The Cyclotron Resonance Hypothesis

Want a sneak peek at one of the new homework problems tentatively included in the 6th edition of Intermediate Physics for Medicine and Biology? Today I present a problem related to the flawed “cyclotron resonance hypothesis.” A lot of nonsense has been written about the idea of extremely low frequency electromagnetic fields influencing biology and medicine, and one of the proposed mechanisms for such effects is cyclotron resonance. 

In Section 8.1 of the 5th edition of IPMB, Russ Hobbie and I discuss the cyclotron.

One important application of magnetic forces in medicine is the cyclotron. Many hospitals have a cyclotron for the production of radiopharmaceuticals, especially for generating positron-emitting nuclei for use in Positron EmissionTomography (PET) imaging (see Chap. 17).

Consider a particle of charge q and mass m, moving with speed v in a direction perpendicular to a magnetic field B. The magnetic force will bend the path of the particle into a circle. Newton’s second law states that the mass times the centripetal acceleration, v²/r, is equal to the magnetic force

      mv²/r = qvB.      (8.5)

The speed is equal to [the] circumference of the circle, 2πr, divided by the period of the orbit, T. Substituting this expression for v into Eq. (8.5) and simplifying, we find

       T = 2π m/(qB).   (8.6)

In a cyclotron particles orbit at the cyclotron frequency, f = 1/T. Because the magnetic force is perpendicular to the motion, it does not increase the particles’ speed or energy. To do that, the particles are subjected periodically to an electric field that changes direction with the cyclotron frequency so that it is always accelerating, not decelerating, the particles. This would be difficult if not for the fortuitous disappearance of both v and r from Eq. (8.6), so that the cyclotron frequency only depends on the charge-to-mass ratio of the particles and the magnetic field, but not on their energy.

This analysis of cyclotron motion works great in a vacuum. The trouble begins when you apply the cyclotron concept to ions in the conducting fluids of the body. The proposed hypothesis says that when an ion is moving about in the presence of the earth’s magnetic field, the resulting magnetic force causes it to orbit about the magnetic field lines, with an orbital period equal to the reciprocal of the cyclotron frequency. If any electric field is present at that same frequency, it could interact with the ion, increasing its energy or causing it to cross the cell membrane.

Below is a draft of the new homework problem, which I hope debunks this erroneous hypothesis.

Section 9.1

Problem 7. One mechanism for how organisms are influenced by extremely low frequency electric fields is the cyclotron resonance hypothesis. 

(a) The strength of the earth's magnetic field is about 5 × 10^–5 T. A calcium ion has a mass of 6.7 × 10^–26 kg and a charge of 3.2 × 10^–19 C. Calculate the cyclotron frequency of the calcium ion. If an electric field exists in the tissue at that frequency, the calcium ion will be in resonance with the cyclotron frequency, which could magnify any biological effect. 

(b) This mechanism seems to provide a way for an extremely low frequency electric field to interact with calcium ions, and calcium influences many cellular processes. But consider this hypothesis in more detail. Use Eq. 4.12 to calculate the root-mean-square speed of a calcium ion at body temperature. Use this speed in Eq. 8.5 to calculate the radius of the orbit. Compare this to the size of a typical cell. 

(c) Now make a similar analysis, but assume the radius of the calcium ion orbit is about the size of a cell (since it would have difficulty crossing the cell membrane). Then use this radius in Eq. 8.5 to determine the speed of the calcium ion. If this is the root-mean-square speed, what is the body temperature? 

(d) Finally, compare the period of the orbit to the time between collisions of the calcium ion with a water molecule. What does this imply for the orbit?

This analysis should convince you that the cyclotron resonance hypothesis is unlikely to be correct. Although the frequency is reasonable, the orbital radius will be huge unless the ions are traveling extraordinarily slowly. Collisions with water molecules will completely disrupt the orbit.

For those who don't have the 5th edition of IPMB handy, Eq. 4.12 says the root-mean-square speed is equal to the square root of 3 times Boltzmann's constant times the absolute temperature divided by the mass of the particle. 

