Hello Freesurfer-experts,
I just analyzed some FreeSurfer cortical thickness data that have been surface-resampled to fsaverage (using mris_surf2surf with -s fsaverage).
For the visualization and reporting of my findings, I have a two questions:
1. Is there anything that conceptually speaks against showing my results on non-inflated surfaces of fsaverage, such as the white matter surface, the pial surface, or even a mid-surface model?
2. I have a couple of ROIs defined on the surface of fsaverage and want to report the surface area of a given ROI in mm^2. Should I calculate the area of a ROI directly from the given surface of fsaverage, or to take the area computations from ?h.pial.avg.area.mgh/?h.white.avg.area.mgh which represent the averages of the individuals that went into fsaverage.
I am asking because I was slightly unclear of the wiki-instructions: https://surfer.nmr.mgh.harvard.edu/fswiki/GroupAverageSurface suggests to use ?h.pial.avg.area.mgh;
on the other hand, the more recently edited http://surfer.nmr.mgh.harvard.edu/fswiki/FsAverage says that "The surface area of the new average subject (fsaverage) is that of a typical subject"
I am using freesurfer 4.5.0.
Hope my questions make sense and thank you very much for answering them, Boris
--- Boris Bernhardt, PhD Max Planck Institute for Human Cognitive and Brain Sciences Stephanstr. 1a, 04103 Leipzig, Germany
p: +(49) 341 9940 2658 e: bernhardt@cbs.mpg.de http://www.cbs.mpg.de/~bernhardt
Hi Boris
1. That's fine. 2. The surface area of fsaverage is less than any individual, so you *definitely* don't want to use it. You should map the ROI back to individuals and compute it in the native space.
cheers Bruce
On Wed, 11 May 2011, Boris Bernhardt wrote:
Hello Freesurfer-experts,
I just analyzed some FreeSurfer cortical thickness data that have been surface-resampled to fsaverage (using mris_surf2surf with -s fsaverage).
For the visualization and reporting of my findings, I have a two questions:
Is there anything that conceptually speaks against showing my results on non-inflated surfaces of fsaverage, such as the white matter surface, the pial surface, or even a mid-surface model?
I have a couple of ROIs defined on the surface of fsaverage and want
to report the surface area of a given ROI in mm^2. Should I calculate the area of a ROI directly from the given surface of fsaverage, or to take the area computations from ?h.pial.avg.area.mgh/?h.white.avg.area.mgh which represent the averages of the individuals that went into fsaverage.
I am asking because I was slightly unclear of the wiki-instructions: https://surfer.nmr.mgh.harvard.edu/fswiki/GroupAverageSurface suggests to use ?h.pial.avg.area.mgh;
on the other hand, the more recently edited http://surfer.nmr.mgh.harvard.edu/fswiki/FsAverage says that "The surface area of the new average subject (fsaverage) is that of a typical subject"
I am using freesurfer 4.5.0.
Hope my questions make sense and thank you very much for answering them, Boris
Boris Bernhardt, PhD Max Planck Institute for Human Cognitive and Brain Sciences Stephanstr. 1a, 04103 Leipzig, Germany
p: +(49) 341 9940 2658 e: bernhardt@cbs.mpg.de http://www.cbs.mpg.de/~bernhardt
Hi Bruce,
I've seen this brought up on the list a few times, and, I have to admit, I've never really been able to wrap my head around it. The naive part of my brain feel like, if fsaverage is an "average" subject, it should be smaller than about half of subjects but also larger than about half of them. I'm sure I'm just not thinking about it quite the right way, but would you mind unpacking this a little bit? I suspect I'm not the only one for whom this is somewhat unintuitive.
Thanks!
Michael
On Wed, May 11, 2011 at 6:05 PM, Bruce Fischl fischl@nmr.mgh.harvard.eduwrote:
- The surface area of fsaverage is less than any individual, so you
*definitely* don't want to use it.
