Happy Birthday Laser!

Quantum Physics of Atoms,
Molecules, Solids, Nuclei, and Particles,
by Eisberg and Resnick.

This month marks the 50^th anniversary of the invention of the laser. In May 1960, Theodore Maiman built the first device to produce coherent light by the mechanism of “Light Amplification by Stimulated Emission of Radiation” at Hughes Research Laboratories in Malibu, making the laser just slightly older than I am. A special website, called laserfest, is commemorating this landmark event. Eisberg and Resnick discuss lasers in Section 11.7 of their textbook Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (quoted from the first edition, 1974).

In the solid state laser that operates with a ruby crystal, some Al atoms in the Al₂O₃ molecules are replaced by Cr atoms. These “impurity” chromium atoms account for the laser action… The level of energy E1 is the ground state and the level of energy E3 is the unstable upper state with a short lifetime (≈10⁻⁸ sec), the energy difference E3-E1 corresponding to a wavelength of about 5500 Å. Level E2 is an intermediate excited state which is metastable, its lifetime against spontaneous decay being about 3 x 10⁻³ sec. If the chromium atoms are in thermal equilibrium, the population number of the states are such that [n3 is less than n2 is less than n1]. By pumping in radiation of wavelength 5500 Å, however, we stimulate absorption of incoming photons by Cr atoms in the ground state, thereby raising the population number of energy state E3 and depleting energy state E1 of occupants. Spontaneous emission, bringing atoms from state 3 to state 2, then enhances the occupancy of state 2, which is relatively long-lived. The result of this optical pumping is to decrease n1 and increase n2, such that n2 is greater than n1 and population inversion exists. Now, when an atom does make a transition from state 2 to state 1, the emitted photon of wavelength 6943 Å will stimulate further transitions. Stimulated emission will dominate stimulated absorption (because n2 is greater than n1) and the output of photons of wavelength 6943 Å is much enhanced. We obtain an intensified coherent monochromatic beam.

Lasers are an important tool in biology and medicine. Russ Hobbie and I discuss their applications in Chapter 14 (Atoms and Light) the 4th edition of Intermediate Physics for Medicine and Biology. In Section 14.5 (The Diffusion Approximation to Photon Transport) we write

A technique made possible by ultrashort light pulses from a laser is time-dependent diffusion. It allows determination of both μ_s and μ_a [the scattering and absorption attenuation coefficients]. A very short (150-ps) pulse of light strikes a small region on the surface of the tissue. A detector placed on the surface about 4 cm away records the multiply-scattered photons… A related technique is to apply a continuous laser beam, the amplitude for which is modulated at various frequencies between 50 and 800 MHz. The Fourier transform of Eq. 14.29 gives the change in amplitude and phase of the detected signal. Their variation with frequency can also be used to determine μ_a and μ_s.

We also mention lasers in Section 14.10 (Heating Tissue with Light).

Sometimes tissue is irradiated in order to heat it; in other cases tissue heating is an undesired side effect of irradiation. In either case, we need to understand how the temperature changes result from the irradiation. Examples of intentional heating are hyperthermia (heating of tissue as a part of cancer therapy) or laser surgery (tissue ablation). Tissue is ablated when sufficient energy is deposited to vaporize the tissue.

Russ and I give many references about lasers in medicine in our Resource Letter (“Resource Letter MP-2: Medical Physics,” American Journal of Physics, Volume 77, Pages 967–978, 2009):

F. Lasers and optics

Lasers have introduced many medical applications of light, from infrared to the visible spectrum to ultraviolet.

150. Lasers in Medicine, edited by R. W. Waynant (CRC, Boca Raton, 2002). (I)

151. Laser-Tissue Interactions: Fundamentals and Applications, M. H. Niemz (Springer, Berlin, 2007). (I)

152. “Lasers in medicine,” Q. Peng, A. Juzeniene, J. Chen, L. O. Svaasand, T. Warloe, K.-E. Giercksky, and J. Moan, Rep. Prog. Phys. 71, Article 056701, 28 pages
(2008). (A)

A fascinating and fast-growing new technique to image biological tissue is optical coherence tomography “OCT.” It uses reflections like ultrasound but detects the reflected rays using interferometry.

153. Optical Coherence Tomography, M. E. Brezinski (Elsevier, Amsterdam, 2006). Overview of the physics of OCT and applications to cardiovascular medicine, musculoskeletal disease, and oncology. (I)

154. “Optical coherence tomography: Principles and applications,” A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239–303 (2003). (I)

With infrared light, scattering dominates over absorption. In this case, light diffuses through the tissue. Optical imaging in turbid media is difficult but not impossible.

155. “Recent advances in diffuse optical imaging,” A. P. Gibson, J. C. Hebden, and S. R. Arridge, Phys. Med. Biol. 50, R1–R43 (2005). (I)

156. “Pulse oximetry,” R. C. N. McMorrow and M. G. Mythen, Current Opinion in Critical Care 12, 269–271 (2006). The pulse oximeter measures the oxygenation of blood and is based on the diffusion of infrared light. (I)

One impetus for medical applications of light has been the development of new light sources, such as free-electron lasers and synchrotrons. In both cases, the light frequency is tunable over a wide range.

157. “Free-electron-laser-based biophysical and biomedical instrumentation,” G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, Rev. Sci. Instrum. 74, 3207–3245 (2003). (I)

158. “Medical applications of synchrotron radiation,” P. Suortti and W. Thomlinson, Phys. Med. Biol. 48, R1– R35 (2003). (I)

Finally, photodynamic therapy uses light-activated drugs to treat diseases.

159. “The physics, biophysics and technology of photodynamic therapy,” B. C. Wilson and M. S. Patterson, Phys. Med. Biol. 53, R61–R109 (2008). (A)

Happy birthday, laser!

The Bragg Peak

In Chapter 16 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the Bragg peak.

Protons are also used to treat tumors (Khan 2010, Ch. 26; Goitein 2008). Their advantage is the increase of stopping power at low energies. It is possible to make them come to rest in the tissue to be destroyed, with an enhanced dose relative to intervening tissue and almost no dose distally (“downstream”) as shown by the Bragg peak in Fig.16.47.

Energy loss versus depth for a 150 MeV proton beam in water, with and without straggling (fluctuations in the range). The Bragg peak enhances the energy deposition at the end of the proton range. Adapted from Fig. 16.47 in Intermediate Physics for Medicine and Biology.

