A framework for identification of brain network dynamics using a novel binary noise modulated electrical stimulation pattern

Modeling and identification of brain network dynamics is of great importance both for understanding brain function and for closed-loop control of brain states. In this work, we present a multi-input-multi-output (MIMO) linear state-space model (LSSM) to describe the brain network dynamics in response to electrical stimulation. The LSSM maps the parameters of electrical stimulation, such as frequency, amplitude and pulse-width to recorded brain signals such as electrocorticography (ECoG) and electroencephalography (EEG). Effective identification of the LSSM in open-loop stimulation experiments, however, is strongly dependent on the open-loop input stimulation design. We propose a novel input design to accurately identify the LSSM by integrating the concept of binary noise (BN) with practical constraints on stimulation waveforms. The designed input pattern is a pulse train modulated by stochastic BN parameters. We show that this input pattern both satisfies the necessary spectral condition for accurate system identification and can incorporate any desired pulse shape. Using numerical experiments, we show that the quality of identification depends heavily on the input signal pattern and the proposed binary noise modulated pattern achieves satisfactory identification results, reducing the relative estimation error more than 300 times compared with step sequence modulated, single-sinusoid modulated and multi-sinusoids modulated input patterns.