Cortical information flow in Parkinson's disease: a composite network/field model

Abstract

The basal ganglia play a crucial role in the execution of movements, as demonstrated by the severe motor deficits that accompany Parkinson's disease (PD). Since motor commands originate in the cortex, an important question is how the basal ganglia influence cortical information flow, and how this influence becomes pathological in PD. To explore this, we developed a composite neuronal network/neural field model. The network model consisted of 4950 spiking neurons, divided into 15 excitatory and inhibitory cell populations in the thalamus and cortex. The field model consisted of the cortex, thalamus, striatum, subthalamic nucleus, and globus pallidus. Both models have been separately validated in previous work. Three field models were used: one with basal ganglia parameters based on data from healthy individuals, one based on data from individuals with PD, and one purely thalamocortical model. Spikes generated by these field models were then used to drive the network model. Compared to the network driven by the healthy model, the PD-driven network had lower firing rates, a shift in spectral power toward lower frequencies, and higher probability of bursting; each of these findings is consistent with empirical data on PD. In the healthy model, we found strong Granger causality between cortical layers in the beta and low gamma frequency bands, but this causality was largely absent in the PD model. In particular, the reduction in Granger causality from the main "input" layer of the cortex (layer 4) to the main "output" layer (layer 5) was pronounced. This may account for symptoms of PD that seem to reflect deficits in information flow, such as bradykinesia. In general, these results demonstrate that the brain's large-scale oscillatory environment, represented here by the field model, strongly influences the information processing that occurs within its subnetworks. Hence, it may be preferable to drive spiking network models with physiologically realistic inputs rather than pure white noise.

Keywords: Granger causality; Parkinsons's disease; basal ganglia; cortex; interlaminar processing; neural field model; spiking neural networks; thalamus.

Figure 1

Schematic of the field model, showing excitatory populations and connections (light colors, diamond arrows) and inhibitory ones (dark colors, round arrows). The key efferent nucleus of the basal ganglia is the internal globus pallidus (GPi), which receives cortical input via direct, indirect, and hyperdirect pathways. The field model drives a spiking network model, shown here schematically (dots at left); the inputs from the field model to the spiking model are indicated by the thin lines. The substantia nigra pars compacta modulates parameters, but is not explicitly modeled. Inputs to the thalamus (yellow arrow) were modeled as white noise.

Figure 2

Layout of the 4950 neurons in the spiking network model (1980 cells shown). Shapes show type (triangle = excitatory pyramidal, E; circle = fast-spiking interneuron, I; star = low-threshold spiking interneuron, IL; square = thalamic reticular, TRN; diamond = thalamocortical relay, TCR). The 28 efferent connections from a single layer 5 pyramidal neuron are shown (black lines). The distance from the thalamus to the cortex is not shown to scale.

Figure 3

Connectivity of the models. Color shows normalized effective connectivity (probability × weight) from rows to columns, with red denoting excitation and blue denoting inhibition. (A) Connections in the field model (CE, cortical excitatory; CI, cortical inhibitory; TCR, thalamocortical relay; TRN, thalamic reticular nucleus; SD1, striatal D1; SD2, striatal D2; GPi, internal globus pallidus; GPe, external globus pallidus; STN, subthalamic nucleus). (B) Connections in the network model. Approximate diagonal symmetry shows that most connections are reciprocal; relatively strong connections along the diagonal indicate high intralaminar connectivity.

Figure 4

Dynamics of the three field models (without the network model). TC, thalamocortical field model; BG, healthy basal ganglia model; PD, Parkinson's disease model; white noise model not shown. “Excitatory” and “inhibitory” refer to cortical subpopulations. (A) Local field potential (LFP) time series, showing phase relationships between populations. Activity in the globus pallidus internal (GPi) and external (GPe) segments is normally in phase (red arrows), but this relationship is lost in PD, since the GPi entrains to the subthalamic nucleus instead (blue arrows). (B) LFP spectra. Except for the subthalamic nucleus, healthy basal ganglia nuclei spectra are similar to the spectrum of the thalamic relay nuclei from 10–40 Hz. This is disrupted in PD (green arrows), especially in the GPi.

Figure 5

Temporal dynamics of the network model with each type of input drive (WN, white noise; TC, thalamocortical; BG, healthy thalamocortical/basal ganglia; PD, Parkinson's disease). (A) Example spike raster from the BG-driven model. Low-frequency oscillations are clearly visible. (B) LFPs from layer 2/3 of each model. The BG case corresponds to the raster shown in (A); peaks in voltage are correlated with peaks in spiking activity. (C) Mean firing rates by cell type (averaged over both cortical and thalamic populations). Overall, the PD-driven model had considerably lower firing rates, which result from excessive inhibition of the thalamic nuclei. (D) Variability in neuronal firing rates on different time scales. The PD- and BG-driven models (which receive the most highly structured input) show the most variability on short and long time scales, respectively; the WN-driven model (which receives the least structured input) shows the least variability on all scales.

Figure 6

Spectral and information-theoretic characteristics of the network model as driven by each field model. (A) Power spectra. The WN- and TC-driven models have fairly featureless spectra, but with different fall-off characteristics at high frequencies. BG- and PD-driven models are similar to the TC-driven spectrum, except for the pronounced peak at ~20 Hz. Spectral power is slightly shifted toward lower frequencies in PD. (B) Population burst frequency, defined as the probability of a given number of cells firing within a 10 ms time window, divided by the corresponding probability for uncorrelated processes. All models are many orders of magnitude more likely to show large bursts than would be predicted from uncorrelated activity; large population bursts are most likely in the PD-driven model.

Figure 7

Spectral Granger causality between cortical layers in each of the models. (A) The BG-driven model shows strong causality from layer 4 to 2/3 in the delta (<5 Hz) and high-beta/low-gamma (20–35 Hz) bands; causality in the latter band is almost entirely lost in Parkinson's disease. (B) The causality from layer 2/3 to layer 5 is slightly reduced in this band in Parkinson's disease. (C) These two effects combine to significantly reduce the total Granger causality from layer 4 to layer 5 in PD, especially in the high-beta/low-gamma band. (D) Similar reductions of Granger causality in this band were seen in other layer pairs, such as layer 6 to layer 2/3. In each case, the high-beta/low-gamma band Granger causality is significantly higher in the BG-driven model than in any of the other models.