“Havana Syndrome”: A post mortem

“Havana Syndrome”: A Post Mortem,
by Bartholomew and Baloh.

Remember the Havana Syndrome? You don’t hear much about it anymore. Recently I read an article titled “‘Havana Syndrome’: A Post Mortem,” by Robert Bartholomew and Robert Baloh. These two researchers are long-time skeptics who don’t believe that the Havana Syndrome was caused by a physical attack on US and Canadian diplomats. They are also critical of the National Academies report that suggested microwave weapons might be responsible for the Havana Syndrome. I came to a similar conclusion in my book Are Electromagnetic Fields Making Me Ill?, where I wrote

At this time, we have no conclusive explanation for the Havana syndrome. We need more evidence. Measuring intense beams of microwaves should be easy to do and would not be prohibitively expensive. Until someone observes microwaves associated with the onset of this illness, I will remain skeptical of the National Academies’conclusion.

Bartholomew and Baloh believe that the Havana Syndrome is psychogenic. In my book, I make an analogy to post traumatic stress syndrome: it’s a real disease, but not one with a simple physical cause. Below I quote the abstract from Bartholomew and Baloh’s paper.

Background: Since 2016, an array of claims and public discourse have circulated in the medical community over the origin and nature of a mysterious condition dubbed “Havana Syndrome,” so named as it was first identified in Cuba. In March 2023, the United States intelligence community concluded that the condition was a socially constructed catch-all category for an array of health conditions and stress reactions that were lumped under a single label.

Aims: To examine the history of “Havana Syndrome” and the many factors that led to its erroneous categorization as a novel clinical entity.

Method: A review of the literature.

Results/Conclusions: Several factors led to the erroneous classification of “Havana Syndrome” as a novel entity including the failure to stay within the limitations of the data; the withholding of information by intelligence agencies, the prevalence of popular misconceptions about psychogenic illness, the inability to identify historical parallels; the role of the media, and the mixing of politics with science.

In Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the health effects of electromagnetic fields. It’s crucial to understand the physics that underlies tissue-field interactions before postulating a nefarious role for electromagnetic fields in human health. If you suggest an idea that is not consistent with physics, prepare to be proved wrong.

A final note: Baloh and Bartholomew write

In September 2021, the head of a U.S. Government panel investigating “Havana Syndrome,” Pamela Spratlen, was forced to resign after refusing to rule out [mass psychogenic illness] as a possible cause... A former senior C.I.A. operative wrote that Spratlen’s position was “insulting to victims and automatically disqualifying.”

I think we all owe Pamela Spratlen an apology. Thank you for your service.

 Was “Havana Syndrome” a case of mass hysteria? DW News.

https://www.youtube.com/embed/ljf1TVWTSlQ

 

Havana Syndrome: Tilting at Windmills?

https://www.youtube.com/watch?v=4IWnhmqVsPc
 

 The Havana Syndrome: A Disorder of Neuropolitics?

https://www.youtube.com/watch?v=izeVdfkYnIo

Craig Henriquez (1959–2023)

I just learned that my friend Craig Henriquez passed away last summer. Craig earned his PhD at Duke University in their Department of Biomedical Engineering under the guidance of the renowned bioelectricity expert Robert Plonsey. His 1988 dissertation, titled “Structure and Volume Conductor Effects on Propagation in Cardiac Tissue,” was closely related to work I was doing at that time. Craig sent me a copy of his dissertation after he graduated. I really wanted to read it, but I was swamped with my my new job at the National Institutes of Health and helping care for my newborn daughter Stephanie. There wasn’t time to read it at work, and when I got home it was my turn to watch the baby, as my wife had been with her all day. The solution was to read Craig’s dissertation out loud to Stephanie as she crawled around in her play pen. She seemed to like the attention and I got to learn about Craig’s work.

Craig and I are nearly the same age. He was born in 1959 and I in 1960. Our careers progressed along parallel lines. After he graduated he stayed at Duke and joined the faculty. I recall he told me at the time that he didn’t know if he would make a career in academia, but he certainly did. He was on the Duke faculty for 35 years. In the early 1990s three young researchers at Duke—Craig, Natalia Trayanova, and Wanda Krassowska—were all from my generation. They were my friends, collaborators, and sometimes competitors as we worked to establish the bidomain model as the state-of-the-art representation of the electrical properties of cardiac tissue.

In my recent review about bidomain modeling (Biophysics Reviews, Volume 2, Article 041301, 2021) , I wrote (referring to myself in third person, as required by the journal; in the quotes below references are removed):

Roth’s calculation was not the first attempt to solve the active bidomain model using a numerical method. In 1984, Barr and Plonsey had developed a preliminary algorithm to calculate action potential propagation in a sheet of cardiac tissue. Simultaneous with Roth’s work, Henriquez and Plonsey were examining propagation in a perfused strand of cardiac tissue. For the next several years, Henriquez continued to improve bidomain computational methods with his collaborators and students at Duke. His 1993 article published in Critical Reviews of Biomedical Engineering remains the definitive summary of the bidomain model.

I’ve cited his 1993 review article (Crit. Rev. Biomed. Eng., Volume 21, Pages 1–77) many times, including in Intermediate Physics for Medicine and Biology. It’s a classic.

Craig and I were both interested in determining if Madison Spach’s electrical potential data from cardiac tissue samples should be interpreted as evidence of discontinuous propagation (Spach’s hypothesis) or a bath effect.

The original calculations of action potential propagation in a continuous bidomain strand perfused by a bath hinted at different interpretations of Spach’s data. As discussed earlier, the wave front is not one-dimensional because its profile varies with depth below the strand surface. The same effect occurs during propagation through a perfused planar slab, more closely resembling Spach’s experiment. The conductivity of the bath is higher than the conductivity of the interstitial space, so the wave front propagates ahead on the surface of the tissue and drags along the wave front deeper below the surface, resulting in a curved front. The extra electrotonic load experienced at the surface slows the rate of rise and the time constant of the action potential foot. Plonsey, Henriquez, and Trayanova analyzed this effect, and subsequently so did Henriquez and his collaborators and Roth.

