People
Christoph
Börgers
Professor
Contact Info:
Tufts University
Department of Mathematics
503 Boston Avenue
BromfieldPearson
Room 215
Medford, MA 02155
Email @tufts.edu:
christoph.borgers
Phone: 6176272366
Personal site
Expertise:
Mathematical neuroscience, applied dynamical systems, numerical analysis, scientific computing
Research:
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 interneuronal 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 HodgkinHuxley 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 HodgkinHuxleylike equations, by means of
computation and mathematical analysis. One must say "HodgkinHuxleylike"
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 HodgkinHuxley 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 shortterm ("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
HodgkinHuxleylike systems of differential equations. At least two features
make the numerical solution of HodgkinHuxleylike 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.
