From Observation to Control of Nonlinear Neuronal Networks in Brain
Open Access
- Author:
- Whalen, Andrew John
- Graduate Program:
- Mechanical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- August 16, 2017
- Committee Members:
- Steven Schiff, Dissertation Advisor/Co-Advisor
Sean N Brennan, Committee Chair/Co-Chair
Reka Z Albert, Committee Member
Alok Sinha, Committee Member
Tim Sauer, Outside Member - Keywords:
- spreading depression
suppression
confinement
electric field
modulation
spreading depolarization
network control
complex networks
nonlinear
symmetry
brain networks
network observation - Abstract:
- Once an adequate understanding of a natural system is reached, laws embodied in computational models can be formulated and the optimal way to observe such systems is to fuse models with measurement data. Common in engineering and physics, such data assimilation has only recently been applied to biology. However, once computational models of biological systems are created, how effectively can the system be reconstructed -- that is, how observable are the models or the real systems they represent? Previously restricted to mathematical physics, quantifying observability for computational neuroscience models and controlling biological tissue in vitro appears tractable from the present results. In constructing a model to observe a system, how does symmetry effect reconstruction? In part one, this manuscript presents the extension of present observability theory to nonlinear network dynamics fundamental to biological dynamics, and fuses it with the symmetry theory appropriate in the analysis of such networks. In constructing a controller from an observer model of a real system, can the system be controlled? Part two of this manuscript validates insights from computational studies of pathological brain waves through careful experiments, establishing the control vector necessary to arrest adverse propagations in vitro.