Craig became an associate editor of the IEEE Transactions on Biomedical Engineering, and he would often send me papers to review. He was a big college basketball fan. We would email each other around March, when our alma maters—my Kansas Jayhawks and his Duke Blue Devils—would face off in the NCAA tournament. His research interests turned to nerves and the brain, and he co-directed a Center of Neuroengineering at Duke. He eventually chaired Duke’s biomedical engineering department, and at the time of his death he was an Associate Vice Provost.

I found out about Craig’s death when I was submitting a paper to a journal. This publication asks authors to suggest potential reviewers, and I was about to put Craig’s name down as a person who would give an honest and constructive assessment. I googled him to get his current email address, and discovered the horrible news. What a pity. I will miss him. 

Short bio published in the IEEE Transactions on Biomedical Engineering in January, 1990.

 Craig Henriquez talking about cardiac tissue and the bidomain model.

https://www.youtube.com/watch?v=OiSiLwP1ZPo

The Alaska Airlines Boeing 737 Max Accident

Last week, the plug door panel on an Alaska Airlines Boeing 737 Max airplane detached during flight, leaving a gaping hole in the side of the fuselage. Fortunately, the plane was able to land safely and no one was seriously injured in the accident. I thought it would be fun to analyze this event from the point of view of physics in medicine and biology. Let me stress that I have no inside information about this accident, and I am not an aviation expert. I’m just an old physics professor playing around trying to make sense of information reported in the press.

Let’s calculate the pressure difference between the normal cabin pressure of a 737 Max and the outside air pressure. The typical pressure at sea level is 1 atmosphere, which is about 100,000 pascals. However, in most planes the cabin pressure is maintained somewhat lower than an atmosphere. Usually the cabin pressure corresponds to the air pressure at about 6000 feet, which is 1800 meters. The air pressure falls exponentially with height. Problem 42 in Chapter 3 of Intermediate Physics for Medicine and Biology asks the reader to calculate the length constant corresponding to this decay. If you solve that problem, you get a length constant of about 8700 meters. So, the cabin pressure in the plane should have been around exp(–1800/8700) = 0.81 atm before the door panel blew out.

The mid-air depressurization occurred at about 16,000 feet (4900 meters). I assume this means 16,000 feet above sea level. Therefore, the air pressure outside the plane just before the door panel failed was about exp(–4900/8700) = 0.57 atmosphere. Thus, the pressure difference between the inside and outside was approximately 0.81 – 0.57 = 0.24 atmospheres, or 24,000 pascals.

Otto von Guerick’s famous 
Magdeburg hemispheres experiment.

The door looks to me like it is about 5 feet by 3 feet, or 15 square feet, which is 1.4 square meters. So, the force acting on the door was (24,000 pascals)×(1.4 square meters) = 34,000 newtons, or 7600 pounds (almost 4 tons). That’s why it’s so important that the door panel be attached securely to the fuselage; air pressure differences can produce large forces, even if the pressure difference is only a quarter of an atmosphere. If you don’t believe me, just ask Otto von Guericke, who in 1654 showed how two hemispheres held together by air pressure could not be pulled apart by two teams of eight horses.

What sort of biological effects would a sudden drop of air pressure have? I expect the biggest effect would be on the ears. The eardrum separates the outside air from an air-filled region in the middle ear. Normally there’s no pressure difference across the ear drum, except for the tiny pressures associated with sound. But pop that door off the plane and you suddenly have a quarter atmosphere pressure difference. Some of the people on the plane complained of plugged ears following the accident. Your Eustachian tubes that connect your ears to your throat will eventually allow you to equilibrate the air pressure across the eardrum, but it may take a while, especially if you have a cold so your tubes are congested.

How significant is an abrupt change of 0.24 atmospheres? The Empire State Building is 1250 feet tall (380 meters), which means the top and bottom of the building have a pressure difference of only about 0.04 atm. If you hop on an express elevator and zoom to the observation deck at the top of the skyscraper, you won’t cry out in pain, but you might notice your ears pop. The cabin pressure in a plane typically falls from 1 atm to about 0.8 atm as the plane rises. That’s why our ears feel uncomfortable. But that change occurs slowly, so it is not too bothersome. Normal skydivers jump at about 10,000 feet (3000 meters), so during their descent they experience a drop in pressure of about 0.3 atm. Skydivers often experience noticeable ear pressure, but any associated pain is not severe enough to keep them from jumping again. Unfortunately, the pressure decompression on the 737 Max happened much more quickly than the decompression during a parachute jump, so I would expect any ear problems would have been greater for the passengers on the plane than for a typical skydiver.

Pressures under water are much greater than those in the air, because water is more dense than air. Dive into a pool to a depth of 32 feet (10 meters) and the pressure on your eardrum increases by one atmosphere. Swimmers typically have worse ear problems than airplane passengers. It is one reason why you have to use scuba equipment if you’re diving deep. It’s also why submarine accidents are so much more severe than airplane depressurizations. Remember last year when that submersible was going down to the wreckage of the Titanic and suffered the catastrophic implosion? It was going to a depth of 13,000 feet (4000 meters), which means the pressure difference between the inside and outside of the sub was about 400 atmospheres! You can survive a hole in the wall of a 737 Max, but not one in a Titanic-visiting submersible.

The airplane’s oxygen masks dropped when the hole opened in the 737 Max. Did people really need the oxygen? The airplane altitude was 16,000 feet when the accident occurred. Mount Everest is 29,000 feet high (8800 meters). A few people have climbed to the peak of Everest without using supplemental oxygen, but most carry an oxygen tank. The Everest base camp is 17,600 feet (5300 meters). Climbers often experience mild symptoms of altitude sickness at base camp, but for most it is not debilitating. I suspect that if the passengers on that 737 Max flight hadn’t put on their mask they would have survived, but it might have had an impact on their ability to think straight. And everyone is different; some are more susceptible to mild oxygen deprivation than others. Certainly, the safe thing to do was to put on the mask.

What would have happened if the door hadn’t blow out until the plane reached its cruising altitude of 35,000 feet (11,000 meters). Now you are well above the height of Mount Everest. The outside air pressure would be about 0.28 atmospheres. You would go unconscious (and probably die) if you didn’t promptly put on your mask. The pressure difference between the outside pressure and the cabin pressure would be over half an atmosphere. The odds of being sucked out of the plane during rapid decompression would have been higher. Yikes! The passengers on that 737 Max were lucky that door was very insecurely attached, and not just modestly insecurely attached. If you are going to have a in-flight disaster, it is best to have it as soon after takeoff as possible, before your altitude gets too high.

