# ico-5 source space (Surface area per source) **URL:** \ **Category:** Support & Discussions\ **Tags:** source-localization, meg\ **Created:** [August 10, 2023, 8:23pm UTC](https://mne.discourse.group/t/ico-5-source-space-surface-area-per-source/7361 "2023-08-10T20:23:58Z")\ **Posts on this page:** 12\ **Page:** 1
**Author:** ![dasdiptyajit](https://yyz2.discourse-cdn.com/free1/user_avatar/mne.discourse.group/dasdiptyajit/32/4796_2.png) [@dasdiptyajit](https://mne.discourse.group/u/dasdiptyajit)\ **Post date:** [August 10, 2023, 8:23pm UTC](https://mne.discourse.group/t/ico-5-source-space-surface-area-per-source/7361/1 "2023-08-10T20:23:58Z")
Hi all, Is there any formula to find out the surface area corresponding to a dipole within a source space? When I am looking at the MNE documentation regarding ico-5 source space, its written as: Source space: ‘ico5’ Sources per hemisphere: 10242 Source spacing: 3.1 mm Surface area per source : 9.8 mm2 (is there any general formula to calculate this?) Thanks, ---
**Author:** ![dasdiptyajit](https://yyz2.discourse-cdn.com/free1/user_avatar/mne.discourse.group/dasdiptyajit/32/4796_2.png) [@dasdiptyajit](https://mne.discourse.group/u/dasdiptyajit)\ **Post date:** [August 10, 2023, 8:24pm UTC](https://mne.discourse.group/t/ico-5-source-space-surface-area-per-source/7361/2 "2023-08-10T20:24:44Z")
@larsoner do you have any idea about it? thanks! ---
**Author:** ![larsoner](https://yyz2.discourse-cdn.com/free1/user_avatar/mne.discourse.group/larsoner/32/3_2.png) [@larsoner](https://mne.discourse.group/u/larsoner)\ **Post date:** [August 14, 2023, 4:08pm UTC](https://mne.discourse.group/t/ico-5-source-space-surface-area-per-source/7361/3 "2023-08-14T16:08:53Z")
There is this info: ```python >>> import mne >>> src = mne.read_source_spaces(mne.datasets.sample.data_path() / 'subjects' / 'fsaverage' / 'bem' / 'fsaverage-ico-5-src.fif', patch_stats=True) >>> src[0].keys() dict_keys(['id', 'type', 'np', 'ntri', 'coord_frame', 'rr', 'nn', 'tris', 'nuse', 'inuse', 'vertno', 'nuse_tri', 'use_tris', 'nearest', 'nearest_dist', 'pinfo', 'patch_inds', 'dist', 'dist_limit', 'subject_his_id', 'tri_area', 'tri_cent', 'tri_nn', 'use_tri_cent', 'use_tri_nn', 'use_tri_area']) >>> src[0]["use_tri_area"].shape (20480,) >>> src[0]["use_tris"].shape (20480, 3) ``` So this could get you the surface area per triangle in the decimated space. But you want it per _vertex_ not per _triangle_. Really the “surface area per source” can be thought of as “total surface area / total number of sources”. So looking at it that way, you could calculate it as: ```python sum(s["tri_area"].sum() for s in src) / sum(s['nuse'] for s in src) * 1e6 6.367790682029399 ``` The `* 1e6` is a conversion from “sources per square m” to sources per square mm". For an `oct-6` for example you’d get: ```python >>> src = mne.read_source_spaces(mne.datasets.sample.data_path() / 'subjects' / 'sample' / 'bem' / 'sample-oct-6-src.fif', patch_stats=True) >>> sum(s["use_tri_area"].sum() for s in src) / sum(s['nuse'] for s in src) * 1e6 20.69581503362706 ``` I’m not sure why the value for the ico-5 doesn’t match, assuming that manual entry is for `fsaverage` (because it will vary by subject). Even that for `sample` wouldn’t be 9.8: ```python >>> sum(s["use_tri_area"].sum() for s in src) / 20484 * 1e6 8.280750830677961 ``` ---
**Author:** ![larsoner](https://yyz2.discourse-cdn.com/free1/user_avatar/mne.discourse.group/larsoner/32/3_2.png) [@larsoner](https://mne.discourse.group/u/larsoner)\ **Post date:** [August 14, 2023, 4:09pm UTC](https://mne.discourse.group/t/ico-5-source-space-surface-area-per-source/7361/4 "2023-08-14T16:09:36Z")
… oh in those last two I errantly used `use_tri_area` – if we use `tri_area` we do get a value that matches (if you `floor` instead of `round`): ```python >>> sum(s["tri_area"].sum() for s in src) / 20484 * 1e6 9.882712190552494 ``` ---
