The Magnetic Field of an Axon: Ampere versus Biot-Savart

In Homework Problem 14 of Chapter 8 in Intermediate Physics for Medicine and Biology, Russ Hobbie and I ask the reader to calculate the magnetic field produced by the action current in a nerve axon using the law of Biot and Savart, and to compare it with the result found using Ampere’s law. This is a useful exercise, but I’ve always been uncomfortable with one aspect of the calculation. I’ll explain what I mean in today’s post.

In the homework problem you assume the intracellular current is uniform along one section of the axon, and is zero elsewhere (this is a big assumption, but it lets you derive an analytical solution). When you calculate the magnetic field using the law of Biot and Savart, you get a smooth, continuous function valid for any position along the axon. However, when you use Ampere’s law the result seems like it should be discontinuous. For some positions the intracellular current contributes to the current enclosed by the Amperian loop, but for other positions the intracellular current is zero and contributes nothing. How can the magnetic field be smooth and continuous if the intracellular current is discontinuous?

Below I’ll show you an elegant way to resolve this paradox. The bottom line is that the magnetic field you calculate using Ampere’s law is the same continuous function that you’d get using the law of Biot and Savart. I’ll change the details so that you don’t solve the homework problem in the book exactly, but the fundamental idea works for the book’s problem too.

Let the intracellular current be I₀ for −b < x < b, and zero elsewhere, where x is the position along the axon (see the figure above). The axon is surrounded by saline with conductivity σ. The calculation consists of four steps: First calculate the extracellular voltage V_e in the saline, then differentiate V_e to find the x-component of the extracellular current density J_x, next integrate the current density across the area of the Amperian loop to get the return current I_ret (that part of the extracellular current that passes through the loop), and finally determine the net current enclosed by the loop and calculate the magnetic field B.

Case 1: x > b

Begin by calculating the magnetic field at point (x,y) where x > b, so you’re in the region where there is no intracellular current threading the Amperian loop (the green circle in the figure above, having radius r). To determine the extracellular voltage, realize that current crosses the membrane at only two locations: x = b (a positive point source when viewed from the extracellular space) and x = −b (a negative point source). The voltage produced by a point source is inversely proportional to the distance, so

(If you don’t follow how I derived this expression, see Section 7.1 in IPMB.)

To find the x-component of the current density, differentiate V_e with respect to x, multiple by σ, and add a minus sign.

The most difficult part of the calculation is integrating the current density over the area enclosed by the loop to find the return current. This is a two-dimensional integral, with an area element of 2πy dy and limits of the integration from 0 to r (see the figure on the right).

You can look up the needed integral in an integral table, evaluate it at the limits, and fill in any missing steps. The result is

The second term in the brackets is equal to minus one and the fourth term is equal to plus one, which cancel. There is no intracellular current for x > b, so the current enclosed by the loop is just the return current. The magnetic field is

(I switched the order of the two surviving terms and brought the minus sign inside the bracket.) This is exactly the solution you get using the law of Biot and Savart; if you don’t believe me, calculate it yourself.

Case 2: −b < x < b

The calculation for the extracellular potential, current density, and return current in the region −b < x < b is exactly as before

Now comes the interesting part. The second term in the brackets is not equal to minus one as it was earlier. Because x < b the numerator is negative, but the denominator is squared inside the square root so it is positive; the term becomes plus one. Because x > −b the fourth term is also equal to plus one, as before (both the numerator and denominator are positive). These two terms no longer cancel, so the return current becomes

This is different than we found for x > b. Don’t panic; remember that the total current enclosed by the loop is the return current plus the intracellular current. In this case, the intracellular current I₀ exactly cancels the +2 term inside the brackets in the expression for I_ret (remember, there is a minus one half in front of the brackets), so the enclosed current is just what we had for the x > b case, and the magnetic field is again

The equation for the magnetic field is the same for any value of x (you can check the x < −b case yourself; you’ll get the same equation). The “magic” comes from the term (x−b)/√(x−b)² switching from negative to positive, which is exactly what it had to do to cancel the intracellular current. The enclosed current is continuous even though the intracellular and return currents are not. The magnetic field calculated using Ampere’s law is a smooth function for all x, and is equivalent to the result obtained using the law of Biot and Savart (as it must be). Nice!

One limitation of this calculation is that the action potential has intracellular current only in one direction; a dipole. For an action potential propagating down an axon, the intracellular current first goes in one direction and then in another as the membrane depolarizes and then repolarizes; a quadrupole.

I’ll leave the calculation for this more complicated current distribution as an exercise for you. I suggest you do the calculation using both the Biot-Savart law and Ampere’s law. Enjoy!

This and That

Most of my blog posts are about a single topic related to Intermediate Physics for Medicine and Biology, but today’s post consists of a dozen brief notes. Read to the end for your Christmas gift.

