Fig 1.
Schematic of the cortico-basal ganglia-thalamic model and fit to empirical data from Parkinsonian rodents.
A model describing the population activity in this circuit was fit to data features (power spectra and directed functional connectivity) of (A) electrophysiological recordings: electrocorticography from motor cortex M2 (blue) as well as local field potentials from striatum (STR; red) external segment of the globus pallidus (GPe; green) and the subthalamic nucleus (STN; yellow) made in a 6-OHDA-lesioned rodent model of Parkinsonism. Data were normalized and band-passed at 4–100 Hz before being transformed to the data features used to estimate parameters. (B) Schematic of model architecture, detailing excitatory/glutamatergic projections (triangular nodes with arrows) and inhibitory/GABAergic projections (circular nodes with ball ended arrows). The motor cortex microcircuit comprises three layers: superficial pyramidal cells (SP; supragranular); middle pyramidal (MP; granular); and deep pyramidal cells (DP; infragranular), plus an inhibitory interneuron population (II). The basal ganglia model comprises four populations: STR, GPe, STN, and internal segment of the pallidus (GPi). The GPi forms the output of the basal ganglia and acts to inhibit relay cells of the ventrolateral thalamus (REL). GPi and REL were treated as hidden nodes and their respective neural activities were inferred from the dynamics of the empirically recorded brain regions. The main subcortical pathways include the direct, indirect, hyperdirect, and cortico-thalamic interactions. The inset graphs indicate the empirical and simulated power spectra in bold and dashed lines, respectively. For the full set of empirical and fitted data features please see S1 Fig. (C) Simulations of this circuit yields time series with transient, burst like behaviour similar to that seen in vivo (A).
Fig 2.
Modulating the strength of inputs to the subthalamic nucleus (STN) from both hyperdirect (HD) and pallidosubthalamic (PS) pathways leaves distinct spectral features in the oscillatory activity and synchronization of cortex (M2) and STN.
Two discrete network states were defined for each pathway: a Down-regulated state fixed at 10% connectivity, as well as an Up-regulated state set at the connection strength eliciting ~200% increase in STN beta power. The fitted model (i.e., the 6-OHDA lesioned state, represented at 100% connectivity) is given in black. (A) Schematic of PS-Up (purple, 145% connection strength) and PS-Down (green, 30% connection strength). (B) Schematic of HD-Down (red, 30% connection strength) and HD-Up (blue, 350% connection strength). (C) Legend to the network states placed on a hypothetical scale from a dopamine intact state associated with a reduction in motor symptoms (far left), to the fitted model (with parameters constrained by data from 6-OHDA rat model of Parkinsonism; middle), to states indicating further progression of the pathology and worsening of motor symptoms (far right). (D) PS network states leave distinct spectral features in the power spectra of STN, with modulation occurring between lower (β1) and upper beta (β2) bands. (E) Similar responses can be seen in the M2 power spectra; as well as in (F) the functional connectivity between STN and M2 in terms of the magnitude squared coherence. (G, H, and I) Same as (D, E, and F) but for the HD defined states. Grey lines show the intermediate spectra generated between Up and Down states.
Fig 3.
Changes in hyperdirect (HD) or pallido-subthalamic (PS) network states result in circuit wide alterations in transient (i.e., within-burst) phase synchronization at beta band frequencies.
Data were simulated using the four predefined network states (see main text and Fig 2) of the CBGT model: PS-Up (purple), PS-Down (green), HD-Up (blue), and HD-Down (red). (A) 120s of data were simulated from each model and then bandpass filtered at lower or upper beta band. The Hilbert envelope was used to defined “burst” epochs as periods of suprathreshold (>75th percentile) activity in the STN (shaded yellow area). Phases across all six sources in the model were reconstructed using the angle of the Hilbert transformed signals. This phase estimate was used to construct connectivity matrices or time-locked statistics of burst activity. (B) Connectivity matrices indicating all possible pairs of within-burst phase synchronization (PLV) across the CBGT circuit. Matrices show the difference in PLV from that of the fitted model, color-coded according to the inset colorbar. The matrix is thresholded to only show significant changes in PLV from those estimated in the fitted model (compared to surrogate distribution, permutation-test (500), α < 0.05). Results for lower and upper beta are shown in the top and bottom diagonals respectively. (C and G) Radar plot of within-burst (i.e., when the STN envelope is suprathreshold) changes in STN/M2 phase difference. Circles indicate median, with bars giving the circular standard deviation. *indicate significant Rayleigh test for difference in mean phase from those computed from length matched, randomly selected out-of-burst data. Note that the radial dimension has no meaning, bars are offset for presentation purposes. Angular lengths should be interpreted with relation to the grid-lines. (D and H) Analysis of the STN amplitude envelope between PS-Up/Down and HD-Up/Down filtered at lower beta frequencies. Traces are mean +/- S.E.M timelocked to burst onset at t = 0. Bars indicate significant cluster-statistics for deviation from length-matched, out-of-burst data (cluster-statistic (500), α < 0.05). (E and I) Analysis of M2/STN phase difference (centred relative to the mean phase at 0°). (F and J) Scatter plots of burst amplitude versus the relative phase stability (estimated as the mean absolute derivative of STN/M2 phase difference in the window 0 to +500 ms). In the case where there was a significant Pearson’s correlation coefficient (R), we plot a regression line. Overall burst amplitude was correlated with phase stability.
