001). Stepping out of the box: information processing in the neural networks of the basal ganglia. Curr Opin Neurobiol 11, 689–695.
Bar-Gad I, Heimer G, Ritov Y & Bergman H (2003). Functional correlations between neighboring neurons in the primate globus pallidus are weak or nonexistent. J Neurosci 23, 4012–4016.
Barnett TP, Johnson LC, Naitoh P, Hicks N & Nute C (1971). Bispectrum analysis of electroencephalogram signals during waking and sleeping. Science 172, 401–402.
, http://www.100md.com
Bergman H, Feingold A, Nini A, Raz A, Slovin H, Abeles M et al. (1998). Physiological aspects of information processing in the basal ganglia of normal and parkinsonian primates. Trends Neurosci 21, 32–38.
Bergman H, Wichmann T, Karmon B & DeLong MR (1994). The primate subthalamic nucleus. II. Neuronal activity in the MPTP model of parkinsonism. J Neurophysiol 72, 507–520.
Brillinger DR (1965). An introduction to polyspectra. Ann Math Stat 36, 1351–1374.
, http://www.100md.com
Brillinger DR & Rosenblatt M (1967). Asymptotic theory of estimates k-th order spectra. Spectral Analysis of Time Series, ed. Harris B, pp. 153–188. Wiley, New York.
Brown P (2003). Oscillatory nature of human basal ganglia activity: relationship to the pathophysiology of Parkinson's disease. Mov Disord 18, 357–363.
Brown P, Oliviero A, Mazzone P, Insola A, Tonali P & Di Lazzaro V (2001). Dopamine dependency of oscillations between subthalamic nucleus and pallidum in Parkinson's disease. J Neurosci 21, 1033–1038.
, http://www.100md.com
Brown P & Williams D (2005). Basal ganglia local field potential activity: Character and functional significance in the human. Clin Neurophysiol 116, 2510–2519.
Cassidy M, Mazzone P, Oliviero A, Insola A, Tonali P, Di Lazzaro V et al. (2002). Movement-related changes in synchronization in the human basal ganglia. Brain 125, 1235–1246.
Courtemanche R, Fujii N & Graybiel AM (2003). Synchronous, focally modulated beta-band oscillations characterize local field potential activity in the striatum of awake behaving monkeys. J Neurosci 23, 11741–11752.
, http://www.100md.com
Creutzfeldt OD, Watanabe S & Lux HD (1966). Relations between EEG phenomena and potentials of single cortical cells. I. Evoked responses after thalamic and erpicortical stimulation. Electroencephalogr Clin Neurophysiol 20, 1–18.
DeLong MR, Crutcher MD & Georgopoulos AP (1985). Primate globus pallidus and subthalamic nucleus: functional organization. J Neurophysiol 53, 530–543.
Donoghue JP, Sanes JN, Hatsopoulos NG & Gaal G (1998). Neural discharge and local field potential oscillations in primate motor cortex during voluntary movements. J Neurophysiol 79, 159–173.
, 百拇医药
Doyle LM, Kühn AA, Hariz M, Kupsch A, Schneider GH & Brown P (2005). Levodopa-induced modulation of subthalamic beta oscillations during self-paced movements in patients with Parkinson's disease. Eur J Neurosci 21, 1403–1412.
Dumermuth G, Huber PJ, Kleiner B & Gasser T (1971). Analysis of the interrelations between frequency bands of the EEG by means of the bispectrum. A preliminary study. Electroencephalogr Clin Neurophysiol 31, 137–148.
, 百拇医药
Egidi M, Rampini P, Locatelli M, Farabola M, Priori A, Pesenti A et al. (2002). Visualization of the subthalamic nucleus: a multiple sequential image fusion (MuSIF) technique for direct stereotaxic localization and postoperative control. Neurol Sci 23, S71–S72.
Elgar S & Guza RT (1988). Statistics for bicoherence. IEEE Trans Acoust Speech Signal Process 36, 1667–1668.
Foffani G, Ardolino G, Egidi M, Caputo E & Priori A (2005a). Subthalamic oscillatory activities at beta or high frequency do not change after high-frequency DBS in Parkinson's disease. Brain Res Bull DOI: 10.1016/j.brainresbull.2005.M.012.
, 百拇医药
Foffani G, Ardolino G, Meda B, Egidi M, Rampini P, Caputo E et al. (2005b). Altered subthalamo-pallidal synchronisation in parkinsonian dyskinesias. J Neurol Neurosurg Psychiatry 76, 426–428.
Foffani G, Ardolino G, Rampini P, Tamma F, Caputo E, Egidi M et al. (2005c). Physiological recordings from electrodes implanted in the basal ganglia for deep brain stimulation in Parkinson's disease. The relevance of fast subthalamic rhythms. Acta Neurochir suppl 93, 97–99.
, http://www.100md.com
Foffani G, Bianchi AM, Baselli G & Priori A (2005d). Movement-related frequency modulation of beta oscillatory activity in the human subthalamic nucleus. J Physiol 568, 699–711.
Foffani G, Bianchi AM, Priori A & Baselli G (2004). Adaptive autoregressive identification with spectral power decomposition for studying movement-related activity in scalp EEG signals and basal ganglia local field potentials. J Neural Eng 1, 165–173.
, 百拇医药
Foffani G, Priori A, Egidi M, Rampini P, Tamma F, Caputo E et al. (2003). 300-Hz subthalamic oscillations in Parkinson's disease. Brain 126, 2153–2163.
Foffani G, Priori A, Rohr M, Pesenti A, Locatelli M, Caputo E et al. (2002). Event-related desynchronization (ERD) in the human subthalamus and internal globus pallidus. J Physiol 539P, 39P.
Fogelson N, Pogosyan A, Kühn AA, Kupsch A, Van Bruggen G, Speelman H et al. (2005). Reciprocal interactions between oscillatory activities of different frequencies in the subthalamic region of patients with Parkinson's disease. Eur J Neurosci 22, 257–266.
, 百拇医药
Fogelson N, Williams D, Tijssen M, Van Bruggen G, Speelman H & Brown P (2006). Different functional loops between cerebral cortex and the subthalamic area in Parkinson's disease. Cereb Cortex 16, 64–75.
Frost JD Jr (1968). EEG-intracellular potential relationships in isolated cerebral cortex. Electroencephalogr Clin Neurophysiol 24, 434–443.
Glass PS, Bloom M, Kearse L, Rosow C, Sebel P & Manberg P (1997). Bispectral analysis measures sedation and memory effects of propofol, midazolam, isoflurane, and alfentanil in healthy volunteers. Anesthesiology 86, 836–847.
, 百拇医药
Godfrey MD (1965). An exploratory study of the bi-spectrum of economic time series. Appl Stat 14, 48–69.
Goldberg JA, Rokni U, Boraud T, Vaadia E & Bergman H (2004). Spike synchronization in the cortex/basal-ganglia networks of Parkinsonian primates reflects global dynamics of the local field potentials. J Neurosci 24, 6003–6010.
Gross J, Schmitz F, Schnitzler I, Kessler K, Shapiro K, Hommel B et al. (2004). Modulation of long-range neural synchrony reflects temporal limitations of visual attention in humans. Proc Natl Acad Sci U S A 101, 13050–13055.
, 百拇医药
Heimer G, Bar-Gad I, Goldberg JA & Bergman H (2002). Dopamine replacement therapy reverses abnormal synchronization of pallidal neurons in the 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine primate model of parkinsonism. J Neurosci 22, 7850–7855.
Hinich MJ (1982). Testing for gaussianity and linearity of a stationary time series. J Time Series Anal 3, 169–176.
Hoover JE & Strick PL (1993). Multiple output channels in the basal ganglia. Science 259, 819–821.
, http://www.100md.com
Huber PJ, Kleiner B, Gasser T & Dumermuth G (1971). Statistical methods for investigating phase relations in stationary stochastic processes. IEEE Trans AU 19, 78–86.
Joel D & Weiner I (1994). The organization of the basal ganglia thalamocortical circuits: open interconnected rather than closed segregated. Neuroscience 63, 363–379.
Kearse LA Jr, Manberg P, Chamoun N, deBros F & Zaslavsky A (1994a). Bispectral analysis of the electroencephalogram correlates with patient movement to skin incision during propofol/nitrous oxide anesthesia. Anesthesiology 81, 1365–1370.
, 百拇医药
Kearse LA Jt, Manberg P, DeBros F, Chamoun N & Sinai V (1994b). Bispectral analysis of the electroencephalogram during induction of anesthesia may predict hemodynamic responses to laryngoscopy and intubation. Electroencephalogr Clin Neurophysiol 90, 194–200.
Kearse LA Jr, Rosow C, Zaslavsky A, Connors P, Dershwitz M & Denman W (1998). Bispectral analysis of the electroencephalogram predicts conscious processing of information during propofol sedation and hypnosis. Anesthesiology 88, 25–34.
, 百拇医药
Kim YC & Powers E (1979). Digital bispectral analysis and its application to nonlinear wave interactions. IEEE Trans Plasma Sci PS1, 120–131.
Kita H & Kitai ST (1994). The morphology of globus pallidus projection neurons in the rat: an intracellular staining study. Brain Res 636, 308–319.
Kühn AA, Trottenberg T, Kivi A, Kupsch A, Schneider GH & Brown P (2005). The relationship between local field potential and neuronal discharge in the subthalamic nucleus of patients with Parkinson's disease. Exp Neurol 194, 212–220.
