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
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
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
Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer
The information in this e-mail is intended only for the person to whom it is addressed. If you believe this e-mail was sent to you in error and the e-mail contains patient information, please contact the Partners Compliance HelpLine at http://www.partners.org/complianceline . If the e-mail was sent to you in error but does not contain patient information, please contact the sender and properly dispose of the e-mail.
Hi Bruce,
In regard to ?h.curv. i extrated the meancurv from aparcstats2table (https://surfer.nmr.mgh.harvard.edu/fswiki/aparcstats2table). Howver, when i run long_mris_slopes, it does not seem to find ?h.meancurv. But i think i need to try ?h.curv instead.
a) What were the thoughts behind using the white surface instead of the pial surface (i.e., both for curvature and surface area)?
b) So a 'higher' number of mean curvature means that the folding is higher?
Thank you.
Best regards Kasper
Sent from [ProtonMail](https://protonmail.com), Swiss-based encrypted email.
Sent with [ProtonMail](https://protonmail.com) Secure Email.
-------- Original Message -------- Subject: Re: [Freesurfer] Curvature in FreeSurfer Local Time: August 16, 2017 4:13 PM UTC Time: August 16, 2017 2:13 PM From: fischl@nmr.mgh.harvard.edu To: Kasper Jessen kasper@brejes.com, Freesurfer support list freesurfer@nmr.mgh.harvard.edu
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
The information in this e-mail is intended only for the person to whom it is addressed. If you believe this e-mail was sent to you in error and the e-mail contains patient information, please contact the Partners Compliance HelpLine at http://www.partners.org/complianceline . If the e-mail was sent to you in error but does not contain patient information, please contact the sender and properly dispose of the e-mail.
a) we use the white surface for many things because it is insensitive to gray matter atrophy (although of course not to wm atrophy)
b) yes, it means that the fold is "sharper" at least in one direction
cheers Bruce On Fri, 18 Aug 2017, Kasper Jessen wrote:
Hi Bruce,
In regard to ?h.curv. i extrated the meancurv from aparcstats2table (https://surfer.nmr.mgh.harvard.edu/fswiki/aparcstats2table). Howver, when i run long_mris_slopes, it does not seem to find ?h.meancurv. But i think i need to try ?h.curv instead.
a) What were the thoughts behind using the white surface instead of the pial surface (i.e., both for curvature and surface area)?
b) So a 'higher' number of mean curvature means that the folding is higher?
Thank you.
Best regards Kasper
Sent from ProtonMail, Swiss-based encrypted email.
Sent with ProtonMail Secure Email.
-------- Original Message --------Subject: Re: [Freesurfer] Curvature in FreeSurfer Local Time: August 16, 2017 4:13 PM UTC Time: August 16, 2017 2:13 PM From: fischl@nmr.mgh.harvard.edu To: Kasper Jessen kasper@brejes.com, Freesurfer support list freesurfer@nmr.mgh.harvard.edu
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
The information in this e-mail is intended only for the person to whom it is addressed. If you believe this e-mail was sent to you in error and the e-mail contains patient information, please contact the Partners Compliance HelpLine at http://www.partners.org/complianceline . If the e-mail was sent to you in error but does not contain patient information, please contact the sender and properly dispose of the e-mail.
b) yes, it means that the fold is "sharper" at least in one direction
I want to underscore Bruce's point. Higher mean curvature could mean that folds are sharper. It does not mean that there are necessarily more folds.
freesurfer@nmr.mgh.harvard.edu
-
Bruce Fischl -
Kasper Jessen -
Rudolph Pienaar