I won’t give away the solution to this problem (once the 6th edition of IPMB is out, instructors can get the solution manual for free by emailing me at roth@oakland.edu). But here are some order-of-magnitude results. The cyclotron frequency is tens of hertz. The root-mean-square (thermal) speed of calcium at body temperature is hundreds of meters per second. The resulting orbital radius is about a meter. That is bigger than the body, and vastly bigger than a cell. To fit the orbit inside a cell, the speed would have to be much slower, on the order of a thousandth of a meter per second, which corresponds to a temperature of about a few nanokelvins. The orbital period is a couple hundredths of a second, but the time between collisions of the ion with a water molecule is one the order of 10^–13 seconds, so there are many billions of collisions per orbit. Any circular motion will be destroyed by collisions long before anything like an orbit is established. I’m sorry, but the hypothesis is rubbish.

Are Electromagnetic Fields
Making Me Ill?

If you want to learn more about how extremely low frequency electric fields interact with tissue, see my book Are Electromagnetic Fields Making Me Ill?

Finally, for you folks who are really on the ball, you may be wondering why this homework problem is listed as being in Chapter 9 when the discussion of the cyclotron is in Chapter 8 of the 5th edition of IPMB. (In this post I changed the equation numbers in the homework problem to match the 5th edition, so you would have them.) Hmm.. is there a new chapter in the 6th edition? More on that later…

 To be fair, I should let my late friend Abraham Liboff tell you his side of the story. In this video, Abe explains how he proposed the cyclotron resonance hypothesis. I liked Abe, but I didn’t like his hypothesis.

https://www.youtube.com/watch?v=YL-wqJ-PMAQ&list=PLCO-VktC6wofkMeEeZknT9Y4WhMnP76Ee&index=6

The Luria-Delbrück Experiment

Introduction

Today’s question is: do mutations happen randomly, or are they caused by some selective pressure? In other words, are mutations a Darwinian event where they happen by chance and then natural selection selects those that are favorable to pass on to the offspring, or are mutations Lamarckian where they happen because they help a species survive (like a giraffe constantly stretching its neck to reach the leaves at the top of the tree, thereby making its neck longer, and then passing that acquired trait to its offspring). To determine which of these two hypotheses is correct, we need an experimental test.

Let’s examine one famous experiment. To make things simple, consider a specific case. Assume we start with just one individual, who is not a mutant. Furthermore, let each parent have two offspring, and only analyze three generations. For the first two generations there is no selective pressure, and only in the third generation the selective pressure is present. To make the analysis really simple, assume the probability of a mutation, p, is very small.

The most common case is shown in the figure below. Blue circles represent the individuals in each generation, starting in the first generation with just one. Locations where lines branch represent births. (Wait, you say, each child should have two parents, not one! Okay, we are making a simple model. Assume an individual reproduces asexually by splitting into two. We should talk about “splittings” and not “births.”) The green dashed line represents when the selective pressure begins. So our picture shows one great-grandparent, two grandparents, four parents, and eight children. A mutation is indicated by changing a blue circle to red. 

Because p << 1, by far the most common result is shown below, with no mutations. 

 

Lamarckian Evolution

In the case when mutations are caused by some selective pressure (Lamarckian), you can get a more interesting situation like shown below. No one above the dashed line undergoes a mutation because there was no selective pressure then. A child below the dashed line in the bottom row might have a mutation. There are eight children, so the probability of one of the eight having a mutation is 8p. The probability of two offspring having mutations will go as p², but since we are assuming p is small the odds of having multiple mutant offspring will be negligible. We’ll ignore those cases.  

Let’s calculate some statistics for this case. Let n be the number of mutant offspring in the last generation (below the dashed line). To find the average value, or mean, of n over several experiments, which we’ll call <n>, you sum up all the possible cases, each multiplied by its probability. In general, we could have n = 0, 1, 2, …, 8, each with probability p₀, p₁, …, p₈, so <n> is 

<n> = p₀ (0) + p₁ (1) + p₂ (2) + … + p₈ (8).