, http://www.100md.com
Kühn AA, Williams D, Kupsch A, Limousin P, Hariz M, Schneider GH et al. (2004). Event-related beta desynchronization in human subthalamic nucleus correlates with motor performance. Brain 127, 735–746.
L.I.M.P.E. (2003). Guidelines for the treatment of Parkinson's disease. Neurol Sci 24, S203–S204.
Latham PE & Nirenberg S (2005). Synergy, redundancy, and independence in population codes, revisited. J Neurosci 25, 5196–5206.
, 百拇医药
Levy R, Ashby P, Hutchison WD, Lang AE, Lozano AM & Dostrovsky JO (2002a). Dependence of subthalamic nucleus oscillations on movement and dopamine in Parkinson's disease. Brain 125, 1196–1209.
Levy R, Hutchison WD, Lozano AM & Dostrovsky JO (2000). High-frequency synchronization of neuronal activity in the subthalamic nucleus of parkinsonian patients with limb tremor. J Neurosci 20, 7766–7775.
Levy R, Hutchison WD, Lozano AM & Dostrovsky JO (2002b). Synchronized neuronal discharge in the basal ganglia of parkinsonian patients is limited to oscillatory activity. J Neurosci 22, 2855–2861.
, http://www.100md.com
Magill PJ, Sharott A, Bevan MD, Brown P & Bolam JP (2004). Synchronous unit activity and local field potentials evoked in the subthalamic nucleus by cortical stimulation. J Neurophysiol 92, 700–714.
Marsden JF, Limousin-Dowsey P, Ashby P, Pollak P & Brown P (2001). Subthalamic nucleus, sensorimotor cortex and muscle interrelationships in Parkinson's disease. Brain 124, 378–388.
Mendel JM (1991). Tutorial on Higher-Order Statistics (Spectra) in signal processing and system theory: theoretical results and some applications. Proc IEEE 79, 278–305.
, 百拇医药
Murthy VN & Fetz EE (1992). Coherent 25- to 35-Hz oscillations in the sensorimotor cortex of awake behaving monkeys. Proc Natl Acad Sci U S A 89, 5670–5674.
Murthy VN & Fetz EE (1996a). Synchronization of neurons during local field potential oscillations in sensorimotor cortex of awake monkeys. J Neurophysiol 76, 3968–3982.
Murthy VN & Fetz EE (1996b). Oscillatory activity in sensorimotor cortex of awake monkeys: synchronization of local field potentials and relation to behavior. J Neurophysiol 76, 3949–3967.
, 百拇医药
Narayanan NS, Kimchi EY & Laubach M (2005). Redundancy and synergy of neuronal ensembles in motor cortex. J Neurosci 25, 4207–4216.
Nikias CL & Mendel JM (1993). Signal processing with higher-order spectra. IEEE Signal Proc Mag 10, 10–37.
Nikias CL & Raghuveer MR (1987). Bispectrum estimation: a digital signal processing framework. Proc IEEE 75, 809–891.
Nini A, Feingold A, Slovin H & Bergman H (1995). Neurons in the globus pallidus do not show correlated activity in the normal monkey, but phase-locked oscillations appear in the MPTP model of parkinsonism. J Neurophysiol 74, 1800–1805.
, 百拇医药
Parent A & Hazrati LN (1993). Anatomical aspects of information processing in primate basal ganglia. Trends Neurosci 16, 111–116.
Percheron G & Filion M (1991). Parallel processing in the basal ganglia: up to a point. Trends Neurosci 14, 55–59.
Percheron G, Yelnik J & Francois C (1984). A Golgi analysis of the primate globus pallidus. III. Spatial organization of the striato-pallidal complex. J Comp Neurol 227, 214–227.
, 百拇医药
Pfurtsheller G & Lopes da Silva FH (1999). Event-related EEG/EMG synchronizations and desynchronization: basic principles. Clin Neurophysiol 110, 1842–1857.
Pfurtsheller G, Stancak A Jr & Edlinger G (1997). On the existence of different types of central beta rhythms below 30 Hz. Electroenceph Clin Neurophysol 102, 316–325.
Priori A, Egidi M, Pesenti A, Rohr M, Rampini P, Locatelli M et al. (2003). Do intraoperative microrecordings improve subthalamic nucleus targeting in stereotactic neurosurgery for Parkinson's diseaseJ Neurosurg Sci 47, 56–60.
, 百拇医药
Priori A, Foffani G, Pesenti A, Bianchi A, Chiesa V, Baselli G et al. (2002). Movement-related modulation of neural activity in human basal ganglia and its L-DOPA dependency: recordings from deep brain stimulation electrodes in patients with Parkinson's disease. Neurol Sci 23, S101–S102.
Priori A, Foffani G, Pesenti A, Tamma F, Bianchi AM, Pellegrini M et al. (2004). Rhythm-specific pharmacological modulation of subthalamic activity in Parkinson's disease. Exp Neurol 189, 369–379.
, 百拇医药
Raghuveer MR & Nikias CL (1985). Bispectrum estimation: a parametric approach. IEEE Trans Acoust 33, 1213–1230.
Rampini PM, Locatelli M, Alimehmeti R, Tamma F, Caputo E, Priori A et al. (2003). Multiple sequential image-fusion and direct MRI localisation of the subthalamic nucleus for deep brain stimulation. J Neurosurg Sci 47, 33–39.
Raz A, Frechter-Mazar V, Feingold A, Abeles M, Vaadia E & Bergman H (2001). Activity of pallidal and striatal tonically active neurons is correlated in MPTP-treated monkeys but not in normal monkeys. J Neurosci 21, RC128.
, 百拇医药
Raz A, Vaadia E & Bergman H (2000). Firing patterns and correlations of spontaneous discharge of pallidal neurons in the normal and the tremulous 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine vervet model of parkinsonism. J Neurosci 20, 8559–8571.
Salinas E & Sejnowski TJ (2001). Correlated neuronal activity and the flow of neural information. Nat Rev Neurosci 2, 539–550.
Schanze T & Eckhorn R (1997). Phase correlation among rhythms present at different frequencies: spectral methods, application to microelectrode recordings from visual cortex and functional implications. Int J Psychophysiol 26, 171–189.
, 百拇医药
Schneidman E, Bialek W & Berry MJ 2nd (2003). Synergy, redundancy, and independence in population codes. J Neurosci 23, 11539–11553.
Schnitzler A & Gross J (2005). Normal and pathological oscillatory communication in the brain. Nat Rev Neurosci 6, 285–296.
Sebel PS, Bowles SM, Saini V & Chamoun N (1995). EEG bispectrum predicts movement during thiopental/isoflurane anesthesia. J Clin Monit 11, 83–91.
, 百拇医药
Sebel PS, Lang E, Rampil IJ, White PF, Cork R, Jopling M et al. (1997). A multicenter study of bispectral electroencephalogram analysis for monitoring anesthetic effect. Anesth Analg 84, 891–899.
Silberstein P, Kühn AA, Kupsch A, Trottenberg T, Krauss JK, Wohrle JC et al. (2003). Patterning of globus pallidus local field potentials differs between Parkinson's disease and dystonia. Brain 126, 2597–2608.
Sochurkova D & Rektor I (2003). Event-related desynchronization/synchronization in the putamen. An SEEG case study. Exp Brain Res 149, 401–404.
, http://www.100md.com
Varela F, Lachaux JP, Rodriguez E & Martinerie J (2001). The brainweb: phase synchronization and large-scale integration. Nat Rev Neurosci 2, 229–239.
Villa AE, Tetko IV, Dutoit P & Vantini G (2000). Non-linear cortico-cortical interactions modulated by cholinergic afferences from the rat basal forebrain. Biosystems 58, 219–228.
Wichmann T & DeLong MR (1996). Functional and pathophysiological models of the basal ganglia. Curr Opin Neurobiol 6, 751–758.
, 百拇医药
Wichmann T & DeLong MR (2003). Pathophysiology of Parkinson's disease: the MPTP primate model of the human disorder. Ann N Y Acad Sci 991, 199–213.
Williams D, Kühn A, Kupsch A, Tijssen M, Van Bruggen G, Speelman H et al. (2003). Behavioural cues are associated with modulations of synchronous oscillations in the human subthalamic nucleus. Brain 126, 1975–1985.
Williams D, Kühn A, Kupsch A, Tijssen M, Van Bruggen G, Speelman H et al. (2005). The relationship between oscillatory activity and motor reaction time in the parkinsonian subthalamic nucleus. Eur J Neurosci 21, 249–258.
, http://www.100md.com
Williams D, Tijssen M, Van Bruggen G, Bosch A, Insola A, Di Lazzaro V et al. (2002). Dopamine-dependent changes in the functional connectivity between basal ganglia and cerebral cortex in humans. Brain 125, 1558–1569.
Yelnik J, Percheron G & Francois C (1984). A Golgi analysis of the primate globus pallidus. II. Quantitative morphology and spatial orientation of dendritic arborizations. J Comp Neurol 227, 200–213.