1. Previously in this blog, I’ve mentioned the website medicalphysicsweb.com. That site no longer exists, but was replaced by a page dedicated to medical physics on the Physics World website. Former medicalphysicsweb editor Tami Freeman is still in charge, and the new site is useful for instructors and students using IPMB. I get updates by email.
2. I taught my Biological Physics class (PHY 3250) this fall at Oakland University, and videos of the class meetings are posted on Youtube. The quality is poor; often the blackboard is difficult to read. But if you want to see how I teach the first half of IPMB, take a look.
3. On the Wednesday before Thanksgiving, my class played Trivial Pursuit IPMB. The students had fun and earned extra credit. Earlier this year my wife and I bought two Trivial Pursuit games—complete with game boards and pieces—at a garage sale for a couple dollars, so I was able to accommodate twelve students. You can download the questions at the IPMB homepage. 
4. In 2012 I wrote about the website iBioMagazine. I no longer can find it, but I believe the website iBiology is related to it. I recommend iBiology for physics students trying to improve their knowledge of biology.
5. Today The Rise of Skywalker opens. It’s the final episode in the Star Wars trilogy of trilogies. I remember watching the first Star Wars movie as a teenager in 1977; I can’t wait to see the latest.
6. From the Oakland University campus you can see the Headquarters and Tech Center of Fiat Chrysler Automobiles. This fall the folks at Chrysler introduced a new advertising blitz called the Dodge Horsepower Challenge. Each week they presented a new physics problem about cars, and those who answered correctly were entered in a drawing for a 2019 Dodge Challenger SRT Hellcat Redeye. They needed a physicist to review their problems and solutions, and somehow I got the job. You can find the problems on Youtube, presented by a colorful wrestler named Goldberg.
7. Lately I’ve been republishing these blog posts on medium.com. Oddly, among my most popular stories on Medium is the one about the Fourier series of the cotangent. It has over 160 reads while others that I think are better have just a handful.
8. The Blogger software keeps its own statistics, and claims that my most popular post is about Frank Netter, with over 6000 page views. I think its popularity has to do with Search Engine Optimization.
9. The IPMB Facebook page now has over 200 members. Thanks everyone, and let’s try to finish 2020 with 220.
10. Regular readers know that my two favorite authors are Isaac Asimov and Charles Dickens. Recently I’ve discovered another: P. G. Wodehouse. His books about Bertie Wooster and Jeeves are hilarious, and a joy to read.
11. If you want to know what books I’m reading, you can follow my Goodreads account. Often books in the category Read More Science become subjects of blog posts.
12. Finally, here’s your Christmas present. Last year Oakland University Professor Andrea Eis organized an event—called Encountering the Rare Book—to highlight the OU Kresge Library’s special collections. I was one of the faculty members Andrea asked to select a book from the collection and write a brief essay about it. I chose A Christmas Carol and my essay is below. A Merry Christmas to you all.

I read A Christmas Carol every December, so I was delighted to find a first edition of Charles Dickens’ classic novella in the Rare Book Collection of Kresge Library. I never tire of Dickens’ “ghostly little book.” I love his language, humor, and wonderfully drawn characters.

I enjoy the Ghosts of Christmas Past and Present best; the Ghost of Christmas Yet to Come frightens me. One of my favorite scenes is when Scrooge’s nephew Fred and the Ghost of Christmas Present collude with Topper to catch Fred’s sister-in-law (the plump one with the lace tucker) during a game of blind man’s bluff. I’m a cheapskate focused on my work, so I have a certain sympathy for Ebenezer. I read the book each year as a reminder to not become a “tight-fisted hand at the grindstone.”

All of us in higher education ought to recall the words of the Ghost of Christmas Present at the end of Stave 3, as he revealed two wretched children hidden in his robes: “This boy is Ignorance. This girl is Want. Beware them both…but most of all beware this boy.”

I sometimes wonder if I should have been born a Victorian. I love their physics—Faraday, Maxwell, and Kelvin are my heroes—as well as their literature. A Christmas Carol was published in 1843, the same year that James Joule measured the mechanical equivalent of heat, George Stokes analyzed incompressible fluids, and Ada Lovelace wrote the first computer program. Holding a first edition in your hands connects you to that time; as if Dickens, like Marley’s Ghost, “sat invisible beside you.” The library’s copy has lovely illustrations, which at that time had to be painstakingly hand-colored.

I intend to continue reading A Christmas Carol each year, with the hope that I, like Scrooge, can “become as good a friend, as good a master, and as good a man, as the good old city knew.”

Encountering the Rare Book, an exhibition celebrating
the Special Collections in Kresge Library at
Oakland University, organized by Andrea Eis.

How Russ Hobbie Came to Write Intermediate Physics for Medicine and Biology

In the preface of Intermediate Physics for Medicine and Biology, Russ Hobbie writes

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. I found a great discrepancy between the physics in some papers in the biological research literature and what I knew to be the level of understanding of most biology majors or premed students who have taken a year of physics. It was clear that an intermediate level physics course would help these students. It would provide the physics they need and would relate it directly to the biological problems where it is useful.

This book is the result of my having taught such a course since 1973…

Want to hear more about how Russ came to write IPMB? You can! Russ was interviewed for the University of Minnesota Oral History Project. Below is an excerpt about the origin of the book.

Interview with Russell Hobbie

Interviewed by Professor Clarke A. Chambers. University of Minnesota

Interviewed on September 29, 1994. University of Minnesota Campus

…I wrote Al Sullivan who was the assistant dean of the Medical School asking if it was possible to snoop around over there. Al asked me to have lunch with him one day—it was in October—and said, “What you really ought to do is to attend Medical School.” I said, “I can’t. I’m director of undergraduate studies in Physics. I’m teaching a full load, which is a course each quarter. There’s just no time to do that.” He said, “You could just audit things and skip the labs.” So, for two years, I did that….

I sat through the remainder of the year in embryology, and biochemistry, and anatomy, and pathology, and physiology, and then, in the second year, the organ systems, the neuro psych, the cardiovascular, the pulmonary, the renal, the dermatology, the bones, the GI [gastrointestinal] ….

I really got a fairly good knowledge there and found that there was just too much physics ever to fit it into the pre-med physics course. I also found that there was a tremendous gap between what we teach the pre-meds, who will take one year of physics and that’s it, and what you found in the physiology and biophysics research literature. I convinced the Physics Department that I ought to try teaching a course to try to fill that gap, a 5000 level course that has a year of general physics and a year of calculus as a prereq[uisite] that would appeal to the physiologists and so on. Probably around 1972 or 1973, I started teaching that course, developing it as I went. That turned into a book [Intermediate Physics for Medicine and Biology] that was published by Wiley in 1978 with a second edition about 1988. I’m trying, without much success, to do a third edition right now….

…after I started teaching the course, I can remember Professor Jack Johnson from Physiology wanted to come and sit it in; and I was quite nervous about this because I was afraid I might get some of the physiology wrong. He reminded me, in no uncertain terms, that I’d been sitting through his course and turnabout really was fair play…

I think that, as I look back at my own career, the thing that I think that was most important, that has certainly given me the greatest intellectual satisfaction is the book.

