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1 Dipartimento di Scienze Neurologiche, Università di Milano, Fondazione IRCCS Ospedale Policlinico, Milano, Italy
2 School of Biomedical Engineering, Science and Health Systems, Drexel University, Philadelphia, PA, USA
3 Dipartimento di Bioingegeneria, Politecnico di Milano, Milano, Italy
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Abstract |
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(Received 3 May 2005;
accepted after revision 18 August 2005;
first published online 25 August 2005)
Corresponding author A. Priori: Dipartimento di Scienze Neurologiche, Clinica Neurologica, Padiglione Ponti, Ospedale Maggiore Policlinico, Via F. Sforza 35, Milano, 20122 Italy. Email: alberto.priori{at}unimi.it
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Introduction |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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Methods |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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Eleven patients (6 females, 5 males) with idiopathic Parkinson's disease were studied after their informed consent and local ethical committee approval. The average age was 56 years (range 38–69), years of disease history 13 (7–20), levodopa equivalent therapy pre-surgery 1438 mg day–1 (750–2800), 15–20 days post-surgery 311 mg day–1 (75–800), Unified Parkinson's Disease Rating Scale (UPDRS) III (motor part) pre-surgery off therapy 43 (27–72.5), pre-surgery on therapy 5 (1–23.5), 1 year after surgery off therapy on stimulation 9 (1.5–20, n = 9), UPDRS IV (complications, A + B) pre-surgery 10 (5–14), 1-year after surgery 2 (0–6, n = 9). Patients were treated with DBS only fulfilling specific inclusion criteria (L.I.M.P.E. 2003). All patients were clinically selected, surgically implanted, neurophysiologically assessed and clinically followed by the Milan DBS Group Policlinico, San Paolo, Politecnico (Italy). Part of the data has been used in previous works. Namely, we described the rest oscillations below 50 Hz of 13 nuclei from nine of these patients (Priori et al. 2004) and the 300 Hz oscillations of 11 nuclei from seven of these patients (Foffani et al. 2003, 2005b), recorded both before and after levodopa.
Surgical procedures
The methods for the localization of DBS electrodes within the STN are extensively reported elsewhere (Foffani et al. 2003). Briefly, the procedures included (a) the preoperative direct visualization of the nucleus through CT-MRI targeting (Egidi et al. 2002; Rampini et al. 2003), (b) the intraoperative neurophysiology with microrecordings (Priori et al. 2003), intraoperative stimulation (i.e. through the explorative microelectrode) and macrostimulation (i.e. through the implanted macroelectrode), (c) the postoperative CT-MRI verification of the final electrode position (Egidi et al. 2002; Rampini et al. 2003), and (d) the postoperative assessment of the optimal DBS contact. The model 3389 electrode (Medtronic, Minneapolis, USA) was implanted, which had four cylindrical contacts (diameter 1.27 mm), each 1.5 mm long and spaced 0.5 mm away from the others (i.e. 2 mm centre to centre). Contacts were denominated 0, 1, 2, and 3 beginning from the more caudal placement. The objective was to place contact 1 into the target position. Double blind assessment revealed marked clinical effects during intraoperative monopolar macrostimulation through contact 1. In all the patients included in this study for STN recordings contact 1 (and consistently less contact 2) induced a remarkably greater clinical effect (scored postoperatively by two independent blind observers) than contacts 0 and 3. All of these procedures taken together were consistent with the localization of contact 1 within the STN (Foffani et al. 2003; Priori et al. 2004). All 11 patients received bilateral STN implants.