William Henry Bragg

Sir William Henry Bragg (1862 – 1942) was an English scientist who shared the 1915 Nobel Prize in Physics with his son Lawrence Bragg for their analysis of crystal structure using X-rays. In 2004, Andrew Brown and Herman Suit published an article commemorating “The Centenary of the Discovery of the Bragg Peak” (Radiotherapy and Oncology, Volume 73, Pages 265-268).

In December 1904, William Henry Bragg, Professor of Mathematics and Physics at the University of Adelaide and his assistant Richard Kleeman published in the Philosophical Magazine (London) novel observations on radioactivity. Their paper “On the ionization of curves of radium,” gave measurements of the ionization produced in air by alpha particles, at varying distances from a very thin source of radium salt. The recorded ionization curves “brought to light a fact, which we believe to have been hitherto unobserved. It is, that the alpha particle is a more efficient ionizer towards the extreme end of its course.” This was promptly followed by further results in the Philosophical Magazine in 1905. Their finding was contrary to the accepted wisdom of the day, viz. that the ionizations produced by alpha particles decrease exponentially with range. From theoretical considerations, they concluded that an alpha particle possesses a definite range in air, determined by its initial energy and produces increasing ionization density near the end of its range due to its diminishing speed.

Although Bragg discovered the Bragg peak for alpha particles, the same behavior is found for other heavy charged particles such as protons. It is the key concept underlying the development of proton therapy. Brown and Suit conclude

The first patient treatment by charged particle therapy occurred within a decade of Wilson’s paper [the first use of protons in therapy, published in 1946]. Since then, the radiation oncology community has been evaluating various particle beams for clinical use. By December 2004, a century after Bragg’s original publication, the approximate number of patients treated by proton–neon beams is 47,000 (Personal communication, Janet Sisterson, Editor, Particles) [over 170,000 today]. There have been several clear clinical gains. None of these would have been possible, were it not for the demonstration that radically different depth dose curves were feasible.

Welcome Home Scott Kelly

Scott Kelly, when he returned to earth
after a year on the space station.

This week astronaut Scott Kelly returned to Earth after nearly a year on the International Space Station. One goal of his mission was to determine how astronauts would function during long trips in space. I suspect we will learn a lot from Kelly about life in a weightless environment. But one of the biggest risks during a mission to Mars would be radiation exposure, and we may not learn much about that from trips to the space station.

In space, the major source of radiation is cosmic rays, consisting mostly of high energy (GeV) protons. Most of these particles are absorbed by our atmosphere and never reach Earth, or are deflected by Earth’s magnetic field. The space station orbits above the atmosphere but within range of the geomagnetic field, so Kelly was partially shielded from cosmic rays. He probably experienced a dose of about 150 mSv. This is much larger than the annual background dose on the surface of the earth. According to Chapter 16 of Intermediate Physics for Medicine and Biology, we all are exposed to about 3 mSv per year.

Scott and Mark Kelly.

Is 150 mSv in one year dangerous? This dose is below the threshold for acute radiation sickness. It would, however, increase your chances of developing cancer. A rule of thumb is that the excess relative risk of cancer is about 5% per Sv. This does not mean Kelly has a 0.75% chance of getting cancer (5%/Sv times 0.15 Sv). Instead, it means that Scott Kelly has a 0.75% higher chance of getting cancer than his brother Mark Kelly, who remained on Earth. This is a significant increase in risk, but may be acceptable if your goal in life is to be an astronaut. The Kelly twins are both 52 years old, and the excess relative risk goes down with age, so the extra risk of Scott Kelly contracting cancer is probably less than 0.5%.

NASA’s goal is to send astronauts to Mars. Such a mission would require venturing beyond the range of Earth’s geomagnetic field, increasing the exposure to cosmic rays. Data obtained by the Mars rover Curiosity indicate that a one-year interplanetary trip would result in an exposure of 660 mSv. This would be four times Kelly's exposure in the space station. 660 mSv would be unlikely to cause serious acute radiation sickness, but would increase the cancer risk. NASA would have to either shield the astronauts from cosmic rays (not easy given their high energy) or accept the increased risk. I’m guessing they will accept the risk.

The Story of the World in 100 Species

The Story of the World
in 100 Species,
by Christopher Lloyd.

I recently finished reading The Story of the World in 100 Species. The author Christopher Lloyd writes in the introduction

This book is a jargon-free attempt to explain the phenomenon we call life on Earth. It traces the history of life from the dawn of evolution to the present day through the lens of one hundred living things that have changed the world. Unlike Charles Darwin’s theory published more than 150 years ago, it is not chiefly concerned with the “origin of species,” but with the influence and impacts that living things have had on the path of evolution, on each other and on our mutual environment, planet Earth.

Of course, I began to wonder how many of the top hundred species Russ Hobbie and I mention in Intermediate Physics for Medicine and Biology. Lloyd lists the species in order of impact. The number 1 species is the earthworm. As Darwin understood, you would have little agriculture without worms churning the soil. The highest ranking species that was mentioned in IPMB is number 2, algae, which produces much of the oxygen in our atmosphere. According to Lloyd, algae might provide the food (ick!) and fuel we need in the future.

Number 6 is ourselves: humans. Although the species name Homo sapiens never appears in IPMB, several chapters—those dealing with medicine—discuss us. Number 8 yeast (specifically, S. cerevisiae) is not in IPMB, although it is mentioned previously in this blog. Number 15 is the fruit fly Drosophila melanogaster, which made the list primarily because it is an important model species for research. IPMB mentions D. melanogaster when discussing ion channels.

Cows are number 17; a homework problem in IPMB contains the phrase “consider a spherical cow.” The flea is number 18, and is influential primarily for spreading diseases such as the Black Death. In IPMB, we analyze how fleas survive high accelerations. Wheat reaches number 19 and is one of several grains on the list. In Chapter 11, Russ and I write: “Examples of pairs of variables that may be correlated are wheat price and rainfall, ….” I guess that wheat is in IPMB, although the appearance is fairly trivial. Like yeast, number 20 C. elegans, a type of roundworm, is never mentioned in IPMB but does appear previously in this blog because it is such a useful model. I am not sure if number 21, the oak tree, is in IPMB. My electronic pdf of the book has my email address, roth@oakland.edu, as a watermark at the bottom of every page. Oak is not in the appendix, and I am pretty sure Russ and I never mention it, but I haven’t the stamina to search the entire pdf, clicking on each page. I will assume oak does not appear.

