Geoffrey D. Clapp, Mathematics
“Modeling Sensory Input to the Lamprey Spinal Cord”
Faculty Mentor: Dr. Kathleen A. Hoffman
Expected Graduation Date: May 2011
We will develop numerical methods to better understand the effects of sensory input on vertebrate locomotion. Sensory input is known to have a profound effect on vertebrate locomotion but is not well understood. The lamprey, a relative of the eel, is a model system for studying vertebrate locomotion because its spinal cord is experimentally accessible and contains the same types of neurons as its human counterpart, except in smaller quantities. Biological experiments reveal an intriguing dependence on position of sensory organs in the lamprey, called edge cells, which measure the bend in the body. To further understand this phenomenon, we model the lamprey spinal cord as a chain of coupled oscillators. Edge cells are simulated by forcing at various positions along the chain, one at a time, as in the experiment. We will develop an algorithm using numerical continuation to determine entrainment ranges, that is, the range of forcing frequencies for which the electrical activity along the spinal cord oscillates with the same constant frequency as the forcer. Previous results using numerical simulation are in good agreement with the theory for sufficiently high connection strength between the forcer and the chain. However, for smaller connection strengths, simulation was not able to produce the theoretical results. Numerical continuation provides a more direct method for determining entrainment ranges in contrast with numerical simulation which depends on accurately computing transient behavior.