Last year, I asked the list about measuring the distributions of objects in
3D space, and got a variety of useful replies which I can re-post if people
are interested, or I can send to individual directly.

One of our problems has been to determine the distribution of synapses over
the complex branching dendrites of nerve cells. Much of the previous work
we examined was difficult to apply in an obvious way to such complex
shapes, especially for mere mortals unversed in more advanced mathematical
analysis. In the end, with a bit of help from a local mathematician /
statistician, we have begun using a sort of primitive Monte Carlo approach.
The idea was to create sets of random distributions of points of various
densities, apply them to samples of our real world containing neurons, and
compare statistically nearest neighbour distributions (and other spatial
parameters) of the real and random points (taking into account the
appropriate assumptions for the statistical tests you use). The random data
sets were generated using SPSS statistics package (it is actually only
pseudo random, but the difference does not really matter...). Tests we have
used include different types of cluster analyses, multivariate ANOVAs and
various comparisions of frequency distributions. We have only done this
properly for two dimensional arrays so far, but extrapolating to 3D is
simple (if tedious), once you have the 3D data in a suitable format (that
is another problem!). Some of the issues we faced in doing the models was
that the things we were interested in (Synapses) cannot appear just any
where in the total 3D space - they have to be on the surface of the
neurons were were looking at. This meant that we used a multi-step
procedure to apply the random points only to the cells we were interested
in and the nearest-neighbour distance paths were restricted by the
geometry of the neurons (ie the path was not straight and could only
traverse space  where synapses could in principle occur.) To do this well
in proper 3D, you must be able to measure the lengths of curved paths
through a 3D model -  which is not always as easy at it should be,a s the
list well knows!! We are just about to send this stuff off for publication,
so I cannot vouch for the validity of our approach in the eyes of others,
but the locals here seem to like it!

I hope that helps a bit. I would welcome any comments / criticism to me or
the list, if all this approach sounds flawed / impossible to understand /
or just plain dumb...

IAN
Professor Ian Gibbins                         Flinders Microscopy &
Department of Anatomy and Histology            Image Analysis Facility
Flinders University of South Australia
GPO Box 2100 Adelaide 5001                    Centre for Neuroscience
AUSTRALIA
Phone:  +61-8-2045271
FAX:    +61-8-2770085
e-mail:  [log in to unmask]