LFP recordings
The postoperative recording sessions took place 2–3 days after patients had received the electrode implants. The patients were comfortably seated on an armchair. LFPs were recorded during the execution of voluntary movements, 8–12 h after overnight withdrawal of dopaminergic medication, before and after administration of 100–200 mg oral fast-acting L-DOPA (Madopar Dispersibile, Roche, Italy). Levodopa dosages were chosen in order to induce a clinical response as similar as possible to the full on-state used for the pre- and postoperative UPDRS evaluation. After-medication recordings started 30–40 min after drug administration, when the patient showed clinical improvement. The latter was evaluated by an experienced neurologist and by self-assessment of the patient. Most patients had some dyskinesias after levodopa but none before. Patients were instructed to extend the second finger from an initial relaxed semiflexed position every 8–10 s as quickly as possible. Movements were self-paced. One extension corresponded to one trial; the mean number of artifact-free trials was 97 ± 40 before levodopa, 84 ± 43 after levodopa. The task execution was interrupted either by the patient will, if tired, or after a block of 50 trials. Multiple blocks of trials were usually recorded from each nucleus before and after levodopa separated by rest periods to avoid fatigue. Dyskinesias, when present, did not interfere with task execution. The EMG signal from the extensor indicis muscle was recorded through a pair of surface non-polarizable Ag–AgCl electrodes with a belly tendon montage. LFPs were captured from the contralateral 3389 electrode using a closely spaced pair of contacts (1–2). Signals were preamplified, differentially amplified and filtered (EMG: 20–1000 Hz, STN: 2–1000 Hz) through a Cambridge 1902 (Cambridge Electronic Design, Cambridge, UK), A/D converted (sampling rate 2500 Hz) through a Cambridge 1401 (Cambridge Electronic Design), on-line analysed on a personal computer and stored by Signal software (version 1.80, Cambridge Electronic Design). All further analysis was conducted off-line with the Matlab software (version 6.5, The Mathworks, Natick, MA, USA) with custom written programs described below unless otherwise specified. Due to time constraints during the experiments, three patients were studied bilaterally both before (6 nuclei) and after (6 nuclei) levodopa, three patients were studied unilaterally both before (3 nuclei) and after (3 nuclei) levodopa, one patient was studied bilaterally before (2 nuclei) and unilaterally after (1 nucleus) levodopa, one patient was studied unilaterally before (1 nucleus) and bilaterally after (2 nuclei) levodopa, two patients were studied unilaterally only before (2 nuclei) levodopa and one patient was studied bilaterally only after (2 nuclei) levodopa. In total, we studied 17 nuclei, 14 before levodopa and 14 after levodopa, from 11 patients.
Data analysis I: preprocessing
As a preprocessing step, LFPs were normalized by subtracting the mean and dividing by the standard deviation of the 600–1000 Hz band-pass filtered signals, in order to minimize variability within and between nuclei (Foffani et al. 2003; Priori et al. 2004). Signals were then low-pass filtered below 45 Hz and down-sampled at 125 Hz. Movement onsets, which triggered the analyses, were evaluated on the EMG signal using the following cumulative sum approach (Foffani et al. 2003): (1) the EMG signal was squared to obtain power; (2) the mean of the resulting signal was subtracted point-by-point; (3) the cumulative sum of the resulting signal was calculated and then smoothed using a moving average forward–backward (zero phase) filter; (4) the movement onsets were defined as the local minima (the signal at the previous and at the next instants is greater than the signal at the current instant) and the offsets as the local maxima (the signal at the previous and at the next instants is lower than the signal at the current instant) in the filtered cumulative sum; and (5) signals were visually inspected, and only epochs free from artifacts were used for the analysis (Fig. 1A).