If you can’t get enough of Russ, watch him in this video about his computer program MacDose.

Russell Hobbie demonstrates MacDose, part 1.

https://www.youtube.com/watch?v=eZGfHBYMuHg&t=8s

Russell Hobbie demonstrates MacDose, part 2.

https://www.youtube.com/watch?v=Rwp8eeKFycQ

Russell Hobbie demonstrates MacDose, part 3.

https://www.youtube.com/watch?v=hB4U7T0gH6M

The Dimensionality of Color Vision in Carriers of Anomalous Trichromacy

Russ Hobbie and I discuss color vision in Chapter 14 of Intermediate Physics for Medicine and Biology.

14.15 Color Vision

The eye can detect color because there are three types of cones in the retina, each of which responds to a different wavelength of light (trichromate vision): red, green, and blue, the primary colors...

From Photon to Neuron:
Light, Imaging, Vision,
by Philip Nelson.

Imagine my shock when I read about possible tetrachromate vision in Philip Nelson’s book From Photon to Neuron. I downloaded the article Phil cited—“The Dimensionality of Color Vision in Carriers of Anomalous Trichromacy,” by Gabriele Jordan, Samir Deeb, Jenny Bosten, and John Mollon, Journal of Vision, Volume 10, doi:10.1167/10.8.12, 2010—and quote the abstract below.

Some 12% of women are carriers of the mild, X-linked forms of color vision deficiencies called “anomalous trichromacy.” Owing to random X chromosome inactivation, their retinae must contain four classes of cone rather than the normal three; and it has previously been speculated that these female carriers might be tetrachromatic, capable of discriminating spectral stimuli that are indistinguishable to the normal trichromat. However, the existing evidence is sparse and inconclusive. Here, we address the question using (a) a forced-choice version of the Rayleigh test, (b) a test using multidimensional scaling to reveal directly the dimensionality of the participants' color space, and (c) molecular genetic analyses to estimate the X-linked cone peak sensitivities of a selected sample of strong candidates for tetrachromacy. Our results suggest that most carriers of color anomaly do not exhibit four-dimensional color vision, and so we believe that anomalous trichromacy is unlikely to be maintained by an advantage to the carriers in discriminating colors. However, 1 of 24 obligate carriers of deuteranomaly exhibited tetrachromatic behavior on all our tests; this participant has three well-separated cone photopigments in the long-wave spectral region in addition to her short-wave cone. We assess the likelihood that behavioral tetrachromacy exists in the human population.

Flatland: A Romance of Many Dimensions,
by Edwin A. Abbott. If you haven’t
read Flatland, ask Santa for a copy
this Christmas (or click on this link).

Wow! IPMB claims that “other animals...[can] have more than three types [of cones]” but offers no hint that people can. How cool is that? This is like finding someone who lives in a four-dimensional world. Would a tetrachromat explaining color to me (a trichromat) be like Square in Flatland describing a sphere to the Triangles? (Square was thrown in prison for that!) What would life be like with four color receptors (red, green, blue, and orange) instead of three? Would you perceive a fundamentally different world, or would any difference be subtle? Could we use CRISPR or some other gene editing tool to expand our color vision? (I’ll take a dozen different cones, please.) Is it fair that only women can be tetrachromats? (No, but let’s not go there.) Is tetrachromacy a superpower?

San Diego woman Concetta Antico diagnosed with “super vision.”

I don’t know how accurate this news story is, but it’s interesting.

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

The Rayl

Section 13.3 of Intermediate Physics for Medicine and Biology discusses acoustic impedance. For an ultrasonic wave the acoustic impedance is the pressure divided by the tissue velocity, so it has units of Pa/(m/s). In terms of kilograms, meters, and seconds, the units of acoustic impedance are kg/(m² s).

Acoustic impedance is analogous to electrical impedance. Voltage over current is like pressure over velocity. Electromagnetic waves propagating through a transmission line reflect when the electrical impedance changes, just as ultrasonic waves propagating through tissue reflect when the acoustic impedance changes. The unit for electrical impedance is the ohm, and the unit for acoustic impedance is the…

Wait! What is the name of the unit for acoustic impedance? According to IPMB the units of acoustic impedance are kg/(m² s). It has no name. The newton is a kg m/s², the joule is a kg m²/s², the pascal is a kg/(m s²), and the watt is a kg m²/s³. Why is there no name for the kg/(m² s)?

There is a name. A kg/(m² s) is called a rayl. It’s pronounced “rail.” I quote the last lines of Section 13.3.1 in IPMB, but using the rayl.

The quantity Z = ρ₀c = √ρ₀ κ is called the acoustic impedance of the medium [ρ₀ is the density, c is the speed of sound, and κ is the compressibility]. The acoustic impedance of water is about (10³ kg m^-3)(1400 m s^-1) = 1.4 × 10⁶ rayl, or 1.4 Mrayl. The acoustic impedance of air is about 400 rayl, so Z_air is much less than Z_water (Denny 1993).

The rayl is also the name for a g/(cm² s). But the rayl in the meter-kilogram-second system of units isn’t the same as the rayl in the centimeter-gram-second system. A CGS rayl is equal to ten MKS rayls. Maybe all this confusion is why no one uses the rayl (including IPMB). My vote is to abolish the CGS rayl. Erase it from history. Make it taboo. Let’s restrict the use of the term rayl to the MKS rayl.

The Theory of Sound,
by Lord Rayleigh.

The unit is named after John William Strutt, better known as Lord Rayleigh (pronounced ray-lee). He is known for Rayleigh waves, Rayleigh scattering, Rayleigh-Benard convection, the Rayleigh criterion, the Rayleigh-Taylor instability, the Rayleigh-Ritz method, and the Rayleigh-Jeans law. His influential textbook The Theory of Sound makes him the logical choice for the unit of acoustic impedance. He won the Nobel Prize in 1904 “for his investigations of the densities of the most important gases and for his discovery of argon in connection with these studies.”

Below are excerpts from Rayleigh’s Nobel biography.

