The Eclipse

A total eclipse of the sun.

On August 21, I’ll be viewing the total eclipse from a location just north of Kansas City. I’ve never seen a total eclipse, and probably never will again (well, maybe in 2024). I have relatives in the Kansas City area, so I don’t have to fight for a hotel room (Thanks, sis!). I already bought my ten-pack of eclipse glasses. The last challenge is the weather: clouds could ruin the experience. Let’s hope for clear sky!

The internet has much information about how to view the eclipse safely. It is one of those topics where physics and medicine collide. In Chapter 14 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the eye and vision. I won’t nag you about all the safety precautions. You can learn about them here.

How intense is the light reaching the retina when you stare at the sun? The intensity of sunlight at the earth’s surface is about 1 kW/m², or 1 mW/mm². The radius of the pupil is about 1 mm, and its area is approximately 3 mm². Therefore, about 3 mW impinges on the retina. To calculate the size of the image spot, treat the eye as a lens (Fig. 14.39a in IPMB). The earth-sun distance is 1.5 × 10⁸ km, the sun radius is 7 × 10⁵ km, and the pupil-retina distance is about 22 mm, implying that the radius of the sun’s image on the retina is (22 mm)(7 × 10⁵)/(1.5 × 10⁸) = 0.1 mm, for an area of about 0.03 mm². The intensity on the retina is thus 3 mW/.03 mm², or 100 mW/mm². This intensity will do damage.

Incidentally, if a 0.5 mW HeNe laser beam is directed into the eye and is focused to a spot with a radius of 0.04 mm, the intensity will be about the same as staring at the sun. Therefore, be as careful when playing with lasers as you are when viewing the eclipse. Both can be unsafe if you are careless.

Path of the total eclipse of the sun
in August 2017.

The light from the sun is about one million times as intense as the light from a full moon. The light from the sun’s corona, visible during a total eclipse, is about as bright as the full moon. So, when the eclipse is 99.99%, the sun is still one hundred times as bright as the moon. It is only when the eclipse is total that you can gaze at it safely. That's why I’m not going to Lawrence, Kansas—home of my alma mater the University of Kansas—for the event; there the eclipse is only 99.3% complete. (Vanderbilt, where I obtained my doctorate, is in the path of totality; my PhD advisor John Wikswo can watch it from his back yard.) We will drive for an hour (perhaps more, if traffic is snarled) to where the eclipse is total.

If you want to learn more, I suggest the “Resource Letter OSE-1: Observing Solar Eclipses,” written Jay Pasachoff and Andrew Fraknoi, and published by my favorite journal: The American Journal of Physics (Volume 85, Pages 485–494, July, 2017).

Enjoy!

Machines In Our Hearts

Machines in Our Hearts:
The Cardiac Pacemaker, the Implantable
Defibrillator, and American Health Care,
by Kirk Jeffrey.

In Chapter 7 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss pacemakers and defibrillators. When introducing this topic, we cite Kirk Jeffrey’s book Machines in Our Hearts: The Cardiac Pacemaker, the Implantable Defibrillator, and American Health Care. The book not only gives a great introduction to these medical devices, but also examines the medical device industry. In his introduction, Jeffrey writes

This book gives an account of the invention of the cardiac pacemaker and the subsequent development and transformation of this machine….The pacemaker was born in 1952 as an appliance the size of a breadbox that stood on a hospital cart and plugged into a wall socket. As it grew, it shrank. Within a few years, medical researchers and engineers had transformed it into a little device that was completely implanted within the patient’s body with one component actually threaded down a vein into the heart’s interior. Today we have a number of implanted machines, such as defibrillators and nerve stimulators, that manage some physiological function, but the pacemaker was the very first of these. Surgeons carried out the earliest implants in human beings between 1958 and 1960.

