[CTN] seminar June 12

[Sue Ann Campbell]

Hello,

Please see below for details of a talk which may be of interest.
I've asked the speaker to make the talk accessible to an interdisciplinary 
audience.  He will be visiting Waterloo for several days, so if you are 
interested in meeting with him, let me know.

Sue Ann

Applied Math Seminar
Tuesday, June 12, 3:30 p.m. MC5158

Optimal Control of Neurons 

Ali Nabi 
Department of Mechanical Engineering 
University of California at Santa Barbara 


Motivated by issues related to treating certain neurological diseases such 
as Parkinson's disease by a method called electrical deep brain stimulation, 
we consider applying optimal control methods to both mathematical models of 
neurons and in vitro neurons.  Patients suffering from Parkinson's disease 
experience involuntary tremors that typically affect the distal portion 
of their upper limbs.  It has been hypothesized that these tremors are 
associated with simultaneous spiking of a cluster of neurons in the thalamus 
and basal ganglia regions of the brain.  In a healthy situation, the periodic 
ring of neurons is not synchronized, but they can engage in a pathological 
synchrony and all fire at the same time which results in release of strong 
action potentials that trigger the downstream muscles with periodic shocks, 
manifested as tremors. 


In this talk, we investigate the control of different neuronal systems 
using methods of optimal control.  The neuronal systems considered range 
from simple one-dimensional phase models to multi-dimensional conductance-based 
models, both on a single neuron level and on a population level.  The 
optimal control methods considered produce event-based, continuous-time, 
typically bounded input stimuli that can optimally achieve the desired 
control objective.  The optimality criterion considered is minimum energy. 
The control objectives of interest are the interspike interval for single 
neurons and desynchrony for populations of neurons.  The applicability of 
the interspike interval controller is shown in practice by testing it 
on single in vitro pyramidal neurons in the CA1 region of rat hippocampus. 



-- 
Dr. S.A. Campbell                   Professor 
Department of Applied Mathematics   office: MC5124
University of Waterloo              email: sacampbell at uwaterloo.ca
Waterloo Ontario                    phone:(519)888-4567 x35461
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