David Pinto pinto at neurocog.lrdc.pitt.edu
Mon Nov 23 14:34:16 EST 1992

In article <astlab3.1 at uci.edu>, astlab3 at uci.edu writes:
|> In article <2B080857.3179 at news.service.uci.edu> mundkur at falcon.eng.uci.edu (Prashanth Mundkur) writes: 
|> >4) When one sets up a "mathematical" model of the operation of a set of neurons
|> >in a particular part of the nervous system, what does one normally take into 
|> >account, and what does one assume to be irrelevant to the modeling objective?
 |> [comments deleted]
|> >Thanks for any advice and/or pointers to literature.
|> >--Prashanth.

|> 4)  Currently the connectionist paradigm is the most popular for modelling
|> 	the functioning of the brain.  The connectionist's bible is 
|> 	"Parallel distributed processing" by some guys at San Diego that
|> 	 I can't recall right now.

If Neurons are being modelled in very large groups, or as node points, without
taking the specifics of each neuron into account, then connectionist models
are the current favorite.

For models of one, two, three or maybe a few more neurons, compartmental models
seem to be prefered.  
   Compartmental models break each neuron down into a series of linked segments
e.g. soma, axon, dendrite branches.  The electrical properties of each segment
can then be represented with a simple (sometimes not so simple) circuit and a 
few equations (e.g. Hodgkin/Huxley, Fitzhugh-Nagumo, etc.).  The segments can
then be linked together to behave as a whole neuron.
   Some really impressive software is around which takes care of all this and
has some nifty graphic displays of things like action potential propagation and
potential spread through dendritic arbors.  Genesis and the Hines Neuron Simulator
come to mind.
   A good reference would be another book by Gorden Shephard "The Synaptic
Organiztion of the Brain" esp the Appendix.  Also the Segev book mentioned 
by someone else, and anything by Wilfred Rall.

As far as what sort of things are taken into account for such models (i.e. 
single neuron), mainly the geometry (obviously) as well as electrical
parameters such as the specific membrane capacitance (generally taken as a
constant 1 uF (micro-Farad), and the input resistance of the membrane.  
    Actually, rather than input resistance, what is needed is both axial
resistance (the resistance down the 'barrel' of the axon, and the specific
membrane resistance.  These can be calculated, however, with knowledge 
of the cell geometry (diameter, lengths, etc.), and the input resistance.

BTW Parallel Distributed Processing is by McClelland & Rumelhart.

"Imagine No Limits" - Company slogan? or mathematicians nightmare?

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