 

Physics With Illustrative Examples
From Medicine and Biology.
by Benedek and Villars.

George Benedek and Felix Villars, in the first volume of their classic textbook Physics With Illustrative Examples From Medicine and Biology, discuss the effects of low oxygen.

Below 10,000 ft (3150) there is no detectable effect on performance and respiration and heart rates are unaffected. Between 10,000 and 15,000 ft (3150–4570 m) is a region of so-called "compensated hypoxia"... There is a measurable increase in heartbeat and breathing rate, but only a slight loss in efficiency in performing complex tasks. Between 15,000 and 20,000 ft (4570–6100 m), however, dramatic changes start to occur. The respiratory and heart rates increase markedly; there is a loss of critical judgment and muscular control, and a dulling of the senses. Emotional states can vary widely from lethargy to excitation with euphoria and even hallucinations... The final fatal regime is the altitude region from 20,000 to 25,000 ft (6100–7620 m).

Perhaps those few Mount Everest climbers who don’t carry an oxygen tank can only survive their ordeal by training their body to adapt to high altitudes.

Benedek and Villars also recount a fascinating story about oxygen deprivation from the early years of ballooning, based on an account written by Gaston Tissandier.

These various symptoms are shown very clearly in the tragic balloon ascent of the “Zenith” carrying the balloon pioneers Tissandier, Sivel, and Croce-Spinelli on April 15, 1875... The balloon’s maximum elevation as recorded on their instruments was 8600 m. Though gas bags containing 70% oxygen were carried by the balloonists, the rapid and insidious effect of hypoxia reduced their judgment and muscular control and prevented their use of the oxygen when it was most needed. Though these balloonists were indeed trying to establish an altitude record, their account shows clearly that their judgment was severely impaired during critical moments near the maximum tolerable altitudes. As they were on the verge of losing consciousness at 7450 m they decided to throw out the ballast and rise even higher. They lost consciousness above this altitude, but by good fortune the balloon descended rapidly after reaching 8600 m. On falling to about 6500 m the balloonists revived and—under the influence of the hypoxia did exactly the wrong thing once again—they threw out ballast! The second rise to high elevation killed Croce-Spinelli and Sivel.

Let us hope we have no more 737 Max door panels detaching in flight. I think we were lucky that no one was hurt this time. 

 

I’ll end with a 737 Max joke. What's the difference between the covid-19 virus and the 737 Max? Covid is airborne. (Rimshot).

 

 A video from inside the plane after the 737 Max door panel detached.

The First Log-Log Plot

In Chapter 2 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss log-log plots. Have you ever wondered who made the first log-log plot? The honor goes to French mathematician and engineer Léon Lalanne (1811–1892), who was interested in using infographics to aid in computation. Let me take you through his idea.

Start with a sheet of log-log graph paper, one cycle in each direction. 

The lines in the bottom left are far apart, so let’s add a few more so it’s easier to make accurate estimates. 

Next, following Lalanne, add a bunch of diagonal lines connecting points of equal value on the vertical and horizontal axes. Label them, so they’re easy to read. 

What we’ve just invented is a log-log plot to do multiplication. For example, suppose we want to multiply 3.2 by 6.8. We find the value of 3.2 on the vertical axis, and draw a horizontal line (solid red). Then we find 6.8 on the horizontal axis and draw a vertical line (dashed red). Where the two lines intersect gives the product. We estimate it by seeing what are the closest diagonal lines. The intersection is between 20 and 22.5. I would guess it’s a little closer to 22.5 than 20, so I’ll estimate the product as 22.0. I’m pretty confident that I have the result correct to within ± 0.5. If I do the calculation on an electronic calculator, I get 21.76. My answer is off by 1.1%. Not bad.

You can do other sorts of calculations with this one sheet of log-log paper. For instance, below I plot a green line with a slope of one half, which lets me calculate square roots. Really, this is just a plot of y = x^1/2 on log-log paper. Because my log-log plot is only one cycle in each direction, the green line lets me calculate square roots of the numbers one through ten. To get the roots of ten through one hundred, I need to add a second, parallel line (green dashed). 

To calculate the square root of 77, I find 7.7 on the horizontal axis, go up to the dashed line, and then extrapolate over to the vertical axis. I estimate the result is about 8.8. When I use my electronic calculator, I get 8.775, so my estimate was accurate to about 0.3%. 

Of course, you could do all sorts of other calculations. Lalanne included many in his “universal calculator” that he had printed and posted in public places. Basically, the universal calculator is meant to compete with the slide rule (see my discussion of IPMB and the slide rule here). His charts never were as popular as the slide rule, perhaps because it’s more fun to slide the little rules than it is to look at a busy chart.

Léon Lalanne’s “Universal Calculator,”
or “Abacus” (1843).

Basic Rheology for Biologists

Cell Mechanics.

In Chapter 1 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss ideal solids and ideal liquids. Ideal solids are covered in Section 1.10, which introduces stress, strain, and their relationship through an elastic modulus. Ideal fluids are discussed in Section 1.16, which introduces a Newtonian fluid where the shear force is related to the flow rate by the coefficient of viscosity.

In the book Cell Mechanics, the chapter “Basic Rheology for Biologists,” by Paul Janmey, Penelope Georges, and Søren Hvidt, focuses on materials that are not ideal solids or liquids.

Real materials are neither ideal solids nor ideal liquids nor even ideal mixtures of the two. There are always effects due to molecular rearrangements and other factors that complicate deformation, transforming elastic and viscous constants to functions of time, and extent of deformation. Real materials, and especially biological materials, exhibit both elastic and viscous responses and are therefore called viscoelastic. They are also often highly anisotropic, showing different viscoelastic properties when deformed in one direction than when deformed in other directions. The goal of rheological experiments is to quantify the viscoelasticity of a material over as wide a range of time and deformation scales as possible, and ultimately to relate these viscoelastic properties to the molecular structure of the material.

IPMB examines only briefly the subject of rheology: the study of how nonideal materials deform and flow.

