Geoffrey Clapp, Mathematics and Computer Science

Modeling Sensory Input to the Lamprey Spinal Cord

Faculty Mentor: Dr. Kathleen Hoffman

*New* - Winner of the National Science Foundation Graduate Research Fellowship

We will develop a mathematical model of the central pattern generator (CPG) of the lamprey spinal cord in order to better understand the effects of sensory input on vertebrate locomotion. The lamprey, a relative of the eel, is a model system for studying vertebrate locomotion because its spinal cord contains the same types of neurons as its human counterpart, except in smaller quantities. Biological experiments have revealed that the lamprey’s swimming behavior is modulated by input to the spinal cord from edge cells, sensory organs that measure the body’s curvature. A mathematical model has become essential to advancing our knowledge on this topic because of the degree of complexity and precision required to obtain accurate experimental data. We will consider both neural and phase models of the CPG. In both cases, the CPG is represented as a chain of connected oscillators. However, a neural model provides representation for multiple groups of neurons within each oscillator, making it more biologically detailed than a phase model, which represents each oscillator by only one variable. Previous work has compared results from our neural model to results from an unrelated phase model. The goal of our project is to derive a phase model from our neural model using phase reduction techniques, which will allow us to make direct comparisons between the models. Our results will help us to determine the appropriate degree of biological detail for a model used to study the role of edge cells in the lamprey swimming behavior.

**How did you find your mentor for this project?**

I took Calculus III and a first year math-biology seminar with my mentor, Dr. Hoffman. During the seminar, she presented some of her research.

**How did you know this was the project you wanted to do?**

The seminar course really sparked my interest in applied math, specifically applications of math in biology. The project was a great opportunity to explore this field.

**How much time do you put into it?**

It really depends on what needs to be done, but I meet with my mentor weekly to provide a status report and to figure out what needs to be done next.

**How did you hear about the Undergraduate Research Award program?**

My mentor noticed it on the UMBC website and suggested that I apply.

**What academic background did you have before you started?**

I had completed courses in math-biology and differential equations. I had also learned Java, C, and Matlab through my coursework, which are important tools for mathematical modeling.

Was the application difficult to do?

No, it wasn't bad at all. Actually, completing the application helped me plan for next year's research.

**How much did your mentor help you with this?**

She provided me with resources on mathematical modeling and the important biology concepts and answered any question I had.

What is your advice to other students about getting involved in research?

Definitely do it if you can - it's a great opportunity to immediately apply what you're learning in class.

**What are your career goals?**

I plan to get my Ph.D. in applied mathematics and to become a professor at the university level.

**What has been the hardest part about your research?**

The hardest part about my research is debugging the code. Sometimes we find a one character mistake that means that we have to redo months of work.

**What was the most unexpected thing?**

The most unexpected part of my research has been that five different universities are working together on this project. Our part of the project is modeling input to the spinal cord, and the other groups are working on fluid dynamics and muscle activity involved in swimming.

How does your research relate to your work in other classes?

Almost all of my math and computer science courses have helped me to better understand various concepts in my research.