Friday, October 11, 2013

How Well Does a Three-Sphere Model Predict Positions of Dipoles in a Realistically Shaped Head?

When I worked at the National Institutes of Health, I collaborated with Susumu Sato, a neurophysiologist interested in electroencephalography and magnetoencephalography. One of Sato’s goals was to develop methods to localize the source of epileptic seizures in the brain. In a small percentage of patients, these seizures cannot be controlled by drugs and are severe enough to be debilitating. In such cases, the best alternative is surgery: remove the region of the brain where the seizure originates, and you stop the seizures. Obviously, in these patients the surgeon must know what part of the brain to remove, and the more accurately that is known the better. Ideally, you want to localize the source using a noninvasive procedure such as electroencephalography. One way to model the sources of electrical activity in the brain is as a single dipole source. Russ Hobbie and I discuss dipoles and the EEG in Chapter 7 of the 4th edition of Intermediate Physics for Medicine and Biology.
Much can be learned about the brain by measuring the electric potential on the scalp surface. Such data are called the electroencephalogram (EEG). Nunez and Srinivasan have written an excellent book about the physics of the EEG. We briefly examine the topic here. The EEG is used to diagnose brain disorders, to localize the source of electrical activity in the brain in patients who have epilepsy, and as a research tool to learn more about how the brain responds to stimuli (“evoked responses”) and how it changes with time (“plasticity”). Typically, the EEG is measured from 21 electrodes attached to the scalp according to the “10–20 system” (Fig. 7.34). A typical signal from an electroencephalographic electrode is shown in the top panel of Fig. 11.38. One difficulty in interpreting the EEG is the lack of a suitable reference electrode. None of the 21 electrodes in Fig. 7.34 qualifies as a distant ground against which all other potential recordings can be measured. One way around this difficulty is to subtract from each measured potential the average of all the measured potentials. In the problems, you are asked to prove that this “average reference recording” does not depend on the choice of reference electrode; it is a reference independent method.
The reference is to Paul Nunez’s book Electric Fields of the Brain (Oxford University Press, 2005), which is a great starting point to learn about the physics of the EEG.

Sato wanted to localize the dipole as accurately as possible, even if that meant moving beyond the three-sphere model. Therefore, I was recruited to write a computer program to solve the EEG problem for a realistically-shaped head. This was not easy, because no software existed at that time for numerically solving the electric potential produced by a dipole in the brain when it is not spherical (at least, Sato and I didn’t have access to such software). I used a boundary element method to perform the calculation. I needed information about the shape of the skull, scalp, and brain surfaces, and I remember painstakingly digitizing those surfaces by hand from magnetic resonance images, and then tessellating the surfaces with triangles. Our resulting image of the brain graced the cover of the journal Electroencephalography and clinical Neurophysiology for several years.

The cover of Electroencephalography and Clinical Neurophysiology, showing a drawing of the brain from the article How Well Does the Three-Sphere Model Predict Dipoles in a Realistically-Shaped Head? (Electroenceph clin Neurophysiol 87:175–184, 1993).
The cover of Electroencephalography
and Clinical Neurophysiology.
This research culminated in a paper published almost exactly 20 years ago: Roth, B. J., M. Balish, A. Gorbach and S. Sato, 1993, “How well does the three-spheres model predict dipoles in a realistically-shaped head?Electroenceph. clin. Neurophysiol., Volume 87, Pages 175–184. The introduction of the paper is presented below, with references removed.
Electroencephalographic data, such as interictal spikes and evoked responses, are increasingly analyzed using the moving dipole method. The source of the EEG activity is represented as one or more dipoles within the brain; their location, orientation and strength are determined using an iterative least-squares algorithm to fit the calculated potential to the measured EEG data. Although the dipole approximation is an oversimplification, it is a convenient representation of the complex cortical sources. Most often, the potential produced by a dipole is calculated using the 3-sphere model. In this model the brain, skull and scalp are represented as concentric, spherical shells that differ in conductivity. More computationally demanding models use a realistically shaped head; the electrical potential produced by a dipole source is computed either by solving a system of integral equations governing the potential on the brain, skull, and scalp surfaces or by using a finite element model of the head.

In this paper, we compare the 3-sphere model to a realistically shaped head model, in which the brain, skull and scalp surfaces are obtained from magnetic resonance images. We consider a dipole in the temporal or frontal lobe of the brain, and perform a forward calculation using the realistically shaped head model to determine the potential at the 10-20 electrode positions. We then use these data to predict the dipole position by performing an inverse calculation with the 3-sphere model. The average difference between the original and predicted dipole positions is about 2 cm, though differences as large as 4 cm are seen under certain circumstances. Our results are particularly significant for localization of EEG sources of epileptic spikes, which commonly lie in the temporal and frontal lobes.


  1. If you had a test electrode at a known position in the brain (e.g. imagine a patient with a deep brain stimulator lead), and you emitted a time varying voltage from that electrode, you would measure a signal at 10 20 leads placed on the scalp.

    Now if you use a pure, computational model based on the MRI geometry, could you indeed accurately predict the potentials at the 10 20 leads given the same driving signal deep in the brain? Is there a way to get the impedance at every point on the interior so you could solve the computational problem?

  2. "Is there a way to get the impedance at every point on the interior so you could solve the computational problem?"

    This is a relevant question. I would ask that 'the computational problem' being referred to be better defined. More to the point, I would ask how many impedance measurements (defined spatially, within a specific volume) are necessary to address the 'computational problem?' While I appreciate that Dr. Roth is explaining how to estimate the location of what is being discussed in brain disorders as the source or the region responsible for the onset of some activity leading to a cascade of activation along some group of cells, it is important for this reader to understand where the actual trigger for this response lies. To discern this point, likely needing to consist of large numbers of individual cells and possibly multiple cell types in order to be something measurable, we must approach the appropriate physiological question with caution - depending heavily on how the solution for the physiological can be compared to the amount of deviation in the computational solutions. These define the limitations in terms of something most useful to the computational scientist. Without these limitations defined, it is impossible to set up relevant experiments - and thus it is impossible to directly address Frankie's question. However, it is not impossible to engage in discussions, whereby these limitations can be defined together - with larger groups of people from different areas within the same field of study. In my opinion, this is what makes the Brain project being undertaken by the NIH so encouraging. We need cross talk.