Mathematical Modeling of How We Hear

For the Applied Mathematics Senior Seminar, I presented a literature review on mathematical modeling of innear ear (cochlea). In this presentation I introduce important figure in the cochlea modeling (George Von Békésy) and cover the basic biology of the ear crucial in sound perception. I investigated on a model proposed by Lesser and Berkley, a two-dimensional cochlea model that is consistent to Békésy's result. The presentation was co-written and co-presented by me (Joowon Park) and a peer in the Applied Mathematics Senior Seminar. A paper version written by me is available.

 
 
 Photo from nobleprize.org

Photo from nobleprize.org

History: Georg Von Békésy

In the late 19th century, scientists had anatomically discovered that nerve ending cells were attached to the basilar membrane in the inner ear. In the mid 20th century, Hungarian biophysicist Georg Von Békésy discovered that the basilar membrane was responsible for frequency selectivity, and received the Nobel Prize for his studies in the inner ear.  

 
 Photo from Dale,  Neuroscience, 3rd Edition,  Sinauer. pg.293

Photo from Dale, Neuroscience, 3rd Edition, Sinauer. pg.293

Biology: The Inner Ear

While external ear (pinna) and middle ear is responsible for sound localization, the inner ear transfers the energy from the sound wave into neural impulses. This presentation focuses on the basilar membrane, a structure that partitions the cochlea. Basilar membrane is wider and more flexible at the apex, and narrower and stiffer at the base. This characteristic contributes to the cochlea's frequency selectivity.

 

Mathematics: PDE with Boundary Conditions

This presentation introduces a simplified model of cochlea proposed by Lesser and Berkley (1972). The reason I chose to present on this was because their mathematical modeling reproduced Békésy's results. Mathematical derivations to the partial differential equations with boundary conditions were done in the chalkboard. The button below directs to my github where I uploaded a python notebook of derivations I presented on chalkboard. 


The following is the presentation given in the senior seminar on November 23rd with my partner. All the references for materials presented can be found in here. I also have written a paper-version of the literature review of mathematical modeling of the inner ear.