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Time–frequency analysis was applied to the movement-related LFPs using a method based on adaptive autoregressive (AAR) identification with spectral power decomposition (Fig. 1B). The method was described in detail and validated elsewhere (Foffani et al. 2004a). In brief, LFPs were modelled using a generic AAR model of the form:
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|
(t) =
[a1(t) a2(t) ... an(t)] is the time-varying autoregressive parameter vector, 
(t) =
[y(t
– 1) y(t
– 2) ... y(t–n)]T is the observation vector, d(t) is a white noise (mean = 0, variance =
2) and n is the model order. The parameter vector (t) was identified from the data using an adaptive algorithm with ‘whale’ forgetting factor (Bianchi et al. 1997), given by the following recursive equations:
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| (1) |
1 and 2 are such that the two roots p1 and p2 of z2
–
1z
–
2
= 0 lie in the interval [0,1], Q is a n-dimensional vector (initialized to zero) and S is an n-by-n square matrix (initialized as a unitary matrix with gain 0.0001). The whale forgetting factor (1
0, 2
0) was preferred to the more standard exponential forgetting factor (1
0, 2
= 0) due to its better performance in terms of disturbance rejection when 1 and 2 are chosen such that the two roots p1 and p2 of z2
–
1z
–
2
= 0 are a couple of coincident roots pp
(0 < pp < 1). As a compromise between tracking capability and disturbance rejection, the whale forgetting factor pp was fixed at 0.93, which corresponds to an approximate memory length of about N
= 55 samples according to the formula N
–4/ln(pp). The values of 1 and 2 were then calculated as 1
= 2pp and 2
=–pp2. Because any movement-related change increases the prediction error, the input error variance 2 was fixed to a normalized constant unitary value in order not to overestimate power increases or underestimate power decreases. This normalization also minimizes the signal-to-noise ratio variability across recordings, facilitating statistical comparisons. Power values were then expressed in arbitrary units (a.u.). The model order was set to n
= 11 for all recordings. This model order is consistent with current neurophysiological knowledge, because the resulting poles match the main STN rhythms previously reported using non-parametric methods (Priori et al. 2004). Namely, one real pole follows the activity at very low frequencies (< 7 Hz), one pair of complex poles follows the alpha activity (7–13 Hz), one pair follows the low-beta (13–20 Hz), one pair follows the high-beta (20–35 Hz), one pair follows the gamma (35–45 Hz) and one pair accounts for residual high-frequencies (see also Foffani et al. 2004a). Trial averaging was performed in the parameter domain: the parameter vector was synchronously averaged across all the available trials triggered on movement onsets, obtaining an average movement-related AAR model given by following parameter vector:
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| (2) |
(t) is the movement-related AAR parameter vector of trial and T is the total number of trials used in the average. The above trial averaging (2) assumes that each single trial is a different independent realization of the same AAR process. The average movement-related AAR parameter vector 
(t)
then contains all the time–frequency spectral information of the signal. The time-varying power spectrum of the average movement-related AAR model (t) was divided into components relevant to real poles or to pairs of complex conjugate poles in the z-domain using the residual method (Baselli et al. 1997; see Foffani et al. 2004a for details). This spectral power decomposition was performed at every time instant t of the average movement-related AAR model (t), so that each real pole i or pair of complex conjugate poles i was characterized by a time-dependent power value Pi(t) and a time-dependent frequency value Fi(t), allowing us to separately describe movement-related amplitude modulations (AMs, measured in log power) and frequency modulations (FMs, measured in Hz). The attention was concentrated on low-beta (13–20 Hz) and high-beta (20–35 Hz) poles (Priori et al. 2002; Foffani et al. 2004a) (i.e. poles whose frequency values Fi(t) varied within the above frequency ranges). Data analysis III: parameter extraction and statistical comparisons
Four main parameters were extracted to quantify the movement-related modulations of each pole: the baseline value ‘b’ (4 s to 2 s before movement onset), the premovement value ‘p’ (0.5 s to 0 s before movement onset), the movement value ‘m’ (0 s to 1 s after movement onset) and the recovery value ‘r’ (2 s to 3 s after movement onset). Two separate statistical analyses were performed: at the single-nucleus level and at the population level. At the single-nucleus level, the significance of AMs and FMs was assessed by challenging the null hypothesis that premovement ‘p’, movement ‘m’ and recovery ‘r’ had the same mean value as the baseline ‘b’, using unpaired t tests (Matlab function ‘ttest2’). Bonferroni correction was applied for multiple comparisons and a cut-off significance value was set at P < 0.00014881. At the population level, the results were analysed with a two-way analysis of variance (ANOVA) design. The first main factor of the ANOVA was the movement-related modulation, with four levels (repeated measures): baseline ‘b’, premovement ‘p’, movement ‘m’ and recovery ‘r’. The second main factor was the dopaminergic condition, with two levels (independent measures): before and after levodopa administration. Each nucleus was considered as an individual sample. Four ANOVAs were separately performed to analyse the movement-related AMs (measured in log power) and FMs (measured in Hz) of the low-beta and high-beta poles. Finally, the latencies of AM and FM onsets (relative to movement onset) were measured as the last zero-crossing before a significant modulation, after subtracting the baseline mean value. This latency estimation is conceptually identical to the approach applied to subthalamic movement-related potentials by Paradiso et al. (2003).
