Hindmarsh-Rose neuronal network with spike-timing-dependent plasticity demonstrates coordinated reset neuromodulation

Computational models of brain structures impacted by Parkinsons disease are useful for exploring potential therapies. We use the Hindmarsh-Rose neuronal model to simulate synchronized activity in the subthalamic nucleus, capturing key features of the pathological rhythms observed in Parkinsons disease using a relatively small network of 100 neurons. Our model incorporates unidirectional excitatory chemical synapses whose strengths evolve according to a spike-timing-dependent plasticity (STDP) rule. To account for inputs from unmodelled neurons, both uniformly distributed white noise and Poisson noise were explored. White noise produced a single stable state of synchronized neuronal activity whereas Poisson noise resulted in two stable states, one synchronized and one desynchronized. We applied coordinated reset stimulation with a rapidly varying sequence (RVS CR) to examine its ability to reduce neuronal synchrony. The neuronal population was divided into subpopulations representing distinct physical sites of stimulation, as in deep brain stimulation therapy, and phase-shifted stimuli were delivered to each subpopulation in a random sequence. We explored how stimulation frequency and the number of stimulation sites affect the efficacy of RVS CR at desynchronizing the network. We demonstrate that RVS CR efficacy is sensitive to the depression-to-potentiation ratio in the STDP rule, which may be an important parameter to tune when reconciling simulations with experimental data. Numerical simulation of neuronal networks is constrained by computational resources when models demand large networks. This work proposes a model that demonstrates similar utility with a relatively small network, enabling researchers to study pathological neuronal activity and treatments more efficiently.