The Physics of Bees

In this third installment of The Physics of Native Gardening series, I look at the physics of bees. Each year we get more and more bees coming to our garden. I especially like the big, fat bumblebees. Some days there are so many bees that they swarm their favorite flowers. You can tell they are hard at work gathering pollen; busy as a bee.

Bumblebee Flight

Sometimes you’ll hear nonsense claiming that according to the laws of physics bumblebees can’t fly. A focus article about a 2016 Physical Review Letters paper states

Relatively small insects, like bees and house flies, have a different flying strategy than larger insects and birds. They have fairly rigid wings, which they flap as much as a hundred times per second. The flapping motion is not strictly up and down like for birds but more forward and backward… Starting with the wings “clapped” together and vertical behind the insect’s back, the wings then tilt steeply away from one another as the forward stroke begins. As they move, the wings produce low pressure in the region just behind the leading edge... The air in front of the wings curls up and over them and forms a horizontal, tornado-like vortex along the back side of the leading edge. Previous experiments and computer simulations have shown that leading edge vortices produce a suction effect that gives the necessary lift for keeping an insect aloft.

Ultraviolet Vision

An Immense World,
by Ed Yong.

Bee vision is different than human vision. The human retina has three color receptors, each sensitive to different frequencies in the visible spectrum (blue, green, and red). The bee also has three receptors, but only two are in the visible spectrum (blue and green); the other is in the ultraviolet (light with a wave length shorter than what the human eye can see). In his book An Immense World: How Animal Senses Reveal the Hidden Realms Around Us, Ed Yong wrote

Flowers use dramatic UV [ultraviolet] patterns to advertise their wares to pollinators. Sunflowers, marigolds, and black-eyed Susans all look uniformly colored to human eyes, but bees can see the UV patches at the bases of their petals, which form vivid bullseyes. Usually, these shapes are guides that indicate the position of nectar.

Oxygen Diffusion

Bees don’t have lungs. Yet, all that flying means they need a lot of oxygen to power their high metabolism. How do they supply oxygen to their muscles?

Instead of having vessels to transport blood, insects use small, air-filled pipes (trachea) that deliver oxygen. The pipes typically have a dead end, so you can’t just flow air through them. The oxygen is supplied by diffusion.

Diffusion is the movement of a molecule from a region of high concentration to low concentration. It works quickly over short distances, but takes a long time over long distances. Russ Hobbie and I discuss diffusion in Chapter 4 of Intermediate Physics for Medicine and Biology. Oxygen can diffuse through air ten thousand times faster than it can diffuse through water. Therefore, filling these insect pipes with blood would make oxygen diffusion way too slow. But having them filled with air means plenty of oxygen can diffuse in, powering flight.

One potential problem for bees would be if water was sucked into their trachea by capillary action. This would drastically lower the diffusion of oxygen. To avoid this, the trachea may be coated by a waxy substance that repels water. The pipes are so small that it is difficult to know for sure, but capillary action is so powerful there must be some way to keep water out.

Thermoregulation of Flight Muscle

Air and Water,
by Mark Denny.

In his book Air and Water, Mark Denny discusses how tiny bees stay warm. As we saw last week when describing hummingbirds, one way to produce a lot of heat is having a high metabolic rate. But it’s complicated. Denny writes

It is a tribute to the metabolic and respiratory machinery of bees and other flying insects that this magnitude of metabolism is possible. Note, however, that this high metabolic rate is closely tied to activity on the part of the bee. It must raise its metabolic rate well above that at rest (by shivering, for instance) to heat itself up. As soon as it becomes inactive, its body temperature returns to that of the ambient air.

There is a flip side to this puzzle. If a flying bee can heat its muscles to 30° C on a cold day, it seems likely that it could overheat on a hot day. Indeed this is the case, and bumblebees have evolved mechanisms that allow them to dump heat effectively from the thorax to the abdomen, from where it is shed to the air.

If you want to learn more about bees, there’s an entire website about physics for beekeepers. It’s mainly about honey bees, which are a little like cattle: non-native domesticated livestock that are commercially important. I’m not so interested in honey bees, but focus more on the many solitary, ground-nesting or cavity-nesting species of bees native to Michigan that live in our yard, such as sweat bees, carpenter bees, mason bees, and miner bees.

Many of the physical constraints faced by bees are shared by their fellow insects, the butterflies. Next week we’ll examine in more detail the physics of butterflies.

