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Christoph Börgers
Christoph Borgers
Contact Info:
Tufts University
Department of Mathematics
503 Boston Avenue
Room 215
Medford, MA 02155

Email @tufts.edu:
Phone: 617-627-2366
Personal site

Mathematical neuroscience, applied dynamical systems, numerical analysis, scientific computing

During the past decade, most of my work has been in the area of Computational Neuroscience.

Arguably the most influential paper in Neuroscience to date is a 1952 article by the physiologists Alan Hodgkin and Andrew Huxley titled A quantitative description of membrane current and its application to conduction and excitation in nerve. At least a decade of highly ingenious experimental and theoretical work by Hodgkin, Huxley, and of course many others, culminated in the 1952 article, which laid out the mechanism of the "firing" of nerve cells, which is the foundation of inter-neuronal communication and therefore of all brain activity. Hodgkin and Huxley summarized their understanding of the firing mechanism by writing down the system of nonlinear partial differential equations nowadays called the Hodgkin-Huxley equations. (Hodgkin and Huxley received the Nobel Prize in Physiology and Medicine for this work in 1963.)

It is only a slight simplification to describe Theoretical Neuroscience as the exploration of solutions of Hodgkin-Huxley-like equations, by means of computation and mathematical analysis. One must say "Hodgkin-Huxley-like" because different neurons have different properties, and are therefore described by different differential equations, but those equations almost always bear close resemblance with the original Hodgkin-Huxley equations, and are inspired by them.

One subject of great interest to both experimental and theoretical neuroscientists are the oscillations in electrical activity in the brain. These oscillations have been observed for a very long time, in EEG and MEG data as well as in more direct measurements, and their causes and functions have been a subject of intense study. The questions that I have worked on in Computational Neuroscience mostly concern oscillations, and specifically gamma (40 Hz) oscillations. This work involves a combination of computation and mathematical analysis of (by necessity) simplified models. Gamma oscillations are known to be correlated with attention and short-term ("working") memory tasks. Pathologies in gamma oscillations are associated with brain disease, in particular with schizophrenia. I have worked on how large numbers of neurons conspire to produce 40 Hz oscillations, and how those oscillations might aid in attention, in protecting signals from distractors, etc. I am interested in the connection between gamma oscillations and schizophrenia as well.

Recently I have also studied issues related to the numerical analysis of Hodgkin-Huxley-like systems of differential equations. At least two features make the numerical solution of Hodgkin-Huxley-like systems challenging. The first is sheer size: A network of a million neurons would represent a very small piece of cortex only, for instance. The second is the discrepancy in relevant time scales between the very fast firing events and the much slower dynamics between firing events.