John William Strutt, third Baron Rayleigh, was born on November 12, 1842 at Langford Grove, Maldon, Essex…

Throughout his infancy and youth he was of frail physique; his education was repeatedly interrupted by ill-health, and his prospects of attaining maturity appeared precarious. After a short spell at Eton at the age of 10, mainly spent in the school sanatorium, three years in a private school at Wimbledon, and another short stay at Harrow, he finally spent four years with the Rev. George Townsend Warner (1857) who took pupils at Torquay.

In 1861 he entered Trinity College, Cambridge, where he commenced reading mathematics, not at first equal in attainments to the best of his contemporaries, but his exceptional abilities soon enabled him to overtake his competitors. He graduated in the Mathematical Tripos in 1865 as Senior Wrangler and Smith’s Prizeman. In 1866 he obtained a fellowship at Trinity which he held until 1871, the year of his marriage.

A severe attack of rheumatic fever in 1872 made him spend the winter in Egypt and Greece. Shortly after his return his father died (1873) and he succeeded to the barony, taking up residence in the family seat, Terling Place, at Witham, Essex… In 1876 he left the entire management of the land to his younger brother.

From then on, he could devote his full time to science again. In 1879 he was appointed to follow James Clerk Maxwell as Professor of Experimental Physics and Head of the Cavendish Laboratory at Cambridge. In 1884 he left Cambridge to continue his experimental work at his country seat at Terling, Essex, and from 1887 to 1905 he was Professor of Natural Philosophy in the Royal Institution of Great Britain, being successor of Tyndall…

Lord Rayleigh’s first researches were mainly mathematical, concerning optics and vibrating systems, but his later work ranged over almost the whole field of physics, covering sound, wave theory, colour vision, electrodynamics, electromagnetism, light scattering, flow of liquids, hydrodynamics, density of gases, viscosity, capillarity, elasticity, and photography… His Theory of Sound was published in two volumes during 1877-1878, and his other extensive studies are reported in his Scientific Papers – six volumes issued during 1889-1920…

He had a fine sense of literary style; every paper he wrote, even on the most abstruse subject, is a model of clearness and simplicity of diction. The 446 papers reprinted in his collected works clearly show his capacity for understanding everything just a little more deeply than anyone else…

Lord Rayleigh… was a Fellow of the Royal Society (1873) and served as Secretary from 1885 to 1896, and as President from 1905 to 1908. He was an original recipient of the Order of Merit (1902), and in 1905 he was made a Privy Councillor. He was awarded the Copley, Royal, and Rumford Medals of the Royal Society, and the Nobel Prize for 1904…

Lord Rayleigh died on June 30, 1919, at Witham, Essex.

Rayleigh has always been a hero of mine. The breadth of his contributions, the quality of his writing, the ability to excel at both theory and experiment, and the service he contributed to his profession amaze me. I’m glad Russ Hobbie and I discuss some of his contributions in Intermediate Physics for Medicine and Biology.

John William Strutt, Lord Rayleigh (1842-1919).

Lord Rayleigh by Peter Wells, Cardiff University

https://www.youtube.com/watch?v=r1x54GeHOTE

Pocket Ultrasound

The November 4, 2019 issue of
TIME magazine, about health innovation.

For decades I’ve been a loyal subscriber to TIME magazine. I read it—more or less cover-to-cover—every week. Most issues have little overlap with Intermediate Physics for Medicine and Biology, but the November 4, 2019 issue is an exception; it focuses on health innovation.

My favorite of the featured innovators is Jonathan Rothberg, who’s developed a handheld ultrasound imager. His device looks like an electric shaver and would fit in your pocket. Don Steinberg writes in TIME 

Jonathan Rothberg, a Yale genetics researcher and serial entrepreneur, figured out how to put ultrasound technology on a chip, so instead of a $100,000 machine in a hospital, it’s a $2,000 go-anywhere gadget that connects to an iPhone app.

On his website, Rothberg says his aim is to make healthcare accessible to everyone around the world. A noble goal, but what’s unique about the physics of Rothberg’s invention? In Chapter 13 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss traditional ultrasound transducers.

Ultrasound is typically produced using a piezoelectric transducer. A piezoelectric material converts a stress (or pressure) into an electric field, and vice versa. A high-frequency oscillating voltage applied across a piezoelectric material creates a sound wave at the same frequency. Conversely, an oscillating pressure applied to a piezoelectric material creates an oscillating voltage across it. Measurement of this voltage provides a way to record ultrasonic waves. Thus, the same piezoelectric material can serve as both source and detector.

According to an article by Eliza Strickland in IEEE Spectrum, Rothberg’s ultrasound device, called the Butterfly iQ, does away with the piezoelectricity.

Today’s ultrasound systems use piezoelectric crystals, which convert electrical energy into vibrations in the form of ultrasonic waves. A typical system has a display screen on a bulky cart with several wands for imaging at different depths within the body. These machines can cost upwards of $100,000…

Developing the iQ’s chip-based technology was a two-step process. First, Butterfly’s engineers replaced the piezoelectrics with a micromachine that acts like a tiny drum to generate vibrations. Inside this “capacitive micromachined ultrasound transducer” (CMUT), an applied voltage moves a membrane to send ultrasonic waves into the body. The waves that bounce back from various body tissues move the membrane and are registered as an electric signal, which creates the image…

Rothberg explains that typical ultrasound systems require separate probes for different clinical applications because the crystals have to be tuned at the time of manufacture to produce the right type of ultrasonic wave for imaging at a particular depth. But the Butterfly iQ can be tuned on the fly. “We have 10,000 of these micromachine transducers on a probe, and that gives us a monster dynamic range,” he says. "We can make them buzz at 1 megahertz if we want to go deep, or 5 megahertz if we want to go shallow.”

The second innovation was to do away with the wiring that connects a typical piezoelectric probe to the electronic controls and displays. Butterfly’s micromachines are attached directly to a semiconductor layer that contains all the necessary amplifiers, signal processors, and so on.