In some materials, the stress depends not only on the strain, but on the rate at which the strain is produced. It may take more stress to stretch the material rapidly than to stretch it slowly, and more stress to stretch it than to maintain a fixed strain. Such materials are called viscoelastic.

Some materials are even more complicated, and the stress is not proportional to the strain or flow, but instead the relationship is nonlinear, demonstrating strain softening or strain stiffening.

Most materials will exhibit strain softening with a smaller [elastic modulus] at large strains. However, some systems exhibit strain stiffening where [the elastic modulus] increases above a critical strain.

Russ and I show an example of strain softening in IPMB’s Fig. 1.21. When stress is plotted versus strain, the stress first rises linearly and then bends over and becomes flatter. 

One rheological concept Russ and I never discuss is creep. Janmey et al. write

Many biological systems experience a sustained force such as gravity or blood pressure. It is therefore useful to monitor how such systems deform under a constant load or stress. This type of measurement is called a creep experiment, and in such an experiment the strain is monitored as a function of time for a fixed stress.

A creep-recovery experiment.

Another type of stress-relaxation experiment is to keep the strain constant and measure the stress.

Stress–relaxation measurements can be performed in both simple shear and simple elongation, and they are of special interest for viscoelastic systems. In a stress–relaxation experiment, the sample is rapidly deformed and the stress is monitored as a function of time, keeping the sample in the deformed state.

 

A stress-relaxation experiment.

Janmey et al. point out that oscillatory behavior is particularly useful when studying nonideal materials.

Rheological information for viscoelastic systems is often obtained by applying small amplitude oscillatory strains or stresses to the sample rather than steady flows.

When a oscillating deformation is applied to a material, the part of the stress in phase with the strain contains information about the material’s elastic behavior and the out-of-phase part contains information about the viscosity. 

Rheology is an advanced topic and probably doesn't belong in an intermediate textbook like IPMB. Yet, in the messy, wet, and sticky world of biology, rheology can often play a major role. Janmey et al. conclude

As cell and tissue mechanics become more of an integral part of basic cell biologic studies, a comprehensive understanding of micro- and macrorheology may help develop a unified model for how specific structural elements are used to form the soft but durable and adaptable materials that make up most organisms. The results of these studies also have potential for developing materials and methods for wound healing, cell differentiation, artificial organ development, and many other applications in biomedical research.

Special Relativity in IPMB

Electricity and Magnetism,
by Edward Purcell.

In Intermediate Physics for Medicine and Biology, Russ Hobbie and I rarely discuss special relativity. We briefly mention that magnetism is a consequence of relativity in Chapter 8 (Biomagnetism) but we don’t develop our study of magnetic fields from this point of view. (If you want to see magnetism analyzed in this way, I suggest looking at the textbook Electricity and Magnetism, by Edward Purcell, which is Volume 2 of the Berkeley Physics Course). We use the relationship between the energy and momentum of a photon, E = pc, in Chapter 15 (Interaction of Photons and Charged Particles with Matter) when analyzing Compton scattering and pair production. And we use Einstein’s famous equation E = mc², relating a particles energy to its rest mass, when calculating the binding energy of nuclei in Chapter 17 (Nuclear Physics and Nuclear Medicine).

The most relativisticish equation we present is in Chapter 15 when analyzing how charged particles (such as protons, electrons, or alpha particles) lose energy when passing through tissue at relativistic speeds. We write

The stopping powers are plotted vs particle speed in the form β = v/c. At low energies (β ≪ 1) β is related to kinetic energy by 

For larger values of β, the relativistically correct expression

was used to convert Fig. 15.17 to 15.18. 

Fig. 15.17

 

Fig. 15.18

Here’s a new homework problem examining the relationship between a particle’s speed and kinetic energy when its speed is near the speed of light.

Section 15.11

Problem 41 ½. A charged particle’s kinetic energy, T, is related to its mass M and its speed, v. We often express speed in terms of the parameter β = v/c, where c is the speed of light.

(a) At low energies (T ≪ Mc², or equivalently β ≪ 1), show that Eq. 15.47 is consistent with the familiar expression from classical mechanics, T = ½ mv².

(b) Show that Equation 15.48 (the relativistically correct relationship between β and T) reduces to Eq. 15.47 when T ≪ Mc².

(c) Plot β versus T/Mc², both in a linear plot (0 < T/Mc² < 3) and in a log-log plot (0.0001 < T/Mc² < 100).

(d) Take a few data points from Fig. 15.17 for a proton, replot them in Fig. 15.18, where the dependent variable is β, not T. See how well they match. Be sure to adjust for the different units for Stopping Power in the two plots.

An IPMB Episode of Meeting of Minds

A few weeks ago, I published a blog post about the television show Meeting of Minds. That show from the late 1970s was created and hosted by Steve Allen and featured historical figures as guests in a talk show format. In my earlier post, I wrote that if I were going to have an episode of Meeting of Minds based on Intermediate Physics for Medicine and Biology, it would include guests Alan Hodgkin, Willem Einthoven, Paul Lauterbur, and Marie Curie.

As your Christmas present, I offer you a script for the IPMB episode of Meeting of Minds.

Enjoy!

***********************************************************

Meeting of Minds, IPMB episode.

Allen: Good evening. I’m Steve Allen and I’d like to welcome you to this week’s episode of Meeting of Minds. Our guests will all be drawn from the field of physics applied to medicine and biology. We have the French physicist Marie Curie, the English physiologist Alan Hodgkin, the Dutch medical doctor Willem Einthoven, and the American chemist Paul Lauterbur. I’d first like to introduce Alan Hodgkin. [applause]

Hodgkin: [Hodgkin enters from stage right, and sits at the table.] Thank you, thank you. It’s such a pleasure to be here, Mr. Allen.

Allen: The pleasure’s all mine, Dr. Hodgkin. Tell me, I understand you were born in the market town of Banbury, England in 1914, the son of Quakers. How did a Quaker upbringing influence your early life?

Hodgkin: It had a huge influence. As you know, Quakers are pacifists, and I was born just as World War I began. When I was only two, my father, George Hodgkin, traveled to Armenia to try to help the many refuges trying to escape genocide committed by the Ottoman Empire. He tried to return to to Armenia two years later, but ended up dying of dysentery in Baghdad. This was just a few weeks after my brother Keith was born. I was only four when dad died.