 

Native bees of Michigan with Dr. Rebecca Tonietto

https://www.youtube.com/watch?v=EICFH-DIYGU 

The Physics of Birds

In this second installment of my series on the physics of native gardening, I’ll talk about the physics of birds. We get a lot of birds in our yard. Robins visit the lawn and our crabapple tree. Too many house sparrows come to our bird feeders; they’re invasive pests. We see lots of blue jays, those big bullies, as well as goldfinches, downy woodpeckers, and black-capped chickadees. Every fall we know that winter is approaching when the dark-eyed juncos come down to Michigan from Canada. Canadian geese fly overhead, but they never stop at our house.

Flight

I often see birds high in the sky, soaring through the air without flapping their wings. I suspect many are red-tailed hawks, but I’ve never gotten close enough to one to say for sure. How does soaring work? First, it requires a thermal updraft. The sun heats the earth and the earth heats the air next to it, resulting in a temperature gradient: the air near the ground is hotter than the cooler air high above. However, hot air is lighter and therefore tends to rise. This unstable situation results in thermal updrafts. Hot air at one location will rise, and then as it cools will sink at some nearby location. The hawk can glide in the uprising air, so it slowly sinks with respect to the air but rises with respect to the ground. Once high up, it can then glide anywhere while searching for food, until it is low enough that it must seek another updraft.

Life in Moving Fluids,
by Steven Vogel.

Most birds don’t soar but instead flap their wings to fly. This flapping is complicated enough that I’ll let Steven Vogel—my favorite expert on biological fluid dynamics—explain it. The following excerpt is from his wonderful book Life in Moving Fluids.

In birds, bats, and insects, flapping wings combine the functions that airplanes divide between fixed wings and propellers—in a sense, they’re closer to helicopters than to airplanes, and it’s all too easy to be misled by our habit of calling the propulsive appendages “wings” rather than “propeller blades.” But they aren’t quite like ordinary propellers either, since flapping wings produce both thrust and lift directly, rather than producing thrust directly and getting lift by diverting some of the thrust to pay for the drag of fixed, lift-producing wings. The composite function, as well as their reciprocating rather than rotational motion, mean that the motion of flapping wings is inevitably complex… The downstroke moves a wing forward as well as downward and produces mainly upward force but usually some rearward force as well. The upstroke goes backward as well as upward, producing mainly rearward force but often some upward force.

Scaling

Scaling,
by Knut Schmidt-Nielsen.

Each summer my wife puts out a feeder filled with sugar water, and near it we plant red cardinal flowers, to attract hummingbirds. The hummingbirds are tiny and are constantly eating. In Intermediate Physics for Medicine and Biology, Russ Hobbie and I explain how an animal’s metabolic rate scales with its size and mass. The heat produced from metabolism increases with the volume of the animal, but heat is lost by an animal at its surface. As you compare larger animals to smaller ones, the volume increases with size faster than the surface area does. This means that large animals have trouble getting rid of excess heat, while small animals find it difficult to stay warm. The tiny hummingbird is smaller than other birds, so it tends to cool down quickly (it has a large surface-to-volume ratio). To keep warm, it has to boost its metabolism, which means it must eat a lot. A high metabolic rate requires not only much food but also oxygen, which implies that the hummingbird’s heart must pump a lot of blood. The heart rate of a hummingbird can be upwards of 1000 beats per minute (a normal heart rate for a human is 60 to 100 bpm).

Scaling relationships like we just saw for the hummingbird are common in biology. If you want to learn more about this topic, I suggest Knut Schmidt-Nielsen’s fascinating book Scaling: Why is Animal Size so Important?

Drinking

My favorite bird is the mourning dove. We sometimes will have eight or more of these sweet, gentle birds around our bird feeder. I love their low-pitched coo… coo… coooooooooo song. They mate for life.

Doves are unique among birds in the way they drink. Most birds fill their bill with water and then gravity pulls it down to their stomach. Sometimes they tilt their head back to help the water flow. Mourning doves, on the other hand, suck water into their bill, like we suck water through a straw. Professor Gart Zweers, from the University of Leiden, took high-speed x-ray photos, and concluded that doves draw a partial vacuum which pulls the water up.

Singing

Bird songs are analyzed using plots of time and frequency. As discussed in Chapter 11 of Intermediate Physics for Medicine and Biology, you can resolve any function of time into its component frequencies: Fourier analysis. If you plot the instantaneous frequency versus time, you get a sonogram. The higher the frequency, the higher the pitch that we hear. The northern cardinal’s song starts on a high pitch (around 4 kilohertz, which is about the frequency of highest pitched note on a piano) and then slurs downward an octave (to 2 kilohertz) in about half a second.