Yoshida S, Nambu A & Jinnai K (1993). The distribution of the globus pallidus neurons with input from various cortical areas in the monkeys. Brain Res 14, 170–174., 百拇医药(S. Marceglia, G. Foffani, A. M. Bianchi,)
2 School of Biomedical Engineering, Science and Health Systems, Drexel University, Philadelphia, PA, USA
3 Fundación del Hospital Nacional de Parapléjicos para la Investigación y la Integración, SESCAM, Toledo, Spain
4 Dipartimento di Bioingegneria, Politecnico di Milano, Milano, Italy
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5 Dipartimento di Neurologia Clinica, Ospedale San Paolo, Milano, Italy
Abstract
The basic information architecture in the basal ganglia circuit is under debate. Whereas anatomical studies quantify extensive convergence/divergence patterns in the circuit, suggesting an information sharing scheme, neurophysiological studies report an absence of linear correlation between single neurones in normal animals, suggesting a segregated parallel processing scheme. In 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP)-treated monkeys and in parkinsonian patients single neurones become linearly correlated, thus leading to a loss of segregation between neurones. Here we propose a possible integrative solution to this debate, by extending the concept of functional segregation from the cellular level to the network level. To this end, we recorded local field potentials (LFPs) from electrodes implanted for deep brain stimulation (DBS) in the subthalamic nucleus (STN) of parkinsonian patients. By applying bispectral analysis, we found that in the absence of dopamine stimulation STN LFP rhythms became non-linearly correlated, thus leading to a loss of segregation between rhythms. Non-linear correlation was particularly consistent between the low-beta rhythm (13–20 Hz) and the high-beta rhythm (20–35 Hz). Levodopa administration significantly decreased these non-linear correlations, therefore increasing segregation between rhythms. These results suggest that the extensive convergence/divergence in the basal ganglia circuit is physiologically necessary to sustain LFP rhythms distributed in large ensembles of neurones, but is not sufficient to induce correlated firing between neurone pairs. Conversely, loss of dopamine generates pathological linear correlation between neurone pairs, alters the patterns within LFP rhythms, and induces non-linear correlation between LFP rhythms operating at different frequencies. The pathophysiology of information processing in the human basal ganglia therefore involves not only activities of individual rhythms, but also interactions between rhythms.
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Introduction
In the classic view of basal ganglia processing, single neurones represent the elementary channels of thalamo-cortico-basal ganglia communication (Albin et al. 1995; Wichmann & Delong, 1996; Wichmann & Delong, 2003). Under physiological conditions in animals, the firing activity between nearby neurones is virtually independent, suggesting that these channels are functionally segregated (Hoover & Strick, 1993; Nini et al. 1995; Bar-Gad et al. 2003) to maximize information transmission (Bar-Gad & Bergman, 2001). In 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) treated monkeys (Bergman et al. 1994; Nini et al. 1995; Raz et al. 2000, 2001; Heimer et al. 2002) and in parkinsonian patients (Levy et al. 2000, 2002a), the firing activity between neurones becomes linearly correlated, suggesting that the lack of dopamine results in a loss of segregation between communication channels (Bergman et al. 1998).
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Recent studies with local field potential (LFP) recordings from electrodes implanted for deep brain stimulation (DBS) in patients with Parkinson's disease are providing a new complementary scenario of information processing in the human basal ganglia (Brown & Williams, 2005). In this scenario, the elementary channels of thalamo-cortico-basal ganglia communication are defined at the network level by LFP rhythms operating at various frequencies (Brown et al. 2001; Marsden et al. 2001; Levy et al. 2002b; Priori et al. 2002, 2004; Cassidy et al. 2002; Williams et al. 2002, 2003, 2005; Silberstein et al. 2003; Kühn et al. 2004, 2005; Foffani et al. 2003, 2004, 2005a,b,c,d; Doyle et al. 2005; Alegre et al. 2005; Fogelson et al. 2005, 2006). LFPs reflect the synchronous presynaptic and postsynaptic activity of large neuronal populations and can detect focal network rhythms that are not necessarily observable in single neurones or neurone pairs (Creutzfeldt et al. 1966; Frost, 1968; Murthy & Fetz, 1992, 1996a,b; Baker et al. 1997; Donoghue et al. 1998; Magill et al. 2004; Goldberg et al. 2004). The presence of multiple LFP rhythms suggests ‘the existence at the network level of multiple functionally independent – but not necessarily spatially separated – subsystems operating at different frequencies’ (Priori et al. 2004). Hence ‘tuning to distinct frequencies may provide a means of marking and segregating related processing, over and above any anatomical segregation of processing streams’ (Fogelson et al. 2006). Little information is available on the segregation between LFP rhythms at different frequencies. This issue is critical for clarifying whether the segregation concept is pathophysiologically relevant for human basal ganglia information processing at the network level.
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In the same way as a loss of segregation at the cellular level induces linear correlation between neurones (i.e. linearly correlates neural signals oscillating at the same frequency), a loss of segregation at the network level presumably induces non-linear synchronization between LFP rhythms (i.e. non-linearly correlates neural signals oscillating at different frequencies). We therefore hypothesized that Parkinson's disease produces non-linear correlations between subthalamic LFP rhythms oscillating at different frequencies and that these non-linear correlations are reversed by dopaminergic medication. A useful approach for studying non-linear correlations is bispectral analysis, a procedure widely used in scalp EEG studies (Dumermuth et al. 1971; Barnett et al. 1971; Kearse et al. 1994a,b, 1998; Sebel et al. 1995, 1997; Glass et al. 1997; Pfurtsheller et al. 1997; Pfurtsheller & Lopes da Silva, 1999; Bannister et al. 2001) and already applied to investigate non-linear cortico-cortical correlations between LFP rhythms in mammals (Schanze & Eckhorn, 1997; Villa et al. 2000). We therefore tested our hypothesis by applying bispectral analysis to LFPs recorded from DBS electrodes implanted in the STN of patients with Parkinson's disease, searching for non-linear correlation between subthalamic rhythms before and after administration of levodopa.
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Methods
Patients and surgical procedure
The study sample consisted of nine patients (four men, five women) with idiopathic Parkinson's disease admitted to the Department of Neurological Science, IRCCS Ospedale Maggiore di Milano and fulfilling the specific inclusion criteria for DBS treatment (L.I.P.E., 2003). All of them were studied after informed consent and local ethical committee approval, and the study conformed with the Declaration of Helsinki. The average age was 55 years (range 44–69 years), years of disease history 12.3 (7–20 years), levodopa equivalent therapy presurgery 1535 mg day–1 (800–2800 mg day–1), after surgery 335 mg day–1 (75–800 mg day–1), Unified Parkinson's Disease Rating Scale (UPDRS) III (motor part) presurgery off therapy 43.7 (27–72.5), on therapy 5.2 (1–23.5), UPDRS III 12 months postsurgery off therapy on stimulation 9.0 (1.5–20), UPDRS IV (complications, A + B) presurgery 10.1 (5–14), and UPDRS IV 12 months postsurgery 2.3 (0–6). Patients were predominantly rigid-akinetic, with severe motor fluctuations not responsive to pharmacological treatment. No patient was on long-acting agonists at the time of surgery. One of the main inclusion criteria was a good response to levodopa, as measured by the UDPRS III.
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All patients were bilaterally implanted in the STN with macroelectrodes for DBS (model 3389 Medtronic, Minneapolis, MN, USA). The STN was targeted by direct visualization through a CT-MRI fusion-based technique before surgery, as extensively reported elsewhere (Egidi et al. 2002; Rampini et al. 2003). The STN position was estimated by matching the CT-MRI fused images with a digitized stereotactic atlas. During surgery, the implant position was assessed by microrecordings from explorative microelectrodes (Priori et al. 2003) and by clinical assessment of the effects induced by stimulation through the implanted macroelectrodes. The implanted 3389 Medtronic electrode has four cylindrical contacts (1.27 mm in diameter, 1.5 mm in length, placed 2 mm apart, centre-to-centre) denominated 0–1–2–3, beginning from the more caudal contact. According to neuroimaging and intraoperative clinical and neurophysiological tests, for all nuclei studied the position of contact 1 was consistent with placement within the STN. Four subjects were studied bilaterally, five only unilaterally, for a total of 13 nuclei.
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Local field potential (LFP) recordings
The LFP recording procedure is described in detail elsewhere (Priori et al. 2004). In brief, LFPs were recorded from the implanted electrodes 2 or 3 days after surgery, before the subcutaneous high-frequency stimulators were connected. LFPs were recorded at rest (60–80 s), 8–12 h after withdrawal of dopaminergic treatment both before (‘off’ therapy condition) and after (‘on’ therapy condition) patients received dopaminergic medication (100–200 mg of oral fast-acting levodopa – Madopar Dispersibile; Roche, Monza, Italy).
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After-medication LFPs were recorded at least 20 min after drug administration, when the patient showed clinical changes, as evaluated by self-scoring and by an experienced neurologist. In order to monitor the temporal dynamics of the dopaminergic effects, in three nuclei from three of the above patients, LFPs were recorded at rest (60–80 s) every 2–5 min from the off-state until the on-state, 33–50 min after levodopa administration.
LFPs were bipolarly captured from the 3389 electrode using the closely spaced pair of contacts 1–2, then preamplified, differentially amplified (100 000x) and filtered (band pass 2–1000 Hz) with an analogical amplifier (Signal Conditioner Cambridge 1902, Cambridge Electronic Design, Cambridge, UK). The output signal was digitized (Cambridge Micro 1402, Cambridge Electronic Design), with sampling rate 2500 Hz and 12 bit quantization with 5 V range. All further analysis was conducted off-line with Matlab software (version 6.5, The Mathworks, Natik, MA, USA). As a preprocessing step, each LFP recording was normalized by subtracting the mean and dividing by the standard deviation of the 600–1000 Hz band-pass filtered signal, which is supposed to contain only background noise. This procedure therefore imposes the same background noise on all recordings, thus reducing the variability between subjects and between pharmacological conditions (Foffani et al. 2003, 2005d; Priori et al. 2004).