Number 24, grass, gets a passing mention: in a homework problem about predator-prey models, we write that “rabbits eat grass…foxes eat only rabbits.” When I searched the book for number 25 ant, I found constant, quantum, implant, elephant, radiant, etc. I gave up after examining just a few pages. Let’s say no for ant. Number 28 rabbit is in that predator-prey problem. Number 32 rat is in my favorite J. B. S. Haldane quote “You can drop a mouse down a thousand-yard mine shaft; and arriving at the bottom, it gets a slight shock and walks away. A rat is killed, and man is broken, a horse splashes.” Number 33 bee is in the sentence “Bees, pigeons, and fish contain magnetic particles,” and number 38 shark is in the sentence “It is possible that the Lorentz force law allows marine sharks, skates, and rays to orient in a magnetic field.” My favorite species, number 42 dog, appears many times. I found number 44 elephant when searching for ant. I am not sure about number 46 cat (complicated, scattering, indicate, cathode, … you search the dadgum pdf!). It doesn’t matter; I am a dog person and don’t care for cats.

Number 53 apple; IPMB suggests watching Russ Hobbie in a video about the program MacDose at the website https://itunes.apple.com/us/itunes-u/photon-interactions-simulation/id448438300?mt=10. No way am I counting that; you gotta draw the line somewhere. Number 58 horse; “…horse splashes…”. Number 59 sperm whale; we mention whales several times, but don’t specify the species—I’m counting it. Number 61 chicken appears in one of my favorite homework problems: “compare the mass and metabolic requirements…of 180 people…with 12,600 chickens…” Number 65 red fox; see predator-prey problem. Number 67 tobacco; IPMB mentions it several times. Number 71 tea; I doubt it but am not sure (instead, steady, steam, ….). Number 77 HIV; see Fig. 1.2. Number 85 coffee; see footnote 7, page 258.

Altogether, IPMB includes twenty of the hundred species (algea, human, fruit fly, cow, flea, wheat, grass, rabbit, rat, bee, shark, dog, elephant, horse, whale, chicken, fox, tobacco, HIV, coffee), which is not as many as I expected. We will have to put more into the 6th edition (top candidates: number 9 influenza, number 10 penicillium, number 14 mosquito, number 26 sheep, number 35 maize aka corn).

Were any important species missing from Lloyd’s list? He includes some well-known model organisms (S. cerevisiae, D. melanogaster, C. elegans) but inexplicably leaves out the bacterium E. coli (Fig. 1.1 in IPMB). Also, I am a bioelectricity guy, so I would include Hodgkin and Huxley’s squid with its giant axon. Otherwise, I think Lloyd’s list is pretty complete.

If you want to get a unique perspective on human history, learn some biology, and better appreciate evolution, I recommend The Story of the World in 100 Species.

Tests for Human Perception of 60 Hz Moderate Strength Magnetic Fields

The first page of “Tests for Human Perception
of 60 Hz Moderate Strength Magnetic Fields,”
by Tucker and Schmitt (IEEE Trans. Biomed. Eng.
25:509-518, 1978).

In Chapter 9 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss possible effects of weak external electric and magnetic fields on the body. In a footnote, we write

Foster (1996) reviewed many of the laboratory studies and described cases where subtle cues meant the observers were not making truly “blind” observations. Though not directly relevant to the issue under discussion here, a classic study by Tucker and Schmitt (1978) at the University of Minnesota is worth noting. They were seeking to detect possible human perception of 60-Hz magnetic fields. There appeared to be an effect. For 5 years they kept providing better and better isolation of the subject from subtle auditory clues. With their final isolation chamber, none of the 200 subjects could reliably perceive whether the field was on or off. Had they been less thorough and persistent, they would have reported a positive effect that does not exist.

In this blog, I like to revisit articles that we cite in IPMB.

Robert Tucker and Otto Schmitt (1978) “Tests for Human Perception of 60 Hz Moderate Strength Magnetic Fields.” IEEE Transactions on Biomedical Engineering, Volume 25, Pages 509-518.

The abstract of their paper states

After preliminary experiments that pointed out the extreme cleverness with which perceptive individuals unintentionally used subtle auxiliary clues to develop impressive records of apparent magnetic field detection, we developed a heavy, tightly sealed subject chamber to provide extreme isolation against such false detection. A large number of individuals were tested in this isolation system with computer randomized sequences of 150 trials to determine whether they could detect when they were, and when they were not, in a moderate (7.5-15 gauss rms) alternating magnetic field, or could learn to detect such fields by biofeedback training. In a total of over 30,000 trials on more than 200 persons, no significantly perceptive individuals were found, and the group performance was compatible, at the 0.5 probability level, with the hypothesis that no real perception occurred.

The Tucker-Schmitt study illustrates how observing small effects can be a challenge. Their lesson is valuable, because many weak-field experiments are subject to systematic errors that provide an illusion of a positive result. Near the start of their article, Tucker and Schmitt write

We quickly learned that some individuals are incredibly skillful at sensing auxiliary non-magnetic clues, such as coil hum associated with field, so that some “super perceivers” were found who seemed to sense the fields with a statistical probability as much as 10^–30 against happening by chance. A vigorous campaign had then to be launched technically to prevent the subject from sensing “false” clues while leaving him completely free to exert any real magnetic perceptiveness he might have.

Few authors are as forthright as Tucker and Schmitt when recounting early, unsuccessful experiments. Yet, their tale shows how experimental scientists work.

Early experiments, in which an operator visible to the test subject controlled manually, according to a random number table, whether a field was to be applied or not, alerted us to the necessity for careful isolation of the test subject from unintentional clues from which he could consciously, or subconsciously, deduce the state of coil excitation. No poker face is good enough to hide, statistically, knowledge of a true answer, and even such feeble clues as changes in building light, hums, vibrations and relay clatter are converted into low but significant statistical biases.

IPMB doesn’t teach experimental methods, but all scientists must understand the difference between systematic and random errors. Uncertainty from random errors is suppressed by taking additional data, but eliminating systematic errors may require you to redesign your experiment.

In a first round of efforts to prevent utilization of such clues, the control was moved to a remote room and soon given over to a small computer. A “fake” air-core coil system, remotely located but matched in current drain and phase angle to the real large coil system was introduced as a load in the no-field cases. An acoustically padded cabinet was introduced to house the experimental subject, to isolate him from sound and vibration. Efforts were also made to silence the coils by clamping them every few centimeters with plastic ties and by supporting them on air pocket packing material. We tried using masking sound and vibrations, but soon realized that this might also mask real perception of magnetic fields.

Designing experiments is fun; you get to build stuff in a machine shop! I imagine Tucker and Schmitt didn’t expect they would have this much fun. Their initial efforts being insufficient, they constructed an elaborate cabinet to perform their experiments in.