Hi Michael,
sure. Partially it's because the way we generate fsaverage is a bit simple-minded as it is only intended for visualization. Each vertex is the average talairach coordinate at that point on the sphere. In general, you can think of averaging as acting as a low-pass filter so that you lose a lot of high-frequency structure. In this case that would mean small, poorly-aligned folds, which means you lose surface area. The average surface is smoother than any of the individuals, and hence has less surface area.
cheers, Bruce
On Thu, 12 May 2011, Michael Waskom wrote:
Hi Bruce,
I've seen this brought up on the list a few times, and, I have to admit, I've never really been able to wrap my head around it. The naive part of my brain feel like, if fsaverage is an "average" subject, it should be smaller than about half of subjects but also larger than about half of them. I'm sure I'm just not thinking about it quite the right way, but would you mind unpacking this a little bit? I suspect I'm not the only one for whom this is somewhat unintuitive.
Thanks!
Michael
On Wed, May 11, 2011 at 6:05 PM, Bruce Fischl fischl@nmr.mgh.harvard.eduwrote:
- The surface area of fsaverage is less than any individual, so you
*definitely* don't want to use it.
Think in 2D about averaging two sine waves that are shifted 90 degrees from one another.
The length of of the resulting line will be far less than that of either curve.
On 05/11/2011 11:20 PM, Michael Waskom wrote:
Hi Bruce,
I've seen this brought up on the list a few times, and, I have to admit, I've never really been able to wrap my head around it. The naive part of my brain feel like, if fsaverage is an "average" subject, it should be smaller than about half of subjects but also larger than about half of them. I'm sure I'm just not thinking about it quite the right way, but would you mind unpacking this a little bit? I suspect I'm not the only one for whom this is somewhat unintuitive.
Thanks!
Michael
On Wed, May 11, 2011 at 6:05 PM, Bruce Fischl <fischl@nmr.mgh.harvard.edu mailto:fischl@nmr.mgh.harvard.edu> wrote:
2. The surface area of fsaverage is less than any individual, so you *definitely* don't want to use it.
Hi Bruce,
Thanks a lot for your reply.
- The surface area of fsaverage is less than any individual, so you *definitely* don't want to use it. You should map the ROI back to individuals and compute it in the native space.
I have two follow-up questions:
1) Do .pial.avg.area.mgh and/or .white.avg.area.mgh then store the mean native space surface areas for the individuals that were used to create fsaverage, and can I use these values to approximate the surface area of my ROIs then?
2) Do the avg.area files also exists somewhere for the half-thickness mid-surface? If not, does it make sense to approximate the mid-thickness surface area at each vertex by taking the mean of the corresponding pial.avg.area and white.avg.area entries?
Many thanks, Boris
cheers Bruce
On Wed, 11 May 2011, Boris Bernhardt wrote:
Hello Freesurfer-experts,
I just analyzed some FreeSurfer cortical thickness data that have been surface-resampled to fsaverage (using mris_surf2surf with -s fsaverage).
For the visualization and reporting of my findings, I have a two questions:
Is there anything that conceptually speaks against showing my results on non-inflated surfaces of fsaverage, such as the white matter surface, the pial surface, or even a mid-surface model?
I have a couple of ROIs defined on the surface of fsaverage and want
to report the surface area of a given ROI in mm^2. Should I calculate the area of a ROI directly from the given surface of fsaverage, or to take the area computations from ?h.pial.avg.area.mgh/?h.white.avg.area.mgh which represent the averages of the individuals that went into fsaverage.
I am asking because I was slightly unclear of the wiki-instructions: https://surfer.nmr.mgh.harvard.edu/fswiki/GroupAverageSurface suggests to use ?h.pial.avg.area.mgh;
on the other hand, the more recently edited http://surfer.nmr.mgh.harvard.edu/fswiki/FsAverage says that "The surface area of the new average subject (fsaverage) is that of a typical subject"
I am using freesurfer 4.5.0.