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Bispectral analysis
Previous studies defined the LFP rhythms in the human basal ganglia by means of power spectral analysis. The power spectrum transforms second-order statistics (i.e. the variance) from the temporal to the frequency domain, assuming that spectral rhythms at different frequencies are statistically independent (i.e. not correlated). Non-linear correlation between spectral rhythms can be detected by means of bispectral analysis (Kim & Powers, 1979; Nikias & Mendel, 1993). The bispectrum (third-order spectrum) transforms third-order statistics (i.e. the skewness) from the temporal to the frequency domain, representing non-linear correlations between spectral components in a two-dimensional (2-D) frequency map, according to the following equation:
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(1)
where f1 and f2 are the frequencies of the spectral components, R(m, n) is the third-order cumulant as a function of the corresponding time lags m and n, and X(t) is the signal, i.e. a zero-mean stationary random process. Non-linear correlation between three spectral rhythms at frequencies f1, f2 and f1+f2 produces a peak in the bispectral frequency map at the intersection between f1 and f2 (Nikias & Raghuveer, 1988) (Fig. 1A). Non-linear correlation between two harmonically related spectral rhythms at frequencies f and 2f produces a peak in the bispectral frequency map at the intersection between f and itself, namely, on the diagonal (Fig. 1B). The bispectrum, similarly to the cross-spectrum in the second-order statistic, can be normalized. The normalized bispectrum is called bicoherence and combines the information from the bispectrum and the power spectrum. The following is a mathematical definition of the bicoherence:
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(2)
where B(f1, f2) is the bispectrum at frequencies (f1, f2) and P(fi) is the power spectrum at frequency fi (Mendel, 1991).
A, bispectral analysis of a simulated signal x characterized by 3 rhythms given by the following formula: x= cos(2F1t+1) + cos(2F2t+2) + cos(2F3t+3) + e(t), where F1= 10 Hz, F2= 25 Hz, F3= 10 + 25 = 35 Hz, t is time, the phases 1 and 2 are independently uniformly distributed between 0 and , 3=1+2 and e(t) is a non-gaussian random noise (Raghuveer & Nikias, 1985; Mendel, 1991). The central 2-D plot shows the bicoherence of the signal as a function of frequencies f1 (x-axis, in Hz) and f2 (y-axis, in Hz). The power spectrum of the signal is shown in the left plot and in the lower plot corresponding to the two frequency axes. The diagonal in the central plot defines the two regions of symmetry of the bicoherence: the peak below the diagonal is exactly the same as the peak above the diagonal. This example illustrates the presence of non-linear correlation between three rhythms at 10 Hz, 25 Hz (dashed arrows) and 35 Hz (continuous arrow). Accordingly, the bicoherence of the signal shows a peak at [10 Hz, 25 Hz] and, symmetrically, at [25 Hz, 10 Hz]. The value of the bicoherence peak is 0.2905. B, bispectral analysis of a simulated signal x characterized by 2 rhythms given by the following formula: x= cos(2F1t+1) + cos(2F2t+2) + e(t), where F1= 15 Hz, F2= 2F1= 15 + 15 = 30 Hz, t is time, the phase 1 is uniformly distributed between 0 and , 2= 21 and e(t) is a non-gaussian random noise (Raghuveer & Nikias, 1985; Mendel, 1991). This example illustrates the presence of harmonic non-linear correlation between two rhythms at 15 Hz (dashed arrows) and at 30 Hz (continuous arrow). Accordingly, the bicoherence of the signal shows a peak on the diagonal at [15 Hz, 15 Hz]. The value of the bicoherence peak is 0.80086. C, regions of interest (ROIs) in the bispectral plane. The diagonal represents a symmetry axis: ROIs in the lower part of the plane (squares with continuous border) are the same as ROIs in the upper part of the plane (squares with dotted border). ROIs on the diagonal are symmetrical, too. ROI 1 =[2–7 Hz, 2–7 Hz]; ROI 2 =[8–12 Hz, 8–12 Hz]; ROI 3 =[13–20 Hz, 13–20 Hz]; ROI 4 =[2–7 Hz, 8–12 Hz]; ROI 5 =[2–7 Hz, 13–20 Hz]; ROI 6 =[8–12 Hz, 13–20 Hz].
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Both the power spectrum P(f) and the bispectrum B(f1, f2) can be directly estimated from the Discrete Fourier Transform coefficients evaluated from the data, according to the following equations:
(3)
where X(k) is the discrete signal, Y(f) values are the Discrete Fourier Transform coefficients, N is the total number of samples and indicates the complex conjugate.
The bicoherence can be estimated by applying eqn (2) with the spectrum and bispectrum estimated with eqn (3). Two main quantitative measures were used in our study: the modulus of the bispectrum, |B(f1, f2)|, and the squared modulus of the bicoherence, |Bic(f1, f2)|2, which throughout this paper will be consistently called bispectrum and bicoherence for simplicity. The bicoherence has three important properties: (i) if the generating process is Gaussian, then the bicoherence is constant, which makes it a useful detector for the gaussianity of a given signal (Godfrey, 1965; Hinich, 1982); (ii) because the bicoherence is normalized by the power spectrum, it provides a measure of non-linear correlation between rhythms that is independent of the peaks in the power spectrum (Godfrey, 1965); (iii) because the asymptotic distribution of the estimated bicoherence is known, its statistical significance is easy to evaluate on a single signal. However, the estimate of the bicoherence is highly dependent on the number of samples per segment and on the total number of samples used in the analysis. We therefore used the bicoherence for quantifying the significance of the results at the single-nucleus level, and used the bispectrum to confirm the results at the population level.
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Parameter extraction and statistical analysis
The data were analysed in the classic EEG range of frequencies (2–40 Hz), consistent with our previous work (Priori et al. 2004). Signals were digitally low-pass filtered (cutoff at 40 Hz) and down-sampled at 125 Hz. To facilitate statistical analyses within and between nuclei, frequencies below 40 Hz were divided into four bands, as previously described (Priori et al. 2004): very-low frequencies (2–7 Hz), alpha (8–12 Hz), low-beta (13–20 Hz) and high-beta (20–35 Hz). Accordingly, we defined six regions of interest (ROIs) in the bicoherence/bispectrum frequency map that represent all the possible intersections of the spectral bands (Fig. 1C): ROI 1 =[2–7 Hz, 2–7 Hz], ROI 2 =[8–12 Hz, 8–12 Hz], ROI 3 =[13–20 Hz, 13–20 Hz], ROI 4 =[2–7 Hz, 8–12 Hz], ROI 5 =[2–7 Hz, 13–20 Hz], and ROI 6 =[8–12 Hz, 13–20 Hz]. Intersections corresponding to the high-beta band were not considered, because the generated harmonics would be within the range of the line noise (50 Hz). The direct non-parametric method (eqn (3)) was applied to estimate both spectra and bispectra, to be consistent with the methodology used in previous studies (Priori et al. 2004). For each nucleus, the LFP signal was divided into segments of 128 samples with no overlap and no tapering; each segment was detrended (i.e. the mean was subtracted); the spectrum and bispectrum were estimated in each segment and then averaged to obtain the spectrum and bispectrum of the whole signal (Nikias & Raghuveer, 1987; Mendel, 1991; Nikias & Mendel, 1993). The frequency resolution is 0.98 Hz.
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Data were analysed statistically at two levels, as previously introduced: at the single-nucleus level using the bicoherence, and at the population level using the bispectrum. At the single nucleus level, significant non-linear correlations between LFP rhythms were identified by the presence of significant bicoherence within the aforementioned ROIs. The bicoherence estimate has an asymptotical chi-squared distribution with 1/2 degrees of freedom, where , N0 is the number of samples per segment (i.e. 128), fs is the sampling frequency (i.e. 125 Hz), N is the total number of samples (about 60–80 s with 125 Hz of sampling frequency), when no tapering or overlapping procedures are applied to the data (Brillinger, 1965; Brillinger & Rosenblatt, 1967; Huber et al. 1971; Kim & Powers, 1979; Elgar & Guza, 1988; Nikias & Mendel, 1993). We therefore used the 95% confidence interval of the chi-squared distribution as the threshold level for the significance of the bicoherence (Huber et al. 1971; Kim & Powers, 1979; Elgar & Guza, 1988; Nikias & Mendel, 1993), given by:
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(4)
The significant threshold used was calculated from eqn (4) applied to our data for each recording, namely 0.12 ± 0.05 for STN LFPs recorded before levodopa and 0.10 ± 0.03 for STN LFPs recorded after levodopa. At the population level, the effect of levodopa on the non-linear synchronizations between LFP rhythms was quantified by submitting the maximum value of the bispectrum (in arbitrary units, AU) in each ROI and each clinical condition to a two-way repeated measures analysis of variance (ANOVA). Each nucleus was considered as a different sample and logarithmic transformation was applied to reduce the variance. The first main factor of the ANOVA was therefore the ROI, with six levels: ROIs 1–6. The second main factor was the clinical condition, with two levels: off (i.e. before levodopa) and on (i.e. after levodopa). Tukey's honestly significant difference test was used for post hoc comparisons. Results were considered significant at P < 0.05. Throughout the text values are means ± standard deviation.