This cabinet was fabricated with four layers of 2 in plywood, full contact epoxy glued and surface coated into a monolithic structure with interleaved corners and fillet corner reinforcement to make a very rigid heavy structure weighing, in total, about 300 kg. The structure was made without ferrous metal fastening and only a few slender brass screws were used. The door was of similar epoxyed 4-ply construction but faced with a thin bonded melamine plastic sheet. The door was hung on two multi-tongue bakelite hinges with thin brass pins. The door seals against a thin, closed-cell foam-rubber gasket, and is pressure sealed with over a metric ton of force by pumping a mild vacuum inside the chamber of means of a remote acoustically silenced hose-connected large vacuum-cleaner blower. The subject received fresh air through a small acoustic filter inlet leak that also assures sufficient air flow to cool the blower. The chosen “cabin altitude” at about 2500 ft above ambient presented no serious health hazard and was fail-safe protected.

An experimental scientist must be persistent. I remember learning that lesson as a graduate student when I tried for weeks to measure the magnetic field of a single nerve axon. I scrutinized every part of the experiment and fixed every problem I could find, but I still couldn’t measure an action current. Finally, I realized the coaxial cable connecting the nerve to the stimulator was defective. It was a rookie mistake, but I was tenacious and ultimately figured it out. Tucker and Schmitt personify tenacity.

As still more isolation seemed necessary to guarantee practically complete exclusion of auxiliary acoustic and mechanical clues, an extreme effort was made to improve, even further, the already good isolation. The cabinet was now hung by aircraft “Bungee” shock cord running through the ceiling to roof timbers. The cabinet was prevented from swinging as a pendulum by four small non-load-bearing lightly inflated automotive type inner tubes placed between the floor and the cabinet base. Coils already compliantly mounted to isolate intercoil force vibration were very firmly reclamped to discourage intracoil “buzzing.” The cabinet was draped inside with sound absorbing material and the chair for the subject shock-mounted with respect to the cabinet floor. The final experiments, in which minimal perception was found, were done with this system.

Once Tucker and Schmitt heroically eliminated even the most subtle cues about the presence of a magnetic field, subjects could no longer detect whether or not a magnetic field was present. People can’t perceive 60-Hz, 0.0015-T magnetic fields.

Russ and I relegate this tale to a footnote, but it’s an important lesson when analyzing the effects of weak electric and magnetic fields. Small systematic errors abound in these experiments, both when studying humans and when recording from cells in a dish. Experimentalists must ruthlessly design controls that can compensate for or eliminate confounding effects. The better the experimentalist, the more doggedly they root out systematic errors. One reason the literature on the biological effects of weak fields is so mixed may be that few experimentalists take the time to eradicate all sources of error.

Tucker and Schmitt’s experiment is a lesson for us all.

Maxwell Equation Sesquicentennial

A Treatise on
Electricity and Magnetism,
by James Clerk Maxwell.

I am a big James Clerk Maxwell fan. In fact, I have made my living applying Maxwell’s equations to biology and medicine. Yes, I own one of those tee shirts with Maxwell’s equations written on it. I keep a copy of Maxwell’s A Treatise on Electricity and Magnetism in my office (although I have never read it in its entirety…Oh how I wish Maxwell had access to modern vector notation!). I have read The Maxwellians (outstanding) and The Man Who Changed Everything: The Life of James Clerk Maxwell (good). So, this month I am celebrating with gusto the sesquicentennial of the publication of Maxwell’s famous equations. The March 17 issue of the journal Nature has a special section containing four articles about Maxwell’s equation. In an editorial titled “A Bold Unifying Leap” (Volume 471, Page 265) the editor writes

In this issue we celebrate the first expression of those equations by Scottish physicist Maxwell in the Philosophical Magazine 150 years ago. There he drew together several strands of understanding about the behaviour of electricity, of magnetism, of light, and of the ways in which these fundamental aspects of nature behave in matter. As Albert Einstein remarked, “so bold was the leap” of this work that it took decades for physicists to grasp its full significance. And although it was a wonderful expression of science at its purest, it was forged in the thoroughly practical culture of intellects at that time.

Russ Hobbie and I mention Maxwell’s equations in the 4th edition of Intermediate Physics for Medicine and Biology. We added a new homework problem to the 4th edition in Chapter 8 (Biomagnetism).

Problem 22 Write down in differential form (a) the Faraday induction law, (b) Ampere’s law including the displacement current term, (c) Gauss’s law, and (d) Eq. 8.7. … These four equations together constitute “Maxwell’s equations.” Together with the Lorentz force law (Eq. 8.2), Maxwell’s equations summarize all of electricity and magnetism.

All four of Maxwell’s equations are discussed in our book. Section 6.3 is dedicated to Gauss’s law, governing the electric field produced by a collection of charges, and we analyze the usual suspects: a line of charge and a charged sheet. Ampere’s law appears in Section 8.2 (The Magnetic Field of a Moving Charge or Current), and—in one of my favorite homework problems—we show in Problem 13 of Chapter 8 how “one can obtain a very different physical picture of the source of a magnetic field using the Biot Savart law than one gets using Ampere’s law, even though the field is the same.” Faraday’s law is presented in Section 8.6 on Electromagnetic Induction, followed by a discussion of magnetic stimulation of the brain. Even Gauss’s law for a magnetic field (Eq. 8.7, stating that the magnetic field has no divergence) is introduced. Maxwell’s great insight was to add the displacement current term to Ampere’s law. We show how the charging of a capacitor implies the existence of this additional term on page 207, and explore its role in biomagnetism (slight).

The Feynman Lectures on Physics,
by Richard Feynman.

Russ and I never analyze what may be the greatest prediction of Maxwell’s equations: the wave nature of light. We state in Section 14.1 that “the velocity of light traveling in a vacuum is given by electromagnetic theory as c = 1/√(ε₀ μ₀)”, but we never derive this result from Maxwell’s equations. Many of the applications of electromagnetic waves—such as wave guides, antennas, diffraction, radiation, and all of optics—are barely mentioned, if mentioned at all, in our text. For those who want to learn these topics (and all students of physics should want to learn these topics), I suggest Griffith’s Introduction to Electrodynamics (undergraduate) or Jackson’s Classical Electrodynamics (graduate). Richard Feynman introduces Maxwell’s equations in his celebrated book The Feynman Lectures on Physics. In Chapter 18 of Volume 2, he writes

It was not customary in Maxwell’s time to think in terms of abstract fields. Maxwell discussed his ideas in terms of a model in which the vacuum was like an elastic solid. He also tried to explain the meaning of his new equation in terms of the mechanical model. There was much reluctance to accept his theory, first because of the model, and second because there was at first no experimental justification. Today, we understand better that what counts are the equations themselves and not the model used to get them. We may only question whether the equations are true or false. This is answered by doing experiments, and untold numbers of experiments have confirmed Maxwell’s equations. If we take away the scaffolding he used to build it, we find that Maxwell’s beautiful edifice stands on its own. He brought together all of the laws of electricity and magnetism and made one complete and beautiful theory.