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Statistical analysis at the single-nucleus level revealed that most nuclei exhibited significant AMs in the low-beta and high-beta poles both before and after levodopa administration. Based on the average baseline ‘b’, pre-movement ‘p’, movement ‘m’ and recovery ‘r’ values, we observed two main movement-related AM patterns (Table 1; cut-off significance P < 0.000148810). The most consistent AM pattern was a movement-related power decrease (P(m) < P(b), i.e. negative AM; Fig. 2A and C, which typically started before movement onset (P(m) < P(b) and P(p) < P(b)) and was followed by a positive post-movement rebound (P(m) < P(b) and P(r) > P(b)). The second AM pattern consisted of a movement-related power increase (P(m) > P(b), i.e. positive AM; Fig. 2B and D, which also typically started before movement onset (P(m) > P(b) and P(p) > P(b)). See Table 1 for details.
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Besides AMs, FMs were also a consistent feature in our dataset. Statistical analysis at the single-nucleus level revealed that most nuclei exhibited significant FMs in the low-beta pole and in the high-beta pole both before and after levodopa administration. Two main movement-related FM patterns were observed (Table 1; cut-off significance P < 0.000148810). The most consistent FM pattern was a movement-related frequency increase (F(m) > P(b), i.e. positive FM; Fig. 2E and G, which typically started before movement onset (F(m) > P(b) & F(p) > P(b)) and was followed by a negative post-movement rebound (F(m) > P(b) and P(r) < P(b)). The second FM pattern consisted of movement-related frequency decrease (F(m) < F(b), i.e. negative FM; Figs 2F and H), which typically started before movement onset (F(m) < F(b) and F(p) < F(b)) with positive post-movement rebounds often observed after levodopa (F(m) < F(b) and F(r) > F(b)). Differently from the AM patterns, levodopa induced consistent effects on the FM patterns, particularly in the low-beta pole, where we observed an inversion of polarity from positive FM (Fig. 2E) to negative FM (Fig. 2F). This result was corroborated by observing that of 11 nuclei recorded in both pharmacological conditions (i.e. both before and after levodopa administration), 7 of the 9 nuclei exhibiting positive FM before levodopa reversed their FM polarity after levodopa, the remaining two nuclei exhibiting positive FM before levodopa decreased the FM after levodopa, and the two nuclei remaining exhibited negative FM both before and after levodopa.
Statistical analysis at the population level (Table 2) confirmed the FM patterns and the effects of levodopa observed at the single-nucleus level. Namely, in the low-beta pole, levodopa reversed the movement-related modulation from a positive FM to a negative FM (ANOVA interaction factor: P = 0.0003) (Fig. 3C). In the high-beta pole, the population exhibited a positive FM both before and after levodopa administration (1st main factor: P = 0.0001) (Fig. 3D). On average, levodopa had no significant effects on baseline frequencies. Latency analysis on all nuclei exhibiting significant movement-related FMs (either F(m) > F(b) or F(m) < F(b)) confirmed that the modulations started well before movement onset (low-beta: 0.63 ± 1.18 s before levodopa, n = 13, and 0.52 ± 0.74 s after levodopa, n = 13; high-beta: 1.05 ± 1.17 s before levodopa, n = 14 and 1.15 ± 1.04 s after levodopa, n = 13).
