S.A. Campbell - Research Program

One aspect of my research program is motivated by some specific biological and mechanical systems: neural networks in the brain, the pupil light reflex, and metal cutting. Although physically unrelated, the behaviour of the these systems is influenced by the same factors: the presence of nonlinearities and time delays. The time delays represent the time it takes information to propagate from one part of the system to another. The nonlinearity represents the fact that in these systems a small change in the state can often result in a large change in behaviour. Another commonality of these systems is that they are all oscillators, i.e., objects that perform a repetitive motion. work is more mathematical in nature and aims to answer general questions about classes models.

Switching Oscillators with Time Delayed Feedback.
The oscillations considered here include the vibrations of a tool used in metal cutting and the dilation and constriction of the pupil of the eye. A notable aspect of these systems is that their defining properties rapidly switch depending on the state of the system. We will examine the role of time delayed feedback in creating, eliminating or reducing the size of oscillations in these systems. Videos
Neural Oscillators with Time Delayed Connections.
The brain is made up of cells called neurons which communicate with each other through electrical signals. It is well known that these signals are oscillatory and that the properties of the oscillations depend on how the characteristics of the individual neurons, how the neurons are connected to each other and the presence of time delays in the connections. We will answer questions such as: Why do neural cells in different brain structures have different characteristics? Why are neural cells connected in certain ways and not others? How do time delays affect the answers to these questions? Animations

A second part of my research program involves building and studying models for specific neural systems. This work is more closely tied to the applications. A significant part of the work is incorporating experimental data into the models. The goal is to use the models to understand mechanisms of neuron communication and answer direct questions about the specific systems.

Mathematical Models of Childhood Absence Epilepsy.
Mathematical Models of Rhythms in the Hippocampus.
This project is being done in collaboration with the lab of Frances Skinner at the Krembil Research Insitute, Toronto Western Hospital.
Computational Model for the Aplysia Bag Cell Neural Network
The bag cells of Aplysia (sea slug/sea hare) form a network of approximately 200 electrically coupled neurons which play a fundamental role in the reproductive behaviour of the animal. When Aplysia is ready to reproduce, the bag cell network undergoes a 20-40 minute period of repetitive firing called an afterdischarge. This afterdischarge causes the neurons to produce hormones which ultimately cause the animal to lay its eggs. Experiments have shown that the individual bag cells undergoe some fundamental changes in electrophysiological properties in order to produce the afterdischarge in the network. However, it is still unknown exactly how the afterdischarge occurs.

This project will investigate these questions by building a computational model for the bag cell network. Using the Hodgkin Huxley formalism and experimental ion channel data, we will build a biophysical differential equation model for a single bag cell. Numerical simulations and mathematical analysis will be carried out to determine the role of the various channels in the excitability of the single cell. Once the single cell is well understood, we will build a network of cells and investigate the afterdischarge behaviour.

This project is being done in collaboration with the lab of Neil Magoski in the Physiology Department at Queen's University.


This page maintained by Sue Ann Campbell.
Last update July 16, 2010.