Anyone with a historical bent may want to read Maxwell’s original papers and accompanying commentary in Maxwell on the Electromagnetic Field: a Guided Study, by Thomas Simpson. The book contains a detailed analysis of Maxwell’s papers, including “On the Physical Lines of Force,” which is the publication we celebrate this month. Simpson’s book is the best place I know of to learn about the “scaffolding” Maxwell used to build his theory.

I will close with one of my favorite quotes, again from The Feynman Lectures. At the end of his first chapter introducing electromagnetism, Feynman writes

From a long view of the history of mankind—seen from, say, ten thousand years from now—there can be little doubt that the most significant event of the 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade.

Facebook

The Intermediate Physics for Medicine and Biology Facebook Group has now reached 150 members.

Yes, IPMB has a Facebook group. I use it to circulate blog posts every Friday morning, but I occasionally share other posts of interest to readers of IPMB. The group photo is my Ideal Bookshelf picture highlighting books about physics applied to medicine and biology.

Group members include my family (including my dog Suki Roth, who has her own Facebook Page) and former students. But members I don’t know come from countries all over the world, including:

• Bangladesh
• Brazil 
• Ecuador
• Egypt 
• France
• Ghana
• Greece
• Guyana
• India 
• Iraq
• Israel
• Jordan
• Malaysia
• Mexico
• Nepal
• Pakistan 
• Palestine 
• South Africa
• South Korea
• Spain
• Taiwan
• Tonga
• Tunisia
• Vietnam

In particular, many members are from India and Pakistan.

I am amazed and delighted to have members from all over the world. I don’t know if universities teach classes based on IPMB in all these places, or if people just stumble upon the group.

The IPMB Facebook group welcomes everyone interested in physics applied to medicine and biology. I am delighted to have you. And for those who are not yet members, just go to Facebook, search for “Intermediate Physics for Medicine and Biology,” and click “Join Group.” Let’s push for 200 members!

Proton Therapy

Section 16.11.3 in the 4th edition of Intermediate Physics for Medicine and Biology discusses proton therapy.

Protons are also used to treat tumors. Their advantage is the increase of stopping power at low energies. It is possible to make them come to rest in the tissue to be destroyed, with an enhanced dose relative to intervening tissue and almost no dose distally (“downstream”) as shown by the Bragg peak.

Proton therapy has become popular recently: see articles in US News and World Report and on MSNBC. There even exists a National Association for Proton Therapy. Their website explains the main advantage of protons over X-rays.

Both standard x-ray therapy and proton beams work on the principle of selective cell destruction. The major advantage of proton treatment over conventional radiation, however, is that the energy distribution of protons can be directed and deposited in tissue volumes designated by the physicians in a three-dimensional pattern from each beam used. This capability provides greater control and precision and, therefore, superior management of treatment. Radiation therapy requires that conventional x-rays be delivered into the body in total doses sufficient to assure that enough ionization events occur to damage all the cancer cells. The conventional x-rays lack of charge and mass, however, results in most of their energy from a single conventional x-ray beam being deposited in normal tissues near the body’s surface, as well as undesirable energy deposition beyond the cancer site. This undesirable pattern of energy placement can result in unnecessary damage to healthy tissues, often preventing physicians from using sufficient radiation to control the cancer.

Protons, on the other hand, are energized to specific velocities. These energies determine how deeply in the body protons will deposit their maximum energy. As the protons move through the body, they slow down, causing increased interaction with orbiting electrons.

Figure 16.51 of the 4th edition of Intermediate Physics for Medicine and Biology shows the dose versus depth from a 150 MeV proton beam, including the all-important Bragg peak located many centimeters below the tissue surface. If you want to understand better why proton energy is deposited in the Bragg peak rather than being spread throughout the tissue, solve Problem 31 in Chapter 16.

To learn more about the pros and cons of proton therapy, I suggest several “point/counterpoint” articles from the journal Medical Physics: “Within the Next Decade Conventional Cyclotrons for Proton Radiotherapy will Become Obsolete and Replaced by Far Less Expensive Machines using Compact Laser Systems for the Acceleration of the Protons,” Chang-Ming Ma and Richard Maughan (Medical Physics, Volume 33, Pages 571–573, 2006), “Proton Therapy is the Best Radiation Treatment Modality for Prostate Cancer,” Michael Moyers and Jean Pouliot (Medical Physics, Volume 34, Pages 375–378, 2007), and “Proton Therapy is Too Expensive for the Minimal Potential Improvements in Outcome Claimed,” Robert Schulz and Alfred Smith (Medical Physics, Volume 34, Pages 1135–1138, 2007).

The Hydrogen Spectrum

One of the greatest accomplishments of atomic physics is Neils Bohr’s model for the structure of the hydrogen atom, and his prediction of the hydrogen spectrum. While Bohr gets the credit for deriving the formula for the wavelengths, λ, of light emitted by hydrogen—one of the early triumphs of quantum mechanics—it was first discovered empirically from the spectroscopic analysis of Johannes Rydberg. In the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I introduce Rydberg’s formula in Homework Problem 4 of Chapter 14.

Problem 4 (a) Starting with Eq. 14.7, derive a formula for the hydrogen atom spectrum in the form

where n and m are integers. R is called the Rydberg constant. Find an expression for R in terms of fundamental constants. 

(b) Verify that the wavelengths of the spectral lines a-d at the top of Fig. 14.3 are consistent with the energy transitions shown at the bottom of the figure.

Our Fig. 14.3 is in black and white. It is often useful to see the visible hydrogen spectrum (just four lines, b-e in Fig 14.3) in color, so you can appreciate better the position of the emission lines in the spectrum.

(Figure from http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch6/graphics/hydrogen.gif).

The hydrogen lines in the visible part of the spectrum are often referred to as the Balmer series, in honor of physicist Johann Balmer who discovered this part of the spectrum before Rydberg. Additional Balmer series lines exist in the near ultraviolet part of the spectrum (the thick band of lines just to the left of line e at the top of Fig. 14.3). All the Balmer series lines can be reproduced using the equation in Problem 4 with n = 2.