Allen: But your Quaker roots didn’t stop you from participating in World War II?

Hodgkin: No, not at all. In fact, I was eager to do my part against the Nazis. I had visited Germany in 1932 and that experience destroyed any pacifist beliefs I might’ve held. During World War II, I worked on radar. In fact, I was on one of the first test flights of a Bristol Blenheim light bomber when it was fitted with our airborne centimetric radar system.

Allen: Going back to your childhood, were there any influences that led you to a scientific career?

Hodgkin: Oh yes. My mother encouraged my scientific interests and so did my Aunt Katie, who used to take me bird watching. In high school, I even got a job surveying rookeries and heronries. I spent many hours wading around in the salt marshes watching birds. This experience kindled my love for science.

Allen: I see you started your career in the biological sciences. Where did you gain the knowledge of the physical sciences that allowed you to work on radar?

Hodgkin: When at college at Cambridge, one of my zoology professors gave me some good advice: study as much math and physics as you can! I also picked up a lot doing student research. And of course, during the war I learned on the job. I’m very interested in learning how my esteemed colleague Willem Einthoven made a similar transition from biology to physics.

Allen: In that case, let’s welcome the father of clinical electrocardiography, Willem Einthoven. [applause]

Einthoven: [Einthoven enters from stage left and sits at the table across from Hodgkin] So good to meet you Mr. Allen. And it is truly a delight to meet the famous Alan Hodgkin, of Hodgkin and Huxley fame. Dr. Hodgkin, I see we have something in common.

Hodgkin: Oh, what’s that?

Einthoven: We both lost our fathers early in our life. My father, Jacob Einthoven, was a doctor, and died when I was only six. I was not born in the Netherlands, but in Java, which at that time was part of the Dutch East Indies. After dad died, we returned to the Netherlands and settled in Utrecht.

Allen: I understand you studied medicine.

Einthoven: Yes, Mr. Allen. When I was 25 I received my medical degree from the University of Utrecht. Then I became a professor at the University of Leiden, where I spent my career. At that time, I married my first cousin Frédérique Jeanne Louise de Vogel.

Hodgkin: First cousin! [giggles from the audience]

Einthoven: Yes, a wonderful woman. [frowning]

Allen: Like Dr. Hodgkin, your biological and medical research required knowledge of physics and math. How did you learn these subjects?

Einthoven: Through self study, Mr. Allen.

Hodgkin: The best type of learning.

Einthoven: I obtained a textbook by the Dutch physicist Hendrik Lorentz and taught myself differential and integral calculus. Thirty years later, I gave a copy of that book to the American cardiologist Frank Wilson (of the Wilson central terminal) with the inscription “May I send you the excellent book of Lorentz’ Differential- und Integralrechnung? I have learned my mathematics from it after my nomination as a professor in this University and I hope you will have as much pleasure and profit by it as I have had myself.” I also benefited from talks with my brother-in-law Julius, a physics professor at Utrecht. My training and degree was in medicine, but in my heart of hearts I was a physicist.

Hodgkin: Fascinating.

Einthoven: What is truly fascinating is how all the guests tonight contributed to the study of bioelectricity and biomagnetism. I developed the electrocardiogram, and you Dr. Hodgkin figured out how nerves work. I am anxious to meet Dr. Lauterbur, who invented magnetic resonance imaging.

Allen: Then without further ado, let me invite Dr. Paul Lauterbur to join our stimulating discussion. [applause]

Lauterbur: [Lauterbur enters from stage right, and sits next to Hodgkin.] Steve Allen [shakes hand]. Drs. Hodgkin and Einthoven [nods]. So happy to be here. Willem, my ancestors came from over in your neck of the woods. They’re from Luxembourg.

Einthoven: Interesting. Luxembourg is more closely related to France and Germany than the Netherlands, but….

Hodgkin: Ha!

Lauterbur: Yeah, we Americans are a little weak on our geography. I was born and raised in the small town of Sidney, Ohio, just north of Dayton.

Einthoven: And how did you become interested in science, Dr. Lauterbur?

Lauterbur: As a teenager I built my own chemistry laboratory in the basement of our house.

Hodgkin: Nice.

Lauterbur: My high school chemistry teacher realized that I liked experimenting, so he let me do my own chemistry experiments in the back of the room during class.

Einthoven: Such a wise teacher.

Lauterbur: I got my bachelor’s degree in industrial chemistry form Case Institute of Technology in Cleveland, which is now part of Case Western Reserve University. Like Dr. Hodgkin, I served in the army. In the early 1950s I was assigned to the army chemical center in Edgewood, Maryland. They let me spend part of my time using an early nuclear magnetic resonance machine. It didn’t do imaging…

Allen: Of course not! You invented imaging.

Lauterbur: …but NMR machines are important for chemical identification. I actually published four papers by the time I was discharged.

Hodgkin: And where did you do your famous work on imaging?

Lauterbur: I was at Stony Brook University for 22 years.

Einthoven: On Long Island?

Lauterbur: Yes, Willem, your geography’s better than mine [quiet laughter from the audience].

Allen: I look forward to hearing about your development of MRI later in our discussion, but now I would like to introduce our last guest, Marie Curie [enthusiastic applause, louder than for any of the other scientists].

Curie: [Curie enters from stage left and sits next to Einthoven] Thank you. Thank you so very much.

Einthoven: The honor is ours, Dr. Curie. Why, you are the only one of us who has an element named for them.

Curie: Yes, element 96 is named curium.

Lauterbur: While on the topic of geography, I seem to associate you with two countries, Marie: France and Poland. Which is your home?

Curie: Well, I was born and raised in Warsaw, which at that time was part of the Russian Empire. It was only when I was 24 that I went to Paris, and I spent the rest of my life in France. But I never lost my Polish heritage. I made sure my daughters learned the Polish language, and we went on trips to Poland. And Dr. Einthoven, you will be interested to know that I managed to get an element, polonium, named after my beloved homeland [scattered applause from the audience].

Einthoven: Nicely done.

Hodgkin: And how did you get started in science, Dr. Curie?

