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

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 substructures of the basal ganglia and thalamus respond differently to various frequencies of DBS. Despite the capability of existing models in qualitatively interpreting experimental data, there are very few unified computational models that quantitatively capture the dynamics of the neuronal activity of varying stimulated substructures—including subthalamic nucleus (STN), substantia nigra pars reticulate (SNr) and ventralis intermedius (Vim)— across different DBS frequencies. Here, we developed a novel mathematical model to represent the firing rate of nuclei receiving DBS (microstimulation), including STN, SNr and Vim—across different DBS frequencies. In our model, the DBS pulses are filtered through a synapse model and a 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. Our model accurately reproduces the firing rates observed and calculated from both experimental and synthetic 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. Our model can be potentially implemented in navigating the DBS parameter space and improves DBS clinical effects.