Using a hybrid neuron in physiologically inspired models of the basal ganglia

Abstract

Our current understanding of the basal ganglia (BG) has facilitated the creation of computational models that have contributed novel theories, explored new functional anatomy and demonstrated results complementing physiological experiments. However, the utility of these models extends beyond these applications. Particularly in neuromorphic engineering, where the basal ganglia's role in computation is important for applications such as power efficient autonomous agents and model-based control strategies. The neurons used in existing computational models of the BG, however, are not amenable for many low-power hardware implementations. Motivated by a need for more hardware accessible networks, we replicate four published models of the BG, spanning single neuron and small networks, replacing the more computationally expensive neuron models with an Izhikevich hybrid neuron. This begins with a network modeling action-selection, where the basal activity levels and the ability to appropriately select the most salient input is reproduced. A Parkinson's disease model is then explored under normal conditions, Parkinsonian conditions and during subthalamic nucleus deep brain stimulation (DBS). The resulting network is capable of replicating the loss of thalamic relay capabilities in the Parkinsonian state and its return under DBS. This is also demonstrated using a network capable of action-selection. Finally, a study of correlation transfer under different patterns of Parkinsonian activity is presented. These networks successfully captured the significant results of the originals studies. This not only creates a foundation for neuromorphic hardware implementations but may also support the development of large-scale biophysical models. The former potentially providing a way of improving the efficacy of DBS and the latter allowing for the efficient simulation of larger more comprehensive networks.

Keywords: Izhikevich neuron; Parkinson's disease; action-selection; basal ganglia models; correlation analysis; deep brain stimulation.

Figure 1

Firing characteristics of single model neurons of the Basal Ganglia. Many of the firing characteristics inherent to neurons of the BG nuclei are captured by the simple hybrid model. The model parameters used to achieve these patterns are Striatum (STR): (a = 0.02, b = 0.2, c = −65.0, d = 8.0), Subthalmic Nucleus (STN): (a = 0.005, b = 0.265, c = −65.0, d = 2.0), Globus Pallidus Externa (GPe): (a = 0.005, b = 0.585, c = −65.0, d = 4.0), Thalamocortical Neuron (TC): (a = 0.002, b = 0.25, c = −65.0, d = 0.05), Substania Nigra pars reticulata (SNr): (a = 0.005, b = 0.32, c = −65.0, d = 2.0). Note that the globus pallidus interna (GPi) response is not shown here but has similar firing characteristics to the GPe neurons only with a higher basal level of firing.

Figure 2

Action-selection network model (Humphries et al., 2006).

Figure 3

(A) Network layout of Rubin and Terman (2004). (B) Individual neuron connections.

Figure 4

Correlation network configuration (Reitsma et al., 2011).

Figure 5

Example GPi spike patterns and TC cell responses for each of the four modes. (A) Example input rate functions. Resulting GPi spike trains, (B), and TC Cell responses, (C).

Figure 6

Basal activity of the model of action-selection. Upper left: The mean rates for the STN, GPe, and SNr qualitatively match the simulated and experimental results of Humphries et al. (2006). Remaining plots: The spike rasters for each of the nuclei are overlaid with the corresponding spike-count firing rates.

Figure 7

Action-selection performance. The model is capable of appropriate selecting the most salient input between two competing channels (A) as well as three competing channels (B).

Figure 8

Network response to competing inputs; spike rasters of the major nuclei of the BG action-selection with the spike count rates overlaid.

Figure 9

Simulated recovery of TC relay fidelity. (A) Under normal BG activity the thalamus is capable of relaying somatomotor inputs. (B) Under Parkinsonian conditions the BG nuclei fall into oscillatory firing patterns TC relay capabilities are greatly diminished. (C) Application of DBS to the STN restores lost TC relay fidelity.

Figure 10

Error index statistics. Allowing the network connection weights to randomly change over 20 simulations results in the Normal and DBS modes operating with less errors than the PD mode.

Figure 11

Parkinsonian fire patterns result in a loss of accurate selection capabilities.

Figure 12

Correlation analysis. Spectral power of the GPi input patterns (A), excitatory input (B) and corresponding TC cell response (C). (D) ISI profile of the TC Cells. (E) Correlation susceptibility for T = 95 ms (F) Susceptibility S of the TC cells based on the analysis window T.

Figure 13

Simplified example of how these models fit in a model based control DBS paradigm.