Abstract
Recent advances in Kalman filtering to estimate system state and parameters in nonlinear systems have offered the potential to apply such approaches to spatiotemporal nonlinear systems. We here adapt the nonlinear method of unscented Kalman filtering to observe the state and estimate parameters in a computational spatiotemporal excitable system that serves as a model for cerebral cortex. We demonstrate the ability to track spiral wave dynamics, and to use an observer system to calculate control signals delivered through applied electrical fields. We demonstrate how this strategy can control the frequency of such a system, or quench the wave patterns, while minimizing the energy required for such results. These findings are readily testable in experimental applications, and have the potential to be applied to the treatment of human disease.
Highlights
In 1809, Carl Frederic Gauss [1] dealt in depth with problem of estimation of planetary and comet orbit parameters when the terrestrial observational data was sparse and imprecise
We here adapt the nonlinear method of unscented Kalman filtering (UKF) to observe the state and estimate parameters in a computational spatiotemporal excitable system that serves as a model of cerebral cortex
We employ the modifications to the Wilson-Cowan equations as suggested by Pinto and Ermentrout [2], to model an experimental system in which we measure the wave dynamics of mammalian middle cortical layers using voltage sensitive dye
Summary
In 1809, Carl Frederic Gauss [1] dealt in depth with problem of estimation of planetary and comet orbit parameters when the terrestrial observational data was sparse and imprecise. Gauss's problem bears strong resemblance to the problem we face in the estimation of neuronal state through electrical or optical measurements. Recent advances in Kalman filtering to estimate system state and parameters in nonlinear systems has offered the potential to apply such approaches to spatiotemporal neuronal systems. We here adapt the nonlinear method of unscented Kalman filtering (UKF) to observe the state and estimate parameters in a computational spatiotemporal excitable system that serves as a model of cerebral cortex
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