numerical density of branching nodes of linear structures, valence of branching nodes

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The linear structures, the implementation of which into gensei is also
desirable, can represent e.g. capillary network. From the point of view of
morphometry, the capillaries can be quantified with:
-length density (length/volume), LV(cap/ref)
-numerical density of capillaries, WV(cap/ref) 
The connectivity of the vascular node-segmented network can be estimated
from the numbers and the valence of branching nodes (for explanation, see
page 728 of the attached article (Stereological estimates of number and
length of capillaries in subdivisions of the human hippocampal region.
Løkkegaard A, Nyengaard JR, West MJ. Hippocampus. 2001;11(6):726-40.).

Therefore it would be very useful to be able to generate a model of such a
linear network with given length density and numerical density of
capillaries (or with the given number of branching nodes with a give valence).

Original issue reported on code.google.com by zto...@gmail.com on 5 Jun 2009 at 12:29

Attachments:

• lokkegard2001.pdf

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Note that no physical 3D structures exist in the code - the objects are just
mathematical objects described by some (simple) equations, and the slices are
generated by examining the slice plane equation and the object equation.

The equation of a general ellipsoid is x^T A x <= 1, which is simple, and 
allows easy
tests like "is this point inside or not?".

I cannot imagine an easy way of doing a similar thing for the general linear
structures like those you describe. We can consider some simplifications (like
straight ellipsoidal/cylindrical/? segments connected together, or branching, 
but
even such an object will not be trivial to implement.

So yes, it could be done somehow, but let us solve the other, easy issues first.

Original comment by robert.c...@gmail.com on 12 Jun 2009 at 8:27

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The thickness of the linear structures could be set by the user (i.e. diameter 
of
1-50 points). 
For the purpose of length density, the linear structures would be considered as
1-dimensional lines only.
For the purpose of volume fraction and surface density, the linear structures 
would
be considered as 3-dimensional objects.

Original comment by zto...@gmail.com on 4 Sep 2009 at 9:46

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