An entire series of spectral lines exists in the extreme ultraviolet, called the Lyman series, shown at the top of Fig. 14.3 as the line labeled a and the lines to its left. These lines are generated by the formula in Problem 4 using n = 1. The new homework problem below will help the student better understand the hydrogen spectrum.

Section 14.2

Problem 4 ½ The Lyman series, part of the spectrum of hydrogen, is shown at the top of Fig. 14.3 as the line labeled a and the band of lines to the left of that line. Create a figure like Fig. 14.3, but which shows a detailed view of the Lyman series. Let the wavelength scale at the top of your figure range from 0 to 150 nm, as opposed to 0-2 μm in Fig. 14.3. Also include an energy level drawing like at the bottom of Fig. 14.3, in which you indicate which transitions correspond to which lines in the Lyman spectrum. Be sure to indicate the shortest possible wavelength in the Lyman spectrum, show what transition that wavelength corresponds to, and determine how this wavelength is related to the Rydberg constant.

Many spectral lines can be found in the infrared, known as the Paschen series (n = 3), the Brackett series (n = 4) and the Pfund series (n = 5). The Paschen series is shown as lines f, g, h, and i in Fig. 14.3, plus the several unlabeled lines to their left. The Paschen, Brackett, and Pfund series overlap, making the hydrogen infrared spectrum more complicated than its visible and ultraviolet spectra. In fact, the short-wavelength lines of the Brackett series would appear at the top of Fig. 14.3 if all spectral lines were shown.

Asimov's Biographical Encyclopedia
of Science and Technology,
by Isaac Asimov.

Rydberg’s formula, given in Problem 4, nicely summarizes the entire hydrogen spectrum. Johannes Rydberg is a Swedish physicist (I am 3/8th Swedish myself). His entry in Asimov's Biographical Encyclopedia of Science and Technology reads

RYDBERG, Johannes Robert (rid’bar-yeh) Swedish physicist Born: Halmstad, November 8, 1854. Died: Lund, Malmohus, December 28, 1919.

Rydberg studied at the University of Lund and received his Ph.D. in mathematics in 1879, and then jointed the faculty, reaching professorial status in 1897.

He was primarily interested in spectroscopy and labored to make sense of the various spectral lines produced by the different elements when incandescent (as Balmer did for hydrogen in 1885). Rydberg worked out a relationship before he learned of Balmer’s equation, and when that was called to his attention, he was able to demonstrate that Balmer’s equation was a special case of the more general relationship he himself had worked out.

Even Rydberg’s equation was purely empirical. He did not manage to work out the reason why the equation existed. That had to await Bohr’s application of quantum notions to atomic structure. Rydberg did, however, suspect the existence or regularities in the list of elements that were simpler and more regular than the atomic weights and this notion was borne out magnificently by Moseley’s elucidation of atomic numbers.

Yesterday was the 158th anniversary of Rydberg’s birth.

Britton Chance (1913-2010)

Britton Chance died late last year. The website www.brittonchance.org states that

Britton Chance, M.D., Ph.D., D.Sc., for more than 50 years one of the giants of biochemistry and biophysics and a world leader in transforming theoretical science into useful biomedical and clinical applications, died on November 16, 2010, at age 97 in Philadelphia, PA. Dr. Chance had the rare distinction of being the recipient of a National Medal of Science (1974), a Gold Medal in the Olympics (1952, Sailing, Men’s 5.5 Meter Class), and a Certificate of Merit for his sensitive work during World War II.

His obituary in the New York Times describes his early work.

Over a lifetime of research, Dr. Chance focused on the observation and measurement of chemical reactions within cells, tissue and the body. But unlike most researchers, he also had expertise in mechanics, electronics and optics, and a great facility in instrument-building. His innovations helped transform theoretical science into biochemical and biophysical principles, the stuff of textbooks, and useful biomedical and clinical applications.

Early in his career he invented a tool, known as a stopped-flow apparatus, for measuring chemical reactions involving enzymes; it led to the establishment of a fundamental principle of enzyme kinetics, known as the enzyme-substrate complex.

Another obituary, in the December 17 issue of Science magazine, observed that

In his mid-70s, Chance (then emeritus) launched a new field of optical diagnostics that rests on the physics of light diffusion through scattering materials such as living tissue. He showed that scattered near-infrared light pulses could not only measure the dynamics of oxy- and deoxyhemoglobin levels in performing muscles, but also reveal and locate tumors and cancerous tissue in muscles and breast as well as injury in the brain. Because changing patterns of oxy- and deoxyhemoglobin in the brain reflect cognitive activity, the applications of this diagnostic approach widened to include assessing neuronal connectivity in premature babies.

Chance appears in the 4th edition of Intermediate Physics for Medicine and Biology because of his research on light diffusion. In Section 14.4 (Scattering and Absorption of Radiation), Russ Hobbie and I analyze the absorption and scattering coefficients of infrared light, and then give typical values that “are eyeballed from data from various tissues reported in the article by Yodh and Chance (1995),” with the reference being to Yodh, A. and B. Chance (1995) “Spectroscopy and Imaging with Diffusing Light,” Physics Today, March, Pages 34–40.

Then in Sec. 14.5 (The Diffusion Approximation to Photon Transport), we analyze pulsed measurements of infrared light.

A technique made possible by ultrashort light pulses from a laser is time-dependent diffusion. It allows determination of both [the scattering coefficient] and [the absorption coefficient]. A very short (150-ps) pulse of light strikes a small region on the surface of the tissue. A detector placed on the surface about 4 cm away records the multiply-scattered photons. A typical plot of the detected photon fluence rate is shown in Fig. 14.13.

Figure 14.13 is a figure from Patterson, M. S., B. Chance, and B. C. Wilson (1989) “Time Resolved Reflectance and Transmittance for the Noninvasive Measurement of Tissue Optical Properties,” Applied Optics, Volume 28, Pages 2331–2336, which has been cited over 1000 times in the scientific literature.

Finally, in Sec. 14.6 (Biological Applications of Infrared Scattering), we reproduce a figure from the Physics Today article by Yodh and Chance, which shows the absorption coefficient for water, oxyhemoglobin and deoxyhemoglobin.

The greater absorption of blue light in oxygenated hemoglobin makes oxygenated blood red…The wavelength 800 nm at which both forms of hemoglobin have the same absorption is called the isosbestic point. Measurements of oxygenation are made by comparing the absorption at two wavelengths on either side of this point.