Pacemakers (or pacers) in the 1990s are no larger than wristwatches with one or two leads instead of a wristband. In the early days of implantable pacers, the devices were thicker and heavier than an old pocket watch; people in fact sometimes called them “heart tickers.” But a pacemaker today can do far more than send little ticks of electricity to the heart. Most pacers implanted in the 1990s coordinate the pumping action of the upper and lower chambers (the atria and ventricles) and change their rate depending on the patient’s activity level. Some can intervene to slow down a dangerously fast heartbeat. We live in “the age of the smart machine”; this phrase certainly applies to the newer pacers, for they include microprocessors and have become, in effect, computers…Once implanted, a pacemaker can be reprogrammed, its behavior completely reconfigured. In the near future, these tiny machines may be smart enough to diagnose the patient’s heart-rhythm problems and choose how to respond by themselves, without the doctor’s needing to intervene at all….

This book shifts its focus midway from the physicians and engineers who invented cardiac pacing and created a technological community to the manufacturing firms that have the greatest degree of control over the technology today. The manufacturers supplemented research physicians as the prime directors of technological change during the 1970s. The upshot is that when it comes to cardiac pacing and defibrillation, doctors are in effect working in alliance with large corporations in determining how best to treat patients.

Anyone interested in working in the medical device industry in general, and in designing new pacemakers and defibrillators in particular, should read Machines in Our Hearts. It is a case study of how physics can be applied to medicine and biology.

Suki is Going Deaf

Suki Roth, in front of a copy of
Intermediate Physics for
Medicine and Biology.

Suki is going deaf. She has not lost all her hearing yet, but when I call her in a normal voice she does not respond. She used to jump up when she heard me get the leash for a walk, but now I have to show it to her. Before she was scared of thunderstorms, but lately she snoozes through all but the loudest rumbles. In the past she got excited when the garage door opened, but nowadays she ignores it. Suki will be 15 years old this October, so such problems are expected. Still, I’m sad to see her sink into silence.

I think my hearing is getting worse too, but slowly. My dad uses a hearing aid, and I take after him. I find myself asking “what did you say?” more often than other people do. I decided to test myself using the website http://www.animations.physics.unsw.edu.au/jw/hearing.html. Below I plot my hearing (red dots) as a function of frequency, and compare it with the normal hearing response of a young adult (solid curve) shown in Figure 13.7 of Intermediate Physics for Medicine and Biology. I normalized the two curves so they are equal at 1 kHz.

My hearing response curve.

My hearing appears normal except for an odd deficit around 3000-4000 Hz. Also, I may be missing some high frequencies, but the loss is not dramatic.

I didn’t follow the website’s instructions exactly. I plotted the lowest intensity tone that I could just hear. I don’t trust this test, performed on myself using a website; it is very subjective and the loudness changes in large 3 dB steps. (In case you do not have IPMB handy, Eq. 13.34 indicates that a ten-fold change in intensity corresponds to a step of 10 in decibels.) I would be interested in hearing (get it?....) if you have a similar result using this website.

Age-related hearing loss is called presbycusis. Wikipedia says it is the second most common illness in the elderly, after arthritis. Normally we lose the high frequencies as we age, which has implications for how teenagers choose ringtones.

On the above video, I could hear the 8 kHz ringtone but not the 12 kHz or higher ones. Can you? I am not sure if it is me, my computer, or the video.

I may be losing some hearing, but probably not much. (Perhaps I just don’t pay attention when my wife talks to me.) Suki, however, is in worse shape. She is the world’s best pet, and I intend to give her extra treats to make up for her lack of hearing.

Do I Make Myself Clear?

Do I Make Myself Clear?
by Harold Evans.

I enjoy reading books about writing. Recently I read Do I Make Myself Clear? Why Writing Well Matters by Harold Evans. One of Evans’s pet peeves is “unnoticed redundancies, such as complete monopoly and awkward predicament, that do not add to the sense of the message.” He provides over 250 examples, with instructions to “strike out the words in italics.”

