Curvature does not really connect simply to folding, although they are
of course related. Nonetheless, one cannot make universal statements
like "A curvature <increase|decrease> means an <increase|decrease> in
folding". Consider for example a pathology like poly-microgryria where
numerous small "bumps" might appear on a brain surface. Though curvature
might change vis-a-vis normal, folding patterns might not.
Also, there are many different functions of curvature. Mean curvature is
the most "obvious", but others, such as the Gaussian curvature are for
some purposes more meaningful.
You might want to take a look here for a background and study on
curvature on brain surfaces and FreeSurfer:
https://surfer.nmr.mgh.harvard.edu/pub/articles/AMethodologyForAnalyzingCurvature.pdf
Best
On 08/16/17 10:13, Bruce Fischl wrote:
Hi Kaspar
if you mean the values we store in the ?h.curv files, those are the
spatially smoothed mean curvature (average of the two principal
curvatures).
a). it is of the white surface, but you can use mris_curvature to
compute the curv of the pial if you want
b) an increase in the curvature means that the radius of curvature
decreases, which usually means the folding has increased (it is sharper)
c) curvature is negatively correlated with thickness, although the
sign is a bit arbitrary (it comes from the arbitrary choice of an
outwards pointing surface normal). Sulci in general are thinner than
gyri.
cheers
Bruce
On Wed, 16 Aug 2017, Kasper Jessen wrote:
Dear FreeSurfer,
We have been discussing the mean curvature provided by FreeSurfer
software.
As i understand the mean curvature is measured as 1/r and has a unit of
1/mm.
But
a) What is the curvature an expression of? Is it the degree of
folding of
the brain and is it the white matter surface or pial surface?
b) An increased value of mean curvature - does that mean an increase in
folding of the brain?
c) What is the expected association between the mean curvature; and
cortical
thickness and surface area? Any suggestions of litterature?
I have read through two webpages below, but unfortunately the confusion
still exist :-)
http://mathworld.wolfram.com/MeanCurvature.html
http://mathworld.wolfram.com/GaussianCurvature.html
I am aware that this may be a simple question but the different
measures of
curvature (fx. gaussian vs mean curvature) made us discuss the
differences
and what it is an expression of.
Best regards,
Kasper
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