Hope my questions make sense and thank you very much for answering them, Boris
Boris Bernhardt, PhD Max Planck Institute for Human Cognitive and Brain Sciences Stephanstr. 1a, 04103 Leipzig, Germany
p: +(49) 341 9940 2658 e: bernhardt@cbs.mpg.de http://www.cbs.mpg.de/~bernhardt
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.
--- Boris Bernhardt Max Planck Institute for Human Cognitive and Brain Sciences Stephanstr. 1a, 04103 Leipzig, Germany
p: +(49) 341 9940 2658 e: bernhardt@cbs.mpg.de http://www.cbs.mpg.de/~bernhardt
Hi Boris,
1. Doug can say for sure, but I believe so. 2. No. The mid surface doesn't correspond to any boundary in the image and so we are always hesitant to provide any morphometric measures for it. We are working on a more explicit estimation of the location of layer IV, but that is a future direction. You could generate it yourself easily enough though.
cheers Bruce
On Thu, 12 May 2011, Boris Bernhardt wrote:
Hi Bruce,
Thanks a lot for your reply.
- The surface area of fsaverage is less than any individual, so you *definitely* don't want to use it. You should map the ROI back to individuals and compute it in the native space.
I have two follow-up questions:
- Do .pial.avg.area.mgh and/or .white.avg.area.mgh then store the mean
native space surface areas for the individuals that were used to create fsaverage, and can I use these values to approximate the surface area of my ROIs then?
- Do the avg.area files also exists somewhere for the half-thickness mid-surface? If not, does it make sense to approximate the mid-thickness surface area at each vertex by taking the mean of the corresponding pial.avg.area and white.avg.area entries?
Many thanks, Boris
cheers Bruce
On Wed, 11 May 2011, Boris Bernhardt wrote:
Hello Freesurfer-experts,
I just analyzed some FreeSurfer cortical thickness data that have been surface-resampled to fsaverage (using mris_surf2surf with -s fsaverage).
For the visualization and reporting of my findings, I have a two questions:
Is there anything that conceptually speaks against showing my results on non-inflated surfaces of fsaverage, such as the white matter surface, the pial surface, or even a mid-surface model?
I have a couple of ROIs defined on the surface of fsaverage and want
to report the surface area of a given ROI in mm^2. Should I calculate the area of a ROI directly from the given surface of fsaverage, or to take the area computations from ?h.pial.avg.area.mgh/?h.white.avg.area.mgh which represent the averages of the individuals that went into fsaverage.
I am asking because I was slightly unclear of the wiki-instructions: https://surfer.nmr.mgh.harvard.edu/fswiki/GroupAverageSurface suggests to use ?h.pial.avg.area.mgh;
on the other hand, the more recently edited http://surfer.nmr.mgh.harvard.edu/fswiki/FsAverage says that "The surface area of the new average subject (fsaverage) is that of a typical subject"
I am using freesurfer 4.5.0.
Hope my questions make sense and thank you very much for answering them, Boris
Boris Bernhardt, PhD Max Planck Institute for Human Cognitive and Brain Sciences Stephanstr. 1a, 04103 Leipzig, Germany
p: +(49) 341 9940 2658 e: bernhardt@cbs.mpg.de http://www.cbs.mpg.de/~bernhardt
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.
Boris Bernhardt Max Planck Institute for Human Cognitive and Brain Sciences Stephanstr. 1a, 04103 Leipzig, Germany
p: +(49) 341 9940 2658 e: bernhardt@cbs.mpg.de http://www.cbs.mpg.de/~bernhardt
Yes, the avg.area files have the average over the input subjects at each vertex. I've used it to overcome this problem. doug
On 5/12/11 8:04 AM, Bruce Fischl wrote:
Hi Boris,
- Doug can say for sure, but I believe so.
- No. The mid surface doesn't correspond to any boundary in the image and
so we are always hesitant to provide any morphometric measures for it. We are working on a more explicit estimation of the location of layer IV, but that is a future direction. You could generate it yourself easily enough though.
cheers Bruce
On Thu, 12 May 2011, Boris Bernhardt wrote:
Hi Bruce,
Thanks a lot for your reply.
