Hi,
in this forum it has been stated that 'Fold Opening" is defined as: "Fold opening, as we calculate it, is a more or less indirect measurement of the width of the CSF in the sulcus: it is the volume of CSF in the sulcus, divided by the surface of the skeleton mesh".
my questions:
what is the exact mathematical formula by which this is done? I.e. are both sides of the skeleton (i.e. median sulcal) mesh used? From the picture in the review by Mangin et al. 2010 ("In-vivo measurement of cortical morphology: means and meanings.") i assume that Fold Opening is the distance between gyral walls, *not* the distance between the skeleton mesh and one of the gyral walls. is this correct?
merci,
-joost
question Fold Opening
Re: question Fold Opening
Hi Prof Mangin and others,
i'll try to clarify my doubts by attaching a drawing, please have a look at it. on the picture you see a rectangular prism, representing a sulcus with a middle wall, representing a median sulcal mesh. the median sulcal mesh has (amongst others) a right and left-handed surface area: Ac1 and Ac2 (we assume that the right- and left-handed sides of the median sulcal mesh are the principal contributors to the surface area of the median sulcal mesh). the Fold Opening includes F01 (right-handed distance of the sulcal median mesh until gyral wall) and F02 (left-handed distance of the median sulcal mesh until gyral wall). we assume in this simplified model that F01=F02 because the median sulcal mesh is exactly in the middle between the right and left gyral walls. the Volume of the sulcal space at the right-handed side (=V1) of the median sulcal mesh equals the Volume of the sulcal space at the left-handed side (=V2) of the median sulcal mesh. then F01=V1/Ac1 and F02=V2/Ac2. then total Fold Opening (F01+F02) = (V1 + V2)/Ac1 (assuming that Ac1=Ac2).
so the question for us is, in this model Fold Opening seems to depend only on Ac1, *not* Ac1+Ac2 (the total surface area of the median sulcal mesh):
is our model correct?
i hope the question makes sense and is clear. we know that the model described in the .jpg is oversimplified but illustrates our doubt about the statement on the forum saying: "Fold opening, as we calculate it, is a more or less indirect measurement of the width of the CSF in the sulcus: it is the volume of CSF in the sulcus, divided by the surface of the skeleton mesh". on the forum it's confirmed that "skeleton mesh" refers to the "mesh that is used for the 3D representation of the sulci."
merci,
-joost
i'll try to clarify my doubts by attaching a drawing, please have a look at it. on the picture you see a rectangular prism, representing a sulcus with a middle wall, representing a median sulcal mesh. the median sulcal mesh has (amongst others) a right and left-handed surface area: Ac1 and Ac2 (we assume that the right- and left-handed sides of the median sulcal mesh are the principal contributors to the surface area of the median sulcal mesh). the Fold Opening includes F01 (right-handed distance of the sulcal median mesh until gyral wall) and F02 (left-handed distance of the median sulcal mesh until gyral wall). we assume in this simplified model that F01=F02 because the median sulcal mesh is exactly in the middle between the right and left gyral walls. the Volume of the sulcal space at the right-handed side (=V1) of the median sulcal mesh equals the Volume of the sulcal space at the left-handed side (=V2) of the median sulcal mesh. then F01=V1/Ac1 and F02=V2/Ac2. then total Fold Opening (F01+F02) = (V1 + V2)/Ac1 (assuming that Ac1=Ac2).
so the question for us is, in this model Fold Opening seems to depend only on Ac1, *not* Ac1+Ac2 (the total surface area of the median sulcal mesh):
is our model correct?
i hope the question makes sense and is clear. we know that the model described in the .jpg is oversimplified but illustrates our doubt about the statement on the forum saying: "Fold opening, as we calculate it, is a more or less indirect measurement of the width of the CSF in the sulcus: it is the volume of CSF in the sulcus, divided by the surface of the skeleton mesh". on the forum it's confirmed that "skeleton mesh" refers to the "mesh that is used for the 3D representation of the sulci."
merci,
-joost
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Re: question Fold Opening
Hi,
Yes, you get it right: the fold opening calculation is a gross approximation of the width of the CSF in the fold, just as in your explanations.
Here the surface we used is actrually Ac1+Ac2 (both sides of the skeleton), which make the "width" half of what it should be. We probably should have used only half of the surface to get closer to a "realistic" width, but as the opening index is quite gross, we did not want to really interpret it as a millimetric distance between the sulcus banks: it is just enough to try to detect variations or rank openings between folds. But, yes, if you really want to get this interpretation, multiply it by 2 (or consider it the distance from the mid-surface of the fold CSF (skeleton) to the sulcus wall.
However, as Jeff told you, there are probably more accurate ways to calculate it as a mean distance, for instrance in Peter Kochunov's RIC toolbox.
Denis
Yes, you get it right: the fold opening calculation is a gross approximation of the width of the CSF in the fold, just as in your explanations.
Here the surface we used is actrually Ac1+Ac2 (both sides of the skeleton), which make the "width" half of what it should be. We probably should have used only half of the surface to get closer to a "realistic" width, but as the opening index is quite gross, we did not want to really interpret it as a millimetric distance between the sulcus banks: it is just enough to try to detect variations or rank openings between folds. But, yes, if you really want to get this interpretation, multiply it by 2 (or consider it the distance from the mid-surface of the fold CSF (skeleton) to the sulcus wall.
However, as Jeff told you, there are probably more accurate ways to calculate it as a mean distance, for instrance in Peter Kochunov's RIC toolbox.
Denis
Re: question Fold Opening
Hi,
thanks. then just to clarify to other people on the forum interested in 'Fold Opening': in the paper by Jouvent et al. ("Longitudinal changes of cortical morphology in CADASIL", NeuroBiology of Aging) where it is stated that: "Fold opening (Fop; distance between each gyral bank defining the cortical sulcus), known to increase with age (Kochunov et al., 2005)" one should interpret this statement with caution as:
- "Fold Opening" isn't really the pure distance between gyral banks (although it *is* a distance in mm, in my opinion)
- The metric used by Peter Kochunov (sulcal span) is something considerably different than Fold Opening, i.e. it is a more direct measurement of sulcal width.
merci,
-joost
thanks. then just to clarify to other people on the forum interested in 'Fold Opening': in the paper by Jouvent et al. ("Longitudinal changes of cortical morphology in CADASIL", NeuroBiology of Aging) where it is stated that: "Fold opening (Fop; distance between each gyral bank defining the cortical sulcus), known to increase with age (Kochunov et al., 2005)" one should interpret this statement with caution as:
- "Fold Opening" isn't really the pure distance between gyral banks (although it *is* a distance in mm, in my opinion)
- The metric used by Peter Kochunov (sulcal span) is something considerably different than Fold Opening, i.e. it is a more direct measurement of sulcal width.
merci,
-joost