About EEG/MEG forward model and dipole position

edelaire · January 28, 2026, 8:13pm

Hello,

This post is about something I have been thinking about on and off since I started learning about MEG, but never formally written. I am finally taking the courage to ask about it.

TLDR: Why, when doing distributed source imaging, with dipole constrained to the cortical surface, are the dipoles placed at the vertex of the cortical mesh and not in the center of each face of the cortical mesh?

Long story:

When doing distributed source imaging, we place dipoles along the cortical surface. Each dipole represents an equivalent patch of cortex with the corresponding cortical column. In the cortex, because the neurons are aligned, this forms an equivalent dipole that is perpendicular to the cortical surface. Now, we describe the cortex as a triangular mesh (a set of vertices and faces). Currently, we place the dipole at each vertex. But I was wondering if we should not, instead, have one vertex per face.

Here are some reasons why I think it would make sense :

Visualization:

When inspecting the head model, we see that there is one dipole per vertex (left – although they don’t appear to be normal to the cortical surface). But when we visualize the result, we dont actually display the dipole’s intensity at each vertex, but smooth the result to color the faces of the mesh (right).

We can see this effect when we apply a threshold and create a scout based on the activated patch:

The activation seems to be larger than the scout. This is minor, but I think I saw multiple questions on the forum asking why Scout seemed to leave empty patches. Notably, here, if we define a second scout for the negative activity. It would seem that a hole would exist between the two scouts (since there is no vertex there).

Putting the dipole at the center of each face would solve the issue since we could then color each face and eventually allow the user to control the amount of spatial smoothing applied. Additionally, defining scout as a set of faces would solve the issue of where to put the boundaries.

Defining the normal vector

When we do ESI/MSI, we often constrain the vector to be normal to the surface. If we consider a face, then defining the normal to that face is easy. But i dont know how to define the normal to a single point when we put the dipoles at the vertex location.

Interpretation:

Each dipole is supposed to represent a volume of cortex. (equivalent area * cortical thickness). However, defining the area covered by each vertex is not evident. (I know brainstorm can give an estimate from tess_area). But to me, it’s not obvious what the equivalent area of cortex is associated with each dipole.

I think this is important as (unless I am mistaken), the activity found after source localization is directly proportional to the area of cortex corresponding to each dipole. If we have 5 dipoles, each with an amplitude A, then modeling them with 1 equivalent dipole would result in an amplitude of 5A. The thing I am not sure about is why the unit after source localization is pA.m when I always thought it should be pA.m^2. Since we have a current over a specific area.

If we place one dipole per face, then it’s direct to see what portion of the cortex is modelled by each dipole (the corresponding triangle), and we can easily associate an area of cortex with each dipole. This means that we can then display the current map (pA.m2) –> meaning that larger triangles will have a bias towards larger amplitudes, but also a normalized map pA where we normalize the amplitude of each dipole using the area of cortex covered by the dipole.

My hypothesis is that doing so would help reduce the impact of the mesh inhomogeneity (e.g., there is variability in the size of each face). In fMRI, people have found that having an homogenous mesh could help reduce some bias when estimating functional connectivity ( A cortical surface template for human neuroscience - PMC )

Conclusion:

From a code perspective i guess there shouldn’t be too much difference from putting the dipole at the mesh edge vs at the center of each triangle. But I guess there is a reason I am missing that leads to that choice? Or was it considered, but both methods are actually leading to the same results?

Thanks for reading
Feel free to let me know if anything is unclear haha

Raymundo.Cassani · January 29, 2026, 4:08pm

Hi @edelaire, that's a interesting question.
Here my comments on the post.

I'm also pinging @John_Mosher, who can certainly give you more details on the topics I am not replying to.

The should figure is not the dipoles, but the leadfields for that sensor (Fp1). For the blue arrows, the orientation will show orientation of the dipole in that direction that will have the maximum influence in the given sensor. While the magnitude shows the sensitivity of the given sensor to that (vertex) location. You can compare the leadfield vectors for EEG and MEG, the EEG ones are radial, while the ones for MEG are tangential.

The normals for the vertices are stored in the surface file. AFAIK there is not a way to plot them from the GUI, but it can be easily done.

Plot the cortical surface
Export that cortical surface to Matlab as variable, e.g., surfo
Plot the normals with this snippet:

hold on
quiver3( ...
    surfo.Vertices(:,1), surfo.Vertices(:,2), surfo.Vertices(:,3), ...
    surfo.VertNormals(:,1), surfo.VertNormals(:,2), surfo.VertNormals(:,3), 3, 'r' ); % Scale by 3, for visualization

That's correct, it's an interpolation for visualization. If it were done face wise, the maps would be piecewise, and that would not really present the data on the cortex that is assumed to be continuous.

Correct, just for visualization. Since the dipole currents are located in the vertices, Scout aggregations are properly handled as the Scouts are sets of vertices.

One potential solution for this visualization issue, that we have not implemented, is to draw the Scouts using the midpoint in the mesh edges.

The normal to the vertex is the average of the normals of the adjacent faces. See tess_normals.m. This measure has smoother transitions (following the assumption of continuos surface) than the face normals which change abruptly between adjacent faces.

Similar to the normals, the areas in the faces can vary a lot for adjacent faces. The area that represents each vertex dipole is set to sum of 1/3 or the adjacent face areas. In this sense, the vertex areas have less variations as it is balanced by the different adjacent face areas.

Have you encounter this post?

In the pragmatic aspect, using vertices as dipoles simplifies the equivalence between the anatomy and the headmodels, this helps to the use of cortical atlases which are defined vertex-wise. Most mesh operations are computing on vertices rather than faces.

I'll let @John_Mosher and @tmedani to provide further comments on this.

tmedani · February 3, 2026, 10:55pm

Hi @edelaire

I agree with Raymundo’s explanation and just wanted to extend/repeat a few points.

About using vertices instead of face centers: this is mainly a practical and conceptual choice: vertices already have well-defined normals (averaged across adjacent triangles), which give a smooth and a stable dipole orientation. Face normals would be discontinuous from triangle to triangle and would make both the forward model assumptions and the visualization noisier. Most cortical data structures (atlases, scouts, smoothing) are also vertex-based, so everything stays consistent.

About the units: reporting source amplitudes in pA·m is correct here, since these are dipole moments (as defined in the forward model). Even though the sources lie on a surface, they are still modeled as equivalent current dipoles (depending on the inverse method), and those are not surface current densities (which would be pA/m²).

Best,