Fig 4.
A model of dual-site controlled motor cortical stimulation phase locked to signals sensed in the subthalamic nucleus, can modulate beta activity across the network.
(A) Schematic for phase specific neuromodulation in the rodent brain. Activity at the STN is used to gate stimulation delivery at M2. (B) Stimulation waveforms were generated using an 18 Hz sinusoid, with phase constructed to be offset against an on-line phase estimate of STN activity. Stimulation was delivered as a direct voltage injection to the stimulated population (superficial layer of M2). Effects upon β power were either amplifying (blue; 330°) or suppressing (orange; 150°) depending on the phase. (C) Amplitude response curves of power in the motor cortex, STN, as well as their synchronization (in terms of coherence) when sweeping across 12 stimulation phases. Curves are shown separately for lower (β1; bold line) or upper beta (β2; dashed line). Corresponding spectra are shown in supplementary S5 Fig. (D) Analysis of mean M2/STN phase difference during stimulation period (centred relative to the mean phase at 0°) filtered at lower beta frequencies. Circular markers indicate median, with bars giving the circular standard deviation. *indicate significant Rayleigh test for difference in phases from the unstimulated, fitted model. Note that the radial dimension has no meaning, bars are offset for presentation purposes. Angular lengths should be interpreted with relation to the grid-lines. (E) Analysis of the STN amplitude envelope during stimulation. (F) Analysis of M2/STN phase difference tracked across time. Traces are mean+/- S.E.M time locked to burst onset at t = 0. Bars indicate significant cluster-statistics for deviation from the unstimulated model (two-sample t-test, n = 500, α < 0.05).
Fig 5.
Stimulation of the cortex phase locked to activity sensed in the STN can induce network-wide patterns of activity that resembles those corresponding to spectral fingerprints of spontaneous activity associated with changes in connection strength.
(A) Data simulated from the four network states PS-Up (purple), PS-Down (green), HD-Up (blue), and HD-Down (red) (see main text and Fig 2) was used to compute spectral fingerprints of spontaneous burst activity which were then compared against those constructed from the outcomes of phase locked stimulation. Only data during which stimulation was delivered (i.e., within a high amplitude STN beta burst event) was analysed. We used two different spectral fingerprints to compare network states with stimulated epochs: (B) the concatenated power spectra of each of the 6 populations in the CBGT circuit. Data were normalized to unit variance prior to concatenation such that comparisons were focused on the shape of spectra rather than large differences in amplitude. (C) Matrices of the pairwise phase synchronization (magnitude of the PLV) were estimated using the Hilbert transformed signals (see Fig 3A) for both β1 and β2 frequencies. (D, E, and F) Stimulation was applied across 12 phases in the fitted model and data were compared (using pooled R2) to each network state using: the concatenated spectra (D); the matrix of PLV magnitudes (E); and the two features combined (F). These results show that spectral fingerprints from stimulation outcomes resembles that from different network states (i.e., a change in synaptic connectivity) depending upon the phase at which stimulation was delivered. (G, H, I) The above was repeated but when varying the connection strength of the PS pathway. Results are plot as a heatmap color-coded to indicate the best fitting state at each phase (x-axis; angle of stimulation relative to STN activity) and connection strength (y-axis; percentage of fitted synaptic strength, dashed line indicates 100%- i.e., the model fit to the 6-OHDA lesion data and plot in D, E, and F). (J, K, and L) Same as G, H, and I, but for modulations of HD pathway strength.