1. Anatomy of the head March 5th 2009
Goal: construct a geometrical model of the head for inverse problem
1. seed the sources in the grey matter according to pyramidal hypothesis of EEG
2. model tissues that contribute to changes in the propagation of the signal
The goal is to construct a geometrical model of the head for source estimation. 2 important issues are to seed the sources in the grey matter in agreement with what is known about the origin of the EEG signal, and to model the tissues that interfere with the propagation of the signal.

2. Overview of the tissues

3. This slide shows the different tissues, skin and periosteum, usually bundled as one tissue, skull (in living being a spongy tissue that is quite resistive to the passage of electrical current and very anisotropic –its conductivity varies greatly from place to place-) meninges, arachnoid space, filled with CSF, grey and white matter.

4. Muscles
A first structure which is visible in MRI but typically not modeled is muscle, there are three groups visible on MRI, temporalis, frontalis and occipitalis.

5. Muscles
Here you see temporalis muscle on the left (red)and their correspondence in the MRI on the right. It lays outside the skull and below the skin, -is thickest in the middle slices of MRI.

6. skull
Here we move to the skull. It is (with white matter) the most anisotropic tissue that contributes to the inverse problem. Plates of bone grow and join, with radial growth patterns and junction sites being large contributors to variance in thickness and in conductivity. There are fine details of the geometry that cannot be captured by MRI (1mm sampling) which are apparent on the right.

7. skull
Since the skull is a major resistor to the EEG signal, breaches/openings are very important structures that contribute to locally-increased passage of the signal and interference patterns.
The upper right picture shows the opening for the arteries, cranial nerves etc… at the base of the skull. These are not important yet since we do not take signal from regions like the chin (Egi pushes in that direction though, with the wise rationale that under-determined inverse problem can be constrained only if we sample from the whole volume –above and below-).
On the left is a picture of parietal foramina -above the lambda, let passage of a vein across the skull-. This kind of structure is extremely variable from one subject to the next. Their position may be asymmetrical (like here), people may not have any distinct foramen, some people have one or two foramina enlarged to a diameter of 1 cm. The presence of this structure probably has a huge influence on amplitude of rhythms like alpha (which power varies across subjects by two orders of magnitude). In most case, it is not detectable in MRI because of the spatial sampling at 1mm.
On the lower right is a picture of frontal foramina above and below the orbit. Same issue re. frontal EEG signals. Anatomical variability as well.

8. skull
Here this picture shows the cast of vascular system passing across the skull (skull was dissolved). This also contributes to the large anisotropy of the skull. Notice again the spongy like texture of the skull. When hydrated in living tissue, this improves the passage of current across the scalp.

9. Vascular system
Here are example of vascular structures, veins, arteries and venous sinuses (e.g superior sagittal sinus quite perceptible in MRI that collects and evacuates blood). Some of the vascular system is in the brain (think of an angiogram), some is outside the skull, and some passes across through the foramina or through capillaries directly in the bone. The major vessels are usually visible in MRI.

10. Frontal sinuses
And here are frontal sinus that greatly attenuate frontal signals. They are cavities that occur directly within the bone, filled with nothing, with conductivity values of zero.
In the old time, neurologists used the horrible naso-pharingeal electrode (spiral passed in the nostril and stucked on the roof by the brain) to get good diagnostic of frontal signal.

11. CSF
Here, to the contrary are the Ventricle and CSF system, very good conductor, and usually modeled as a separate compartment because its conductivity value is very different from its neighbors. 4 Ventricles (left, right, 3rd and 4th) and CSF passing by the arachnoid space above the grey matter.

12. Seeding the sources in the grey matter,
Constraint 1:
Seeding the sources in the grey matter,
with their proper 3D orientation

13. Current theory posits that most (not all) EEG signal comes from the open-field generated by pyramidal neurons (because of their nice spatial order, their signal don’t cancel out). There are two layers of the cerebral cortex with dense representation of pyramidal neurons, III and V.
Sources should be constrained to these structures.

14. Dipoles should also have a direction in 3D space that correspond to the local geometry. Lower right picture shows a segmentation of the outer grey matter boundary. We see that the grey/meninges case is easy, the grey-grey boundary however (sulci) is sometimes very difficult. The grey-white boundary is not always clear especially in 3T MRI.

15. Issues: resolution, outer and inner boundary crossing, etc…
Other issues come up depending on MRI spatial resolution, contrast, and problem occur during automatic segmentation such as this outer and inner boundary crossing, error that needs to be fixed …

16. Constraint 2: compartmental or voxel-based anisotropy

17. Constraint 2: compartmental or voxel-based anisotropy
Another domain of future improvement is the anisotropy. Now, most models include a compartment-based conductivity values (each compartment,-grey matter, white, CSF, skull etc…- has one parameter of conductivity). The figure on the left is a forward model that shows diversion of current as a function of voxel-based anisotropy (each voxel has its own conductivity value). We see that it makes a difference although the skull remain the largest contributor. In the future, EIT and DTI will be used to specify empirical values of conductivities at each voxel.
EIT, DTI

18. Annotated transversal head shape.