Fine temporal structure of beta oscillations synchronization in subthalamic nucleus in Parkinson's disease

Abstract

Synchronous oscillatory dynamics in the beta frequency band is a characteristic feature of neuronal activity of basal ganglia in Parkinson's disease and is hypothesized to be related to the disease's hypokinetic symptoms. This study explores the temporal structure of this synchronization during episodes of oscillatory beta-band activity. Phase synchronization (phase locking) between extracellular units and local field potentials (LFPs) from the subthalamic nucleus (STN) of parkinsonian patients is analyzed here at a high temporal resolution. We use methods of nonlinear dynamics theory to construct first-return maps for the phases of oscillations and quantify their dynamics. Synchronous episodes are interrupted by less synchronous episodes in an irregular yet structured manner. We estimate probabilities for different kinds of these "desynchronization events." There is a dominance of relatively frequent yet very brief desynchronization events with the most likely desynchronization lasting for about one cycle of oscillations. The chances of longer desynchronization events decrease with their duration. The observed synchronization may primarily reflect the relationship between synaptic input to STN and somatic/axonal output from STN at rest. The intermittent, transient character of synchrony even on very short time scales may reflect the possibility for the basal ganglia to carry out some informational function even in the parkinsonian state. The dominance of short desynchronization events suggests that even though the synchronization in parkinsonian basal ganglia is fragile enough to be frequently destabilized, it has the ability to reestablish itself very quickly.

Fig. 1.

Diagram of the 1st-return plot (the phase space). This phase space is partitioned into 4 regions (coinciding with each quadrant, but numbered in a clockwise manner: I–IV). The arrows indicate all possible transitions from one region to another and the expressions next to the arrows indicate the rates for these transitions, computed from experimental data (see First-return maps for the phases and desynchronization events). The sum of the rates for all possible transitions for a given region is equal to 1.

Fig. 2.

Raw and processed data for a short piece of a synchronized episode. A and C: plots contain raw and filtered data. A contains the spikes (gray line) and the spiking signal filtered to 10–30 Hz band (black line); C contains raw local field potential (LFP) signal (gray line) and LFP filtered to 10–30 Hz band (black dotted line). The amplitude is measured in relative units. B: the sines of the phases of the both filtered signal. There is no amplitude information here (both signals vary in between −1 and 1), but the phase information is preserved. One can see that although the signals are not perfectly phase-locked, the deviation of one phase from the other is not very large and is kept constrained. Stars indicate the phases of the filtered spiking signal, when the phase of filtered LFP signal is 0. Thus stars give {φ_spikes,i}, i = 1, N, from which (φ_spikes,i,φ_spikes,i+1) are constructed (see First-return maps for the phases and desynchronization events). The first-return map for this piece of data are presented in Fig. 3.

Fig. 3.

The first-return map for the data from the Fig. 2. The points in the depicted phase space are coming from the sequence of the {φ_spikes,i}, i = 1,…, N indicated by stars at the Fig. 2. All points are within the first region of the phase space, which corresponds to phase-locking, as seen in the Fig. 2.

Fig. 4.

An example of the first-return map for the phases of spikes and LFP for 1 of the recorded episodes (cf. Fig. 1). All 4 first-return plots have the same data points, 4 different plots are presented to illustrate the transitions from each of the regions. In each of the plots all points in one region (A, 4th region; B, first region; C, 3rd region, and D, 2nd region) are represented by ○, the points to which they evolve in 1 cycle are represented by *, and all other points are . Lines connect each circle to a star—the point, to which this circle evolves. Thus each plot shows the transitions from a corresponding part of the phase space. Note the high density of the circles, stars, and lines in the B; this is due to the fact that this part of the phase space (1st region) contains the synchronized state.

Fig. 5.

The mean transition rates r₁, r₂, r₃, r₄. and ◽, represent different lengths of the time window used to compute the synchronization index γ (1 s and 1.5, respectively) and thus represent the results of different inclusion criteria for the original data. Vertical lines indicate SD.

Fig. 6.

The weighted averages of the transition rates r₁, r₂, r₃, r₄. The averaging weights are equal to the number of points in the 1st-return plots for each episode. and ◽, different lengths of the time window used to compute the synchronization index γ (1 s and 1.5, respectively). Note the qualitative similarity with the Fig. 5.

Fig. 7.

The histogram of probabilities of desynchronization events of different durations (measured in cycles of oscillations). For the duration >5, all durations are pooled together, so that the last bin counts all durations >5. Different shades of gray correspond to different evaluation methods: weighted and nonweighted, from data directly and from transition rates. The data are for the window length for the computation of synchronization index γ equal to 1.5 s.