The Rest of the Story 5

Bill grew up in Schenectady, New York, the youngest of four children. While a child he became interested in science because of his fascination with telescopes. He was smart; he graduated from high school at the age of 15, and then attended Schenectady’s Union College, finishing in just three years. By the age of 22 he had graduated with an M.D. from the Albany Medical College. Many of his friends didn’t realize how bright Bill was, because he was so modest and friendly, and had such a wonderful sense of humor.

Bill became an active duty medical officer posted at the U.S. Naval Hospital in Newport, Rhode Island. After a fellowship in neurology at the University of Minnesota, he joined the new medical school at UCLA. He was much loved as a medical doctor and a mentor, but he disliked many of the invasive procedures that he had to perform as a clinical neurologist.

In 1959, Bill had an idea how to noninvasively image the brain using multiple x-ray beams in different directions. After two years of effort he had a working prototype, applied for a patent, and published an article about this work. But when he approached a leading x-ray manufacturer, the company president couldn’t image there would ever be a market for such a device. Frustrated, Bill turned his attention to other things.

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Bill’s idea for how to image the brain did not go away. Other scientists took up the challenge. Physicist Allan Cormack and engineer Ronald Bracewell each developed detailed mathematical techniques for obtaining an image from beams in different directions. Engineer Godfrey Hounsfield built the first brain scanner in 1971. And the rest is history. Bill’s invention is now known as Computed Tomography (originally called a CAT scan and now referred to as CT for short). It has revolutionized medicine. In 1979, Cormack and Hounsfield won the Nobel Prize in Physiology or Medicine for their contributions to CT. William (“Bill”) Oldendorf did not share the prize, but he shared in the discovery.

William Oldendorf.

And now you know the rest of the story.

Good day! 

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This blog post was written in the style of Paul Harvey’s The Rest of the Story radio program. You can find four other of my The Rest of the Story posts here, here, here, and here. 

You can learn more about Computed Tomography in Chapter 16 of Intermediate Physics for Medicine and Biology.

William Oldendorf was born March 27, 1925, one hundred years ago yesterday. Happy birthday Bill!

Dipole-Dipole Interaction

One strength of Intermediate Physics for Medicine and Biology is its many homework problems. The problems stress (but perhaps not enough) the ability to make general arguments about how some quantity will depend on a variable. Often getting a calculation exactly right is not as important as just knowing how something varies with something else. For instance, you could spend all day learning how to compute the volume and surface area of complicated objects, but it’s still useful simply to know that volume goes as size cubed and surface area as size squared. Below is a new homework problem that emphasizes the ability to determine a functional form.

Section 6.7

Problem 20½. Consider an electric dipole p a distance r from a small dielectric object. Calculate how the energy of interaction between the dipole and the induced dipole in the dielectric varies with r. Will the dipole be attracted to or repelled from the dielectric? Use the following facts:

1. The energy U of a dipole in an electric field E is U = – p · E,

2. The net dipole induced in a dielectric, p', is proportional to the electric field the dielectric experiences,

3. The electric potential produced by a dipole is given by Eq. 7.30.

Let’s take a closer look at these three facts.

1. When discussing magnetic resonance imaging in Chapter 18 of IPMB, we give the energy U of a magnetic dipole μ in a magnetic field B as U = – μ · B (Eq. 18.3). An analogous relationship holds for an electric dipole in an electric field. The energy is lowest when the dipole and the electric field are in the same direction, and varies as the cosine of the angle between them. I suggest treating the original dipole p as producing the electric field E, and the induced dipole p' as interacting it. 

2. Section 6.7 of IPMB discusses how an electric field polarizes a dielectric. The net dipole p' induced in the dielectric object will depend on the electric field and the objects shape and volume. I don’t want you to have to worry about the details, so the problem simply says that the net dipole is proportional to the electric field. You might get worried and say “wait, the electric field in the dielectric is not uniform!” That’s why I said the dielectric object is small. Assume that it’s small enough compared to the distance to the dipole that the electric field is approximately uniform over the volume of the dielectric. 

3. What is the electric field produced by a dipole? Russ Hobbie and I don’t actually calculate that, but we do give an equation for a dipole’s electrical potential, which falls off as one over the square of the distance. (It may look like the cube of the distance in Eq. 7.13, but there’s a factor of distance in the numerator that cancels one factor of distance cubed in the denominator, so it’s an inverse square falloff.) The electric field is the negative gradient of the potential. Calculating the electric field can be complicated in the general case. I suggest you assume the dipole p points toward the dielectric. Fortunately, the functional dependence of the energy on the distance r does not depend on the dipole direction.