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Discussion |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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Methodological considerations
The concept of FM as used in this paper refers to the modulation of the frequency of neural oscillatory rhythms distributed in large populations of neurones and should not be confused with the modulation of single-neurone firing rates (Riehle et al. 1997). This difference should be taken into account when comparing our results at the LFP level with studies at the single-neurone level (Amirnovin et al. 2004). LFPs represent the synchronous presynaptic and postsynaptic activity of large populations of neurones and can detect focal network oscillatory behaviours that are not necessarily observable in single neurones or in 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). In the human STN, the local action of LFP beta oscillations is strongly supported by polarity reversals and amplitude gradients between adjacent electrode contacts (Brown et al. 2001; Levy et al. 2002a; Kühn et al. 2004; Doyle et al. 2005), and by the synchronization between LFP beta oscillations and single-neurone activity, reflecting focal topography (Levy et al. 2002a; Kühn et al. 2005). The possibility that these oscillations represent volume conduction from cortical or nearby brainstem regions is therefore unlikely. In fact, when simultaneous (differential) recordings are performed from several of these regions in humans (e.g. STN, globus pallidus internus (GPi) and cortex), the phase differences of beta oscillations between regions are typically consistent with synaptic transmission, being too long for volume conduction (Brown et al. 2001; Cassidy et al. 2002; Williams et al. 2002). Possible sources of variability involved with LFP recordings from DBS electrodes in human patients were discussed in our previous works and include the time elapsed from electrode implant, the clinical features of the patients and possible biases in the localization of the electrodes within the STN (Foffani et al. 2003, 2005b; Priori et al. 2004). Of note, the possible subtle variability in the localization of the electrodes could have contributed to the variability in the patterns of movement-related modulation described in the present study, which is consistent with the increase in complexity of STN processing that is emerging from LFP studies. As we previously remarked, ‘this variability is an important result by itself, as it suggests that the human STN is not a single homogeneous nuclear structure but it contains multiple, functionally segregated subsystems’ (Priori et al. 2004). Two additional aspects should be specifically considered in this study. Firstly, from the experimental point of view, we asked our patients to perform fine self-paced movements (second finger extensions), which require much smaller and more focal muscular activation than the hand-held joystick movements employed in previous studies (Cassidy et al. 2002; Doyle et al. 2005). Differences in muscular activation patterns are likely to produce differences in the STN LFP modulation patterns. Secondly, from the data analysis point of view, we employed a novel approach (adaptive autoregressive identification with spectral power decomposition, Foffani et al. 2004a) that describes the movement-related behaviour of LFP rhythms in terms of ‘poles’, which can vary both in amplitude and frequency, instead of the classical frequency bands, which can vary only in amplitude. This allowed us to study not only the movement-related AM but also the movement-related FM of subthalamic beta LFP activity. Nonetheless, it should be remarked that all studies based on LFP recordings from DBS electrodes, including the present work, are performed in patients with movement disorders and the extension to physiological conditions should be cautious.
Movement-related amplitude modulations (AMs)
In scalp EEG studies, the idea of event-related AM is almost as old as EEG itself. Since the pioneering works by Berger (1929), EEG rhythms have been described to be modulated in amplitude by a great variety of events, including attention, cognitive tasks and movement executions (Pfurtscheller & Lopes da Silva, 1999). Movement-related AM can be easily observed over the sensorimotor cortex, most consistently in the alpha, beta and gamma frequency ranges (Pfurtscheller & Aranibar, 1979; Defebvre et al. 1994; Toro et al. 1994; Defebvre et al. 1998; Crone et al. 1998a,b; Magnani et al. 1998; Wang et al. 1999; Pfurtscheller & Lopes da Silva, 1999; Ohara et al. 2000; Alegre et al. 2003; Devos et al. 2003; Pfurtscheller et al. 2003; Szurhaj et al. 