- The surface area of fsaverage is less than any individual, so you *definitely* don't want to use it. You should map the ROI back to individuals and compute it in the native space.
I have two follow-up questions:
- Do .pial.avg.area.mgh and/or .white.avg.area.mgh then store the mean
native space surface areas for the individuals that were used to create fsaverage, and can I use these values to approximate the surface area of my ROIs then?
- Do the avg.area files also exists somewhere for the half-thickness mid-surface? If not, does it make sense to approximate the mid-thickness surface area at each vertex by taking the mean of the corresponding pial.avg.area and white.avg.area entries?
Many thanks, Boris
cheers Bruce
On Wed, 11 May 2011, Boris Bernhardt wrote:
Hello Freesurfer-experts,
I just analyzed some FreeSurfer cortical thickness data that have been surface-resampled to fsaverage (using mris_surf2surf with -s fsaverage).
For the visualization and reporting of my findings, I have a two questions:
Is there anything that conceptually speaks against showing my results on non-inflated surfaces of fsaverage, such as the white matter surface, the pial surface, or even a mid-surface model?
I have a couple of ROIs defined on the surface of fsaverage and want
to report the surface area of a given ROI in mm^2. Should I calculate the area of a ROI directly from the given surface of fsaverage, or to take the area computations from ?h.pial.avg.area.mgh/?h.white.avg.area.mgh which represent the averages of the individuals that went into fsaverage.
I am asking because I was slightly unclear of the wiki-instructions: https://surfer.nmr.mgh.harvard.edu/fswiki/GroupAverageSurface suggests to use ?h.pial.avg.area.mgh;
on the other hand, the more recently edited http://surfer.nmr.mgh.harvard.edu/fswiki/FsAverage says that "The surface area of the new average subject (fsaverage) is that of a typical subject"
I am using freesurfer 4.5.0.
Hope my questions make sense and thank you very much for answering them, Boris
Boris Bernhardt, PhD Max Planck Institute for Human Cognitive and Brain Sciences Stephanstr. 1a, 04103 Leipzig, Germany
p: +(49) 341 9940 2658 e: bernhardt@cbs.mpg.de http://www.cbs.mpg.de/~bernhardt
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.
Boris Bernhardt Max Planck Institute for Human Cognitive and Brain Sciences Stephanstr. 1a, 04103 Leipzig, Germany
p: +(49) 341 9940 2658 e: bernhardt@cbs.mpg.de http://www.cbs.mpg.de/~bernhardt
Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer
Hi Bruce and Doug,
thank you both so much for your help.
You could generate it yourself easily enough though.
For now I am taking the geometric average between pial and white surface coordinates. Is that the right way to do it, or is there a more precise way?
Also: If I decided to represent the stuff on the mid-surface, would it then also make sense to also take the average of pial.avg.area.mgh white.avg.area.mgh as the area estimation at each vertex?
Many thanks, Boris
On 2011-05-12, at 4:08 PM, Douglas Greve wrote:
Yes, the avg.area files have the average over the input subjects at each vertex. I've used it to overcome this problem. doug
On 5/12/11 8:04 AM, Bruce Fischl wrote:
Hi Boris,
- Doug can say for sure, but I believe so.
- No. The mid surface doesn't correspond to any boundary in the image and
so we are always hesitant to provide any morphometric measures for it. We are working on a more explicit estimation of the location of layer IV, but that is a future direction. You could generate it yourself easily enough though.
cheers Bruce
On Thu, 12 May 2011, Boris Bernhardt wrote:
Hi Bruce,
Thanks a lot for your reply.
- The surface area of fsaverage is less than any individual, so you *definitely* don't want to use it. You should map the ROI back to individuals and compute it in the native space.