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Results
Off condition
In the off clinical state, after overnight withdrawal of dopaminergic therapy, the power spectrum evidenced activity in the four frequency bands previously described (Priori et al. 2004), namely very-low frequencies (2–7 Hz), alpha band (8–12 Hz), low-beta band (13–20 Hz) and high-beta band (20–35 Hz) (Fig. 2A and Fig. 3A, left and lower plots). In the analysis seeking non-linear correlations between LFP rhythms, all nuclei and ROIs displayed significant bicoherence (ROI 1 =[2–7 Hz, 2–7 Hz]; ROI 2 =[8–12 Hz, 8–12 Hz]; ROI 3 =[13–20 Hz, 13–20 Hz]; ROI 4 =[2–7 Hz, 8–12 Hz]; ROI 5 =[2–7 Hz, 13–20 Hz]; ROI 6 =[8–12 Hz, 13–20 Hz]; Fig. 1C), suggesting that the off condition led to numerous non-linear correlations between LFP rhythms. More specifically, 11 nuclei (of 13) displayed significant bicoherence in ROI 1 (max bicoherence = 0.26 ± 0.17 at [3.46 ± 0.8 Hz, 3.46 ± 0.8 Hz]), five nuclei in ROI 2 (0.31 ± 0.23 at [9.2 ± 1.3 Hz, 9.2 ± 1.3 Hz]), 12 nuclei in ROI 3 (0.36 ± 0.19 at [14.9 ± 2.0 Hz, 14.9 ± 2.0 Hz]), two nuclei in ROI 4 (0.23 at [6.8 Hz, 10.7 Hz] and 0.31 at [4.9 Hz, 8.8 Hz]), two nuclei in ROI 5 (0.12 at [5.8 Hz, 17.6 Hz] and 0.28 at [5.8 Hz, 14.6 Hz]) and three nuclei in ROI 6 (0.11 ± 0.01 at [10.4 ± 1.1 Hz, 15.6 ± 1.7 Hz]). Of 13 nuclei, 11 displayed significant bicoherence in more than one ROI, and seven nuclei in three or more ROIs (see Fig. 2 for a representative example). Despite the frequency variability between nuclei, the mean bispectrum clearly showed the most consistent peaks of non-linear correlation (i.e. in ROIs 1, 2, 3) thus indicating exactly how bicoherence behaved in the population as a whole (Fig. 3A). The mean bispectral peak in ROI 1 suggests that the broad peak in the low-frequency band (2–7 Hz) of the power spectrum reflects complex activity resulting from non-linear correlations within this frequency band. The mean bispectral peak in ROI 2 suggests that alpha LFP rhythms (8–12 Hz) can produce harmonic non-linear correlation with the low-beta range (13–20 Hz) or even with the high-beta range (20–35 Hz). The mean bispectral peak in ROI 3 was remarkably consistent, suggesting that in the off state the LFP activity in the high-beta range (20–35 Hz) is, partially, a harmonic of the LFP activity in the low-beta range (13–20 Hz).
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The figure is organized as in Fig. 1A and B and shows a representative example of bicoherence in one nucleus in the off condition. The central 2-D plot shows the bicoherence of the LPF signal as a function of frequencies f1 (x-axis, in Hz) and f2 (y-axis, in Hz). The level-lines in the plot represent bicoherence values colour coded as indicated in the colour-bar on the right. Only bicoherence values greater than the threshold for significance (see methods) are shown. The power spectrum of the signal is presented in the left plot and in the lower plot corresponding to the two frequency axes. The diagonal in the central plot defines the two regions of symmetry of the bicoherence. The arrows indicate the harmonic non-linear correlation between the LFP rhythm in the low-beta range (13–20 Hz, dashed lines) and the LFP rhythm in the high-beta range (20–35 Hz, continuous line). This non-linear correlation is evidenced by the bicoherence peak in ROI 3 [13–20 Hz, 13–20 Hz]. In this nucleus significant bicoherence can also be observed in other ROIs. Most notably, a marked bicoherence peak is present in ROI 2 [8–12 Hz, 8–12 Hz], indicating a non-linear correlation between the LFP rhythm in the alpha range and its harmonic around 20 Hz.
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Mean bispectrum in 13 nuclei before (A) and after (B) levodopa administration. Each panel is organized similarly to Figs 1A and B and 2. The central 2-D plot shows the mean bispectrum of the LFP signals as a function of frequencies f1 (x-axis, in Hz) and f2 (y-axis, in Hz). The level lines in the plot represent bispectrum values colour coded as indicated in the colour bar on the right (log transform of the average bispectrum, expressed in log arbitrary units, log AU). The mean power spectrum is presented in the left plot and in the lower plot corresponding to the two frequency axes. The diagonal in the central plot defines the two regions of symmetry of the bispectrum. A, before levodopa administration, the arrows indicate the harmonic non-linear correlation between the LFP rhythm in the low-beta range (13–20 Hz, dashed lines) and the LFP rhythm in the high-beta range (20–35 Hz, continuous line). This non-linear correlation is evidenced by the bispectral peak in ROI 3 [13–20 Hz, 13–20 Hz]. Note that this bispectral peak appears broad due to the frequency variability between nuclei. Bispectral peaks are also present in other ROIs, most notably ROI 1 [2–7 Hz, 2–7 Hz], ROI 2 [8–12 Hz, 8–12 Hz] and ROI 4 [2–7 Hz, 8–12 Hz], suggesting the presence of non-linear correlations between different LFP rhythms in the off parkinsonian state. B, after levodopa administration, the mean bispectrum in ROI 1 is increased but no peaks appear in the other ROIs. The mean spectral peak that is evident in the high-beta range is therefore independent of activity at lower frequencies.
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The effect of levodopa
As previously described (Priori et al. 2004), after patients received levodopa the frequency patterns in the power spectrum changed (Fig. 3B, left and lower plots): the spectral power at very-low frequencies dramatically increased, while the spectral power in the low-beta band decreased; oscillations in the alpha range remained almost unchanged; spectral power in the high-beta range tended to decrease, but a low-amplitude peak persisted. Bispectral analysis showed that levodopa administration also altered the non-linear correlation between rhythms: significant bicoherence remained in ROI 1 (11 of 13 nuclei; max bicoherence = 0.53 ± 0.50 at [4.7 ± 1.0 Hz, 4.7 ± 1.0 Hz]) and in ROI 2 (6 nuclei; 0.16 ± 0.08 at [11.1 ± 1.2 Hz, 11.1 ± 1.2 Hz]), but only few nuclei exhibited significant bicoherence in ROI 3 (2 nuclei; 0.46 at [17.6 Hz, 17.6 Hz] and 0.36 at [17.6, 17.6]) and in ROI 4 (1 nucleus; 0.20 at [3.9 Hz, 8.8 Hz]) and no significant bicoherence was found in ROI 5 and 6. These dopamine-dependent changes were clearly detectable in the mean bispectrum (Fig. 3B). The two-way ANOVA (Fig. 4) showed a significant interaction factor (P < 0.000001), between ROIs (6 levels: 1, 2, 3, 4, 5, 6) and the clinical condition (2 levels: off, on). The post hoc test (Tukey's HSD) revealed that after levodopa administration the max bispectrum significantly increased in ROI 1 (2–7 Hz, 2–7 Hz; P= 0.0114) and significantly decreased in ROI 3 (13–20 Hz, 13–20 Hz; P= 0.0001) and in ROI 6 (8–12 Hz, 13–20 Hz; P= 0.0003). The results obtained with the analysis at the population level using the bispectrum therefore confirmed the results obtained with the analysis at the single-nucleus level using the bicoherence. In three nuclei from three patients, we also studied the temporal dynamics of the dopaminergic effects. The non-linear correlation between the low-beta rhythm and the high-beta rhythm was very stable in the off state and it abruptly disappeared with the on state (Fig. 5), paralleling the abrupt changes observed in the power spectrum (Priori et al. 2004). In synthesis, levodopa increased non-linear correlations within the low-frequency band and decreased (or left unchanged) all the other non-linear correlations, thereby increasing segregation between LFP rhythms operating at different frequencies.
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Results of the two-way repeated measures ANOVA, illustrating the interaction factor between region of interest (ROI) and the clinical condition. The average max bispectrum, calculated after logarithmic transformation (y-axis, in log arbitrary units, AU) is reported for each ROI (x-axis, 1–6), separating the data recorded before levodopa administration (circles, continuous line) from the data recorded after levodopa administration (squares, dotted line). Error bars correspond to 95% confidence intervals. The single star indicates significant difference at P < 0.05, the double stars indicate significant difference at P < 0.001 (Tukey's honestly significant difference test, comparing before versus after levodopa; n= 13 nuclei).
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Both panels show the temporal evolution of the bicoherence (higher plots) and of the corresponding power spectrum (middle plots) from the off clinical state before levodopa administration to the on clinical state after levodopa administration. Each plot represents 60–80 s of LFP signal recorded at the time instants indicated on the time arrow (lower plot). Time 0 represents the instant of levodopa administration. The bicoherence 2-D plots are organized as in Figure 2. The red arrows indicate the consistent bicoherence peak corresponding to the non-linear correlation between the low-beta rhythm and the high-beta rhythm (ROI3), which abruptly disappeared when the two patients transitioned from the off state to the on state, respectively 26 min (A) and 39 min (B) after levodopa administration.
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Discussion
Our main finding is that Parkinson's disease produces non-linear correlations between subthalamic LFP rhythms oscillating at different frequencies. After levodopa administration these non-linear correlations decrease. The most marked non-linear correlation was found between the low-beta rhythm (13–20 Hz) and the high-beta rhythm (20–35 Hz). More precisely, we provide evidence that in the off state the high-beta rhythm is distorted by a harmonic of the low-beta rhythm and that this distortion is virtually eliminated by levodopa administration. When patients were in the off state, non-linear correlations were also observed between the low-beta rhythm and other rhythms at very-low frequencies (2–7 Hz) or in the alpha range (8–12 Hz). After levodopa administration non-linear correlation within very-low frequencies increased, but non-linear correlations between rhythms all decreased or remained unchanged. These results support the hypothesis that the lack of dopamine determines a loss of segregation between rhythms operating at different frequencies in the basal ganglia circuit in patients with Parkinson's disease. This dopamine-dependent segregation between STN rhythms opens a new level of pathophysiological information processing in the human basal ganglia.