2003; Alegre et al. 2004; Foffani et al. 2004a,b). Thanks to the advent of DBS for treating movement disorders, these concepts have been deepened into the human basal ganglia – in particular STN and GPi – through LFP recordings from electrodes implanted for DBS (Brown, 2003). Subthalamo-pallidal rhythms encompass a wide range of frequencies, from as low as a few Hz (Silberstein et al. 2003; Priori et al. 2004; Foffani et al. 2005a) to as high as 300 Hz (Foffani et al. 2003, 2005b). However, the highest degree of attention has been devoted to the beta frequency range (13–35 Hz). LFP beta oscillations in the human STN are tightly related to local single-unit activity (Levy et al. 2002a; Kühn et al. 2005), display long-range synchronization across multiple structures in the cortico-basal ganglia loop (Brown et al. 2001; Cassidy et al. 2002; Williams et al. 2002; Brovelli et al. 2004; Schnitzler & Gross, 2005; Foffani et al. 2005a), and are modulated in amplitude by both dopaminergic medication (Brown et al. 2001; Levy et al. 2002a; Priori et al. 2004) and movement execution (Foffani et al. 2002, 2004a; Levy et al. 2002a; Priori et al. 2002; Cassidy et al. 2002; Kühn et al. 2004; Williams et al. 2005; Doyle et al. 2005). Here we corroborated that the low-beta (13–20 Hz) rhythm has a greater baseline sensitivity to levodopa than the high-beta (20–35 Hz) rhythm (Priori et al. 2004), showed that movement-related AMs in these two rhythms can display different patterns, and confirmed that movement-related beta AM are present not only at off in the full parkinsonian state (Foffani et al. 2002; Cassidy et al. 2002), but also at on after dopaminergic medication, consistent with our preliminary observations (Priori et al. 2002) and with recent findings (Doyle et al. 2005). These results support the idea that beta rhythms can play an important – not only pathological – role in basal ganglia motor control, which is consistent with the movement-related beta AM observed in the globus pallidus internus (GPe) of epileptic patients (Sochurkova & Rektor, 2003) and with the widespread modulation of beta activity observed in the striatum of normal primates (Courtemanche et al. 2003).
Movement-related frequency modulations (FMs)
Very little evidence about event-related FM can be found in EEG studies. This probably has a methodological rather than physiological explanation, as in classical Fourier time-frequency analysis (or similar approaches) frequency and time are the independent variables whereas the spectral amplitude (or power) is the dependent variable. New methodological approaches recently allowed EEG researchers to observe phase-resetting phenomena in alpha oscillations (
10 Hz) when studying brain dynamics in terms of event-related alterations of ongoing-rhythms (Makeig et al. 2002, 2004; Gruber et al. 2005). From a communication theory point of view, FM is a more general principle than phase-resetting, in the sense that phase-resetting is a sufficient but not necessary condition for FM. FM phenomena have also been observed at very-low frequencies (1 Hz) in the Limax olfactory lobe (Kimura et al. 1998; Cooke & Gelperin, 2001), at theta frequencies (3–10 Hz) in guinea pig inferior olive neurones (Benardo & Foster, 1986), in the rat hippocampus (Kirk, 1998) and in the primate occipitotemporal pathway (Purpura et al. 2003), and at beta/gamma frequencies (20–80 Hz) in the cat auditory cortex (Karmos et al. 2002; Lakatos et al. 2004), in the rabbit sensory cortices (Freeman & Rogers, 2002) and, most notably, in the rat subthalamic nucleus (Sharott et al. 2005). This evidence – although sparse, non-systematic and mostly related to sensory processing – suggests that FM could serve as a general principle for brain information processing and communication. By combining adaptive autoregressive identification with spectral power decomposition (Foffani et al. 2004a) we found that FMs could contribute to the involvement of the human STN in movement preparation, execution and recovery (Foffani et al. 2002, 2003; Priori et al. 2002; Levy et al. 2002a; Cassidy et al. 2002; Paradiso et al. 2003; Kühn et al. 2004; Amirnovin et al. 2004; Williams et al. 2005; Doyle et al. 2005). Moreover, we showed that dopaminergic medication induces significant changes in the FM patterns, particularly in the low-beta (13–20 Hz) rhythm. Even though the FMs could be an epiphenomenon of movement-related network changes (i.e. of the AMs), the different effects induced by levodopa on beta frequencies (movement-related modulation) compared to beta amplitudes (baseline modulation) suggest that FM could represent a new domain for information processing in the human basal ganglia.