I have two follow-up questions:
- Do .pial.avg.area.mgh and/or .white.avg.area.mgh then store the mean
native space surface areas for the individuals that were used to create fsaverage, and can I use these values to approximate the surface area of my ROIs then?
- Do the avg.area files also exists somewhere for the half-thickness mid-surface? If not, does it make sense to approximate the mid-thickness surface area at each vertex by taking the mean of the corresponding pial.avg.area and white.avg.area entries?
Many thanks, Boris
cheers Bruce
On Wed, 11 May 2011, Boris Bernhardt wrote:
Hello Freesurfer-experts,
I just analyzed some FreeSurfer cortical thickness data that have been surface-resampled to fsaverage (using mris_surf2surf with -s fsaverage).
For the visualization and reporting of my findings, I have a two questions:
Is there anything that conceptually speaks against showing my results on non-inflated surfaces of fsaverage, such as the white matter surface, the pial surface, or even a mid-surface model?
I have a couple of ROIs defined on the surface of fsaverage and want
to report the surface area of a given ROI in mm^2. Should I calculate the area of a ROI directly from the given surface of fsaverage, or to take the area computations from ?h.pial.avg.area.mgh/?h.white.avg.area.mgh which represent the averages of the individuals that went into fsaverage.
I am asking because I was slightly unclear of the wiki-instructions: https://surfer.nmr.mgh.harvard.edu/fswiki/GroupAverageSurface suggests to use ?h.pial.avg.area.mgh;
on the other hand, the more recently edited http://surfer.nmr.mgh.harvard.edu/fswiki/FsAverage says that "The surface area of the new average subject (fsaverage) is that of a typical subject"
I am using freesurfer 4.5.0.
Hope my questions make sense and thank you very much for answering them, Boris
Boris Bernhardt, PhD Max Planck Institute for Human Cognitive and Brain Sciences Stephanstr. 1a, 04103 Leipzig, Germany
p: +(49) 341 9940 2658 e: bernhardt@cbs.mpg.de http://www.cbs.mpg.de/~bernhardt
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.
Boris Bernhardt Max Planck Institute for Human Cognitive and Brain Sciences Stephanstr. 1a, 04103 Leipzig, Germany
p: +(49) 341 9940 2658 e: bernhardt@cbs.mpg.de http://www.cbs.mpg.de/~bernhardt
Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer
Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer
Hi Boris,
For now I am taking the geometric average between pial and white surface coordinates. Is that the right way to do it, or is there a more precise way?
To obtain a surface that lies in the geometric middle between white and pial surfaces, it is correct to take the average of the coordinates. This surface is not guaranteed to coincide with any biologically meaningful cortical layer, but it has advantages over pial or white for not over/under-representing gyri or sulci.
Also: If I decided to represent the stuff on the mid-surface, would it then also make sense to also take the average of pial.avg.area.mgh white.avg.area.mgh as the area estimation at each vertex?
No no, to take the average of the areas is not the same as take the average of the coordinates, because the areas depend quadratically on linear distances. An average of the areas would not necessarily represent a surface at the middle, most likely representing an (invisible) surface that would be closer to the white in some places and closer to the pial in others, depending on local folding.
Hope this helps!
All the best,
Anderson
On 2011-05-12, at 4:08 PM, Douglas Greve wrote:
Yes, the avg.area files have the average over the input subjects at each vertex. I've used it to overcome this problem. doug
On 5/12/11 8:04 AM, Bruce Fischl wrote:
Hi Boris,
- Doug can say for sure, but I believe so.
- No. The mid surface doesn't correspond to any boundary in the
image and so we are always hesitant to provide any morphometric measures for it. We are working on a more explicit estimation of the location of layer IV, but that is a future direction. You could generate it yourself easily enough though.
cheers Bruce
On Thu, 12 May 2011, Boris Bernhardt wrote:
Hi Bruce,
Thanks a lot for your reply.
- The surface area of fsaverage is less than any individual, so
you *definitely* don't want to use it. You should map the ROI back to individuals and compute it in the native space.