Of course, I became curious how Intermediate Physics for Medicine and Biology fared with these redundancies. So I hunted for them using the search box in my pdf version of IPMB. Most were absent, but a few appeared. I’m not sure they are always bad; you can decide for yourself. I enjoy doing this sort of thing, but is it fair to subject my dear readers to this analysis? I believe that writing well is critical for scientists; if pointing out some sloppy writing in IPMB can help others tighten their prose, the effort is worthwhile.

all of

Russ Hobbie and I occasionally include the unnecessary “of,” such as on page 59, “all of the external parameters,” which would sound tighter with no loss of meaning as “all the external parameters.”

a distance of

Evans puts the whole phrase in italics, which must mean he thinks it is unnecessary. Our text would probably be better by deleting “a distance of” from the homework problem on page 497: “Use the appropriate values for striated muscle to estimate the dose to the gonads if they are at a distance of 50 cm from the x-ray tube."

a number of examples

While Russ and I don’t use “a number of” with the word “examples,” we often write “a number of.” Sometimes we mean “several,” which I think is OK (although it sounds slightly pompous). My guess is that Evans is concerned primarily with cases when “a number of” could be deleted with no loss of meaning. I found a few examples in IPMB, such as on page 489, “irradiating the patient through a number of absorbers of different thickness spreads out the region of maximum dose” (and should it be “thicknesses”?), and especially page 514, “A number of more complicated situations are solved by Loevinger et al.”

a period of

I suspect that Evans is irritated by authors who write “a period of time,” which Russ and I never do. Sometimes we use “a period of” in the mathematical sense of the repeat time of a periodic function, such as on page 342: “If you are told that there is a signal in these data with a period of 4 s, you can group them together and average them.” No change is needed there. On the other hand, this text from page 39 is a borderline case: “figure 2.10 shows the survival of patients with congestive heart failure for a period of 9 years.” To me our prose sounds fine; I’m not sure what Evans would say.

appear to be

I admit, we occasionally have the unneeded “to be” after “appear,” such as on page 178 “does the charge distribution appear to be continuous or discrete?” and page 297 “do the results appear to be chaotic?” I write mainly be ear, and my ear isn’t bothered by “appear to be.” I am left wondering: “to be,” or not “to be,” that is the question.

as yet

On page 134 we write “There is evidence that some as yet unidentified toxin of medium molecular weight accumulates in the blood.” Yes, I concede the sentence would sound better if we delete the “as.”

close proximity

I agree with Evans that the “close” is bothersome. Russ and I never include a “close” with our “proximity,” except once on page 483 when we had no choice, it was inside a quote: “The bystander effect in radiobiology refers to the ‘induction of biological effects in cells that are not directly traversed by a charged particle, but are in close proximity to cells that are.’”

completely untrue

I think Evans’s point is that a statement can be either true or untrue, with no intermediate case, so completely is redundant. I’m not sure science is so black and white. Sometimes you can have an approximation that is very accurate, but technically untrue (Newtonian mechanics is almost true for speeds much less than the speed of light, but not completely true). Perhaps a better example is the cliché “completely pregnant.”

We have a lot of “completely”s in IPMB, most of which I am comfortable with. One questionable case appears on page 125: “if a solute is present to which the membrane is completely impermeable...” At first the completely sounds unneeded—a membrane is either permeable or it is not—but we had just introduced the hydraulic permeability, a parameter that can be very small without being zero. Saying “completely impermeable” is probably fine when we mean the limit as the hydraulic permeability goes to zero. I side with Evans that completely is unnecessary on page 88 “this differential form of the continuity equation is completely equivalent to the integral form,” and on page 279 “Jules Henri Poincaré realized around 1900 that systems described exactly by the completely deterministic equations of Newton’s laws could exhibit wild behavior.

depreciated in value

Although we don’t use “depreciated,” this wordy sentence from page 33 would be improved by deleting “in value”: “if the interest rate is 5% and if the interest is credited to the account once a year, the account increases in value by 5% of its present value each year.”

divide up

Russ and I sin only once, on page 144: “Divide up any closed surface into elements of surface area...”

end up

You tell me if this sentence form page 510 sounds better without the “up”; my ear can’t decide: “When a radiopharmaceutical is given to a patient for either diagnosis or therapy, the nuclei end up in different organs in varying amounts.”