This property of infrared absorption of light is the basis for pulse oximeters that measure oxygenation. Not all measurements of blood oxygen use pulsed light. Russ and I cite one of Chance’s papers that uses a continuous source: Liu, H., D. A. Boas, Y. Zhang, A. G. Yodh, and B. Chance (1995) “Determination of Optical Properties and Blood Oxygenation in Tissue Using Continuous NIR Light,” Physics in Medicine and Biology, Volume 40, Pages 1983–1993. A fourth of Chance’s paper that we include in our references is Sevick, E. M., B. Chance, J. Leigh, S. Nioka, and M. Maris (1991) “Quantitation of Time- and Frequency-Resolved Optical Spectra for the Determination of Tissue Oxygenation,” Analytical Biochemistry, Volume 195, Pages 330–351.

In 1987, Chance won the Biological Physics Prize (now known as the Max Delbruck Prize in Biological Physics) from the American Physical Society

for pioneering application of physical tools to the understanding of Biological phenomena. The early applications ranged from novel spectrometry that elucidated electron transfer processes in living systems to analog computation of nonlinear processes. Later contributions have been equally at the forefront.

The Constituents of Blood

I’m a big supporter of blood donation. This week I gave another pint to the Red Cross, which brings my total to 8 gallons. As I lay there with a needle stuck in my arm, I began to wonder “what’s in this blood they’re squeezing out of me?”

Table 3.1 in Intermediate Physics for Medicine and Biology lists some constituents of blood. I reproduce the table below, with revisions.

Constituent	Density in mg/cm3	Number in 1 μm3
Water	1000	33,000,000,000
Sodium	3	83,000,000
Glucose	1	3,300,000
Cholesterol	2	3,100,000
Hemoglobin	150	1,400,000
Albumin	45	390,000

This version of the table highlights several points. Water molecules outnumber all others by a factor of four hundred. Sodium ions are sixty times more common than hemoglobin molecules, but the mass density of hemoglobin is over fifty times that of sodium. In other words, if judged by number of molecules (and therefore the osmotic effect) sodium is most important, but if judged by mass or volume fraction, hemoglobin dominates. Glucose and cholesterol are intermediate cases. Albumin has a surprisingly small number of molecules, given that I thought it was one of the main contributors to osmotic pressure. It is a big molecule, however, so by mass it contributes nearly a third as much as hemoglobin.

Are other molecules in blood important? You can find a comprehensive list of blood constituents beautifully illustrated here. When judged by number, sodium is the most important small ion, but the chloride ion contributes nearly as much. Carbon dioxide and bicarbonate are also significant, and potassium has about the same number of molecules as glucose. If you drive drunk, you may have twice as many ethyl alcohol molecules as potassium ions (if the number of ethanol molecules reaches the level of sodium or chloride ions, you die). Urea has a similar number of molecules as hemoglobin.

Judged by mass, you get an entirely different picture. Large protein molecules dominate. Hemoglobin is by far the largest contributor to blood by mass (after water, of course), followed by albumin and another group of proteins called globulins. Next are glycoproteins such as the clotting factor fibrinogen and iron-binding transferrin.

Many trace constituents hardly affect the osmotic pressure or density of blood, but are excellent biomarkers for diagnosing diseases.

If you’re starting to think that blood is awfully crowded, you’re right. The picture below is by David Goodsell. No scale bar is included, but each candy-apple-red hemoglobin molecule in the lower left has a diameter of about 6 nm. The water, ions, and other small molecules such as glucose are not shown; if they had been they would produce a fine granular appearance (water has diameter of about 0.3 nm) filling in the spaces between the larger macromolecules.

Blood. Serum is in the upper right and a red blood cell is in the lower left. In the serum, the Y-shaped molecules are antibodies (an immunoglobulin), the long thin light-red molecules are fibrinogen (a glycoprotein), and the numerous potato-like yellow proteins are albumin. The red blood cell is filled with red hemoglobin molecules. The cell membrane is in purple. The illustration is by David S. Goodsell of the Scripps Research Institute.

In another eight weeks I will get free juice and cookies be eligible to give blood again. It doesn’t hurt (much) or take (too) long. If you want to donate, contact the American Red Cross. Give the gift of life.

Retinal Injuries from a Handheld Laser Pointer

Are laser pointers safe? Apparently, it depends on the laser pointer. A recent article by Christine Negroni in the New York Times (Feb. 28, 2011) states that

Eye doctors around the world are warning that recent cases of teenagers who suffered eye damage while playing with high-power green laser pointers are likely to be just the first of many.

Negroni cites a letter that appeared last September in the New England Journal of Medicine (Wyrsch, Baenninger, and Schmid, “Retinal Injuries from a Handheld Laser Pointer,” N. Engl. J. Med., Volume 363, Pages 1089–1091, 2010), which says

In the past, laser pointers sold to the public had a maximal output of 5 mW, which is regarded as harmless because the human eye protects itself with blink reflexes. The measured output of the laser in [the case of a person who was injured] was 150 mW. The use of lasers that are threatening to the eye is normally restricted to occupational and military environments; laser accidents outside these fields are very rare. However, powerful laser devices, with a power of up to 700 mW, are now easily obtainable through the Internet, despite government restrictions. These high-power lasers are advertised as “laser pointers” and look identical to low-power pointers. The much higher power of such devices may produce immediate, severe retinal injury. Despite their potential to cause blinding, such lasers are advertised as fun toys and seem to be popular with teenagers. In addition, Web sites now offer laser swords and other gadgets that use high-power lasers.

I attended a talk just last week where the speaker waved his green laser pointer around like a light saber. I don’t know the power of his pointer, but I wonder if I was in danger.

One concern arises from the bozos who point lasers at airplanes. The U.S. Congress plans to toughen the laws on this sort of horseplay, making shining a laser at a plane a federal crime with up to five years imprisonment. I’m all for high school students learning science by hands-on activities, but do it right. Buy a 5 mW red helium-neon laser pointer and use it safely to do some optics experiments (I suggest observing Young’s double slit interference pattern). Don’t buy a 700 mW green laser pointer and start shining it up into the sky! Do you think I’m being a schoolmarm out to ruin your fun? Consider this: the website laserpointersafety.com reports that

A $5000 reward is being offered for information leading to the arrest of the person(s) who aimed a laser into the cockpit of a Southwest Airlines flight approaching Baltimore-Washington International Airport. The flight, which originated in Milwaukee, was 2000 feet over the town of Millersville, near Old Mill Road and Kenora Drive, when it was illuminated around 6:45 pm on Sunday, Feb. 20, 2011. Millersville is about 8 miles from BWI Airport.

You better be careful; someone may be watching.