But in this case p₂, p₃, …, p₈ are all negligibly small, so we have only the first two terms in the sum to worry about.

For each individual, the odds of not mutating is (1 – p). In the last generation below the dashed line there are 8 offspring, so the probability of none of them having a mutation, p₀, is (1 – 8p). The probability for one mutation (p₁) is 8p because there are 8 offspring, each with probability p of mutating. So

<n> = (1 – 8p) (0) + 8p (1) = 8p .

We will also be interested in the variation of results between different trials. For this, we need <n²>

<n²> = (1 – 8p) (0)² + 8p (1)² = 8p .

The variance is the mean of the square of the variation from the mean. In Appendix G of Intermediate Physics for Medicine and Biology, Russ Hobbie and I call the variance σ² and we prove that σ² = <n²> – <n>². In our case

σ² = <n²> – <n>² = 8p – (8p)² .

But remember, p << 1 so the last term is negligible and the variance is 8p. Therefore, the mean and variance are the same. You may have seen a probability distribution with this property before. Appendix J of IPMB states that the Poisson distribution has the same mean and variance. Basically, the Lamarckian case is a Poisson process. 

 

Darwinian Evolution

Now consider the case when mutations occur randomly (Darwinian). You still can get all the results shown earlier in the Lamarckian case, but you get others too because mutations can happen all the time, not just when the selective pressure is operating. Suppose one of the parents (just above the dashed line) mutates. Their mutation gets passed to both offspring. The odds of mutating back (changing from red to blue) are very small (p << 1), so we assume both offspring of a mutant inherit the mutation, as shown below. 

You could also have one of the two grandparents give rise to four mutant offspring below the dashed line, as shown below.

Let’s do our statistics again. As before, the vast majority of the cases have no mutations. There are now 14 cases, each of which could have the mutation in one of the offspring. All the cases are shown below.

The probability of having no mutations ever (the bottom right case) is (1 – 14p). The probability of one of the offspring having a mutation is 8p (the eight cases in the top row). The probability of any one of the parents having a mutation is p and there are 4 parents, so the probability of a mutation among the parents is 4p, and each would give rise to two mutants below the dashed line (the four cases on the left in the bottom row). Finally, one of the two grandparents could mutate (the fifth and sixth cases in the bottom row), each with probability p. If a grandparent mutates it results in 4 mutants below the dashed line. So, the mean number of mutants in the final generation is

<n> = (1 – 14p) (0) + 8p (1) + 4p (2) + 2p (4) = 24p .

The odds of a mutant appearing in the final generation is three times higher in the Darwinian case than in the Lamarckian case. What about the variance?

<n²>  = (1 – 14p) (0)² + 8p (1)² + 4p (2)² + 2p (4)² = 56p .

The variance is

σ² = <n²> – <n>²  = 56p – 24²p² = 56p

(remember, terms in p² are negligible). Now the variance (56p) is over twice the mean (24p). It is not a Poisson process. It’s something else. There is much more variation in the number of mutants because of mutations happening early in the family tree that pass the mutation to all of the subsequent offspring. 

 

Conclusion

In an experiment, p may not be easy to determine. You need to know how many individuals you start with (in our example, one) and how many generations you examine (in our example, three), as well as how many mutants you end up with. But you can easily compare the variance to the mean; just take their ratio (variance/mean). If they are the same, you suspect a Lamarckian Poisson process. If the variance is significantly more than the mean, you suspect Darwinian selection.  In our example, variance/mean = 2.3.

There are some limitations. The probability is not always very small, so you might need to extend this analysis to cases where you have more than one mutation occurring. Also, in many experiments you will want to let the number of generations be much larger than three. There is also the possibility of a mutant mutating back to its original state. Finally, during sexual reproduction you have the in-laws to worry about, and you could have more than two offspring. So, to be quantitative you have some more work to do. But even in the more general case, the qualitative conclusion remains the same: Darwinian evolution results in a larger variance in the number of mutants than does Lamarckian evolution.

