Hobbie and Roth, Back in the Saddle Again

In the November, 2009 issue of the American Journal of Physics, Russ Hobbie and I published “Resource Letter MP-2: Medical Physics.” Our resource letter “provides a guide to the literature on the uses of physics for the diagnosis and treatment of disease.” Think of it (along with Ratliff’s “Resource Letter MPRT-1: Medical Physics in Radiation Therapy” discussed in the August 28, 2009 entry to this blog) as an updated bibliography to the 4th edition of Intermediate Physics for Medicine and Biology. Together, these two publications provide over 300 citations to the best and most recent books, articles, and websites about medical physics. We even slipped a mention of this blog into the list of references.

Felix Bloch

One hundred and four years ago today, Felix Bloch (1905–1983) was born in Zurich, Switzerland. Bloch received his PhD in physics in 1928 from the University of Leipzig working under Werner Heisenberg, and then immigrated to the United States after Hitler came to power in Germany. He worked for a time at Los Alamos on the Manhattan Project, and had a long career in the Physics Department at Stanford University.

Bloch is most familiar to readers of the 4th edition of Intermediate Physics in Medicine and Biology because of his contributions to our understanding of nuclear magnetic resonance. He shared the 1952 Nobel Prize with Edward Purcell for “their development of new ways and methods for nuclear magnetic precision measurements.” In Chapter 18 on Magnetic Resonance Imaging, Russ Hobbie and I present the Bloch Equations (Eq. 18.15), which govern the magnetization of a collection of spins in a static magnetic field. Essentially all of MRI begins with the Bloch equations, so they are part of the essential toolkit for any medical physicist. Bloch’s most cited paper is “Nuclear Induction” (Physical Review, Volume 70, Pages 460–474, 1946). The abstract is reproduced below.

The magnetic moments of nuclei in normal matter will result in a nuclear paramagnetic polarization upon establishment of equilibrium in a constant magnetic field. It is shown that a radiofrequency field at right angles to the constant field causes a forced precession of the total polarization around the constant field with decreasing latitude as the Larmor frequency approaches adiabatically the frequency of the r-f field. Thus there results a component of the nuclear polarization at right angles to both the constant and the r-f field and it is shown that under normal laboratory conditions this component can induce observable voltages. In Section 3 we discuss this nuclear induction, considering the effect of external fields only, while in Section 4 those modifications are described which originate from internal fields and finite relaxation times.

Bloch also appears in Chapter 15 of Intermediate Physics for Medicine and Biology, because of his contribution to the development of the Bethe-Bloch formula (Eq. 15.58) governing the stopping power of a charged particle by interaction with a bound electron. He is also known for his fundamental contributions to solid state physics, including his seminal calculation of the electron wave function in a periodic potential, derived when he was only 23. You can download a Biographical Memoir about Bloch by Robert Hofstadter at books.nap.edu/html/biomems/fbloch.pdf.

I have an indirect connection to Felix Bloch. When in graduate school at Vanderbilt University in the 1980s, I had several classes from Ingram Bloch, who—if I recall correctly—was Felix’s cousin. At that time, Ingram Bloch was teaching many of the graduate classes, so I took classical mechanics, two semesters of quantum mechanics, and general relativity from him. I remember spending days working on his infamous “take-home” exams. They weren’t easy. With two physicists in the family, the Blochs made quite an impact on 20th century physics.


P.S. Right now, amazon.com has the 4th edition of Intermediate Physics for Medicine and Biology on sale at 40% off. I have no control over if and when amazon reduces prices on books, so the price may go back up anytime.

P.P.S. Last night I finished Steven Strogatz’s book The Calculus of Friendship: What a Teacher and a Student Learned About Life While Corresponding About Math, mentioned in the July 3rd entry to this blog. In a word, the book is charming.

The Klein-Nishina Formula

In Chapter 15 of the 4^th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I present the Klein-Nishina formula (Eq. 15.17).

The inclusion of dynamics, which allows us to determine the relative number of photons scattered at each angle, is fairly complicated. The quantum-mechanical result is known as the Klein-Nishina formula.

At first glance, Eq. 15.17 doesn’t look quantum-mechanical, because it does not appear to contain Planck’s constant, h. However, closer inspection reveals that the variable x in the equation, defined on the previous page (Eq. 15.15), does indeed contain h. Russ and I don’t derive the Klein-Nishina formula, nor do we give much background about it. Yet, this equation played an important role in the development of quantum mechanics, and specifically of quantum electrodynamics.

In the book Nishina Memorial Lectures: Creators of Modern Physics, the Nobel Prize winning physicist Chen Ning Yang wrote a chapter about “The Klein-Nishina Formula and Quantum Electrodynamics.”