Trevisan and Mindlin (Philosophical Transactions A, Volume 367, Pages 3239–3254, 2009) have modeled the bird’s vocal organ, called the syrinx. Their model might be familiar to physics students: it is Newton’s second law, force equals mass times acceleration. The important parameters that enter the model are the mass, stiffness, and a constant characterizing the dissipation or attenuation of the motion. The dissipation can be nonlinear, leading to all sorts of complex dynamics. The model predicts an oscillatory behavior (like that for a mass on a spring). Furthermore, the beak acts as a resonance tube (somewhat like an organ pipe).

We get majestic red cardinals visiting our birdfeeders all the time. Next time you hear a cardinal singing, think of all the physics going on.

Magnetoreception

Are Electromagnetic Fields
Making Me Ill?

Many birds make long migrations, and one wonders how they find their way. One method is magnetoreception: the sensing of magnetic fields. Most organisms cannot detect magnetic fields, but some birds can. Magnetoreception is possible because the birds have small particles of magnetite, called magnetosomes, which provide a magnetic moment that can interact with a magnetic field. I discussed magnetoreception in my book Are Electromagnetic Fields Making Me Ill?

In 1963, German zoologist Wolfgang Wiltschko placed European robins inside a chamber and turned on a magnetic field comparable in strength to the earth’s field. He did not expect a response, but to his surprise the birds oriented with the field… The robins proved adept at sensing magnetic signals during their annual migration.

Some researchers believe there are other mechanisms for magnetoreception besides magnetite particles. I wrote

A few animals, including the European robin, may take advantage of free radical reactions instead of magnetite for magnetoreception. Sonke Johnsen and Kenneth Lohmann [Physics Today, Volume 61, Pages 29–35, 2008], after reviewing the data, conclude that “the current evidence for the radical-pair hypothesis is maddeningly circumstantial…” The jury is still out on this issue.

To tell you the truth, I’m skeptical that free radical reactions are important.

Another animal that may detect the earth’s magnetic field and use it to navigate is the bee. Next week we will continue this series on the physics of native gardening by examining the physics of bees.

 Northern cardinal song

https://www.youtube.com/watch?v=e_b4PkcpDe0

The Physics of Native Gardening

Since my retirement, I’ve started gardening with native plants. Originally this was an interest of my wife’s, but through her I became interested too. We live in a traditional suburban neighborhood, with most of the homes having primarily turf grass lawns that are maintained with a lot of water, fertilizer, and herbicides. But whether the neighbors like it or not, we have changed. Each year, we convert more and more of our yard to native flower gardens. We have a rain garden in a low spot in the back yard, and several other gardens are back there too. In the front, under our crabapple and serviceberry trees, we have all sorts of flowers, including goldenrods and asters.

A garden in our back yard with swamp milkweed,
purple cone flowers, and black-eyed Susans.

Nature's Best Hope,
by Doug Tallamy.

The point of native gardening is not just to have pretty flowers. Our main goal is to support the native birds, butterflies, bees, and other animals. Evolution creates complex and interdependent ecosystems, where the flowers rely on the bees and butterflies for pollination, the bees and butterflies need the pollen and nectar for food, and the birds eat the caterpillars (soon to be butterflies) and flower seeds. We face a biodiversity crisis in our society that we can address, in a small way, with native gardening. One book that influenced me in this endeavor is Doug Tallamy’s Nature’s Best Hope: A New Approach to Conservation that Starts in Your Yard. I highly recommend it.

I’m still a physicist, interested in the applications of physics to medicine and biology. There’s lots of physics in native gardening, which I intend to explore. So, over the next few weeks I’ll post a series of essays about the physics of native gardening. Next week will be the physics of birds, the following week the physics of bees, and the third week the physics of butterflies. Some topics will be drawn from Intermediate Physics for Medicine and Biology, but most will come from other sources.

You might ask, why just birds, bees, and butterflies? Why not bats, beavers, and beetles? Fair question. We have many other animals visiting our yard. We’ve been trying to attract frogs and toads, but without a pond or stream it is difficult. Worms are a crucial asset for any gardener, especially if you maintain a compost heap like we do. Other insects we often see include the desirable dragonflies, moths, and lightning bugs, and some undesirable ones like wasps, flies, and mosquitoes. We have small mammals such as squirrels (who do their best to invade our bird feeders, but that’s another story), rabbits, and chipmunks. Our yard is too small to support larger predators, like foxes or coyotes, but we do occasionally have a Cooper’s hawk visit. On rare occasion, we see a raccoon, skunk, possum, or ground hog, but I don’t think they live here. One large mammal that comes a lot is white-tailed deer, which wander in from a nearby forest. They only eat plants, and act like giant rabbits as far as their ecological niche. I would enjoy having a big oak tree, but we don’t. We do have a couple maples, and a linden tree growing up in the middle of our deck. We love all these plant and animals.

