The following is adapted from a short overview of my research I gave at the 2017 Swarthmore College Faculty Showcase (Nov 10, 2017)
Three ways in which I apply mathematics to understand the auditory system
Analyze neural dynamics
I develop mathematical models to describe the dynamics of neurons in the auditory pathway. The neuron pictured in the first column is in a region of the brain called the medial superior olive (or MSO). What’s remarkable about these neurons, is that they are able to compare the timing of sounds arriving at our two ears with microsecond-scale temporal precision. This exquisite timing calculation allows us to sense the spatial locations from which sounds originate.
I am currently working to understand how the structure of these cells affects their dynamics and function. Specifically, I am determining how the coupling between the axon and the cell affects the temporal precision of MSO neurons. To do this, I construct an idealized mathematical model of the neuron. I imagine that the cell can be lumped, roughly, into two regions: the axon (output) region and the remaining (input) regions. I then systematically explore the behavior of my mathematical neuron model as I change the connection between these regions.
This approach of formulating minimal, or idealized models, is a common strategy across my work. I use it to uncover essential properties of complex systems.
Understand neural data
I also develop mathematical models and methods to understand neural data recorded by experimental collaborators. One type of data that is relatively easy to obtain but difficult to understand is extracellular voltage. Extracellular voltages are recorded in the space between neurons. These signals represent a complicated mixture of the activity of many neurons.
I recently worked with expert collaborators who recorded extracellular voltage signals in auditory regions of the brain. I developed a model that successfully reproduced the spatial-temporal patterns of extracellular voltages recorded by my collaborators, as shown in the middle column. Using this model, we gained new understanding of these complicated neural signals.
Improve neural prostheses
Unfortunately, the auditory system does not always work flawlessly. For some individuals with profound hearing loss, surgically implanted devices called cochlear implants can restore a sense of hearing by electrically activating neurons in the inner ear. I have developed models to accurately simulate the responses of auditory neurons to cochlear implants, as shown here. I can then use this model to evaluate cochlear implant designs, by quantifying how effectively sound information is provided to users of these devices.
This project is especially gratifying because it represents an opportunity to use mathematics to improve the quality of life of individuals with hearing impairment.