One of the greatest scientific revolutions in the history of mankind was the development of Quantum Mechanics. Its birth was a very difficult process, extending from Planck’s paper of 1900 to the papers of Einstein, Bohr, Heisenberg, Schrodinger, Dirac, and many others. After 1925–1927, a successful theory was in place, explaining many complicated phenomena in atomic spectra. Then attention moved to higher energy phenomena. It was in this period, 1928–1932, full of great ideas and equally great confusions, that the Klein-Nishina formula played a crucial role. The formula was published in 1929, in the journals Nature and Z. Physik. It dealt with the famous classical problem of the scattering of light rays by a charged particle…

Oskar Klein and Yoshio Nishina derived their formula starting from the Dirac equation, which is a relativistic version of Schrodinger’s equation for an electron, including the effect of spin. During the summer of 1928, Klein and Nishina performed the lengthy calculations necessary to derive their formula. They would work independently during the day, and then compare results each evening (as Russ and I say, the calculation is “fairly complicated”). The final result was published in the German journal Zeit. f. Phys. (“Streuung von Strahlung durch freie Elektronen nach der neuen relativistischen Quantendynamik von Dirac,” Volume 52, Pages 853–868, 1929). I don’t read German, so I can’t enjoy the original.

Later, the theory of Quantum Electrodynamics (QED) was developed to more completely describe the quantum mechanical interactions of electrons and photons. For an elementary introduction to this subject, see Richard Feynmann’s book QED. (Although I took several semesters of quantum mechanics in graduate school, I never really mastered quantum electrodynamics.) When the problem of the scattering of light by electrons was reexamined using QED, the result was identical to the Klein-Nishina formula derived earlier. To learn more about how these results were obtained, see “The Road to Stueckelberg's Covariant Perturbation Theory as Illustrated by Successive Treatments of Compton Scattering,” by J. Lacki, H. Ruegg, and V. Telegdi (http://arxiv.org/abs/physics/9903023). But beware, the paper is quite mathematical and not for the faint of heart.

Who were the two men who derived this formula? Oskar Klein (1894–1977) was a Swedish theoretical physicist. He is known for the Kaluza-Klein theory, the Klein-Gordon equation, and the Klein paradox. Yoshio Nishina (1890–1951) was a Japanese physicist. He was a friend of Niels Bohr, and a close associate of Albert Einstein. The crater Nishina on the Moon is named in his honor. During World War II he was the head of the Japanese atomic program.

Let me share one last anecdote about Klein, Nishina, and Paul Dirac that I find amusing. Gosta Ekspong tells the story in his chapter “The Klein-Nishina Formula,” in the book The Oskar Klein Memorial Lectures.

When Dirac paid a short visit to Copenhagen in 1928, he met Klein and Nishina. The three of them were once conferring in the library of the Bohr Institute. Dirac was a man of few words, so when the remark came from Nishina that he had found an error of sign in the new Dirac paper on the electron, Dirac drily answered: “But the result is correct.” Nishina, in an attempt to be helpful, said: “There must be two mistakes,” only to get Dirac’s reply that “there must be an even number of mistakes.”

Steven Chu, Biological Physicist

Readers of the 4th edition of Intermediate Physics for Medicine and Biology may wish to see examples of physicists who have contributed to biology. One excellent example is Steven Chu, who until recently was professor of physics and professor of molecular and cellular biology at the University of California, Berkeley. Chu describes his biological physics research on his Berkeley website:

We apply single molecule techniques such as fluorescence resonance energy transfer, atomic force microscopy and optical tweezers, we study enzyme activity, and protein and RNA folding at the single bio-molecule level. Systems being studied include how the ribosome reads m-RNA and manufactures proteins, how vesicles fuse into the cell wall at the synapse of neurons, how cells adhere to each other via adhesive molecules, and how RNA molecules fold into active enzymes.

If you want to hear Chu talk about his biological physics research, watch this video on YouTube.

 Steven Chu asks What Can Physics Say About Life?
https://www.youtube.com/watch?v=lUR3WgVh-Hc

Some of his best known biological physics papers, published while on the faculty at Stanford, are:

• Zhuang XW, Bartley LE, Babcock HP, Russell R, Ha TJ, Herschlag D, Chu S (2000) “A Single-Molecule Study of RNA Catalysis and Folding,” Science, Volume 288, Pages 2048–2051.


• Zhuang XW, Kim H, Pereira MJB, Babcock HP, Walter NG, Chu S (2002) “Correlating structural dynamics and function in single ribozyme molecules,” Science, Volume 296, Pages 1473–1476.


• Ha T, Rasnik I, Cheng W, Babcock HP, Gauss GH, Lohman TM, Chu S (2002) “Initiation and re-initiation of DNA unwinding by the Escherichia coli Rep helicase,” Nature, Volume 419, Pages 638–641.


• Blanchard SC, Gonzalez RL, Kim HD, Chu S, Puglisi JD (2004) “tRNA selection and kinetic proofreading in translation,” Nature Structural and Molecular Biology, Volume 11, Pages 1008–1014.

Steven Chu exemplifies how physicists can contribute to our understanding of biology.


....Oh, did I forget to mention something? Chu is best known for his work on the “development of methods to cool and trap atoms with laser light,” for which he shared the Nobel Prize in Physics in 1997. He is currently Secretary of Energy in the Obama administration, and is leading the US effort to move away from fossil fuels and toward alternative energy sources, thereby combating global warming.

