Modelling Instantaneous Firing Rate of DBS Target Neuronal Ensembles in Basal Ganglia and Thalamus

ABSTRACT Objective Deep Brain Stimulation (DBS) is an effective treatment for movement disorders, including Parkinson’s disease and essential tremor. However, the underlying mechanisms of DBS remain elusive. Despite the capability of existing models in interpreting experimental data qualitatively, there are very few unified computational models that quantitatively capture the dynamics of the neuronal activity of varying stimulated nuclei—including subthalamic nucleus (STN), substantia nigra pars reticulata (SNr) and ventral intermediate nucleus (Vim)—across different DBS frequencies. Materials and Methods Both synthetic and experimental data were utilized in the model fitting; the synthetic data were generated by an established spiking neuron model that was reported in our previous work 1 , and the experimental data were provided using single-unit microelectrode recordings (MER) during DBS (microelectrode stimulation). Based on these data, we developed a novel mathematical model to represent the firing rate of neurons receiving DBS, including neurons in STN, SNr and Vim—across different DBS frequencies. In our model, the DBS pulses were filtered through a synapse model and a nonlinear transfer function to formulate the firing rate variability. For each DBS-targeted nucleus, we fitted a single set of optimal model parameters consistent across varying DBS frequencies. Results Our model accurately reproduced the firing rates observed and calculated from both synthetic and experimental data. The optimal model parameters were consistent across different DBS frequencies. Conclusion The result of our model fitting were in agreement with experimental single-unit microelectrode recording data during DBS. Reproducing neuronal firing rates of different nuclei of the basal ganglia and thalamus during DBS can be helpful to further understand the mechanisms of DBS, and to potentially optimize stimulation parameters based on their actual effects on neuronal activity.