Multivariate autoregressive models with exogenous inputs for intracerebral responses to direct electrical stimulation of the human brain

A multivariate autoregressive (MVAR) model with exogenous inputs (MVARX) is developed for describing the cortical interactions excited by direct electrical current stimulation of the cortex. Current stimulation is challenging to model because it excites neurons in multiple locations both near and distant to the stimulation site. The approach presented here models these effects using an exogenous input that is passed through a bank of filters, one for each channel. The filtered input and a random input excite a MVAR system describing the interactions between cortical activity at the recording sites. The exogenous input filter coefficients, the autoregressive coefficients, and random input characteristics are estimated from the measured activity due to current stimulation. The effectiveness of the approach is demonstrated using intracranial recordings from three surgical epilepsy patients. We evaluate models for wakefulness and NREM sleep in these patients with two stimulation levels in one patient and two stimulation sites in another resulting in a total of 10 datasets. Excellent agreement between measured and model-predicted evoked responses is obtained across all datasets. Furthermore, one-step prediction is used to show that the model also describes dynamics in pre-stimulus and evoked recordings. We also compare integrated information—a measure of intracortical communication thought to reflect the capacity for consciousness—associated with the network model in wakefulness and sleep. As predicted, higher information integration is found in wakefulness than in sleep for all five cases.