have got

Sometimes Evans is like the Lorax: correct but annoying. I suppose this sentence from page 607 should not have the “gotten,” but the change seems so picky: “This is the same answer we would have gotten if h had been regarded as a constant.”

it is interesting to note that

We never use this exact phrase, but on page 248 “it is interesting to compare this to Eq. 9.38” would sound better as the command “compare this to Eq. 9.38.” I probably would not change page 11: “it is interesting to read what an orthopedic surgeon had to say about the use of a cane.”

past history

I hadn’t really thought about this redundancy until Evans pointed it out. He is right that “past history” is redundant, and I would change several such cases in IPMB, including page 57, “it is independent of the past history of the system and is specified by a few macroscopic parameters.”

Do I Make Myself Clear? is a fine book, although in my opinion it is not as good as Zinsser’s On Writing Well. Scientists are judged by their journal papers and grant proposals, both written documents. You need to write well, or your reputation will suffer. Eliminating minor redundancies is one way to make your writing clearer and more concise. Train your ear to listen for them.

Nerve, Muscle, and Synapse

Nerve, Muscle, and Synapse,
by Bernard Katz.

In Intermediate Physics for Medicine and Biology, Russ Hobbie ad I include a footnote at the start of Chapter 6:

A good discussion of the properties of nerves and the Hodgkin–Huxley experiments is found in Katz (1966).

Why do we cite a book that is over 50 years old? One reason is nostalgia. In 1982 I graduated from the University of Kansas with a physics major and entered graduate school at Vanderbilt. I began working with John Wikswo, who was measuring the magnetic field produced by a nerve axon, so I had to learn quickly how nerves work. One of the first books I read was Nerve, Muscle and Synapse. What a lucky choice.

The author, Bernard Katz, led an interesting and productive life. Because of his Jewish background, in 1935 he fled Germany for England. There he worked with physiologist Archibald Hill (Katz dedicates Nerve, Muscle, and Synapse “to my friend and teacher, A. V. Hill”). He collaborated with Alan Hodgkin, and was a coauthor on one of the five famous papers from 1952 that established the Hodgkin and Huxley model (see Chapter 6 of IPMB for more on this model). He also published a paper with Hodgkin about electric current flowing through a membrane, leading to the Goldman-Hodgkin-Katz equation discussed in Sec. 9.6 of IPMB (Goldman derived this equation independently of Hodgkin and Katz).

Katz won his Nobel Prize for discovering the discrete nature of acetylcholine release at the nerve-muscle synapse, which explains the book’s title. I was glancing through his Chapter 9 on the Quantal Nature of Chemical Transmission when I saw an example analyzed using Poisson statistics and I thought to myself “Hey, that looks familiar.” His example uses the same data that Russ and I present in our Appendix J about the Poisson Distribution. We had a common source: IPMB and Katz both cite work by Boyd and Martin.

One reason I like Nerve, Muscle and Synapse is that it contains a lot of physics. In his foreword, George Wald writes

Professor Katz has produced here the elementary text we asked of him, but also much more. He goes far beyond the first essentials to develop the subject in depth. He has the gift of a graphic style and the apt phrase. What impresses me particularly is that each idea is pursued to the numerical level. Each theoretical development comes out in this form, in clearly stated problems worked through with the relevant numbers. But the treatment as a whole extends beyond this also, asking and answering the basic questions that few workers in electrophysiology probably have taken the trouble to pursue so far. All this is done with an easy mastery of the underlying physics and physical chemistry.

That’s high praise. Russ and I take a similar approach in IPMB, pursuing topics to the numerical level (sometimes in the text, and sometimes in the homework). Nerve, Muscle, and Synapse shares another trait with IPMB: it uses calculus without apology.

If you are looking for the most up-to-date textbook on nerve electrophysiology, you should search for a more recent publication (perhaps the latest edition of From Neuron to Brain). But, if you’re a physicist trying to learn something about how nerves work, Katz’s book remains a useful introduction. That’s why Russ and I still cite it.