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Abstract. Deep brain stimulation (DBS) of the subthalamic nucleus (STN) or the internal segment of the globus pallidus (GPi) has recently been recognized as an important form of intervention for alleviating motor symptoms associated with Parkinson's disease, but the mechanism underlying its effectiveness remains unknown. Using a computational model, this paper considers the hypothesis that DBS works by replacing pathologically rhythmic basal ganglia output with tonic, high frequency firing. In our simulations of parkinsonian conditions, rhythmic inhibition from GPi to the thalamus compromises the ability of thalamocortical relay (TC) cells to respond to depolarizing inputs, such as sensorimotor signals. High frequency stimulation of STN regularizes GPi firing, and this restores TC responsiveness, despite the increased frequency and amplitude of GPi inhibition to thalamus that result. We provide a mathematical phase plane analysis of the mechanisms that determine TC relay capabilities in normal, parkinsonian, and DBS states in a reduced model. This analysis highlights the differences in deinactivation of the low-threshold calcium T -current that we observe in TC cells in these different conditions. Alternative scenarios involving convergence of thalamic signals in the cortex are also discussed, and predictions associated with these results, including the occurrence of rhythmic rebound bursts in certain TC cells in parkinsonian states and their drastic reduction by DBS, are stated. These results demonstrate how DBS could work by increasing firing rates of target cells, rather than shutting them down.

Based on recent experimental data, we have developed a conductance-based computational network model of the subthalamic nucleus and the external segment of the globus pallidus in the indirect pathway of the basal ganglia. Computer simulations and analysis of this model illuminate the roles of the coupling architecture of the network, and associated synaptic conductances, in modulating the activity patterns displayed by this network. Depending on the relationships of these coupling parameters, the network can support three general classes of sustained firing patterns: clustering, propagating waves, and repetitive spiking that may show little regularity or correlation. Each activity pattern can occur continuously or in discrete episodes. We characterize the mechanisms underlying these rhythms, as well as the influence of parameters on details such as spiking frequency and wave speed. These results suggest that the subthalamopallidal circuit is capable both of correlated rhythmic activity and of irregular autonomous patterns of activity that block rhythmicity. Increased striatal input to, and weakened intrapallidal inhibition within, the indirect pathway can switch the behavior of the circuit from irregular to rhythmic. This may be sufficient to explain the emergence of correlated oscillatory activity in the subthalamopallidal circuit after destruction of dopaminergic neurons in Parkinson's disease and in animal models of parkinsonism. Key words: basal ganglia; subthalamic nucleus; globus pallidus; computational models; oscillations; synchrony; Parkinson's diseaseMost current models of the basal ganglia are static models, in that they represent the inputs and outputs of the component nuclei as firing rates. For example, the Albin et al. (1989) model, commonly used to explain the symptoms of Parkinsonism, views the interactions of the direct and indirect pathway as constant in time and explains the symptoms of Parkinson's disease in terms of changes in mean rate of the basal ganglia output (Wichmann and DeLong, 1996). In contrast, recent experimental studies have not strongly confirmed the predicted changes in mean rate in these structures under dopamine depletion, but have instead revealed prominent low-frequency periodicity (4 -30 Hz) of firing and dramatically increased correlations among neurons in the external segment of the globus pallidus (GPe) and the subthalamic nucleus (STN) (Bergman et al., 1994;Nini et al., 1995;Magnin et al., 2000;Raz et al., 2000;Brown et al., 2001). It is remarkable that the changes in firing pattern seen in those structures do not appear to be attributable to comparable changes in the firing patterns of striatal output cells, although cholinergic striatal interneurons show changes comparable with those seen in the globus pallidus (Raz et al., 1996). The authors of those studies have proposed that a rate model of the basal ganglia is inadequate to capture the dynamic interaction of the STN and GPe that may generate these pathological changes.In particular, such dynamic interactions ma...

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