Curie: “Dr. Curie.” That still seems strange to hear. You see, it wasn’t as easy for a young lady to start a career in science as it was for you men.

Allen: I’m sure it wasn’t.

Curie: Also, my education was difficult because my parents were involved in uprisings to gain Polish independence. We lost much of the family fortune. My father was a physics teacher. When Russia eliminated laboratory instruction from Polish schools, dad brought all the lab equipment home for us kids to use. The Russians finally fired my father. Like Drs. Hodgkin and Einthoven, I lost a parent when I was young. For me, it was my mother, who died of tuberculosis when I was ten. I couldn’t pursue higher education then, because I was a woman…

Einthoven: So unfair.

Curie: I did become involved with the clandestine Flying University, a Polish patriotic institution that admitted women. Eventually my sister Bronislawa and I made a deal. I stayed in Poland and made money to pay for her medical studies in Paris. In exchange, she agreed to help me pay for my education two years later.

I got a job tutoring for some wealthy relations of my father. I fell in love with one of the sons, Kazimierz, but his family wouldn’t allow a marriage to a poor tutor. Kazimierz later became a famous mathematician. When he was an old man and I had died, he would come sit and stare at my statue at the Radium Institute.

I eventually was able to go to Paris and join my sister. Still, life was hard. I studied so hard I often forgot to eat! I hit the books all day and tutored in the evenings to pay the bills.

Hodgkin: How did you meet your husband Pierre Curie?

Curie: We met through our mutual love of science. When Pierre proposed, I was reluctant to accept because I planned to return to Poland. Pierre said he would give up his distinguished physics career to join me! [applause from the audience]. We eventually were married. One smart aleck called me “Pierre’s greatest discovery” but his work in magnetism was very important in its own right.

Allen: Now I would like to switch the conversation to the science that made each of you famous. Dr. Hodgkin, you first. Tell us a little about your work with the squid nerve axon.

Hodgkin: I’d love to. Yes, Dr. Curie, some people think they’re so witty. In my case, one wise guy said that “it’s the squid who really deserved the Nobel Prize” [polite laughter from the audience]. I must admit he had a point. We conducted our experiments using the giant axon of the squid, which is up to one millimeter in diameter.

Einthoven: One millimeter!? For a nerve axon, that is huge!

Hodgkin: Yes, that’s the point. It was big enough that we could stick electrodes down its length.

Curie: Who is “we,” Dr. Hodgkin?

Hodgkin: I worked mainly with my collaborator, Andrew Huxley. He was a little younger than me and started as my student, but eventually became a true collaborator. He was an excellent experimentalist, but one of his greatest strengths was his skill in mathematics.

Lauterbur: Do go on, Alan. What did ya do with those axons?

Hodgkin: We developed a technique called the “voltage clamp” in which we used two electrodes, one to measure the voltage across the axon membrane and the other to pass current across the membrane. The electrodes were attached to a feedback circuit, which applied whatever current was necessary to keep the voltage constant. With this device, we could monitor both the current and voltage, and thus determine the membrane conductance.

Allen: But Dr. Hodgkin, wasn’t the voltage clamp originally invented by Kenneth Cole at Woods Hole in the United States?

Hodgkin: Yes, he did some of the early work. And it’s true I visited Woods Hole and learned the technique from Cole. But some of his measurements were questionable. He reported action potentials that went positive by over 100 millivolts!

Einthoven: Oh my.

Hodgkin: An action potential that positive would have invalidated the idea that the membrane depolarized until it reached the sodium equilibrium voltage, which was the basis for the Hodgkin and Huxley model. In any case, we were able to calculate the membrane conductance and could determine how the membrane changed its conductance for both sodium and potassium individually.

Lauterbur: Because the sodium and potassium ions passed through selective ion channels?

Hodgkin: Yes, but we didn’t know it at the time. We just knew that two ions were involved: sodium and potassium. At rest the axon was primarily permeable to potassium and during the action potential it became permeable to sodium. We imagined that “gates” allowed the current to pass through the membrane: the m and h gates for sodium, and the n gate for potassium. It may sound a bit ad hoc, but our Hodgkin and Huxley model was really a gigantic curve-fitting exercise.

When the membrane was slightly depolarized—that is, when the membrane voltage was made slightly positive compared to its resting value—the m gate began to open, letting in sodium. The positive charge of the sodium ions raised the membrane voltage further, resulting in the m gate opening more, allowing more sodium to enter…

Einthoven: Positive feedback!

Hodgkin: Yes, the upstroke of the action potential is a positive feedback loop.

Lauterbur: But Alan, positive feedback can be explosive. What stopped the rise in membrane voltage?

Hodgkin: When the membrane voltage reached the sodium equilibrium voltage, there was no longer a tendency for sodium to enter the nerve. Even though there was more sodium outside the axon than inside, the high positive voltage in the axoplasm prevented any more positive sodium ions from diffusing in. That’s why Cole’s huge action potentials didn’t make any sense. Their reported action potentials went above the sodium equilibrium voltage.

Curie: But Dr. Hodgkin, what then caused the voltage to return to rest?

Hodgkin: Well, the n gate slowly opened, allowing potassium to leave the axon (carrying positive charge with it). But more importantly, the h gate slowly closed, preventing any further sodium current.

Einthoven: But if the h gate closes, would not that destroy the positive feedback loop of the action potential?

Hodgkin: Yes indeed. The closing of h made the axon “refractory.” It couldn’t fire another action potential until the h gate finally opened again and the membrane returned to its resting state.

Allen: Interesting, Dr. Hodgkin. And you made a mathematical model of this?

Hodgkin: Yes. Much of that was Andrew’s work.

Lauterbur: Don’t some people call Huxley the “greatest mathematical biologist ever”?

Hodgkin: They do. Our model required solving a set of nonlinear differential equations. This was back in the days before digital computers were available. You should’ve seen Andrew working that hand-held mechanical calculating machine to solve those equations numerically. Boy, did his fingers fly!

Allen: Dr. Einthoven, you also worked in bioelectricity. Perhaps you could tell us about your discoveries?

Einthoven: Well, I was the first to record the electrocardiogram, which is the electrical signal produced by the heart.

Lauterbur: I often had an ECG taken during my yearly physical.