It’s not my habit to do a series of postings on related topics. But biodiversity is important. Moreover, it’s cold and snowy here in Michigan right now so I can’t go out and dig, weed, water, or plant. I’ll do the next best thing and write. I hope you enjoy it.

Tune in next week as we explore the physics of birds. 

Our rain garden. A big swamp milkweed is in the center,
surrounded by nodding onions and golden Alexanders.
Blue flag irises are in the back (difficult to see in this photo).

Nature’s Best Hope: Conservation That Starts in Your Yard, with Doug Tallamy.

https://www.youtube.com/watch?v=CBWhaTbe_x0 

 

Edward O. Wilson discusses the half-earth project.

https://www.youtube.com/watch?v=lmoD-pNANWo
 

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.

Willi Kalender (1949–2024)

Medical physicist Willi Kalender died on October 20 at the age of 75. Kalender was an inventor of spiral computed tomography. Russ Hobbie and I describe spiral CT in Chapter 16 of Intermediate Physics for Medicine and Biology.

Figure 16.25 shows the evolution of the detector and source configurations [of CT]. The third generation configuration is the most popular. All of the electrical connections are made through slip rings. This allows continuous rotation of the gantry and scanning in a spiral as the patient moves through the machine. Interpolation in the direction of the axis of rotation (the z axis) is used to perform the reconstruction for a particular value of z. This is called spiral CT or helical CT. Kalender (2011) discusses the physical performance of CT machines, particularly the various forms of spiral machines.

Computed Tomography,
by Willi Kalender.

The citation is to Kalender’s well-known textbook Computed Tomography: Fundamentals, System Technology, Image Quality and Applications. According to Google Scholar, it has been cited over 1800 times. Russ and I reference it often.

Kalender obtained his PhD in 1979 from the University of Wisconsin’s famous medical physics program. He then went to the University of Tübingen in Germany. There, according to Wikipedia, “he took and successfully completed all courses in the pre-clinical medicine curriculum.” This is interesting, because just a few years earlier Russ Hobbie did the same thing in Minnesota.

Between 1971 and 1973 I audited all the courses medical students take in their first 2 years at the University of Minnesota. I was amazed at the amount of physics I found in these courses and how little of it is discussed in the general physics course.

Kalender was much loved in the radiology community. The European Society of Radiology wrote

With deep sadness, the ESR announces the passing of Prof. Willi Kalender on October 20, 2024 at the age of 75. A pioneering figure in diagnostic imaging and medical physics, Prof. Kalender significantly influenced the field through his groundbreaking research and leadership.

You can find a memorial page with many more tributes to Kalender here: https://www.kudoboard.com/boards/xqZwpoWO

Prof. Willi Kalender — Dedicated Breast CT — Interview at RSNA 2013

https://www.youtube.com/watch?v=9Ay-Ry6a8C0 

 

From Brownian Motion to Virtual Biopsy: A Historical Perspective from 40 years of Diffusion MRI

From Brownian Motion to Virtual Biopsy:
A Historical Perspective from 40 years
of Diffusion MRI, by Denis Le Bihan

Denis Le Bihan recently published an open access review article in the Japanese Journal of Radiology titled “From Brownian Motion to Virtual Biopsy: A Historical Perspective from 40 years of Diffusion MRI” (https://doi.org/10.1007/s11604-024-01642-z). The article explores in depth several of the concepts that Russ Hobbie and I describe in Section 18.13 (Diffusion and Diffusion Tensor MRI) of Intermediate Physics for Medicine and Biology. The introduction begins (references removed)

Diffusion MRI was born in the mid-1980s. Since then, it has enjoyed incredible success over the past 40 years, both for research and in the clinical field. Clinical applications began in the brain, notably in the management of acute stroke patients. Diffusion MRI then became the standard for the study of cerebral white-matter diseases, through the diffusion tensor imaging (DTI) framework, revealing abnormalities in the integrity of white-matter fibers in neurologic disorders and, more recently, mental disorders. Over time, clinical applications of diffusion MRI have been extended, notably in oncology, to diagnose and monitor cancerous lesions in almost all organs of the body. Diffusion MRI has become a reference-imaging modality for prostate and breast cancer. Diffusion MRI began in my hands in 1984 (I was then a radiology resident and a PhD student in nuclear and particle physics) with my intuition that measuring the molecular diffusion of water would perhaps allow to characterize solid tumors due to the restriction of molecular motion and vascular lesions where in circulating blood “diffusion” would be somewhat enhanced. This idea was to become the cornerstone of diffusion MRI. This article retraces the early days and milestones of diffusion MRI which spawned over 40 years.

