Paper on connectivity of the brain

[Jaap Murre]

The following paper has been added to our ftp-site:

J.M.J. Murre, & D.P.F. Sturdy (submitted). The connectivity of the
      brain: multi-level quantitative analysis. Revised version submitted
      to Biological Cybernetics.


Abstract 
We develop a mathematical formalism for calculating connectivity
volumes generated by specific topologies with various physical packing
strategies. We consider four topologies (full, random, nearest neighbor,
and modular connectivity) and three physical models: (i) interior
packing, where neurons and connection fibers are intermixed, (ii)
sheeted packing where neurons are located on a sheet with fibers
running underneath, and (iii) exterior packing where the neurons are
located at the surfaces of a cube or sphere with fibers taking up the
internal volume. By extensive cross-referencing of available human
neuroanatomical data we produce a consistent set of parameters for the
whole brain, the cerebral cortex, and the cerebellar cortex. By comparing
these inferred values with those predicted by the expressions, we draw
the following general conclusions for the human brain, cortex,
cerebellum: (i) Interior packing is less efficient than exterior packing (in
a sphere). (ii) Fully and randomly connected topologies are extremely
inefficient. More specifically we find evidence that different topologies
and physical packing strategies might be used at different scales. (iii)
For the human brain at a macrostructural level, modular topologies on
an exterior sphere approach the data most closely. (iv) On a
mesostructural level, laminarization and columnarization are evidence of
the superior efficiency of organizing the wiring as sheets. (v) Within
sheets, microstructures emerge in which interior models are shown to be
the most efficient. With regard to interspecies similarities and
differences we conjecture (vi) that the remarkable constancy of number
of neurons per underlying mm2 of cortex may be the result of evolution
minimizing interneuron distance in grey matter, and (vii) that the
topologies that best fit the human brain data should not be assumed to
apply to other mammals, such as the mouse for which we show that a
random topology may be feasible for the cortex.

The paper is 39 pages, single spaced. The postscript file and its
compressed versions are called:


  ftp://ftp.mrc-apu.cam.ac.uk/pub/nn/murre/connect.ps     (940 Kb)
  ftp://ftp.mrc-apu.cam.ac.uk/pub/nn/murre/connect.ps.Z   (327 Kb)
  ftp://ftp.mrc-apu.cam.ac.uk/pub/nn/murre/connect.zip    (223 Kb)

(with PKZIP 2.04g)

      -- Jaap Murre             jaap.murre at mrc-apu.cam.ac.uk 

After 1 June 1995:              pn_murre at macmail.psy.uva.nl