I won’t work out all theentire solution here. When all is said and done, the energy falls off as 1/r⁶, and the dipole is attracted to the dielectric. It doesn’t matter if the dipole originally pointed toward the dielectric or away from it, the force is always attractive.

This result is significant for a couple reasons. First, van der Waals interactions are important in biology. Two dielectrics attract each other with an energy that falls as 1/r⁶. Why is there any interaction at all between two dielectrics? Because random thermal motion can create a fluctuating dipole in one dielectric, which then induces a dipole in a nearby dielectric, causing them to be attracted. These van der Waals forces play a role in how biomolecules interact, such as during protein folding.

From Photon to Neuron:
Light, Imaging, Vision.

Second, there is a technique to determine the separation between two molecules called fluorescence resonance energy transfer (FRET). The fluorescence of two molecules, the donor and the acceptor, is affected by their dipole-dipole interaction. Because this energy falls off as the sixth power of the distance between them, FRET is very sensitive to distance. You can use this technique as a spectroscopic ruler. It’s not exactly the same as in the problem above, because both the donor and acceptor have permanent dipole moments, instead of one being a dielectric in which a dipole moment is induced. But nevertheless, the 1/r⁶ argument still holds, as long as the dipoles aren’t too close together. You can learn more about FRET in Philip Nelson’s book From Photon to Neuron: Light, Imaging, Vision.

The First Measurement of the Magnetocardiogram

Biomagnetism: The First Sixty Years.

A couple years ago, I published a review article titled “Biomagnetism: The First Sixty Years.” I wrote about that article before in this blog, but I thought it was time for an update. The paper is popular: according to Google Scholar it has been cited 28 times in two years, which is more citations than any other of my publications in the last decade. I remember working on this paper because it was my Covid project. That year I got Covid for the first—and, so far, only—time. I quarantined myself in our upstairs bedroom, wore a mask, and somehow avoided infecting my wife. I remember having little to do except work on my biomagnetism review.

As a treat, I thought I would reproduce one of the initial sections of the article (references removed) about the first measurement of the magnetocardiogram. Russ Hobbie and I talk about the MCG in Chapter 8 of Intermediate Physics for Medicine and Biology. This excerpt goes into more detail about how MCG measurements began. Enjoy!

2.1. The First Measurement of the Magnetocardiogram

In 1963, Gerhard Baule and Richard McFee first measured the magnetic field generated by the human body. Working in a field in Syracuse, New York, they recorded the magnetic field of the heart: the magnetocardiogram (MCG). To sense the signal, they wound two million turns of wire around a dumbbell-shaped ferrite core that responded to the changing magnetic field by electromagnetic induction. The induced voltage in the pickup coil was detected with a low-noise amplifier.

The ferrite core was about one-third of a meter long, so the magnetic field was not measured at a single point above the chest, but instead was averaged over the entire coil. One question repeatedly examined in this review is spatial resolution. Small detectors are often noisy and large detectors integrate over the area, creating a trade-off between spatial resolution and the signal-to-noise ratio.

The heart’s magnetic field is tiny, on the order of 50–100 pT (Figure 1). A picotesla (pT) is less than a millionth of a millionth as strong as the magnetic field in a magnetic resonance imaging machine. The magnetic field of the earth is about 30,000,000 pT (Figure 1), and the only reason it does not obscure the heart’s field is that the earth’s field is static. That is not strictly true. The earth’s field varies slightly over time, which causes geomagnetic noise that tends to mask the magnetocardiogram (Figure 1). Moreover, even a perfectly static geomagnetic field would influence the MCG if the pickup coil slightly vibrated. A key challenge in biomagnetic recordings, and a major theme in this review, is the battle to lower the noise enough so the signal is detectable

Figure 1. Noise sources in biomagnetism.

Most laboratories contain stray magnetic fields from sources such as electronic equipment, elevators, or passing cars (Figure 1). Baule and McFee avoided much of this noise by performing their experiments at a remote location. Even so, they had to filter out the ubiquitous 60 Hz magnetic field arising from electrical power distribution. A magnetic field changing at 60 Hz is a particular nuisance for biomagnetism because the magnetic field typically exists in a frequency band extending from 1 Hz (1 s between heartbeats) to 1000 Hz (1 ms rise time of a nerve or muscle action potential).