I suspect you now are saying “this is an interesting result; has anyone done this experiment?” The answer is yes! Salvador Luria and Max Delbrück did the experiment using E. coli bacteria (so the asexual splitting of generations is appropriate). The selective pressure applied at the end was resistance to a bacteriophage (a virus that infects bacteria). Their result: there was a lot more variation than you would expect from a Poisson process. Evolution is Darwinian, not Lamarckian. Mutations happen all the time, regardless of if there is some evolutionary pressure present.

 

The Luria-Delbrück experiment, described by Doug Koshland of UC Berkeley. 

https://www.youtube.com/watch?v=slfLeKqE3Bg

Electromagnetic Hypersensitivity

What is electromagnetic hypersensitivity? It’s an alleged condition in which a person is especially sensitive to weak radiofrequency electromagnetic fields, such as those emitted by a cell phone or other wireless technology. All sorts of symptoms are claimed to be associated with electromagnetic hypersensitivity, such as headaches, fatigue, anxiety, and sleep disturbances. An example of a person who says he has electromagnetic hypersensitivity is Arthur Firstenberg, author of The Invisible Rainbow, a book about his trials and tribulations. Many people purportedly suffering from electromagnetic hypersensitivity flock to Green Bank, West Virginia, because a radiotelescope there requires that the surrounding area being a “radio quiet zone.”

Is electromagnetic hypersensitivity real? Answering this question should be easy. Take people who claim such hypersensitivity, sit them down in a lab, turn a radiofrequency device on (or just pretend to), and ask them if they can sense it. Ask them about their symptoms. Of course, you must do this carefully, avoiding any subtle cues that might signal if the radiation is present. (For a cautionary tale about why such care is important, read this post.) You should do the study double blind (neither the patient nor the doctor who asks the questions should be told if the radiation is or is not on) and compare the patients to control subjects.

The effects of
radiofrequency
electromagnetic fields
exposure on human
self-reported symptoms.

Many such experiments have been done, and recently a systematic review of the results was published.

Xavier Bosch-Caplanch, Ekpereonne Esu, Chioma Moses Oringanje, Stefan Dongus, Hamed Jalilian, John Eyers, Christian Auer, Martin Meremikwu, and Martin Röösli (2024) The effects of radiofrequency electromagnetic fields exposure on human self-reported symptoms: A systematic review of human experimental studies. Environment International, Volume 187, Article number 108612.

This review is part of an ongoing project by the World Health Organization to assess potential health effects from exposure to radiofrequency electromagnetic fields. The authors come from a variety of countries, but several work at the respected Swiss Tropical and Public Health Institute. I’m particularly familiar with the fine research of Martin Röösli, a renowned leader in this field.

The authors surveyed all publications on this topic and established stringent eligibility criteria so only the highest quality papers were included in their review. A total of 41 studies met the criteria. What did they find? Here’s the key conclusion from the author’s abstract.

The available evidence suggested that study volunteers could not perceive the EMF [electromagnetic field] exposure status better than what is expected by chance and that IEI-EMF [Idiopathic environmental intolerance attributed to electromagnetic fields, their fancy name for electromagnetic hypersensitivity] individuals could not determine EMF conditions better than the general population.

The patients couldn’t determine if the fields were on or off better than chance. In other words, they were right about the field being on or off about as often as if they had decided the question by flipping a coin. The authors added

Available evidence suggests that [an] acute RF-EMF [radiofrequency electromagnetic field] below regulatory limits does not cause symptoms and corresponding claims in... everyday life are related to perceived and not to real EMF exposure status.

Let me repeat, the claims are related “to perceived and not to real EMF exposure.” This means that electromagnetic hypersensitivity is not caused by an electromagnetic field being present, but is caused by thinking that an electromagnetic field is present.

Yes, there are some limitations to this study, which are discussed and analyzed by the authors. The experimental conditions might differ from real-life exposures in the duration, frequency, and location of the field source. Most of the subjects were young, healthy volunteers, so the authors could not make conclusions about the elderly or chronically ill. The authors could not rule out the possibility that a few super-sensitive people are mixed in with a vast majority who can’t sense the fields (although they do offer some evidence suggesting that this is not the case).