**Author:** ![dasdiptyajit](https://yyz2.discourse-cdn.com/free1/user_avatar/mne.discourse.group/dasdiptyajit/32/4796_2.png) [@dasdiptyajit](https://mne.discourse.group/u/dasdiptyajit)\ **Post date:** [August 16, 2023, 1:16pm UTC](https://mne.discourse.group/t/ico-5-source-space-surface-area-per-source/7361/5 "2023-08-16T13:16:49Z")
@larsoner Thanks a lot for the explanation. `It works with sample data but not the 'fsaverge'` ```python In [38]: src= read_source_spaces('/home/dip_meg/mne_data/MNE-sample-data/subjects/fsaverage/bem/fsaverage-ico-5-src.fif') Reading a source space... [done] Reading a source space... [done] 2 source spaces read In [39]: src Out[39]: , ] MRI (surface RAS) coords, subject 'fsaverage', ~21.9 MB> In [40]: sum(s["tri_area"].sum() for s in src) / 20484 * 1e6 --------------------------------------------------------------------------- KeyError Traceback (most recent call last) Cell In[40], line 1 ----> 1 sum(s["tri_area"].sum() for s in src) / 20484 * 1e6 Cell In[40], line 1, in (.0) ----> 1 sum(s["tri_area"].sum() for s in src) / 20484 * 1e6 KeyError: 'tri_area' In [41]: sum(s["use_tri_area"].sum() for s in src) / 20484 * 1e6 --------------------------------------------------------------------------- KeyError Traceback (most recent call last) Cell In[41], line 1 ----> 1 sum(s["use_tri_area"].sum() for s in src) / 20484 * 1e6 Cell In[41], line 1, in (.0) ----> 1 sum(s["use_tri_area"].sum() for s in src) / 20484 * 1e6 KeyError: 'use_tri_area' ``` It seems like `use_tri_area` or `tri_area` attributes are missing in the `src`. Am I missing something? thanks! ---
**Author:** ![larsoner](https://yyz2.discourse-cdn.com/free1/user_avatar/mne.discourse.group/larsoner/32/3_2.png) [@larsoner](https://mne.discourse.group/u/larsoner)\ **Post date:** [August 16, 2023, 1:28pm UTC](https://mne.discourse.group/t/ico-5-source-space-surface-area-per-source/7361/6 "2023-08-16T13:28:26Z")
> [@dasdiptyajit](#): > > Am I missing something? You have to pass `patch_stats=True` to the `read_source_spaces` call ---
**Author:** ![dasdiptyajit](https://yyz2.discourse-cdn.com/free1/user_avatar/mne.discourse.group/dasdiptyajit/32/4796_2.png) [@dasdiptyajit](https://mne.discourse.group/u/dasdiptyajit)\ **Post date:** [August 16, 2023, 2:10pm UTC](https://mne.discourse.group/t/ico-5-source-space-surface-area-per-source/7361/7 "2023-08-16T14:10:25Z")
I can print the values now but for ico-5 for `fsaverage`, it doesn’t give the same value of 9.8 as documented in MNE. Would that mean the value is rather based on the `sample subject src` and not for `fsaverage`? ```python In [3]: from mne import read_source_spaces In [4]: src= read_source_spaces('/home/dip_meg/mne_data/MNE-fsaverage-data/fsave ...: rage/bem/fsaverage-ico-5-src.fif', patch_stats=True) Reading a source space... [done] Completing triangulation info... [done] Completing selection triangulation info... [done] Reading a source space... [done] Completing triangulation info... [done] Completing selection triangulation info... [done] 2 source spaces read In [5]: src Out[5]: , ] MRI (surface RAS) coords, subject 'fsaverage', ~59.1 MB> In [6]: src.info Out[6]: {'fname': '/home/dip_meg/mne_data/MNE-fsaverage-data/fsaverage/bem/fsaverage-ico-5-src.fif', 'working_dir': '/autofs/space/megmix_002/users/mluessi/data/code/mne-scripts', 'command_line': 'mne_make_source_space --surf lh.white:rh.white --ico 5 --src /cluster/fusion/mluessi/MNE-sample-data-build/MNE-sample-data/subjects/fsaverage/bem/fsaverage-ico-5-src.fif'} In [7]: sum(s["tri_area"].sum() for s in src) / 20484 * 1e6 Out[7]: 6.367790682029399 In [8]: sum(s["use_tri_area"].sum() for s in src) / 20484 * 1e6 Out[8]: 6.246565416014217 ``` ---
**Author:** ![larsoner](https://yyz2.discourse-cdn.com/free1/user_avatar/mne.discourse.group/larsoner/32/3_2.png) [@larsoner](https://mne.discourse.group/u/larsoner)\ **Post date:** [August 16, 2023, 3:02pm UTC](https://mne.discourse.group/t/ico-5-source-space-surface-area-per-source/7361/8 "2023-08-16T15:02:47Z")
I guess it must be. It’ll depend on the brain surface area since the number of vertices for `ico-5` is always the same… ---
