The investigator and his collaborator, Joseph Blum, have offered the only proposal for how the neurons in the lateral superior olive collectively compute and encode azimuthal location based on sound level difference at the ears. Recent experimental evidence indicates that their proposal may be correct. In the first part of this project, the investigator works with collaborators to compare the model predictions with experimental results. Analytical investigations explain why the model encoding is very independent of sound level and exceptionally robust to parameter variations and synapse and cell death. A second part of the project uses mathematical models and machine computation to investigate neural processing in the dorsal nucleus of the lateral lemniscus, DNLL, an important intermediary processing region between the superior olivary complex and the midbrain. Recent experimental studies have shed new light on the anatomy and physiology of the DNLL, but no modelling studies have been performed to understand how the DNLL neurons process their inputs and influence the encoding of a map of space in the auditory midbrain. Using mathematics and computation, the investigator studies the structure and function of specific groups of nerve cells. The main focus of this project is to understand how groups of nerve cells in the brain perform together calculations that individual nerve cells cannot do. These investigations not only help us understand normal brain function, but should also enable the design of prosthetic devices and treatment strategies in certain cases of brain injury. In connection with these research activities, the investigator trains mathematics Ph.D. students and post-doctoral associates in the applications of mathematics to biological systems and medicine. In addition, he teaches a freshman course entitled "Applications of Mathematics to Physiology and Medicine," which introduces excellent college freshmen to this new and exciting field.
