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This article is part of the Research Topic Manipulative approaches to human brain dynamics


Front. Hum. Neurosci., 30 November 2012 | http://dx.doi.org/10.3389/fnhum.2012.00317

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

  • 1Department of Electrical and Computer Engineering, University of Wisconsin, Madison, WI, USA
  • 2Department of Clinical Sciences, University of Milan, Milan, Italy
  • 3Department of Psychiatry, University of Wisconsin, Madison, WI, USA
  • 4Centre of Epilepsy Surgery “C. Munari”, Niguarda Hospital, Milan, Italy

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.

Keywords: intracerebal EEG, evoked response, MVARX model, cross-validation, integrated information

Citation: Chang J-Y, Pigorini A, Massimini M, Tononi G, Nobili L and Van Veen BD (2012) Multivariate autoregressive models with exogenous inputs for intracerebral responses to direct electrical stimulation of the human brain. Front. Hum. Neurosci. 6:317. doi: 10.3389/fnhum.2012.00317

Received: 24 August 2012; Accepted: 07 November 2012;
Published online: 30 November 2012.

Edited by:

Keiichi Kitajo, RIKEN Brain Science Institute, Japan

Reviewed by:

Stefan Haufe, Berlin Institute of Technology, Germany
Adam Barrett, University of Sussex, UK

Copyright © 2012 Chang, Pigorini, Massimini, Tononi, Nobili and Van Veen. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in other forums, provided the original authors and source are credited and subject to any copyright notices concerning any third-party graphics etc.

*Correspondence: Barry D. Van Veen, Department of Electrical and Computer Engineering, University of Wisconsin, 3611 Engineering Hall, 1415 Engineering Drive, Madison, WI 53706, USA. e-mail: vanveen@engr.wisc.edu