**Author:** ![dasdiptyajit](https://yyz2.discourse-cdn.com/free1/user_avatar/mne.discourse.group/dasdiptyajit/32/4796_2.png) [@dasdiptyajit](https://mne.discourse.group/u/dasdiptyajit)\ **Post date:** [August 16, 2023, 4:21pm UTC](https://mne.discourse.group/t/ico-5-source-space-surface-area-per-source/7361/9 "2023-08-16T16:21:10Z")
Yes, you are right. I looked it up with my subjects data. thanks for helping. ---
**Author:** ![dasdiptyajit](https://yyz2.discourse-cdn.com/free1/user_avatar/mne.discourse.group/dasdiptyajit/32/4796_2.png) [@dasdiptyajit](https://mne.discourse.group/u/dasdiptyajit)\ **Post date:** [August 17, 2023, 4:48pm UTC](https://mne.discourse.group/t/ico-5-source-space-surface-area-per-source/7361/10 "2023-08-17T16:48:20Z")
@larsoner sorry, I have a follow up question. If I look at the [mne.setup\_source\_space — MNE 1.5.0 documentation](https://mne.tools/stable/generated/mne.setup_source_space.html) , MNE creates (at-least with default setup) source space at the interface between gray and white matter, i.e. at the white surface (decimated surface, more suitable for morphological feature)? and not at the middle surface, i.e. a surface that runs at the mid-distance between white and pial?? I am looking at the `mne code` to compute `Cortical surface area` for the triangulation. If I understand the code properly, then this means (I put the comments at the side): ```python def _complete_source_space_info(this, verbose=None): """Add more info on surface.""" # Main triangulation logger.info(" Completing triangulation info...") this["tri_area"] = np.zeros(this["ntri"]) r1 = this["rr"][this["tris"][:, 0], :] r2 = this["rr"][this["tris"][:, 1], :] r3 = this["rr"][this["tris"][:, 2], :] this["tri_cent"] = (r1 + r2 + r3) / 3.0 this["tri_nn"] = fast_cross_3d((r2 - r1), (r3 - r1)) this["tri_area"] = _normalize_vectors(this["tri_nn"]) / 2.0 logger.info("[done]") # Selected triangles logger.info(" Completing selection triangulation info...") if this["nuse_tri"] > 0: r1 = this["rr"][this["use_tris"][:, 0], :] >>>>>>>>> a triangular face say, r1r2r3; vertex coordinates r2 = this["rr"][this["use_tris"][:, 1], :] >>>>>>>>> vertex coordinates r3 = this["rr"][this["use_tris"][:, 2], :] >>>>>>>>> vertex coordinates this["use_tri_cent"] = (r1 + r2 + r3) / 3.0 >>>>>>>>> Conversion from facewise to vertexwise each vertex one-third of the sum of the areas of all faces that meet at that vertex this["use_tri_nn"] = fast_cross_3d((r2 - r1), (r3 - r1)) >>>>>>>>>>> computes the triangle vector normal this["use_tri_area"] = np.linalg.norm(this["use_tri_nn"], axis=1) / 2.0 >>>>>>>>>>> computes The triangle areas from vector normal in m2 logger.info("[done]") ``` Am I correct? I am following this paper : [https://s3.us-east-2.amazonaws.com/brainder/publications/2012/winkler2012\_facewise\_surface\_area.pdf](https://s3.us-east-2.amazonaws.com/brainder/publications/2012/winkler2012_facewise_surface_area.pdf) to understand the logic. Highly appreciate your help. Dip ---
**Author:** ![larsoner](https://yyz2.discourse-cdn.com/free1/user_avatar/mne.discourse.group/larsoner/32/3_2.png) [@larsoner](https://mne.discourse.group/u/larsoner)\ **Post date:** [August 17, 2023, 5:03pm UTC](https://mne.discourse.group/t/ico-5-source-space-surface-area-per-source/7361/11 "2023-08-17T17:03:42Z")
> [@dasdiptyajit](#): > > MNE creates (at-least with default setup) source space at the interface between gray and white matter, i.e. at the white surface (decimated surface, more suitable for morphological feature)? and not at the middle surface, i.e. a surface that runs at the mid-distance between white and pial?? That sounds right, the `white` surface should be the white/gray interface > [@dasdiptyajit](#): > > Am I correct? I am following this paper I don’t have the bandwidth to “check your work” so-to-speak on this – it’s probably better to convince yourself using more reading and/or checking against other libraries (like `vtk`) anyway! ---
**Author:** ![dasdiptyajit](https://yyz2.discourse-cdn.com/free1/user_avatar/mne.discourse.group/dasdiptyajit/32/4796_2.png) [@dasdiptyajit](https://mne.discourse.group/u/dasdiptyajit)\ **Post date:** [August 17, 2023, 5:07pm UTC](https://mne.discourse.group/t/ico-5-source-space-surface-area-per-source/7361/12 "2023-08-17T17:07:15Z")
Thanks! I will do that.