Are Electromagnetic Fields
Making Me Ill?

Their results do not prove that a condition like electromagnetic hypersensitivity is impossible. Impossibility proofs are always difficult in science, and especially in medicine and biology. But the evidence suggests that the patients’ symptoms are related “to perceived and not to real EMF exposure.” While I don’t doubt that these patients are suffering, I’m skeptical that their distress is caused by electromagnetic fields. 

To learn more about potential health effects of electromagnetic fields, I refer you to Intermediate Physics for Medicine and Biology (especially Chapter 9) or Are Electromagnetic Fields Making Me Ill?

Martin Röösli - Electromagnetic Hypersensitivity and Vulnerable Populations

https://www.youtube.com/watch?v=UPXY0WQJ37Q

Is Electromagnetic Hypersensitivity Real?

https://www.youtube.com/watch?v=IrkL1Hm5myE

J. Patrick Reilly (1937—2024)

J. Patrick Reilly died on October 28 in Silver Spring, Maryland, at the age of 87. He was a leader in the field of bioelectricity, and especially the study of electrical stimulation.

Russ Hobbie and I didn’t mention Reilly in Intermediate Physics for Medicine and Biology, but I did in my review paper “The Development of Transcranial Magnetic Stimulation.”

J. Patrick Reilly of the Johns Hopkins Applied Physics Laboratory calculated electric fields in the body produced by a changing magnetic field, although primarily in the context of neural stimulation caused by magnetic resonance imaging (MRI) [54, 55].

[54] Reilly, J. P. (1989). Peripheral nerve stimulation by induced electric currents: Exposure to time-varying magnetic fields. Med. Biol. Eng. Comput., 27, 101–110.

[55] Reilly, J. P. (1991). Magnetic field excitation of peripheral nerves and the heart: A comparison of thresholds. Med. Biol. Eng. Comput., 29, 571–579.

The papers included this biography of the author. 

 

Applied Bioelectricity,
by J. Patrick Reilly.

Reilly was also known for his 1998 book Applied Bioelectricity: From Electrical Stimulation to Electropathology, which covered many of the same topics as Chapters 6–8 in IPMB: The Hodgkin-Huxley model of a nerve action potential, the electrical properties of cardiac tissue, the strength-duration curve, the electrocardiogram, and magnetic stimulation. However, you can tell that Russ and I are physicists while Reilly is an engineer. Applied Bioelectricity focuses less on deriving equations from fundamental principles and providing insights using toy models, and more on predicting stimulus thresholds, analyzing stimulus wave forms, examining electrode types, and assessing electrical injuries. That’s probably why he included the word “Applied” in his title. Compared to IPMB, Applied Bioelectricity has no homework problems, fewer equations, a similar number of figures, more references, and way more tables.

Reilly’s preface begins

The use of electrical devices is pervasive in modern society. The same electrical forces that run our air conditioners, lighting, communications, computers, and myriad other devices are also capable of interacting with biological systems, including the human body. The biological effects of electrical forces can be beneficial, as with medical diagnostic devices or biomedical implants, or can be detrimental, as with chance exposures that we typically call electric shock. Whether our interest is in intended or accidental exposure, it is important to understand the range of potential biological reactions to electrical stimulation.

In 2018, Reilly was the winner of the d’Arsonval Award, presented by the Bioelectromagnetic Society for outstanding achievement in research in bioelectromagnetics. The award puts him in good company. Other d’Arsonval Award winners include Herman Schwan, Thomas Tenforde, Elanor Adair, Shoogo Ueno, and Kenneth Foster.

I don’t recall meeting Reilly, which is a bit surprising given the overlap in our research areas. I certainly have been aware of his work for a long time. He was a skilled musician as well as an engineer. I would like to get a hold of his book Snake Music: A Detroit Memoir. It sounds like he had a difficult childhood, and there were many obstacles he had to overcome to make himself into a leading expert in bioelectricity. Thank goodness he persevered. J. Patrick Reilly, we’ll miss ya.