Articulo

J Comput Neurosci DOI 10.1007/s10827-010-0215-x

A model of feedback control for the charge-balanced suppression of epileptic seizures
Beth A. Lopour · Andrew J. Szeri

Received: 3 April 2009 / Revised: 6 October 2009 / Accepted: 7 January 2010 © The Author(s) 2010. This article is published with open access at Springerlink.com

Abstract Here we present several refinements to a model offeedback control for the suppression of epileptic seizures. We utilize a stochastic partial differential equation (SPDE) model of the human cortex. First, we verify the strong convergence of numerical solutions to this model, paying special attention to the sharp spatial changes that occur at electrode edges. This allows us to choose appropriate step sizes for our simulations; because the spatialstep size must be small relative to the size of an electrode in order to resolve its electrical behavior, we are able to include a more detailed electrode profile in the simulation. Then, based on evidence that the mean soma potential is not the variable most closely related to the measurement of a cortical surface electrode, we develop a new model for this. The model is based on the currentsflowing in the cortex and is used for a simulation of feedback control. The simulation utilizes a new control algorithm incorporating the total integral of the applied electrical potential. Not only does this succeed in suppressing the seizure-like oscillations, but it guarantees that the applied signal will be charge-balanced and therefore unlikely to cause cortical damage.

Keywords Epilepsy ·Seizure · Feedback · Control · Electrocorticogram · Human

1 Introduction The recurrent, unprovoked seizures associated with epilepsy can have a devastating effect on those with this disorder. Basic parts of every day life such as driving and obtaining employment become very difficult. While many people with epilepsy can control their seizures with medication, roughly thirty percent do not respond tothis type of treatment and therefore seek out alternatives such as surgery (The Epilepsy Foundation 2009). The surgical procedure involves resecting the seizing portion of the brain, often part of the cortex, while avoiding any areas that provide vital functions such as speech, memory, and vision (The Epilepsy Foundation 2009). Because this is a very invasive procedure that does not guaranteesuccess, other alternatives are being investigated. One of these is automatic feedback control, where subdural electrodes on the cortical surface would detect the seizure and apply an electrical signal to disrupt the abnormal electrocorticogram (ECoG) activity. This method of treatment is currently being studied by experimentalists. It has been shown that the application of electric fields to ratcortex in vitro can modulate the behavior of seizure-like waves (Richardson et al. 2005). In vivo experiments on rats demonstrated that stimulation via proportional feedback can temporarily suppress seizure activity (Gluckman et al. 2001). A subsequent set of experiments showed that an increase in the amplitude of the proportional control feedback gain corresponds to decreases in both seizureamplitude

Action Editor: Steven J. Schiff B. A. Lopour · A. J. Szeri (B) Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA e-mail: aszeri@me.berkeley.edu B. A. Lopour e-mail: bethlopour@berkeley.edu

J Comput Neurosci

(measured as a reduction in the amplitude variance) and Teager energy (Colpan et al. 2007). The Teager energy can be reduced by a decrease inthe amplitude of a signal or a lowering of the frequencies in its power spectrum. While these experiments suggest further exploration, they are all restricted to animal implementation. Therefore, to gain insight into the feasibility of human use, we turn first to mathematical models. The stochastic partial differential equation (SPDE) model of the cortex used here can support seizure-like...