I have two follow-up questions:
- Do .pial.avg.area.mgh and/or .white.avg.area.mgh then store the mean
native space surface areas for the individuals that were used to create fsaverage, and can I use these values to approximate the surface area of my ROIs then?
- Do the avg.area files also exists somewhere for the
half-thickness mid-surface? If not, does it make sense to approximate the mid-thickness surface area at each vertex by taking the mean of the corresponding pial.avg.area and white.avg.area entries?
Many thanks, Boris
cheers Bruce
On Wed, 11 May 2011, Boris Bernhardt wrote:
Hello Freesurfer-experts,
I just analyzed some FreeSurfer cortical thickness data that have been surface-resampled to fsaverage (using mris_surf2surf with -s fsaverage).
For the visualization and reporting of my findings, I have a two questions:
- Is there anything that conceptually speaks against showing my
results on non-inflated surfaces of fsaverage, such as the white matter surface, the pial surface, or even a mid-surface model?
- I have a couple of ROIs defined on the surface of fsaverage
and want
to report the surface area of a given ROI in mm^2. Should I calculate the area of a ROI directly from the given surface of fsaverage, or to take the area computations from ?h.pial.avg.area.mgh/?h.white.avg.area.mgh which represent the averages of the individuals that went into fsaverage.
I am asking because I was slightly unclear of the wiki-instructions: https://surfer.nmr.mgh.harvard.edu/fswiki/GroupAverageSurface suggests to use ?h.pial.avg.area.mgh;
on the other hand, the more recently edited http://surfer.nmr.mgh.harvard.edu/fswiki/FsAverage says that "The surface area of the new average subject (fsaverage) is that of a typical subject"
I am using freesurfer 4.5.0.
Hope my questions make sense and thank you very much for answering them, Boris
Boris Bernhardt, PhD Max Planck Institute for Human Cognitive and Brain Sciences Stephanstr. 1a, 04103 Leipzig, Germany
p: +(49) 341 9940 2658 e: bernhardt@cbs.mpg.de mailto:bernhardt@cbs.mpg.de http://www.cbs.mpg.de/~bernhardt http://www.cbs.mpg.de/%7Ebernhardt
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.
Boris Bernhardt Max Planck Institute for Human Cognitive and Brain Sciences Stephanstr. 1a, 04103 Leipzig, Germany
p: +(49) 341 9940 2658 e: bernhardt@cbs.mpg.de mailto:bernhardt@cbs.mpg.de http://www.cbs.mpg.de/~bernhardt http://www.cbs.mpg.de/%7Ebernhardt
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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,
No no, to take the average of the areas is not the same as take the average of the coordinates, because the areas depend quadratically on linear distances. An average of the areas would not necessarily represent a surface at the middle, most likely representing an (invisible) surface that would be closer to the white in some places and closer to the pial in others, depending on local folding. Hope this helps!
yes - that helps and clarifies things.
Thank you all for your help and patience, Boris
On 2011-05-12, at 11:57 PM, Anderson Winkler wrote:
Hi Boris,
For now I am taking the geometric average between pial and white surface coordinates. Is that the right way to do it, or is there a more precise way?
To obtain a surface that lies in the geometric middle between white and pial surfaces, it is correct to take the average of the coordinates. This surface is not guaranteed to coincide with any biologically meaningful cortical layer, but it has advantages over pial or white for not over/under-representing gyri or sulci.
Also: If I decided to represent the stuff on the mid-surface, would it then also make sense to also take the average of pial.avg.area.mgh white.avg.area.mgh as the area estimation at each vertex?
No no, to take the average of the areas is not the same as take the average of the coordinates, because the areas depend quadratically on linear distances. An average of the areas would not necessarily represent a surface at the middle, most likely representing an (invisible) surface that would be closer to the white in some places and closer to the pial in others, depending on local folding.
Hope this helps!
All the best,
Anderson
freesurfer@nmr.mgh.harvard.edu