Optimal Control of Models of Neural Population Dynamics
Experimental and Theoretical Network Neuroscience
Final Report Abstract
The stimulation of neural systems plays a crucial role in both experimental and theoretical research in neuroscience. Mathematical modeling provides valuable insights into the mechanisms that drive local or global neural responses to targeted perturbations. Optimal Control Theory (OCT) offers a framework for designing efficient stimulation protocols to induce or suppress specific neural dynamics. In this context, control inputs are optimized based on cost functionals that balance achieving the desired target activity with minimizing the intensity of the applied control. In this project, we developed and implemented tools to study optimal control (OC) of neural population dynamics. To this end, the open-source software framework neurolib was extended by an OC module. The OC module is implemented in a user-friendly and modular way, allowing for straightforward usage and for easy modification and extension to fit the needs of new research questions. Furthermore, the OC module enables the computation of OC signals in noisy systems. We focused on two representatives of the common motif of recurrently coupled populations of excitatory and inhibitory neurons. The Wilson-Cowan (WC) model is a low-dimensional, comparatively simple, phenomenological model. By contrast, the mean-field adaptive exponential integrate-and-fire (AdEx) model is a high-dimensional model, which describes the collective dynamics of sparsely and randomly coupled excitatory and inhibitory AdEx neurons in the limit of infinite network size. The broad applicability of our methods is thus demonstrated through successful application to one simple and one complex model. Oscillations and synchrony frequently emerge and spread over large parts of the brain. They play a pivotal role in ensuring the well-functioning of neural systems. However, OC of oscillatory phenomena is technically challenging because of the necessity to apply appropriate cost functionals. We systematically studied and evaluated various options for cost functionals to control oscillations and (de-)synchronization. Results have been published in Frontiers in Computational Neuroscience. Three cost functionals have proven useful for the study of the control of oscillations and synchrony: The Fourier cost evaluates the Fourier spectrum of the system activity. It is applicable to enforce oscillations at a specific frequency and to synchronize networks, if the synchronization frequency is known. The cross-correlation cost and the variance cost enable to (de-)synchronize networks by evaluating either the pairwise cross-correlation of the activity of nodes or the variance of the activity throughout a network. Finally, we studied optimal (de-)synchronization of a whole-brain (WB) network model. Our results suggest that both shape and timing of the optimal (de-)synchronization control signals are primarily determined by the phase response curve (PRC) of the isolated neural population at the respective point in state space. Furthermore, we find that the importance of a specific node for efficient network control can be estimated from their connection strength in the network.
Publications
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A framework for optimal control of oscillations and synchrony applied to non-linear models of neural population dynamics. Frontiers in Computational Neuroscience, 18.
Salfenmoser, Lena & Obermayer, Klaus
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Optimal Control of Nonlinear Models of Neural Population Dynamics. PhD thesis at the Technische Universität Berlin
L. Salfenmoser