Einthoven: Yes, it has become one of the most important diagnostic tools of modern medicine. But unlike Dr. Hodgkin, I didn’t have fancy voltmeters and oscilloscopes that I could use to measure electrical current. I had to invent an improved “string galvanometer.”

Hodgkin: Yes, yes. You passed a current through a wire in a magnetic field, causing a force on the wire proportional to the current.

Enithoven: Indeed, Dr. Hodgkin. We could not measure currents that changed too rapidly or that were too weak, but the device was sufficient to record the electrocardiogram. Unlike Hodgkin and Huxley, I could not insert an electrode into a heart cell, so I had to be content with measuring the voltage produced on the body surface by the electrical activity of the distant heart.

Curie: And wasn’t it you, Dr. Einthoven, who assigned the names P-wave, QRS-complex, and T-wave to the various electrocardiogram deflections?

Enithoven: Yes it was. The P-wave corresponded to the atria depolarizing, the QRS-complex to the ventricles depolarizing, and the T-wave to the ventricles repolarizing.

Allen: And what about the atria repolarizing?

Einthoven: That tiny signal was buried in the QRS-complex.

Lauterbur: And how did ya interpret your data?

Einthoven: I imagined that the heart produced a dipole, which just means current passed out of the heart cells at one point and reentered the cells at another, like an electric dipole made from two charges separated by a distance. Really, the ECG is produced by tiny dipoles associated with each cardiac cell, but there are billions of cells so I simplified the situation by representing the current source as a single dipole.

Hodgkin: A “toy model”!

Einthoven: Yes, sometimes we must make approximations to simplify a complicated situation so we can understand it better. A dipole is a vector, meaning it has a magnitude and a direction. To determine its direction, I placed electrodes on the left arm, right arm, and left leg. These three electrodes roughly form an equilateral triangle…

Lauterbur: Einthoven’s triangle!

Einthoven: Some people started calling it that, which was quite an honor. The signal from the three electrodes forming “Einthoven’s” triangle, if you will, determine the dipole direction.

Curie: Can’t the electrocardiogram be used to treat diseases?

Einthoven: Not really treat, but diagnose. The details of the electrical signal provide information about heart arrhythmias. Once you know the type of arrhythmia, then you can treat it properly.

Allen: I believe that our modern artificial pacemakers and defibrillators are what you are referring to.

Einthoven: Yes. These miraculous devices can use ECG recordings to determine the correct place and time to stimulate the heart to overcome the arrhythmia. It is all quite wonderful, but those devices were invented long after I had left the scene.

Curie: But they’re based on your work, Dr. Einthoven. We all owe you a great debt of gratitude.

Einthoven: And to you, Dr. Curie, for your work on…

Allen: Before we discuss Dr. Curie’s research, I would like to hear from Dr. Lauterbur about his studies that led to magnetic resonance imaging.

Lauterbur: Steve, I’d love to talk about it. Some nuclei have a property called “spin.” A nucleus with spin, such as that of the hydrogen atom, precesses, or rotates, about a magnetic field, with its precession frequency proportional to the magnetic field strength. This precession is the basis for nuclear magnetic resonance.

Now, the secret to magnetic resonance imaging is to apply a large, static magnetic field that causes the spins to precess, plus a magnetic field gradient that you can turn on and off. The gradient makes the magnetic field larger in one location than another; it maps magnetic field strength to position. This causes the precession frequency to also vary with position. It’s the frequency that we measure during MRI. Therefore, the gradient maps frequency to position, allowing you to determine a nucleus’s location from its frequency.

Hodgkin: Wonderful! Why didn’t they call the method “nuclear magnetic resonance imaging”?

Lauterbur: Ha! People are so afraid of the word “nuclear” that they dropped it and renamed the technique “magnetic resonance imaging,” or MRI. Some people have such irrational fears of anything having to do with the nucleus or radiation.

Curie: I know what you mean, I remember when…

Allen: Yes, but let Dr. Lauterbur finish his story.

Lauterbur: I remember the day I came up with the idea of using gradient fields to do MRI. I was sitting in a Big Boy restaurant and it just came to me: Eureka! I immediately scribbled the thought down on the only thing I had available: a paper napkin.

Hodgkin: I’m glad they didn’t use cloth napkins.

Lauterbur: Ha. Not likely at a Big Boy. I would’ve walked out with it if they had. So I built the first simple MRI machine and started creating images. I tried to publish my initial results in the journal Nature…

Einthoven: Ah, that English journal is one of the finest in all of science.

Lauterbur: Perhaps, but they initially rejected my manuscript.

Curie: Goodness!

Lauterbur: They thought my images were too fuzzy. But they were the very first magnetic resonance images, for crying out loud. I persisted and asked them to review it again. It was finally published in Nature, and the article became a classic. I believe you could write the entire history of science in the last 50 years in terms of papers rejected by Science or Nature.

Allen: Really?

Lauterbur: Yes. I tried to patent my ideas, but Stony Brook decided not to pursue it. Patents are expensive, and they didn’t expect the potential earnings justified the cost of the lawyers and filing fees.

Curie: What a mistake.

Allen: Can you tell us a little about your controversy with Raymond Damadian regarding the invention of MRI.

Lauterbur: Steve, I thought ya might bring that up [audience laughs awkwardly]. Yes, Damadian also was working on imaging using MRI. He was particularly interested in finding if signals from a tumor were different from normal tissue. It was nice work, but it didn’t contain the idea of using a magnetic field gradient to map frequency to position, which is the essence of my method. When Peter Mansfield and I each received the Nobel Prize for developing MRI, Damadian took out a full-page ad in the New York Times claiming the prize should have gone to him too! He was bitter about it all his life. But I think history is on my side.

Einthoven: What about Herman Carr?

Lauterbur: Carr’s work was a precursor to mine and he probably had a better claim to the Nobel Prize than Damadian did. I should’ve cited Carrr’s work. And Mansfield thought Erwin Hahn deserved a piece of the prize for his discovery of spin echo. Scientific discoveries and inventions are complex processes, and the credit must often be shared among many researchers.

Hodgkin: Yes, I know. Besides Huxley, my work was assisted by Bernard Katz and William Rushton among others.