I’m not expert enough to judge how revolutionary this device really is, but it sure sounds cool! One thing I know for certain: when you mix physics with medicine, the results can be astounding. 

Three issues behind in reading TIME magazine;
I've got my work cut out for me.

Thank goodness Christmas break is approaching, because I’m three issues behind with TIME. I try to keep up, I really do; it’s a challenge. But you never know what you’ll find when you open a new issue. Sometimes you find physics applied to medicine and biology!

Listen to Jonathan Rothberg talk about his ultrasound device, Butterfly iQ.

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

Jonathan Rothberg, 2013 National Medal of Technology and Innovation.
https://www.youtube.com/watch?v=hVV80xl-rNU

Thomas Tenforde (1940-2019) and The Wonders of Magnetism

Thomas Tenforde (1940-2019).
Photo used with permission of the
Health Physics Society.

Thomas Tenforde—an expert on the interaction of magnetic fields with biological tissue—died this fall.

When I was looking for employment in the late 1980s just after getting my PhD, I had a fellowship opportunity at the Pacific Northwest National Laboratory in Richland, Washington, where Tom Tenforde worked. At that time a debate raged about the health risks of 60-Hz power-line fields, and I recall having much respect for Tenforde’s research on this topic; his work seemed more rigorous and physics-based than many other studies. I ended up taking a position at the National Institutes of Health, but I seriously considered working for Tenforde.

When Russ Hobbie and I discuss power-line electric and magnetic fields in Intermediate Physics for Medicine and Biology, we cite a review by Tenforde.

9.10.2  Power Frequency (50-60 Hz) Fields

9.10.2.1 Fields in Homes are Weak

Much weaker fields in homes are produced by power lines, house wiring, and electrical appliances. Barnes (1995) found average electric fields in air next to the body of about 7 V m⁻¹, with peak values of 200 V m⁻¹. (We will find that since the body is a conductor, the fields within the body are much less.) Average residential magnetic fields are about 0.1 μT, with peaks up to four times as large. Within the body they are about the same. Tenforde (1995) reviews both power-line and radio-frequency field intensities.

Electromagnetic Fields:
Biological Interactions and Mechanisms,
edited by Martin Blank.

The reference is to

Tenforde TS (1995) Spectrum and intensity of environmental electromagnetic fields from natural and man-made sources. In: Blank M (ed.) Electromagnetic Fields: Biological Interactions and Mechanisms. American Chemical Society, Washington, DC, pp 13–35.

An obituary for Tenforde published online by the Health Physics Society begins

Thomas S. Tenforde died on 6 September 2019 in Berkeley, California, at the age of 78. He was born in Middletown, Ohio, on 15 December 1940. He received his BA degree from Harvard University with a major in physics. He earned a PhD in biophysics at the University of California at Berkeley. He was a senior scientist at the Lawrence Berkeley National Laboratory from 1969 to 1988. He moved to Richland, Washington, where he was a fellow at Battelle's Pacific Northwest National Laboratory from 1988 to 2002. His special areas of research included health effects of nonionizing radiation and the role of radionuclides for medical applications. He received the d’Arsonval Medal from the Bioelectromagnetics Society in 2001. He also received awards from the US Department of Energy in 2000 and the Federal Laboratory Consortium in 2001 for leading the development of ⁹⁰Y as a therapeutic medical isotope that is used worldwide for the treatment of cancer and other medical disorders...

Jacques-Arsène d’Arsonval
(1851-1940).
Photo from Wikipedia.

The d’Arsonval Medal is the most prestigious award bestowed by the Bioelectromagnetics Society. It’s named after French physician and physicist Jacques-Arsène d’Arsonval, a pioneer in electrophysiology. (Two scientists mentioned in last week's post—Eleanor Adair and Ken Foster—also were awarded the d'Arsonval Medal.) Tenforde’s award announcement states

Thomas S. Tenforde, senior chief scientist in the environmental technology division, Pacific Northwest National Laboratory, Richland, Wash., will receive the eighth d’Arsonval Award, presented by the Bioelectromagnetics Society to recognize “extraordinary accomplishment within the discipline of bioelectromagnetics.” This award recognizes Tenforde’s extensive research on dosimetry and biophysical interaction of static and low-frequency electric and magnetic fields with living systems….

Tenforde’s strong interest in bioelectromagnetics began with the use of static electric fields for single-cell micro-electrophoresis during his doctoral thesis work. In the 1970s and 1980s at Lawrence Berkeley National Laboratory he conducted a broad range of biological studies on static and ELF [extremely low frequency] magnetic fields. Tom and his colleagues at the Donner Laboratory at the University of California developed what soon became the foremost program investigating the biological effects of strong static magnetic fields. These studies looked at the cardiovascular system, the nervous system, thermoregulation, circadian rhythmicity, lipid bilayer membrane permeability, and animal behavior.

This work initially began because of concerns about human exposure to strong magnetic fields near thermonuclear fusion reactors, magneto-hydrodynamic power systems, and high-energy physics facilities such as cyclotrons and bubble chambers. Tom and his colleagues played a key role in the evaluation of potential risks to patients and workers from MRI facilities…

As manager of PNNL’s Hanford Radioisotopes Program, Tenforde supervised work which produced the medical isotope yttrium-90, which is now being used worldwide to treat cancer…

Tenforde provides yet another example of a scientist who made the transition from physics to biology. His career indicates how working at this interface can lead to new insights and great accomplishments. His interest in how magnetic fields affect animals overlaps with my work on the magnetic field of a nerve axon, magnetic stimulation and magnetoacoustic imaging. I think he would have enjoyed Chapter 8 of Intermediate Physics for Medicine and Biology, about biomagnetism.

I will let Tenforde have the last word. In an article based on his speech accepting the d’Arsonval Medal (Bioelectromagnetics, Volume 24, Pages 3-11, 2003), he wrote

A recurring theme of my work during the past 25 years has been the beneficial uses of magnetism in advancing our scientific knowledge of living systems, and hence I have chosen the title, “The Wonders of Magnetism.”