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Methodological considerations
The concept of non-linear correlation as used in this paper refers to non-linear phase coupling between LFP rhythms operating at different frequencies, as detected by applying higher-order spectral analysis – bicoherence and bispectrum – to single LFP signals. In parallel, we have employed the expression linear correlation to refer to the linear coupling between neural rhythms operating at the same frequency, frequently described in the literature by applying second-order spectral analysis – cross-correlation function and coherence – to pairs of neural signals. It is worth mentioning that the coupling between neural rhythms, either linear or non-linear, is often described in terms of synchronization (Varela et al. 2001; Gross et al. 2004; Schnitzler & Gross, 2005; Foffani et al. 2005b). However, the word synchronization is used in neuroscience literature with a variety of slightly different meanings (Salinas & Sejnowski, 2001). We have therefore preferred the term ‘correlation’, interpreted in its more rigorous and general sense, as absence of statistical independence between communication channels (Schneidman et al. 2003; Latham & Nirenberg, 2005; Narayanan et al. 2005).
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Patterns of non-linear correlation between LFP rhythms in our patients showed variability. Possible reasons for variability within and between studies using LFP recordings in humans include the time elapsed from electrode implant, the clinical features of the patients and possible biases in the localization of electrodes within the STN (Foffani et al. 2003, 2005c; Priori et al. 2004). In relation to the clinical conditions of the patients, even though the Parkinsonism substantially worsened after overnight withdrawal of levodopa and no patient was on long-acting agonists at the time of surgery, our experimental design leaves open the possibility that long-term drug effects influenced LFP activity. Nevertheless if they did we would probably have underestimated the non-linear correlations between LFP rhythms in the off state and the segregating effects of levodopa, variables that both yielded statistically significant results. More important, studies on polarity reversals, amplitude gradients between adjacent electrode contacts and topographical synchronization between LFP oscillations and single-neurone activity supported the hypothesis that LFP oscillations in the alpha and beta range originate in the subthalamic nucleus (Brown et al. 2001; Levy et al. 2002a; Kühn et al. 2004; Doyle et al. 2005; Fogelson et al. 2006), whereas the origin of LFP oscillations at very-low frequencies is still not well defined. The non-linear correlations we observed between the alpha, low-beta and high-beta LFP rhythms probably therefore reflect non-linear interactions within the subthalamic nucleus, whereas the strong correlations we observed at low frequencies might have been more broadly distributed in nearby brainstem regions. Another possibility we cannot exclude is that the correlation between LFP rhythms at least in part reflected the non-linear behaviour of a single oscillator. Nevertheless, the presence of non-linear correlation between LFP rhythms should be carefully considered to interpret correctly the results obtained with traditional spectral analysis. Finally, even though our results strongly suggest that independence between LFP rhythms is physiologically relevant, studies based on LFP recordings from DBS electrodes have been conducted exclusively in patients with movement disorders. Caution is therefore needed in extending these findings to physiological conditions.
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Multiple rhythms in the human subthalamic nucleus
In this study we show that in the parkinsonian off state the low-beta rhythm in the human STN harmonically distorts the high-beta rhythm; the distortion disappears after dopaminergic medication. This distortion is probably responsible for the small power decreases already observed in the high-beta rhythm after dopaminergic medication (Priori et al. 2004), for the correlation between the two beta rhythms in their dopamine-dependent power-changes (Priori et al. 2004) and for at least part of the subthalamo-pallido-cortical coherence overlapping from the low-beta band to the high-beta band (Brown et al. 2001; Williams et al. 2002; Foffani et al. 2005b; Fogelson et al. 2006). Previous studies of human subthalamic activity showed that LFP beta oscillations (frequency range 13–35 Hz) are tightly related to local single-unit activity (Levy et al. 2002a; Kühn et al. 2005), are coherent across multiple structures in the cortico-basal ganglia loop (Brown et al. 2001; Cassidy et al. 2002; Williams et al. 2002; Foffani et al. 2005b; Fogelson et al. 2006), and are typically decreased by dopaminergic medication (Brown et al. 2001; Levy et al. 2002a; Priori et al. 2004; Foffani et al. 2005a) and movement execution (Priori et al. 2002; Cassidy et al. 2002; Levy et al. 2002a; Foffani et al. 2002, 2004, 2005d; Kühn et al. 2004; Williams et al. 2005; Doyle et al. 2005). These observations implied that beta oscillations could be essentially ‘antikinetic’, directly contributing to the bradykinetic parkinsonian symptomatology (Brown, 2003). This pathological interpretation nevertheless seemingly contrasts with the widespread modulation of beta activity observed in the striatum of normal primates (Courtemanche et al. 2003), with the remarkably small differences observed in the movement-related amplitude modulation of beta activity in the human STN during the off and on states (Priori et al. 2002; Doyle et al. 2005; Foffani et al. 2005d; Alegre et al. 2005), and with the presence of (probably physiological) movement-related beta modulations in the external pallidum of patients with epilepsy (Sochurkova & Rektor, 2003). By separating the subthalamic beta activity into two rhythms – low-beta and high-beta (Priori et al. 2002, 2004; Foffani et al. 2004, 2005a,d; Fogelson et al. 2006) – our study may help to solve the discrepancy. Overall, our results suggest that the previously postulated pathological ‘antikinetic’ role of beta activity in the human STN (Brown, 2003) could be more specifically played by the low-beta rhythm, whereas the high-beta rhythm could be essentially physiological. The significant decrease in non-linear correlation between the high-beta rhythm and rhythms at lower frequencies in the on state supports the idea that under physiological conditions multiple rhythms operate independently in the human STN (Priori et al. 2004; Foffani et al. 2005d; Fogelson et al. 2006).
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Pathophysiological implications
The presence of multiple physiological LFP rhythms is in agreement with the idea that LFP rhythms not only reflect pathological linear correlation between single neurone pairs but also represent independent physiological channels of information. This duality in the pathophysiological interpretation of LFP rhythms (i.e. pathological or physiological) could shed new light on an old debate about information processing in the basal ganglia circuit: information sharing versus segregated parallel processing (Alexander & Crutcher, 1990; Percheron & Filion, 1991; Parent & Hazrati, 1993; Joel & Weiner, 1994; Bergman et al. 1998). The information sharing view (i.e. great overlap in incoming information to different cells at the basal ganglia output) is supported by the bulk of anatomical studies describing the convergence/divergence from the input to the output of the basal ganglia (Yelnik et al. 1984; Percheron et al. 1984; Parent & Hazrati, 1993; Kita & Kitai, 1994). The segregated parallel processing view is supported by neurophysiological studies showing the absence of linear correlation between neurones at the basal ganglia output in normal animals (DeLong et al. 1985; Hoover & Strick, 1993; Yoshida et al. 1993; Bergman et al. 1994; Nini et al. 1995; Bar-Gad et al. 2003). How can our results reconcile these conflicting views The wide convergence/divergence in the basal ganglia anatomical pathways could be necessary to sustain ‘normal’ LFP rhythms distributed in large ensembles of neurones (e.g. the ‘physiological’ high-beta rhythm), but not sufficient to induce correlated firing between pairs of neurones. The loss of dopamine in Parkinson's disease alters this equilibrium, generating pathological linear correlation between pairs of neurones (Bergman et al. 1994; Nini et al. 1995; Levy et al. 2000, 2002a; Raz et al. 2000, 2001; Heimer et al. 2002), inducing important alterations in the patterns of LFP rhythms (e.g. the pathological increase in the low-beta rhythm) and provoking the appearance of non-linear correlations between different LFP rhythms (e.g. the harmonic distortion of the low-beta rhythm onto the high-beta rhythm). In other words, our results suggest that Parkinson's disease determines a loss of segregation not only between different neurones, but also between different LFP rhythms. The present study therefore confirms and extends to the LFP level the idea that ‘the normal dopaminergic system supports segregation of the functional subcircuits of the basal ganglia, and that a breakdown of this independent processing is a hallmark of Parkinson's disease’ (Bergman et al. 1998). Intriguingly, the disruption of non-linear correlations between different LFP rhythms in the human STN could be critical not only for improving the clinical efficacy of dopaminergic medication, but also for understanding the mechanisms responsible for the action of deep brain stimulation. In conclusion, the dopamine-dependent non-linear correlations between LFP rhythms in the human STN open a non-linear dimension for rhythm-based pathophysiological models of basal ganglia processing, pointing out the importance of interactions between rhythms.
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Footnotes
S. Marceglia and G. Foffani contributed equally to this work.
References
Albin RL, Young AB & Penney JB (1995). The functional anatomy of disorders of the basal ganglia. Trends Neurosci 18, 63–64.
Alegre M, Alonso-Frech F, Rodriguez-Oroz MC, Guridi J, Zamarbide I, Valencia M, Manrique M Obeso JA & Artieda J (2005). Movement-related changes in the oscillatory activity in the human subthalamic nucleus: ipsilateral vs. contralateral movements. Eur J Neurosci 22, 2315–2324.
, http://www.100md.com
Alexander GE & Crutcher MD (1990). Functional architecture of basal ganglia circuits: neural substrates of parallel processing. Trends Neurosci 13, 266–271.
