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/AMethodologyForAnalyzingCurv...
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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