Response of neuronal populations to phase-locked stimulation: model-based predictions and validation.

Modulation of neuronal oscillations holds promise for the treatment of neurological disorders. Nonetheless, conventional stimulation in a continuous open-loop manner can lead to side effects and suboptimal efficiency. Closed-loop strategies such as phase-locked stimulation aim to address these shortcomings by offering a more targeted modulation. While theories have been developed to understand the neural response to stimulation, their predictions have not been thoroughly tested using experimental data. Using a mechanistic coupled oscillator model, we elaborate on two key predictions describing the response to stimulation as a function of the phase and amplitude of ongoing neural activity. To investigate these predictions, we analyze electrocorticogram recordings from a previously conducted study in Parkinsonian rats, and extract the corresponding phase and response curves. We demonstrate that the amplitude response to stimulation is strongly correlated to the derivative of the phase response ([Formula: see text] > 0.8) in all animals except one, thereby validating a key model prediction. The second prediction postulates that the stimulation becomes ineffective when the network synchrony is high, a trend that appeared missing in the data. Our analysis explains this discrepancy by showing that the neural populations in Parkinsonian rats did not reach the level of synchrony for which the theory would predict ineffective stimulation. Our results highlight the potential of fine-tuning stimulation paradigms informed by mathematical models that consider both the ongoing phase and amplitude of the targeted neural oscillation. This study validates a mathematical model of coupled oscillators in predicting the response of neural activity to stimulation for the first time. Our findings also offer further insights beyond this validation. For instance, the demonstrated correlation between phase response and amplitude response is indeed a key theoretical concept within a subset of mathematical models. This prediction can bring about clinical implications in terms of predictive power for manipulation of neural activity. Additionally, while phase dependence in modulation has been previously studied, we propose a general framework for studying amplitude dependence as well. Lastly, our study reconciles the seemingly contradictory views of pathologic hypersynchrony and theoretical low synchrony in Parkinson's disease.