Evoked Resonant Neural Activity Long-Term Dynamics can be Reproduced by a Computational Model with Vesicle Depletion

Subthalamic deep brain stimulation (DBS) robustly generates high-frequency oscillations known as evoked resonant neural activity (ERNA). Recently the importance of ERNA has been demonstrated through its ability to predict the optimal DBS contact in the subthalamic nucleus in patients with Parkinson’s disease. However, the underlying mechanisms of ERNA are not well understood, and previous modelling efforts have not managed to reproduce the wealth of published data describing the dynamics of ERNA. Here, we therefore aim to present a minimal model capable of reproducing the characteristics of the slow ERNA dynamics published to date. We make biophysically-motivated modifications to the Kuramoto model and fit its parameters to the slow dynamics of ERNA obtained from data. We further validate the model against experimental data from Parkinson’s disease patients by simulating variable stimulation and medication states, as well as the response of individual neurons. Our results demonstrate that it is possible to reproduce the slow dynamics of ERNA with a single neuronal population, and, crucially, with vesicle depletion as the key mechanism behind the ERNA frequency decay. We provide a series of predictions from the model that could be the subject of future studies for further validation. Author Summary ERNA is a high amplitude response to stimulation of deep brain structures, with a frequency over twice that of the frequency of stimulation. While the underlying mechanisms of ERNA are still unclear, recent findings have demonstrated its importance as the best indicator of which stimulation contact to select for DBS therapy in patients with Parkinson’s disease. Previous modelling studies of ERNA focus on the immediate responses to stimulation ( < 200ms) and rely on interconnected neural structures and delays. Our work shows that the long-term (on the scale of one or more seconds) ERNA response to continuous stimulation can be modelled using a single neural structure. The proposed model also captures the long-term frequency and amplitude characteristics of ERNA with variable stimulation and medication paradigms. The key features of the model, in particular the depletion of vesicles carrying neurotransmitters between neurons by high-frequency stimulation, may provide insights into the underlying mechanisms of ERNA and inform future investigations into this neural response. ### Competing Interest Statement TD is a founder, director, and shareholder of Amber Therapeutics, Ltd, which also has a controlling interest in Bioinduction Ltd and Finetech Medical Ltd, the respective designers and manufacturers of the Picostim DyNeuMo system. TD is also an advisor for Synchron and Cortec Neuro.