Baker SN, Olivier E & Lemon RN (1997). Coherent oscillations in monkey motor cortex and hand muscle EMG show task-dependent modulation. J Physiol 501, 225–241.
Bannister CF, Brosius KK, Sigl JC, Meyer BJ & Sebel PS (2001). The effect of bispectral index monitoring on anesthetic use and recovery in children anesthetized with sevoflurane in nitrous oxide. Anesth Analg 92, 877–881.
, 百拇医药
Bar-Gad I & Bergman H (2001). Stepping out of the box: information processing in the neural networks of the basal ganglia. Curr Opin Neurobiol 11, 689–695.
Bar-Gad I, Heimer G, Ritov Y & Bergman H (2003). Functional correlations between neighboring neurons in the primate globus pallidus are weak or nonexistent. J Neurosci 23, 4012–4016.
Barnett TP, Johnson LC, Naitoh P, Hicks N & Nute C (1971). Bispectrum analysis of electroencephalogram signals during waking and sleeping. Science 172, 401–402.
, http://www.100md.com
Bergman H, Feingold A, Nini A, Raz A, Slovin H, Abeles M et al. (1998). Physiological aspects of information processing in the basal ganglia of normal and parkinsonian primates. Trends Neurosci 21, 32–38.
Bergman H, Wichmann T, Karmon B & DeLong MR (1994). The primate subthalamic nucleus. II. Neuronal activity in the MPTP model of parkinsonism. J Neurophysiol 72, 507–520.
Brillinger DR (1965). An introduction to polyspectra. Ann Math Stat 36, 1351–1374.
, http://www.100md.com
Brillinger DR & Rosenblatt M (1967). Asymptotic theory of estimates k-th order spectra. Spectral Analysis of Time Series, ed. Harris B, pp. 153–188. Wiley, New York.
Brown P (2003). Oscillatory nature of human basal ganglia activity: relationship to the pathophysiology of Parkinson's disease. Mov Disord 18, 357–363.
Brown P, Oliviero A, Mazzone P, Insola A, Tonali P & Di Lazzaro V (2001). Dopamine dependency of oscillations between subthalamic nucleus and pallidum in Parkinson's disease. J Neurosci 21, 1033–1038.
, http://www.100md.com
Brown P & Williams D (2005). Basal ganglia local field potential activity: Character and functional significance in the human. Clin Neurophysiol 116, 2510–2519.
Cassidy M, Mazzone P, Oliviero A, Insola A, Tonali P, Di Lazzaro V et al. (2002). Movement-related changes in synchronization in the human basal ganglia. Brain 125, 1235–1246.
Courtemanche R, Fujii N & Graybiel AM (2003). Synchronous, focally modulated beta-band oscillations characterize local field potential activity in the striatum of awake behaving monkeys. J Neurosci 23, 11741–11752.
, http://www.100md.com
Creutzfeldt OD, Watanabe S & Lux HD (1966). Relations between EEG phenomena and potentials of single cortical cells. I. Evoked responses after thalamic and erpicortical stimulation. Electroencephalogr Clin Neurophysiol 20, 1–18.
DeLong MR, Crutcher MD & Georgopoulos AP (1985). Primate globus pallidus and subthalamic nucleus: functional organization. J Neurophysiol 53, 530–543.
Donoghue JP, Sanes JN, Hatsopoulos NG & Gaal G (1998). Neural discharge and local field potential oscillations in primate motor cortex during voluntary movements. J Neurophysiol 79, 159–173.
, 百拇医药
Doyle LM, Kühn AA, Hariz M, Kupsch A, Schneider GH & Brown P (2005). Levodopa-induced modulation of subthalamic beta oscillations during self-paced movements in patients with Parkinson's disease. Eur J Neurosci 21, 1403–1412.
Dumermuth G, Huber PJ, Kleiner B & Gasser T (1971). Analysis of the interrelations between frequency bands of the EEG by means of the bispectrum. A preliminary study. Electroencephalogr Clin Neurophysiol 31, 137–148.
, 百拇医药
Egidi M, Rampini P, Locatelli M, Farabola M, Priori A, Pesenti A et al. (2002). Visualization of the subthalamic nucleus: a multiple sequential image fusion (MuSIF) technique for direct stereotaxic localization and postoperative control. Neurol Sci 23, S71–S72.
Elgar S & Guza RT (1988). Statistics for bicoherence. IEEE Trans Acoust Speech Signal Process 36, 1667–1668.
Foffani G, Ardolino G, Egidi M, Caputo E & Priori A (2005a). Subthalamic oscillatory activities at beta or high frequency do not change after high-frequency DBS in Parkinson's disease. Brain Res Bull DOI: 10.1016/j.brainresbull.2005.M.012.
, 百拇医药
Foffani G, Ardolino G, Meda B, Egidi M, Rampini P, Caputo E et al. (2005b). Altered subthalamo-pallidal synchronisation in parkinsonian dyskinesias. J Neurol Neurosurg Psychiatry 76, 426–428.
Foffani G, Ardolino G, Rampini P, Tamma F, Caputo E, Egidi M et al. (2005c). Physiological recordings from electrodes implanted in the basal ganglia for deep brain stimulation in Parkinson's disease. The relevance of fast subthalamic rhythms. Acta Neurochir suppl 93, 97–99.
, http://www.100md.com
Foffani G, Bianchi AM, Baselli G & Priori A (2005d). Movement-related frequency modulation of beta oscillatory activity in the human subthalamic nucleus. J Physiol 568, 699–711.
Foffani G, Bianchi AM, Priori A & Baselli G (2004). Adaptive autoregressive identification with spectral power decomposition for studying movement-related activity in scalp EEG signals and basal ganglia local field potentials. J Neural Eng 1, 165–173.
, 百拇医药
Foffani G, Priori A, Egidi M, Rampini P, Tamma F, Caputo E et al. (2003). 300-Hz subthalamic oscillations in Parkinson's disease. Brain 126, 2153–2163.
Foffani G, Priori A, Rohr M, Pesenti A, Locatelli M, Caputo E et al. (2002). Event-related desynchronization (ERD) in the human subthalamus and internal globus pallidus. J Physiol 539P, 39P.
Fogelson N, Pogosyan A, Kühn AA, Kupsch A, Van Bruggen G, Speelman H et al. (2005). Reciprocal interactions between oscillatory activities of different frequencies in the subthalamic region of patients with Parkinson's disease. Eur J Neurosci 22, 257–266.
, 百拇医药
Fogelson N, Williams D, Tijssen M, Van Bruggen G, Speelman H & Brown P (2006). Different functional loops between cerebral cortex and the subthalamic area in Parkinson's disease. Cereb Cortex 16, 64–75.
Frost JD Jr (1968). EEG-intracellular potential relationships in isolated cerebral cortex. Electroencephalogr Clin Neurophysiol 24, 434–443.
Glass PS, Bloom M, Kearse L, Rosow C, Sebel P & Manberg P (1997). Bispectral analysis measures sedation and memory effects of propofol, midazolam, isoflurane, and alfentanil in healthy volunteers. Anesthesiology 86, 836–847.
, 百拇医药
Godfrey MD (1965). An exploratory study of the bi-spectrum of economic time series. Appl Stat 14, 48–69.
Goldberg JA, Rokni U, Boraud T, Vaadia E & Bergman H (2004). Spike synchronization in the cortex/basal-ganglia networks of Parkinsonian primates reflects global dynamics of the local field potentials. J Neurosci 24, 6003–6010.
Gross J, Schmitz F, Schnitzler I, Kessler K, Shapiro K, Hommel B et al. (2004). Modulation of long-range neural synchrony reflects temporal limitations of visual attention in humans. Proc Natl Acad Sci U S A 101, 13050–13055.
, 百拇医药
Heimer G, Bar-Gad I, Goldberg JA & Bergman H (2002). Dopamine replacement therapy reverses abnormal synchronization of pallidal neurons in the 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine primate model of parkinsonism. J Neurosci 22, 7850–7855.
Hinich MJ (1982). Testing for gaussianity and linearity of a stationary time series. J Time Series Anal 3, 169–176.
Hoover JE & Strick PL (1993). Multiple output channels in the basal ganglia. Science 259, 819–821.
, http://www.100md.com
Huber PJ, Kleiner B, Gasser T & Dumermuth G (1971). Statistical methods for investigating phase relations in stationary stochastic processes. IEEE Trans AU 19, 78–86.
Joel D & Weiner I (1994). The organization of the basal ganglia thalamocortical circuits: open interconnected rather than closed segregated. Neuroscience 63, 363–379.
Kearse LA Jr, Manberg P, Chamoun N, deBros F & Zaslavsky A (1994a). Bispectral analysis of the electroencephalogram correlates with patient movement to skin incision during propofol/nitrous oxide anesthesia. Anesthesiology 81, 1365–1370.
, 百拇医药
Kearse LA Jt, Manberg P, DeBros F, Chamoun N & Sinai V (1994b). Bispectral analysis of the electroencephalogram during induction of anesthesia may predict hemodynamic responses to laryngoscopy and intubation. Electroencephalogr Clin Neurophysiol 90, 194–200.
Kearse LA Jr, Rosow C, Zaslavsky A, Connors P, Dershwitz M & Denman W (1998). Bispectral analysis of the electroencephalogram predicts conscious processing of information during propofol sedation and hypnosis. Anesthesiology 88, 25–34.
, 百拇医药
Kim YC & Powers E (1979). Digital bispectral analysis and its application to nonlinear wave interactions. IEEE Trans Plasma Sci PS1, 120–131.
