Friday, April 14, 2023

The Magnetoencephalogram is Not Sensitive to a Radial Dipole

One of the key limitations of the magnetoencephalogram (MEG) is that it’s not sensitive to a radial dipole. What does this mean? The MEG is the magnetic field outside the head produced by the electrical activity of neurons in the brain. Often the source of this activity can be described by a current dipole, p, representing the intracellular current in the neurons. Because current flows in continuous loops, a dipole is surrounded by extracellular “return currents” flowing throughout the brain. Often the brain can be approximated as a sphere.

In Intermediate Physics for Medicine and Biology, Russ Hobbie and I explain the lack of a magnetic signal from a radial dipole this way:
One can see from the symmetry argument in the caption of Fig. 8.19 that in a spherically symmetric conducting medium the radial component of p and its return currents do not generate any magnetic field outside the sphere. Therefore the MEG is most sensitive to detecting activity in the fissures of the cortex, where the trunk of the postsynaptic dendrite is perpendicular to the surface of the fissure. A tangential component of p does produce a magnetic field outside a spherically symmetric conductor.

Figure 8.19 from IPMB is shown below.

While this text and figure do explain why a radial dipole has zero magnetic field, the explanation is a bit cryptic. Here is an alternative explanation that I wrote for another publication, and a better (or at least more colorful) figure.

A radial dipole produces no magnetic field (Fig. 8). This result is best proved using Ampere’s law: the magnetic field integrated along a closed loop is proportional to the net current threading the loop. The symmetry is sufficient that the integral over the path (dashed circle in Fig. 8) equals the path length times the magnetic field. The current produced by a dipole, including the return current, must be contained within the sphere because the region outside is not conducting. Hence, the net current threading the loop (the dipole plus the return current) is zero, so the magnetic field of a radial dipole vanishes.

Figure 8. The magnetic field of a radial dipole is zero outside a spherical conductor.

I hope this description is clearer!

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