DynSyst Special Topics: Mathematical Modeling of Nonlinear Dynamics and Bifurcation Control of Epileptic Seizures
Location(s): United States
In preliminary work, we have adapted a stochastic, nonlinear, partial differential equation model of mesoscale cortical dynamics to study seizure waves. We have applied the model to the sleeping cortex, and developed the capacity for automatic, continuous, real-time sleep staging. We have made a significant advance in model reduction using Locally Linear Embedding to associate patient EEG data and model dynamics. We have developed an understanding of how to apply ideas from feedback control theory to ameliorate?or eliminate?seizure waves rapidly in the model. To do so, we have understood the role of uncertainty or fluctuations on bifurcations. We have examined the model to consider possible pathways to changes in cortical physiology (mathematical bifurcations of the infinite dimensional model) from a normal state to one that can support seizures. Our technical goals for the project include the following: to explore propensity for seizure dynamics at different parts of the sleep cycle (in the model and in patients); to develop further our seizure control algorithms to more closely track designs of sense and actuation electrodes; and to explore the ways in which electrophysiological data of seizure onset in patients is related to cortical seizure susceptibility via different kinds of bifurcations in the model.
Over 50M people worldwide suffer from epileptic seizures. Of 2.5M Americans so afflicted, 20% suffer epilepsy that does not respond well to pharmacological treatment; they may undergo surgery to remove the affected part of the brain as a last resort. Our work to improve understanding of epilepsy will aid in the challenge to find a better form of treatment. Our approach is to explore seizure occurrence and control through a computer model, along with patient observations in a hospital setting. Eventually, seizure control may prove to be possible by sensing and application of electrical fields in affected parts of the brain. Appropriate methodologies will depend on brain state, the details of electrode placement and design, and how measurements might reveal they way in which seizure onset occurs. These are all points of study in project. These investigations will provide the foundation for new understanding of brain dynamics and will contribute to the development of a pathway to effective treatment.