Kita H & Kitai ST (1994). The morphology of globus pallidus projection neurons in the rat: an intracellular staining study. Brain Res 636, 308–319.
Kühn AA, Trottenberg T, Kivi A, Kupsch A, Schneider GH & Brown P (2005). The relationship between local field potential and neuronal discharge in the subthalamic nucleus of patients with Parkinson's disease. Exp Neurol 194, 212–220.
, http://www.100md.com
Kühn AA, Williams D, Kupsch A, Limousin P, Hariz M, Schneider GH et al. (2004). Event-related beta desynchronization in human subthalamic nucleus correlates with motor performance. Brain 127, 735–746.
L.I.M.P.E. (2003). Guidelines for the treatment of Parkinson's disease. Neurol Sci 24, S203–S204.
Latham PE & Nirenberg S (2005). Synergy, redundancy, and independence in population codes, revisited. J Neurosci 25, 5196–5206.
, 百拇医药
Levy R, Ashby P, Hutchison WD, Lang AE, Lozano AM & Dostrovsky JO (2002a). Dependence of subthalamic nucleus oscillations on movement and dopamine in Parkinson's disease. Brain 125, 1196–1209.
Levy R, Hutchison WD, Lozano AM & Dostrovsky JO (2000). High-frequency synchronization of neuronal activity in the subthalamic nucleus of parkinsonian patients with limb tremor. J Neurosci 20, 7766–7775.
Levy R, Hutchison WD, Lozano AM & Dostrovsky JO (2002b). Synchronized neuronal discharge in the basal ganglia of parkinsonian patients is limited to oscillatory activity. J Neurosci 22, 2855–2861.
, http://www.100md.com
Magill PJ, Sharott A, Bevan MD, Brown P & Bolam JP (2004). Synchronous unit activity and local field potentials evoked in the subthalamic nucleus by cortical stimulation. J Neurophysiol 92, 700–714.
Marsden JF, Limousin-Dowsey P, Ashby P, Pollak P & Brown P (2001). Subthalamic nucleus, sensorimotor cortex and muscle interrelationships in Parkinson's disease. Brain 124, 378–388.
Mendel JM (1991). Tutorial on Higher-Order Statistics (Spectra) in signal processing and system theory: theoretical results and some applications. Proc IEEE 79, 278–305.
, 百拇医药
Murthy VN & Fetz EE (1992). Coherent 25- to 35-Hz oscillations in the sensorimotor cortex of awake behaving monkeys. Proc Natl Acad Sci U S A 89, 5670–5674.
Murthy VN & Fetz EE (1996a). Synchronization of neurons during local field potential oscillations in sensorimotor cortex of awake monkeys. J Neurophysiol 76, 3968–3982.
Murthy VN & Fetz EE (1996b). Oscillatory activity in sensorimotor cortex of awake monkeys: synchronization of local field potentials and relation to behavior. J Neurophysiol 76, 3949–3967.
, 百拇医药
Narayanan NS, Kimchi EY & Laubach M (2005). Redundancy and synergy of neuronal ensembles in motor cortex. J Neurosci 25, 4207–4216.
Nikias CL & Mendel JM (1993). Signal processing with higher-order spectra. IEEE Signal Proc Mag 10, 10–37.
Nikias CL & Raghuveer MR (1987). Bispectrum estimation: a digital signal processing framework. Proc IEEE 75, 809–891.
Nini A, Feingold A, Slovin H & Bergman H (1995). Neurons in the globus pallidus do not show correlated activity in the normal monkey, but phase-locked oscillations appear in the MPTP model of parkinsonism. J Neurophysiol 74, 1800–1805.
, 百拇医药
Parent A & Hazrati LN (1993). Anatomical aspects of information processing in primate basal ganglia. Trends Neurosci 16, 111–116.
Percheron G & Filion M (1991). Parallel processing in the basal ganglia: up to a point. Trends Neurosci 14, 55–59.
Percheron G, Yelnik J & Francois C (1984). A Golgi analysis of the primate globus pallidus. III. Spatial organization of the striato-pallidal complex. J Comp Neurol 227, 214–227.
, 百拇医药
Pfurtsheller G & Lopes da Silva FH (1999). Event-related EEG/EMG synchronizations and desynchronization: basic principles. Clin Neurophysiol 110, 1842–1857.
Pfurtsheller G, Stancak A Jr & Edlinger G (1997). On the existence of different types of central beta rhythms below 30 Hz. Electroenceph Clin Neurophysol 102, 316–325.
Priori A, Egidi M, Pesenti A, Rohr M, Rampini P, Locatelli M et al. (2003). Do intraoperative microrecordings improve subthalamic nucleus targeting in stereotactic neurosurgery for Parkinson's diseaseJ Neurosurg Sci 47, 56–60.
, 百拇医药
Priori A, Foffani G, Pesenti A, Bianchi A, Chiesa V, Baselli G et al. (2002). Movement-related modulation of neural activity in human basal ganglia and its L-DOPA dependency: recordings from deep brain stimulation electrodes in patients with Parkinson's disease. Neurol Sci 23, S101–S102.
Priori A, Foffani G, Pesenti A, Tamma F, Bianchi AM, Pellegrini M et al. (2004). Rhythm-specific pharmacological modulation of subthalamic activity in Parkinson's disease. Exp Neurol 189, 369–379.
, 百拇医药
Raghuveer MR & Nikias CL (1985). Bispectrum estimation: a parametric approach. IEEE Trans Acoust 33, 1213–1230.
Rampini PM, Locatelli M, Alimehmeti R, Tamma F, Caputo E, Priori A et al. (2003). Multiple sequential image-fusion and direct MRI localisation of the subthalamic nucleus for deep brain stimulation. J Neurosurg Sci 47, 33–39.
Raz A, Frechter-Mazar V, Feingold A, Abeles M, Vaadia E & Bergman H (2001). Activity of pallidal and striatal tonically active neurons is correlated in MPTP-treated monkeys but not in normal monkeys. J Neurosci 21, RC128.
, 百拇医药
Raz A, Vaadia E & Bergman H (2000). Firing patterns and correlations of spontaneous discharge of pallidal neurons in the normal and the tremulous 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine vervet model of parkinsonism. J Neurosci 20, 8559–8571.
Salinas E & Sejnowski TJ (2001). Correlated neuronal activity and the flow of neural information. Nat Rev Neurosci 2, 539–550.
Schanze T & Eckhorn R (1997). Phase correlation among rhythms present at different frequencies: spectral methods, application to microelectrode recordings from visual cortex and functional implications. Int J Psychophysiol 26, 171–189.
, 百拇医药
Schneidman E, Bialek W & Berry MJ 2nd (2003). Synergy, redundancy, and independence in population codes. J Neurosci 23, 11539–11553.
Schnitzler A & Gross J (2005). Normal and pathological oscillatory communication in the brain. Nat Rev Neurosci 6, 285–296.
Sebel PS, Bowles SM, Saini V & Chamoun N (1995). EEG bispectrum predicts movement during thiopental/isoflurane anesthesia. J Clin Monit 11, 83–91.
, 百拇医药
Sebel PS, Lang E, Rampil IJ, White PF, Cork R, Jopling M et al. (1997). A multicenter study of bispectral electroencephalogram analysis for monitoring anesthetic effect. Anesth Analg 84, 891–899.
Silberstein P, Kühn AA, Kupsch A, Trottenberg T, Krauss JK, Wohrle JC et al. (2003). Patterning of globus pallidus local field potentials differs between Parkinson's disease and dystonia. Brain 126, 2597–2608.
Sochurkova D & Rektor I (2003). Event-related desynchronization/synchronization in the putamen. An SEEG case study. Exp Brain Res 149, 401–404.
, http://www.100md.com
Varela F, Lachaux JP, Rodriguez E & Martinerie J (2001). The brainweb: phase synchronization and large-scale integration. Nat Rev Neurosci 2, 229–239.
Villa AE, Tetko IV, Dutoit P & Vantini G (2000). Non-linear cortico-cortical interactions modulated by cholinergic afferences from the rat basal forebrain. Biosystems 58, 219–228.
Wichmann T & DeLong MR (1996). Functional and pathophysiological models of the basal ganglia. Curr Opin Neurobiol 6, 751–758.
, 百拇医药
Wichmann T & DeLong MR (2003). Pathophysiology of Parkinson's disease: the MPTP primate model of the human disorder. Ann N Y Acad Sci 991, 199–213.
Williams D, Kühn A, Kupsch A, Tijssen M, Van Bruggen G, Speelman H et al. (2003). Behavioural cues are associated with modulations of synchronous oscillations in the human subthalamic nucleus. Brain 126, 1975–1985.
Williams D, Kühn A, Kupsch A, Tijssen M, Van Bruggen G, Speelman H et al. (2005). The relationship between oscillatory activity and motor reaction time in the parkinsonian subthalamic nucleus. Eur J Neurosci 21, 249–258.
, http://www.100md.com
Williams D, Tijssen M, Van Bruggen G, Bosch A, Insola A, Di Lazzaro V et al. (2002). Dopamine-dependent changes in the functional connectivity between basal ganglia and cerebral cortex in humans. Brain 125, 1558–1569.
Yelnik J, Percheron G & Francois C (1984). A Golgi analysis of the primate globus pallidus. II. Quantitative morphology and spatial orientation of dendritic arborizations. J Comp Neurol 227, 200–213.
Yoshida S, Nambu A & Jinnai K (1993). The distribution of the globus pallidus neurons with input from various cortical areas in the monkeys. Brain Res 14, 170–174., 百拇医药(S. Marceglia, G. Foffani, A. M. Bianchi,)