Modulation of Nonlinear Neural Dynamics for Closed-Loop Deep Brain Stimulation Systems

Accurate modeling of complex neural dynamics can advance closed-loop neuromodulation systems for the treatment of neurological and neuropsychiatric disorders. Recent efforts have shown the potential of closed-loop deep brain stimulation (DBS) as a promising treatment in human studies. However, these studies have largely focused on turning the DBS on and off based on a threshold on a neural biomarker. In parallel, computational efforts in-silico or in animal models have explored the use of linear state-space models (LSSMs) to describe neural dynamics and develop standard controllers. However, such linear models fall short of capturing the inherent nonlinearities of neural dynamics. Here we design modeling and neuromodulation strategies that can capture nonlinear dynamics and test them in biologically inspired closed-loop DBS simulations. We first design a Koopman operator-based approach, which is a linear operator capable of representing nonlinear systems in a higher-dimensional space, thus allowing for the use of well-established linear control tools. We find that despite its advantages over LSSMs, the Koopman operator struggles with complex neural dynamics, which may be due to challenges in observation function selection and data collection constraints. We then design a neural network-based approach, which first learns recurrent neural networks (RNNs) to effectively capture nonlinear dynamic patterns and then couples the RNNs with the iterative linear quadratic regulator (iLQR), a locally optimal feedback control strategy. We find that the RNN-iLQR framework outperforms the Koopman operator and LSSM-based approaches in system identification and control accuracy in our biologically inspired closed-loop DBS simulations. This work shows the potential of this method for developing future closed-loop neuromodulation systems.