A Town Hall About The Health Risks of 5G Cell Phone Technology

5G Town Hall
Rochester, Michigan
November 7, 2019.

Yesterday I participated in a town hall meeting in Rochester, Michigan to discuss the new 5G cell phone technology. I was invited to attend in part because of my contributions to the book Intermediate Physics for Medicine and Biology, which discusses the health risks of electromagnetic fields.

When preparing for the event, I created a list of frequently asked questions (well, these were the questions I thought people would ask). Not wanting to waste this effort, I reproduce my FAQ below.

The event was....interesting. I was impressed by the passion of these concerned citizens, who packed a large room on a cold Thursday evening and for over two hours asked questions and voiced their opinions (mostly voiced their opinions). I’ve taught plenty of apathetic 20-something-year-olds who don’t engage with the lecture or challenge what I say, so I found this feisty crowd refreshing. Unfortunately, I was not convinced by their claims of dire health effects from 5G technology, and they were not convinced by me. The most disturbing moment was when I said something along the lines of “if you want to know more about the risks of cancer, consult the National Cancer Institute” and the response was a chorus of “No, No, No!” Goodness, if we can’t trust the National Cancer Institute to understand cancer, who can we trust? But no one threw a tomato at me, so I’ll call the evening a success. The FAQ below summarizes my view on this matter.

FAQ: 5G Cell Phone Health Effects

What is 5G?

5G is the fifth generation of technology for cell phones. It uses higher frequencies of electromagnetic radiation than 4G technology (up to 300 GHz, with a wave length of 1 mm).

What does IPMB say about the health risks from cell phones?

Section 9.10.5 of Intermediate Physics for Medicine and Biology addresses possible health risks from microwaves, mobile phones, and wi-fi. Russ Hobbie and I cite a 2005 review by John Moulder, Ken Foster, and their colleagues, which concludes that “Overall, a weight-of-evidence evaluation shows that the current evidence for a causal association between cancer and exposure to RF [radiofrequency] energy is weak and unconvincing.” We also cite “an exhaustive (390 page) report…by the International Committee on Non-Ionizing Radiation Protection (Vecchia et al. 2009)” that reaches a similar conclusion. Next we write that “Sheppard et al. (2008) evaluated all the proposed mechanisms for radio-frequency interactions with biological molecules and processes…[and conclude that] the principal mechanism for biological effects, and the only well-established mechanism, is the heating of tissues.” Finally, “Foster and Moulder (2013) reviewed the current state of research [on the health effects of wi-fi, and conclude that the evidence provides] ‘no basis to anticipate any biological effects.’”

The 2013 review by Foster and Moulder summarizes my opinion on this topic.

“Impossibility” arguments are difficult to sustain in biology; but the lack of a generally-accepted mechanism by which low-level (below ICNIRP and IEEE limits) RF fields in the GHz frequency range could produce biological effects, after many years of sustained efforts to uncover such mechanisms, makes it increasingly unlikely that any mechanism will be found.

What have Foster and Moulder said lately about health risks from wi-fi?

Ken Foster and John Moulder are experts on the interaction of electromagnetic radiation with the body. They are skeptical about many claims of health risks caused by power-line, cell-phone, and wi-fi radiation. Both are now emeritus professors; Foster at the University of Pennsylvania and Moulder at the University of Wisconsin. Intermediate Physics for Medicine and Biology cites Foster and Moulder several times, but the 5th edition of IPMB was published in 2015. What have they said lately?

Foster published a post two months ago in a Scientific American blog looking specifically at 5G technology and health risks. His conclusion: “So far, at least, there’s little evidence of danger.”

The most interesting development is a critique of Foster and Moulder’s 2013 review by Martin Pall, an emeritus professor at Washington State University. He concludes that “there are seven repeatedly found Wi-Fi effects which have also been shown to be caused by other similar EMF [electromagnetic field] exposures. Each of the seven should be considered, therefore, as established effects of Wi-Fi.” Pall’s central hypothesis is that cell phone radiation affects calcium ion channels, which if true could trigger a cascade of biological effects. In a rebuttal, Foster and Moulder (2018) write

Pall (2018) criticizes our 5-year-old review of studies related to Wi-Fi and health (Foster and Moulder 2013). We respond to his critique, and also note weaknesses in his selection and interpretation of studies on biological and health effects of Wi-Fi type signals...

Having examined the additional papers that Pall cites, we reaffirm our earlier conclusion: a number of studies have reported bioeffects of Wi-Fi exposures, but technical limitations make many of them difficult to interpret and artifacts cannot be excluded. We are not aware of any health-agency warnings about health risks of Wi-Fi technology. Despite some level of public controversy and an ongoing stream of reports of highly variable quality of biological effects of RF energy (e.g. articles in a recent special issue of the Journal of Chemical Neuroanatomy, Volume 75, 2016) health agencies consistently conclude that there are no proven hazards from exposure to RF fields within current exposure limits (even as they consistently call for more research).

My advice is to read the review, the critique, and the rebuttal, and then draw your own conclusion. You may find many of the technical details difficult to understand (I do), but you will better appreciate the complexity if these issues, and the difficulty in drawing definite conclusions from imperfect data. I don’t agree with Pall’s claims.

What does Bob Park have to say about the health risks from cell phones?

Robert Park is an emeritus professor of physics at the University of Maryland, and was the director of public information at the Washington office of the American Physical Society. He is the author of Voodoo Science, and wrote a weekly column titled “What’s New” debunking pseudoscience. His health has not allowed him to contribute to the recent discussion about the risks of cell phones and 5G technology (and, oh, how we miss him). Here’s what he wrote in “What’s New” on Sunday, May 6, 2012.