How do you tell the difference between a safe, educational experience and a potentially disastrous prank? You begin by learning about light and its biological impact. Russ Hobbie and I discuss light in Chapter 14 of the 4th edition of Intermediate Physics for Medicine and Biology. We address topics related to light and safety, although we don’t analyze the particular concern of laser damage to the eye. For instance, we discuss how ultraviolet light damages the eye (Section 14.9.6) and how light can be used to heat tissue (Section 14.10), as well as a detailed discussion of radiometry (the measurement of radiant energy, Section 14.11) and the anatomy and optics of the eye (Section 14.12).

In another New York Times article, Negroni relates how high powered laser pointers can pose a risk to pilots. And on her blog, she explains why helicopters may be at a greater risk than airplanes.

A helicopter cockpit has glass extending below the level of the pilots' eyes toward the ground exactly where the lasers are. Rotor craft fly at low altitudes over residential areas and busy highways. They are not flying autopilot and they may be piloted by a single person. They hover and may make inviting targets. That was the case on Tuesday when a Los Angeles television station sent its chopper to follow and report on the police activity and it was hit by a laser.

The interaction of laser light and vision is one more example of why a firm understanding of physics applied to medicine and biology is so important.

The Radiation Dose from Radon: A Back-of-the-Envelope Estimation

I like Fermi problems: those back-of-the-envelope order-of-magnitude estimates that don’t aim for accuracy, but highlight underlying principles. I also enjoy devising new homework exercises for the readers of this blog. Finally, I am fascinated by radon, that radioactive gas that contributes so much to the natural background radiation. Ergo, I decided to write a new homework problem about estimating the radiation dose from breathing radon.

What a mistake. The behavior of radon is complex, and the literature is complicated and confusing. Part of me regrets starting down this path. But rather than give up, I plan to forge ahead and to drag you—dear reader—along with me.

Section 17.12

Problem 57 1/2. Estimate the annual effective dose (in Sv yr^-1) if the air contains a trace of radon. Use the data in Fig. 17.27, and assume the concentration of radon corresponds to an activity of 150 Bq m^-3, which is the action level at which the Environmental Protection Agency suggests you start to take precautions. Make reasonable guesses for any parameters your need.

Here is my solution (stop reading now if you first want to solve the problem yourself). In order to be accessible to a wide audience, I avoid jargon and unfamiliar units.

One bequerel is a decay per second, and a cubic meter is 1000 liters, so we start with 0.15 decays per second per liter. The volume of air in your lungs is about 6 liters, implying that approximately one atom of radon decays in your lungs every second.

Radon decays by emitting an alpha particle. You don’t, however, get just one. Radon-222 (the most common isotope of radon) alpha-decays to polonium-218, which alpha-decays to lead-214, which beta-decays twice to polonium-214, which alpha-decays to lead-210 (see Fig 17.27 in Intermediate Physics for Medicine and Biology). The half-life of lead-210 is so long (22 years) that we can treat it as stable. Each decay of radon therefore results in three alpha particles. An alpha particle is ejected with an energy of about 6 MeV. Therefore, roughly 18 MeV is deposited into your lungs each second. If we convert to SI units (1 MeV = 1.6 × 10^-13 joule), we get about 3 × 10^-12 joules per second.

Absorbed dose is expressed in grays, and one gray is a joule per kilogram. The mass of the lungs is about 1 kilogram. So, the dose rate for the lungs is 3 × 10^-12 grays per second. To find the annual dose, multiply this dose rate by one year, or 3.2 × 10⁷ seconds. The result is about 10^-4 gray, or a tenth of a milligray per year.

If you want the equivalent dose in sieverts, multiply the absorbed dose in grays by 20, which is the radiation weighting factor for alpha particles. To get the effective dose, multiply by the tissue weighting factor for the lungs, 0.12. The final result is 0.24 mSv per year.

This all seems nice and logical, except the result is a factor of ten too low! It is probably even worse than that, because my initial radon concentration was higher than average and in Table 16.6 of IPMB Russ Hobbie and I report a value of 2.28 mSv for the average annual effective dose. My calculation here is an estimate, so I don’t expect the answer to be exact. But when I saw such a low value I was worried and started to read some of the literature about radon dose calculations. Here is what I learned:

1. The distribution of radon progeny (such as ²¹⁴Po) is complicated. These short-lived isotopes are charged and behave differently than an unreactive noble gas like radon. They stick to particles in the air. Your dose depends on how dusty the air is.
2. How these particles interact with our lungs is even more difficult to understand. Some large particles are filtered out by the upper respiratory track. 
3. The range of a 6-MeV alpha particle is only about 50 microns, so some of the energy is deposited harmlessly into the gooey mucus layer lining the airways (see https://www.ncbi.nlm.nih.gov/books/NBK234233). Ironically, if you get bronchitis your mucus layer thickens, protecting you from radon-induced lung cancer.  
4. The progeny and their dust particles stick to the bronchi walls like flies to flypaper, increasing their concentration.
5. Filtering out dust and secreting a mucus layer reduces the dose to the lungs, while attaching the progeny to the airway lining increases it. My impression from the literature is that the flypaper effect dominants, and explains why my estimate is so low.
6. The uranium-238 decay chain shown in Fig. 17.27 is the source of radon-222, but other isotopes arise from other decay chains. The thorium-232 decay chain leads to radon-220, called thoron, which also contributes to the dose.
7. I am not confident about my value for the mass. The lungs are a bloody organ; about half of their mass is blood. I don’t know whether or not the blood is included in the reported 1 kg mass. The radon literature is oddly silent about the lung mass, and I don’t know how these authors calculate the dose without it. 
8. I ignored the energy released when progeny beta-decay, which would cause a significant error if my aim was to calculate the absorbed dose in grays. But if I want the effective dose in sieverts I should be alright, because the radiation weighting factor for electrons is 1 compared to 20 for alpha particles. 
9. The radon literature is difficult to follow in part because of strange units, such as picocuries per liter and working level months (see https://www.ncbi.nlm.nih.gov/books/NBK234224).
10. Radon can get into the water as well as the air. If you drink the water, your stomach gets a dose. With a half-life of days, the radon in this elixir has time to enter your blood and irradiate your entire body.
11. Does the dose from radon lead to lung cancer? That depends on the accuracy of the linear no-threshold model. If there is a threshold, then such a small dose may not represent a risk.
12. If you want to learn more about radon, read NCRP Report 160, ICRP Publication 103, or BEIR VI. Of course, you should start by reading Section 17.12 in IPMB.

What do I take away from this estimation exercise? First, radon dosimetry is complicated. Second, biology problems are messy, and while order-of-magnitude estimates are still valuable, your results need large error bars.