The lasttwo blog posts have dealt with biomagnetism: the magnetic fields produced by our bodies. Some of you might have noticed hints about how these posts originated in “another publication.” That other publication is now published! This week, my review article “Biomagnetism: The First Sixty Years” appeared in the journal Sensors. The abstract is given below.
Biomagnetism is the measurement of the weak magnetic fields produced by nerves and muscle. The magnetic field of the heart—the magnetocardiogram (MCG)—is the largest biomagnetic signal generated by the body and was the first measured. Magnetic fields have been detected from isolated tissue, such as a peripheral nerve or cardiac muscle, and these studies have provided insights into the fundamental properties of biomagnetism. The magnetic field of the brain—the magnetoencephalogram (MEG)—has generated much interest and has potential clinical applications to epilepsy, migraine, and psychiatric disorders. The biomagnetic inverse problem, calculating the electrical sources inside the brain from magnetic field recordings made outside the head, is difficult, but several techniques have been introduced to solve it. Traditionally biomagnetic fields are recorded using superconducting quantum interference device (SQUID) magnetometers, but recently new sensors have been developed that allow magnetic measurements without the cryogenic technology required for SQUIDs.
The “First Sixty Years” refers to this year (2023) being six decades since the original biomagnetism publication in 1963, when Baule and McFee first measured the magnetocardiogram.
My article completes a series of six reviews I’ve published in the last few years.
When I was on the faculty at Vanderbilt University, my student Marcella Woods and I examined the magnetic field produced by electrical activity in a sheet of cardiac muscle. I really like this analysis, because it provides a different view of the mechanism producing the magnetic field compared to that used by other researchers studying the magnetocardiogram. In another publication, here is how I describe our research. I hope you find it useful.
Roth and Marcella Woods examined an action potential propagating through a two-dimensional sheet of cardiac muscle [58]. In Fig. 6, a wave front is propagating to the right, so the myocardium on the left is fully depolarized and on the right is at rest. Cardiac muscle is anisotropic, meaning it has a different electrical conductivity parallel to the myocardial fibers than perpendicular to them. In Fig. 6, the fibers are oriented at an angle to the direction of propagation. The intracellular voltage gradient is in the propagation direction (horizontal in Fig. 6), but the anisotropy rotates the intracellular current toward the fiber axis. The same thing happens to the extracellular current, except that in cardiac muscle the intracellular conductivity is more anisotropic than the extracellular conductivity, so the extracellular current is not rotated as far. Continuity requires that the components of the intra- and extracellular current densities in the propagation direction are equal and opposite. Their sum therefore points perpendicular to the direction of propagation, creating a magnetic field that comes out of the plane of the tissue on the left and into the plane on the right (Fig. 6) [58–60].
Figure 6. The current and magnetic field produced by a planar wave front
propagating in a two-dimensional sheet of cardiac muscle. The muscle is
anisotropic with a higher conductivity along the myocardial fibers.
This perspective of the current and magnetic field in cardiac muscle is unlike that ordinarily adopted when analyzing the magnetocardiogram, where the impressed current is typically taken as in the same direction as propagation. Nonetheless, experiments by Jenny Holzer in Wikswo’s lab confirmed the behavior shown in Fig. 6 [61].
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.
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.
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.
For three years I’ve dodged the bullet, but no more; I have covid. I’m doing fine, thank you. For me the symptoms were similar to a moderate cold. My doctor put me on a five-day regimen of the antiviral drug Paxlovid plus some supplements to support my immune system (vitamin C, vitamin D3, and zinc). I’ve been isolating in our spare bedroom, which is boring but otherwise comfortable. I think I’m over the hump.
During the last few days I’ve taken several of those at-home covid rapid antigen tests. There’s some interesting physics at work in them. The figure below illustrates how they’re constructed.
To perform a test, you typically swab your nose, dip the swab in saline, stir, and then place a few drops of the solution onto the sample pad (A). You’re not detecting the virus itself, but instead the SARS-Cov 2antibody. To explain what that means, I need to delve into a bit of immunology.
Our immune system produces a Y-shaped protein called an antibody, or immunoglobulin, that can selectively bind to an antigen, which is typically a protein that’s part of the coronavirus. The beauty of the antibody-antigen reaction is that it’s so specific: it lets the immune system attack a particular virus, bacteria, or other pathogen, ignoring everything else.