One limitation of a metal pickup coil is the thermal currents in the winding due to the random motion of electrons, creating extraneous magnetic fields caused by the measuring device itself. The ultimate source of noise is thermal currents in the body, but fortunately, their magnetic field is minuscule (Figure 1).

Baule and McFee suppressed background noise by subtracting the output of two pickup coils. A distant source of noise gave the same signal in both coils and did not contribute to their difference. One coil was placed over the heart, and the magnetocardiogram was larger there and did not cancel out. The two coils formed a rudimentary type of gradiometer (Figure 2).

The magnetocardiogram resembled the electrocardiogram (ECG) sensed by electrodes attached to the skin. Baule and McFee speculated that the MCG might contain different information than the ECG, another idea that reappears throughout this review. In a followup article, they theoretically calculated the magnetic field produced by the heart. The interplay between theory and experiments is yet one more subject that frequently arises in this article.

Figure 2. Types of gradiometers.

Einstein and Smoluchowski

In Chapter 4 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the Einstein relationship between diffusion and viscosity. We wrote

The diffusion constant…is closely related to the viscosity, as was first pointed out by Albert Einstein. This is not surprising, since diffusion is caused by the random motion of particles under the bombardment of neighboring atoms, and viscous drag is also caused by the bombardment of neighboring atoms.

All this random bombardment is also related to Brownian motion: the random movement of small particles when they collide with many water molecules.

What is typically referred to as the Einstein relationship is given by our Eq. 4.22,

      D = kT/β,       (4.22)

where D is the diffusion constant, k is Boltzman’s constant, T is the absolute temperature, and β is a factor relating the viscous force to the drift velocity, sometimes called the frictional drag coefficient. Essentially, β is like the reciprocal of the mobility. This equation doesn’t contain the viscosity, but if you use Stokes’ law for β you get

      D = kT/6πηa,     (4.23)

where a is the radius of the particle being considered and η is the coefficient of viscosity.

Russ and I refer to Eq. 4.22 as the Einstein relationship. However, if you look in Howard Berg’s marvelous book Random Walks in Biology, you find this expression is called the Einstein-Smoluchowski relationship. So the natural question is: just who is this Smoluchowski?

To answer that question, I consulted my favorite biography of Einstein, Abraham Pais’s Subtle is the Lord. Pais writes

If Marian Ritter von Smolan-Smoluchowski had been only an outstanding theoretical physicist and not a fine experimentalist as well, he would probably have been the first to publish a quantitative theory of Brownian motion.

Smoluchowski, born to a Polish family, spent his early years in Vienna, where he also received a university education. After finishing his studies in 1894, he worked in several laboratories abroad, and then returned to Vienna, where he became Privatdozent. In 1900 he became professor of theoretical physics in Lemberg (now Lvov), where he stayed until 1913. In that period he did his major work. In 1913 he took over the directorship of the Institute for Experimental Physics at the Jagiellonian University in Cracow. There he died in 1917, victim of a dysentery epidemic.

It is quite remarkable how often Smoluchowski and Einstein simultaneously and independently pursued similar if not identical problems. In 1904 Einstein worked on energy fluctuations, Smoluchowski on particle number fluctuations of an ideal gas. Einstein completed his first paper on Brownian motion in May 1905; Smoluchowski his in July 1906.

So even the great Einstein had competition for many of his ideas. In fact, Smoluchowski nearly derived the relationship first. Pais continues

Smoluchowski began his 1906 paper by referring to Einstein’s two articles of 1905: “The findings [of those papers] agree completely with some results which I had… obtained several years ago and which I consider since then as an important argument for the kinetic nature of this phenomenon.” Then why had he not published earlier? “Although it has not been possible for me till now to undertake an experimental test of the consequences of this point of view, something I originally intended to do, I have decided to publish these considerations…”

Apparently he wanted to get experimental support for his ideas, and by waiting he got scooped.

Both Einstein and Smoluchowski went on to independently study critical opalescence: how the scattering of light passing through a gas increases in the neighborhood of a critical point. Pais concludes

Smoluchowski’s last contribution to this problem [of critical opalescence] was experimental: he wanted to reproduce the blue of the sky in a terrestrial experiment. Preliminary results looked promising, and he announced that more detailed experiments were in progress. He did not live to complete them.

After Smoluchowski’s death, Sommerfeld and Einstein wrote obituaries in praise of a good man and a great scientist. Einstein called him an ingenious man of research and a noble and subtle human being.