1. ALBERT WHO? DEAD PHYSICIST DISPELS MOBILE-PHONE MYTH. According to news reports last week: "There is still no evidence of harm to health from mobile-phone technologies," or other wireless devices such as Wi-Fi. A study for the UK's Health Protection Agency (HPA) is said to be the most complete review yet and new evidence is still being examined, according to Professor Anthony Swerdlow of the Institute of Cancer Research, who chaired the study. I once had a rubber stamp made that said: “More research is needed,” since its found at the end of every science paper. The unanswered question is why anyone thought microwave radiation might be a cancer agent in the first place? Cancer is linked to the formation of mutant strands of DNA. More than 100 years ago in his 1905 paper on the photoelectric effect, Albert Einstein predicted an abrupt threshold for photoemission at about 5 eV, just above the lovely blue limit of the visible spectrum, demonstrating wave-particle duality. He was awarded the 1923 Physics Nobel Prize [actually, Einstein received the Nobel Prize in 1921, and Robert Millikan received it in 1923, in part for his experimental work on the photoelectric effect]. Its also the threshold for the emission of invisible ultraviolet radiation that causes hideous skin cancers. The cancer threshold, is therefore, 1 million times higher than the microwaves band. The same enormous mistake was made in the 1980s when epidemiologists falsely warned that exposure to power line emission can cause cancer. Power lines abruptly stopped causing cancer in 1997 after the U.S. National Cancer Institute conducted a better study. Its painful to witness this sad history being replayed with mobile-phone radiation. Aside: My apologies to regular readers who have heard this 20 times before, but it has not gotten through to everyone.

Park’s argument remains as true now as eight years ago, except that a 300 GHz photon has an energy of one-thousandth of an electron volt, which is “only” a few thousand times less than the threshold for photoemission or UV skin cancer (and is about 25 times smaller than thermal energy, 0.025 eV). The possibility of DNA damage—the underlying cause of cancer—remains extraordinarily remote, but not as ridiculously remote as it was for cell phone technology ten years ago.

Electromagnetic radiation is considered a possible carcinogen. What’s that mean?

Something that is “possibly carcinogenic to humans” doesn’t probably cause cancer. It probably doesn’t cause cancer, but we can’t say for certain. RF radiation was not placed into two more threatening categories: “probably carcinogenic to humans” and “carcinogenic to humans.”

The website Science-Based Medicine states that

Despite the negative evidence to date, in 2011, the International Agency for Research on Cancer classified EMF [low-frequency electromagnetic fields] as a “possible” carcinogen. They have a low threshold for this category, which is rather long. It requires limited evidence of carcinogenic potential in humans and inadequate evidence in animals. This is the, “Probably should do more research just to be sure, but basically don’t worry about it,” category.

Who was Eleanor Adair, and what did she think about microwaves?

I have written about Eleanor Adair before in this blog. She was a leading expert on the interaction of microwaves with biological tissue, and was skeptical of any health hazards claims. A New York Times interview included this exchange:

Q. If I were to say to people, “Hey there’s this really cool idea: Why heat your whole house when you could use microwaves to heat yourself?” they would say: “You’ve got to be kidding. Don’t you know that microwaves are dangerous? They can even cause cancer.” What do you say to people who respond like that?

 A. I try to educate them in exactly what these fields are. That they are part of the full electromagnetic spectrum that goes all the way from the radio frequency and microwave bands, through infrared, ultraviolet, the gamma rays and all that.

And the difference between the ionizing X-ray, gamma ray region and the microwave frequency is in the quantum energy. The lower you get in frequency the lower you get in quantum energy and the less it can do to the cells in your body.

If you have a really high quantum energy such as your X-rays and ionizing-radiation region of the spectrum, this energy is high enough that it can bump electrons out of the orbit in your cells and it can create serious changes in the cells of your body such that they can turn into cancers and various other things that are not good for you.

But down where we are working, in the microwave band, you are millions of times lower in frequency and there the quantum energy is so low that they can’t do any damage to the cells whatsoever. And most people don’t realize this.

Somehow, something is missing in their basic science education, which is something I keep trying to push. Learn the spectrum. Learn that you’re in far worse shape if you lie out on the beach in the middle of summer and you soak up that ultraviolet radiation than you are if you use your cell phone.

Any new data about health effects of electromagnetic fields in the last few years?

A recent article examining the “Occupational Exposure to High-Frequency Electromagnetic Fields and Brain Tumor Risk in the INTEROCC Study: An Individualized Assessment Approach,” (Vila et al., 2018) provides the following highlights

• Evidence on health effects of long-term occupational exposure to high-frequency EMF remains weak

• Individualized cumulative occupational RF [radiofrequency, 10 MHz–300 GHz] and IF [intermediate frequency, 3 kHz–10 MHz] exposure indices were assigned to study subjects

• No clear associations with RF or IF EMF and glioma or meningioma risk were observed

• The possible role of RF magnetic fields on brain tumor promotion/progression should be further investigated.

As Bob Park said, everyone supports doing additional research (as do I). But I don’t see a lot to be worried about here.

Bill Curry concluded that 5G technology “is likely to be a serious health hazard.” Well?

I’ve written about physicist Bill Curry and his claims previously in this blog. That post begins

A recent article by William Broad in the New York Times—titled “The 5G Health Hazard That Isn’t”—tells the sad story of how unfounded fears of radiofrequency radiation were stoked by one mistaken scientist.

What is electromagnetic hypersensitivity?

Some people claim they’re extremely sensitive to weak electromagnetic fields. The SkepDoc Harriet Hall wrote a blog post titled “Myths About Electromagnetic Hypersensitivity and Multiple Chemical Sensitivity.” She begins

As if we didn’t have enough things to worry about already, now we are being told to fear our toasters. A typical headline trumpets “The Effects of Invisible Waves.” We are increasingly exposed to electromagnetic radiation from cell phones, cell phone towers, wireless Internet routers, cordless phones, and power lines. Other sources ... are our household appliances: TVs, hairdryers, light bulbs, and yes, your trusty toaster. These invisible villains are said to lead to a variety of symptoms, including poor sleep, fatigue, heart palpitations, headache, nausea, dizziness, memory impairment, prickling and burning sensations, along with skin rashes. They’ve even been blamed for depression, anxiety, colds, digestive disorders, and chronic pain. It’s called electromagnetic hypersensitivity or EHS.

