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

Objective Parkinson’s disease (PD) is the second most common neurodegenerative disorder symptom, and is closely related to the dysfunction of the basal ganglia-thalamocortical network. Deep Brain Stimulation (DBS) is an effective treatment for suppressing PD motor symptoms; however, the underlying mechanisms of DBS remain elusive. A recent study demonstrated that different nuclei of the basal ganglia and thalamus respond differently to various frequencies of DBS. 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 reticulate (SNr) and ventralis intermedius (Vim)—across different DBS frequencies. Materials and Methods Both synthetic and experimental data were utilized in model fits; the synthetic data were the simulations from an established spiking neuron model, and the experimental data were the single-unit recordings during DBS (microstimulation). 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 are filtered through a synapse model and a nonlinear transfer function to formulate the firing rate variability. To consistently fit the model in varying frequencies of DBS, we developed a novel parameter optimization method based on the concatenated data from all DBS frequencies. Results Our model accurately reproduces the firing rates observed and calculated from both synthetic and experimental data. The optimal model parameters are consistent across different DBS frequencies, and this consistency conforms to the relatively static synaptic structures in short durations of DBS. Conclusion Our model can detect the firing rate dynamics in response to DBS, and potentially implemented in navigating the DBS parameter space and improving DBS clinical effects. ### Competing Interest Statement The authors have declared no competing interest.