Neurophysiological significance
The classical basal ganglia model (Albin, 1995; Brooks, 1995; Chesselet & Delfs, 1996; Wichmann & Delong, 1996) is exclusively based on firing rates, which are modulated in each nucleus by excitatory or inhibitory inputs from other nuclei. The limits of the classical model are apparent, and it is becoming progressively clear that rhythms and oscillations play a primary role in the pathophysiology of the human basal ganglia (Brown & Marsden, 1998; Wichmann & Delong, 1999; Bevan et al. 2002; Brown, 2003; Dovstrovsky & Bergman, 2004; Hutchison et al. 2004). Alternative rhythm-based models of basal ganglia pathophysiology are emerging from LFP studies in DBS patients (Brown, 2003; Priori et al. 2004). Intriguingly, Hoppensteadt and Izhikevich mathematically demonstrated that FM is a general principle of interaction between brain structures when the following two main assumptions are verified: (1) each structure can be considered as an autonomous oscillator, and (2) oscillators are weakly connected (Hoppensteadt & Izhikevich, 1997, 1998; Izhikevich, 1999). Their study was focused on thalamo-cortical interactions, but it can be easily generalized to cortico-basal ganglia processing. In this circuit, the assumption about autonomous oscillations is supported by modelling studies suggesting that ‘different parts of the STN-GPe system may oscillate separately from each other’ (Terman et al. 2002), by experimental work in vitro showing the autonomous oscillatory behaviour of single cells in the STN–GP circuit (Plenz & Kital, 1999; Beurrier et al. 1999; Stanford, 2003) and by the evidence of independent oscillators in the pathophysiology of tremor (Hurtado et al. 1999, 2000, 2005). The assumption of weak connections is experimentally verified in the human basal ganglia, as LFP beta oscillations are transmitted throughout the STN–GP–cortical circuit (Brown et al. 2001; Cassidy et al. 2002; Williams et al. 2002; Foffani et al. 2005a), but pairs of single neurones in STN, GPi and GPe are not necessarily correlated at beta frequencies (Levy et al. 2000, 2002a,b). According to Hoppensteadt and Izhikevich, the FM interaction between brain structures/oscillators occurs when there is a certain nearly resonant relation between their frequencies, which well agrees with FMs in the order of 1 Hz as observed in our study. Our finding that beta subthalamic rhythms can represent information not only in AM but also in FM therefore suggests that movement execution is associated not only with linear modulations of ongoing rhythms, but also with non-linear interactions between nearly resonant, independent and weakly coupled oscillators in the cortico-basal ganglia circuit. Hence, movement-related AMs and FMs in the human STN might reflect the presence of linear and non-linear communication channels, which could separately or complementarily contribute to subthalamic information processing. The actual way by which FMs might exert their putative mechanistic influence is suggested by Hoppensteadt & Izhikevich (1998): ‘An entire cortex can be dynamically partitioned into interwoven, but relatively independent, ensembles that process information without cross-interference. A cortical oscillator may participate in different ensembles by changing its frequency, without changing the strengths of synaptic connections.... The functional partition of the cortex may be dynamically reorganized by a rhythmic input from the thalamus. Indeed, the thalamus can link any "non-interacting" cortical columns if it has an appropriate frequency’. These considerations can be easily extended to the STN: if multiple beta rhythms operate in the human STN (Terman et al. 2002) and control different body parts in a somatotopically segregated fashion (Rodriguez-Oroz et al. 2001; Romanelli et al. 2005), then movement-related FMs could serve to regulate the degree of synchrony between rhythms and therefore between body parts for coordinated movement control. The excitatory nature of the human STN and its widespread efferent connectivity to most of the basal ganglia and other structures in the brainstem (Hamani et al. 2004) suggest that beta FMs could be relevant for the ‘normal and pathological oscillatory communication in the brain’ (Brown & Marsden, 1998; Brown, 2003; Schnitzler & Gross, 2005). In conclusion, the subthalamic FM mode provides a novel informational domain for rhythm-based pathophysiological models of cortico-basal ganglia processing.
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