Deep brain stimulation pulse sequences to optimally modulate frequency-specific neural activity

Objective. Precise neuromodulation systems are needed to identify the role of neural oscillatory dynamics in brain function and to advance the development of brain stimulation therapies tailored to each patient's signature of brain dysfunction. Low-frequency, local field potentials (LFPs) are of increasing interest for the development of these systems because they can reflect the synaptic inputs to a recorded neuronal population and can be chronically recorded in humans. In this computational study, we aim to identify stimulation pulse patterns needed to optimally maximize the suppression or amplification of frequency-specific neural activity.Approach. We derived DBS pulse patterns to minimize or maximize the 2-norm of frequency-specific neural oscillations using a generalized mathematical model of spontaneous and stimulation-evoked LFP activity, and a subject-specific model of neural dynamics in the pallidum of a Parkinson's disease patient. We leveraged convex and mixed-integer optimization tools to identify these pulse patterns, and employed constraints on the pulse frequency and amplitude that are required to keep electrical stimulation within its safety envelope.Main results. Our analysis revealed that a combination of phase, amplitude, and frequency pulse modulation is needed to attain optimal suppression or amplification of the targeted oscillations. Phase modulation is sufficient to modulate oscillations with a constant amplitude envelope. To attain optimal modulation for oscillations with a time-varying envelope, a trade-off between frequency and amplitude pulse modulation is needed. The optimized pulse sequences were invariant to changes in the dynamics of stimulation-evoked neural activity, including changes in damping and natural frequency or complexity (i.e. generalized vs. patient-specific model).Significance. Our results provide insight into the structure of pulse patterns for future closed-loop brain stimulation strategies aimed at controlling neural activity precisely and in real-time.