I knew Le Bihan when I worked at the intramural program of the National Institutes of Health in the late 1980s and early 1990s. To me, he was mainly Peter Basser’s French friend. Peter was my colleague who worked in the same section as I did (his office was the second office down the hall from mine), and was my best friend at NIH. Le Bihan describes the start of his collaboration with Basser this way:

During the “NIH Research Festival” of October 1990 I met Peter Basser who had a poster on ionic fluxes in tissues while I had a talk on our recent diffusion MRI results. Peter appropriately commented that the correct way to deal with anisotropic diffusion was to estimate the full diffusion tensor , not just the ADC [apparent diffusion constant], as the approach of the time provided. Basically, ADCs are not sufficient in the presence of diffusion anisotropy, except in particular cases where the main diffusion directions coincide with those of the diffusion MRI measurements. To solve this issue Peter and I came with a new paradigm, the Diffusion Tensor Imaging (DTI) framework. By applying simultaneous diffusion-sensitizing gradient pulses along the X, Y and Z axes the diffusion MRI signal would become a linear combination of the diffusion tensor components. From the diffusion MRI signals acquired along a set of non-colinear directions, encoding multiple combinations of diffusion tensor components weighted by the corresponding b values, it would be possible to retrieve the individual diffusion tensor components at each location.

In Le Bihan’s Figure 3, he includes a photo of Basser, Jim Mattiello, and himself doing an early diffusion tensor imaging experiment. Le Bihan was the diffusion MRI expert and Mattiello (who worked in the same section as Basser and I did at NIH, and who I’ve written about before) was skilled at writing MRI pulse sequences. When they started collaborating, Basser knew little about magnetic resonance imaging, but he understood linear algebra and its relationship to anisotropy, and realized that by making the “b vector” a matrix he could obtain important information (such as its eigenvalues and eigenvectors) that would determine the fiber direction. 

Denis Le Bihon (left), Peter Basser (center)
and Jim Mattiello (seated), circa 1991.

Diffusion MRI works because spins that are excited by a radiofrequency pulse will then diffuse away from the tissue voxel being imaged, degrading the signal. The degradation is exponential and given by e^–bD, where D is the diffusion constant and b is the “b-factor” that depends on the magnetic field gradient used to extract the diffusion information and the timing of the gradient pulse. I had always thought that this notation went way back in the MRI literature, but according to Le Bihon’s article he named the “b-factor” after himself (“B”ihon)!

Le Bihon describes how the clinical importance of diffusion MRI was demonstrated in 1990 when it was found that stroke victims showed a big change in the diffusion signal while having little change in the traditional magnetic resonance image. In fact, Le Bihon claims that the other big advance in MRI of that era—the development of functional MRI based on the blood oxygenation level dependent (BOLD) imaging—has not yet led to any clinical applications, while diffusion imaging has several.

Le Bihon’s article concludes

Diffusion MRI, as its additions, DTI and IVIM [IntraVoxel Incoherent Motion] MRI, has become a pillar of modern medical imaging with broad applications in both clinical and research settings, providing insights into tissue integrity and structural abnormalities. It allows to detect early changes in tissues that may not be visible with other imaging modalities. Diffusion imaging first revolutionized the management of acute cerebral ischemia by allowing diagnosis at an acute stage when therapies can still work, saving the outcomes of many patients. Diffusion imaging is today extensively used not only in neurology but also in oncology throughout the body for detecting and classifying various kinds of cancers, as well as monitoring treatment response at an early stage. The second major impact of diffusion imaging concerns the wiring of the brain, allowing to obtain non-invasively images in 3 dimensions of the brain connections. DTI has opened up new avenues of clinical diagnosis and research to investigate brain diseases, revealing for the first time how defects in white-matter track integrity could be linked to mental illnesses.

If you want to learn more about diffusion MRI, I recommend Le Bihon’s article. It provides an excellent introduction to the subject, with a fascinating historical perspective.