When you get covid, your body launches an immune attack by producing SARS-Cov 2 antibodies. In the illustration above, the yellow Y is the antibody you are trying to detect. See David Goodsell’s marvelous painting of a virus being attacked by antibodies at the bottom of this post.
In the above figure, the conjugate pad (B) is where much of the physics lives. The pad contains gold nanoparticles (AuNP) that are coated with anti-human antibodies. An “anti-human antibody” is a molecule that binds selectively to a human antibody. In the figure, a red dot with a blue Y sticking out is a gold nanoparticle with an anti-human antibody bound to it.
A nitrocellulose membrane (NC membrane) is made from a mesh of nitrocellulose fibers (C). The mesh is porus
and acts something like a wick, pulling the fluid from left to right by capillary action. This is why a device like that in the figure above is sometimes called a lateral flow test. The mesh also provides protected space for the nanoparticles and molecules to move around and interact in. The absorbent pad (D) acts like a sponge, soaking up the fluid
as it reaches the right end of the detector, contributing to the
capillary action and preventing any back flow.
As any SARS-Cov 2 antibody passes by a gold nanoparticle/anti-human antibody, it binds and the entire complex flows to the right together (in the figure, a combined red dot/blue Y/yellow Y).
Some additional molecules are bound to two spots on the nitrocellulose membrane. One,
the test strip, has the SARS-cov 2 antigen. If any SARS-Cov 2 antibody
passes by, it will bind to the antigen, immobilizing the gold
nanoparticles. The other strip is goat
anti-mouse antibody. How did a goat and mouse get involved? I don’t know. As I understand it, gold nanoparticles with antibodies that bind to the goat anti-mouse antibody are included in the conjugate pad, so regardless of if you have covid or not it serves as a control. If the nanoparticles
don’t collect at the control strip, something is wrong.
Why bother with the gold nanoparticles? Their role is to transduce the signal so it becomes visible. Nanoparticles have interesting optical properties. When exposed to an electromagnetic field such as light, the electric field causes electrons to accumulate on one side of the particle creating a negative surface charge, leaving the opposite side positive from a lack of electrons. Such a distribution of charge oscillates at its own natural frequency (its plasma frequency), and when this frequency matches the driving frequency of the light there is a resonance. This “localized surface plasmon resonance” is effective at absorbing or scattering light. Scattering is particularly important because Rayleigh scattering (the scattering of light by particles with a radius much smaller than the wavelength of the light) depends on the sixth power of the particle radius. The binding of nanoparticles (which typically have a diameter of tens of nanometers) with large antibodies and antigens, and the aggregation of these complexes, can increase their effective size, accentuating scattering. In addition, the high concentration of the nanoparticles at the test and control strips enhance any optical effect. The end result is that you see a dark line if the nanoparticles are present.
So swab your nose, swish it in some saline, add a few drops to the sample pad, and wait. After about 15 minutes look at the results. If there is no control line, you’ve messed up. Throw the test away and try again. If there’s a control line but no test line, you’re negative. Be happy (but not too happy, because these tests are prone to false negatives). If there’s both a control line and a test line, you’ve got covid. The tests don’t give false positives too often, so you can be fairly confident you have the disease. Isolate yourself and talk to you doctor.
Where is the physics in all this? First, in the flow, which results from the surface tension created by the mesh of fibers, leading to capillary action. Second, in the optical properties of the nanoparticles, which provide the color that you see in the test and control strips. Unfortunately, Intermediate Physics for Medicine and Biology doesn’t discuss capillary action or surface plasmons, so you can’t learn about them there. Sorry; no book can cover everything. But there is interesting physics hidden in these tests.
Stay safe, dear reader, and may all your covid tests be negative.
This painting shows a cross section through a coronavirus surrounded by
blood plasma, with neutralizing antibodies in bright yellow. The painting was commissioned for the cover of a special COVID-19 issue of Nature. From: David S. Goodsell, RCSB Protein Data Bank and Springer Nature; doi: 10.2210/rcsb_pdb/goodsell-gallery-025
A chemist explains how at-home covid tests work. From WIRED.
I am an emeritus professor of physics at Oakland University, and coauthor of the textbook Intermediate Physics for Medicine and Biology. The purpose of this blog is specifically to support and promote my textbook, and in general to illustrate applications of physics to medicine and biology.