Hall concludes

The symptoms described by “electromagnetic hypersensitivity” sufferers can be severe and are sometimes disabling. However, it has proved difficult to show under blind conditions that exposure to EMF can trigger these symptoms. This suggests that “electromagnetic hypersensitivity” is unrelated to the presence of EMF.

I recommend you read the entire article.

IPMB cited a point-counterpoint article that suggests cell phones are dangerous. True?

Point-counterpoint articles appear every month in the journal Medical Physics. They are a wonderful teaching tool, allowing students to consider and discuss questions at the cutting edge of medical physics. The one cited in Chapter 9 of IPMB is by Khurana, Moulder, and Orton (2008), titled “There is Currently Enough Evidence and Technology Available to Warrant Taking Immediate Steps to Reduce Exposure of Consumers to Cell-Phone-Related Electromagnetic Radiation.” Every point-counterpoint article pits one researcher against another, arguing opposing sides of the claim made in the article title. In this case, Vini Khurana supports the proposition, and John Moulder opposes it; Colin Orton is the moderator. I encourage you to read the article for yourself. I agree with Moulder’s conclusion that

weak epidemiological evidence of an association of mobile phone use with brain cancer incidence, when combined with the biophysical implausibility of a causal link and the strongly unsupportive animal studies, does not support the case that regulation of mobile phone use is urgently needed.

Last year I saw an article that says 5G cell phone radiation is unsafe! What’s up?

The Nation published an article titled “How Big Wireless Made Us Think That Cell Phones Are Safe: A Special Investigation. The Disinformation Campaign—and Massive Radiation Increase—Behind the 5G Rollout,” by Mark Hertsgaard and Mark Dowie. David Gorski published a critique of this article for the website Science-Based Medicine. He writes

The Nation indulges in fear mongering about cell phones and cancer An article published last week in The Nation likens wireless telephone companies to tobacco and fossil fuel episodes in their tactics of spreading fear, misinformation, and doubt regarding the science of cell phone radiation and health. To produce this narrative, the investigation’s authors rely on unreliable sources and cherry pick scientific studies, ignoring the scientific consensus that cell phone radiation almost certainly doesn’t cause cancer, all the while disingenuously claiming that they aren’t taking a position on the health effects of radio waves.

Read The Nation article and the critique and decide for yourself. At the least, you’ll learn how physics can be applied to medicine and biology.

What’s the bottom line regarding the risk of cancer from 5G cell phones?

Electromagnetic radiation consists of packets of energy called photons. The energy of a photon increases with the frequency of the radiation. Cancer is caused when DNA is damaged by very-high-frequency photons, such as x-rays (ionizing radiation). If the frequency is in the range of 300 GHz, the energy of a photon is far too small to disrupt bonds in DNA. It is, in fact, smaller than the energies associated with thermal motion of molecules. So, photons associated with 300 GHz radiation cannot cause cancer by damaging DNA. Of course, you could have a whole lot of 300 GHz photons, and they might pool their effort and together have enough energy to break bonds. We have a word for that: heat. 300 GHz radiation can heat tissue, but such heating is well understood and easily measured; Cell phone radiation is too weak to cause a significant temperature increase. So, we are left with no plausible mechanism for health risks from cell phone radiation. Perhaps some secondary effect could make your body less able to fight off cancer once it is induced by other mechanisms, but no one really knows how that might occur. Moreover, the epidemiological evidence suggests there is little risk. Cell phone use has increased dramatically since the turn of the century, but the incidence of brain cancer hasn’t increased. The National Cancer Institute says “The only consistently recognized biological effect of radiofrequency radiation in humans is heating... There are no other clearly established effects on the human body from radiofrequency radiation.” I wouldn’t say it’s impossible that cell phones put you at risk for cancer, but it’s unlikely. In my opinion, it’s exceedingly unlikely. We have many other things to worry about instead.

References

Foster KR, Moulder JE (2013) “Wi-Fi and Health: Review of Current Status of Research,” Health Physics, Volume 105, Pages 561-575.

Foster KR, Moulder JE (2018) “Response to Pall, ‘Wi-Fi is an Important Threat to Human Health’,” Environmental Research, Volume 445-447, Pages 445-447.

Khurana VG, Moulder JE, Orton CG (2008) “There is Currently Enough Evidence and Technology Available to Warrant Taking Immediate Steps to Reduce Exposure of Consumers to Cell-Phone-Related Electromagnetic Radiation,” Medical Physics, Volume 35, Pages 5203-5206.

Moulder JE, Foster KR, Erdreich LS, McNamee JP (2005) “Mobile Phones, Mobile Phone Base Stations and Cancer: A Review,” International Journal of Radiation Biology, Volume 81, Pages 189-203.

Pall ML (2018) “Wi-fi is an Important Threat to Human Health,” Environmental Research, Volume 164, Pages 405-416.

Sheppard AR, Swicord ML, Balzano Q (2008) “Quantitative evaluation of mechanisms of radiofrequency interactions with biological molecules and processes,” Health Physics, Volume 95, Pages 365-396.

Vecchia P, Matthes R, Ziegelberger G, Lin J, Saunders R, Swerdlow A (2009) “Exposure to High Frequency Electromagnetic Fields, Biological Effects and Health Consequences (100 kHz – 300 GHz),” Munich: International Commission on Non-ionizing Radiation Protection.

Vila, J, Turner MC, Gracia-Lavedan E, Figuerola J, Bowman JD, Kincl L, Richardson L, Benke G, Hours M, Krewski D, McLean D, Parent M-E, Sadetzki S, Schlaefer K, Schlehofer B, Schuz J, Siemiatycki J, Tongeren M, Cardis, E (2018) Occupational exposure to high-frequency electromagnetic fields and brain tumor risk in the INTEROCC study: An individualized assessment approach. Environment International, Volume 119, Pages 353-365.