Allen: Including Kenneth Cole.

Hodgkin: [Sighs] And Cole.

Allen: Now, Dr. Curie, could you tell us a little of your important work.

Curie: Yes. I’ve been waiting patiently for my turn [quiet laughter]. First a little background. I lived in an exciting time for science…

Einthoven: I believe all times are exciting for science.

Curie: I agree, but the end of the 19th century was a particularly exciting time for physics. In 1895 Wilhelm Rontgen discovered x-rays (a type of very high frequency electromagnetic radiation) and then in 1896 Henri Becquerel discovered radiation from uranium. I decided to examine uranium in more detail.

Lauterbur: Didn’t you find three types of radiation: alpha, beta, and gamma?

Curie: No, Dr. Lauterbur, that was found by my good friend Ernest Rutherford. But back to my work. I started with a ton of pitchblende (an ore containing uranium) and analyzed it chemically, separating the radioactive and nonradioactive parts. My husband Pierre was so interested in this work that he abandoned his own research to help me. After years of analysis, we finally ended up with less than a gram of a new element we named radium. It was highly radioactive. Along the way, we also discovered another element, polonium, which I mentioned previously.

Hodgkin: Those discoveries must’ve made you very famous.

Curie: Well, it did allow me to finally obtain my doctorate from the University of Paris. I was then invited to the Royal Institution in London to lecture about radioactivity. But since I was a woman, I was not allowed to speak, and Pierre alone gave the presentation [indignant murmur from the audience]. The committee that decides the Nobel Prize was going to award it to only Pierre and Henri Becquerel, but Pierre put a stop to that. I miss Pierre so much. In 1906, he was killed in a road accident. It was devastating…

Allen: I’m so sorry, Dr. Curie [Allen pats Curie on the shoulder].

Curie: But I soldiered on. Almost immediately x-rays and radium began to be used in medicine, creating the new discipline of medical physics. During the First World War, my daughter Irene and I developed x-ray imaging equipment mounted on trucks that could be used as mobile radiography units at the front. They were known as “petites Curies,” or “Little Curies.” [Curie smiles.]

Einthoven: Was not Irene herself a famous scientist?

Curie: Yes, Irene and her husband won their own Nobel Prize for discovering artificial radioisotopes.

Allen: I know this may be a delicate subject, but could you tell us about your relationship with physicist Paul Langevin?

Curie: Mr. Allen, I’m surprised you have so little tact [audience laughs nervously]. But I suppose if you must know, Paul was a former student of Pierre’s. He was married, but was estranged from his wife. After Pierre died, Paul and I were lovers. The press got a hold of the news (by that time I was quite famous) and started calling it the “Langevin affair.” They tortured me about that relationship.

Allen: Thank you, Dr. Curie, for sharing that difficult part of your past. [Looking up at the entire group] There is one thing all four of you have in common. You all won a Nobel Prize.

Lauterbur: Yes, you’ve already heard my embarrassing story about the prize. I received mine, jointly with Mansfield, for Physiology and Medicine.

Hodgkin: I also received mine in Physiology or Medicine, along with Huxley and neurophysiologist John Eccles.

Einthoven: Mine was for Physiology or Medicine too, but it was a solo award.

Curie: I’m so proud of you all. But gentlemen, do any of you have two Nobel Prizes [all laugh]?

Hodgkin: Yes, Dr. Curie, you were the first woman to receive a Nobel Prize, and you ended up with two: one in physics and one in chemistry [several young female members of the audience start stomping their feet and cheering for Curie; one yells “girl power!”].

Allen: [Laughing] With that thought, my friends, I fear we have run out of time. I hope you will join us again next week for another episode of Meeting of Minds.

The Three Laws of Thermodynamics

Thermodynamics is often summarized in three laws. Do Russ Hobbie and I discuss the three laws of thermodynamics in Intermediate Physics for Medicine and Biology? Yes!

The First Law

We state the first law on page 58.

The most general way the energy of a system can change [ΔU] is to have both work [W] done by the system and heat [Q] flow into the system. The statement of the conservation of energy in that case is called the first law of thermodynamics: ΔU = Q − W. 

The Second Law

The 2nd Law, by Peter Atkins.

On page 75 of IPMB, Russ and I write

The total entropy [of a system] remains the same or increases. This is one form of the second law of thermodynamics. For a fascinating discussion of the second law, see Atkins (1994).

The book we cite by Peter Atkins, The 2nd Law: Energy, Chaos and Form (Scientific American, 1994) is excellent and I highly recommend it.

An Introduction to
Thermal Physics,
by Daniel Schroeder.

When Daniel Schroeder talks about the efficiency of a heat engine in his textbook An Introduction to Thermal Physics, he states the first two laws this way:

In deriving the limit… on the efficiency of an engine, we used both the first and second laws of thermodynamics. The first law told us that… we can’t get more work out than the amount of heat put in. In this context, the first law is often paraphrased, “You can’t win.” The second law, however, made matters worse. It told us that we can’t even achieve [an efficiency of one, meaning all the heat is converted to work] unless [the heat engine operates between a cold reservoir at zero absolute temperature and a hot reservoir at an arbitrarily high absolute temperature], both of which are impossible in practice. In this context, the second law is often paraphrased, “You can’t even break even.”

The second law is one of the most famous principles of science. In his book The Two Cultures, C. P. Snow writes

A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is the scientific equivalent of: Have you read a work of Shakespeare’s?

The Third Law

Russ and I don’t state the third law of thermodynamics, but it is inherent in the definition of entropy we give on page 62.

The entropy S is defined by S = k_B ln Ω.

In this equation, k_B is Boltzmann's constant and Ω is the number of possible states of the system.

Here is what Schroeder writes.

At zero temperature [absolute zero] a system should settle into its unique lowest-energy state, so [the number of states is one] and [the entropy, which is proportional to the logarithm of the number of states, is therefore zero]. This fact is often called the third law of thermodynamics.

The third law was discovered by the German physicist Walther Nernst, whose Nernst equation for the equilibrium potential across a membrane plays such a big role IPMB’s analysis of bioelectricity.

Summary

To summarize, the three laws of thermodynamics are

1. Energy is conserved
2. Entropy increases
3. The entropy is zero at absolute zero.