Who says we don’t have wonderful role models anymore?

Are Static Magnetic Fields Dangerous?

Are static magnetic fields dangerous? This question has recently taken on added importance because a European directive is limiting a worker’s exposure to the strong static magnetic field in a magnetic resonance imager, thereby impeding research with MRI. A recent article by Denis Le Bihan on medicalphysicsweb.org asserts that

those limits could end up preventing the technique from being used—just when European scientists are starting to lead the world in ultra-high-field (UHF) MRI magnet research. The initially proposed limits will immediately put the brakes on progress and, moreover, be a big blow to companies that make MRI scanners and magnets, such as Siemens, Philips, Bruker and Magnex. These firms could end up being unable to meet the growing global demand for clinical UHF MRI scanners, the high fields from which could boost the potential of MRI for healthcare and biomedical sciences, particularly for neurological applications.

Voodoo Science,
by Robert Park.

Physicist Bob Park, the author of Voodoo Science and the weekly newsletter What’s New, writes

MAGNETIC FIELDS: THE PRECAUTIONARY PRINCIPLE IN ACTION. According to Denis Le Bihan at the CEA-Saclay Centre, a European directive to prevent workers from being exposed to high magnetic fields could severely impact research into Ultrahigh-Field MRI which shows great promise particularly in neurological applications. It is particularly frustrating that limits on static magnetic fields resulted from the paranoia surrounding EMF, which was associated with everything from power lines to cell phones, Wi-Fi, Bluetooth, and other wireless devices. As I pointed out in an editorial in the Journal of the National Cancer Institute eight years ago, “there will always be some who will argue that the issue has not been completely settled. In science, few things ever are.”

Are these limits justified? Based on my knowledge of biomagnetism, I think not. There are few known mechanisms by which a static magnetic field can have a significant biological impact, except in unusual cases such as a person with a ferromagnetic medical implant, or in some animals (such as magnetotactic bacteria) that are believed to sense magnetic fields, presumably by the presence of ferromagnetic or superparamagnetic nanoparticles (magnetosomes). Russ Hobbie and I discuss the possible effects of weak magnetic fields in Chapter 9 of the 4th edition of Intermediate Physics for Medicine and Biology.

Denis Le Bihan is a leader in the field of MRI, known for his development of diffusion weighted imaging. He is director of NeuroSpin, a French institute aimed at developing and using ultra high field Magnetic Resonance to understand the brain. I knew Denis when we were both working at the National Institutes of Health in the 1990s. He was a close collaborator with my friend Peter Basser, and together they developed diffusion tensor imaging. (Incidentally, one of their early papers on this topic just received its 1000th citation in the citation index!) Let us hope that Le Bihan’s important research is not interrupted unnecessarily by misguided government regulations.

Cochlear Implants

Russ Hobbie and I discuss the ear and hearing in Chapter 13 of the 4th edition of Intermediate Physics for Medicine and Biology. Last Wednesday, Russ attended a colloquium at the University of Minnesota titled “Bionic Hearing: The Science and the Experience,” presented by Ian Shipsey of Purdue University. The talk was about cochlear implants, at topic we mention briefly in Section 7.10 on Electrical Stimulation. You can download the entire powerpoint presentation from the colloquium. Shipsey’s story is itself inspirational. On his website he writes “I had cochlea implant surgery in November 2002 at the Riley Hospital for Children in Indianapolis, IN. The surgeon was Professor Richard Miyamoto. The device was activated in late December. I am now able to hear my daughter for the first time and my wife for the first in 12 years.”

In order to understand cochlear implants, you need to understand how the ear works. For a short lesson, you should watch an absolutely incredible video on YouTube. This animation is a wonderful example of what can happen when science education meets modern technology, and it was selected by Science Magazine as the first place winner in its 2003 Science and Engineering Visualization Challenge. Don’t miss it; especially you Beethoven fans!

Auditory Transduction.

https://www.youtube.com/watch?v=46aNGGNPm7s

You can learn more about cochlear implants by viewing a video of a lecture by Richard Miyamoto titled “Cochear Implants: Past, Present, and Future,” which you can download from a website about cochlear implants maintained by the National Institute of Deafness and Other Communication Disorders, one of the National Institutes of Health. More information is available on a Food and Drug Administration webpage. Also interesting is a National Public Radio report about cochlear implants.

When I worked at NIH in the 1990s, I used to attend the Neural Prosthesis Program workshops held in Bethesda every fall. I recall listening to the researchers each year report on how they were developing these incredible devices to restore hearing. From those workshops, I gained a great appreciation for cochlear implants, and I have come to view them as a prototypical example—along with the cardiac pacemaker—of how physics and engineering can contribute to medicine.

More on "Is Computed Tomography Safe?"

The December 7, 2007 entry to this blog was titled “Is Computed Tomography Safe?” As is often the case with such a difficult question, the answer is yes and no. No—there are risks associated with any exposure to ionizing radiation, so no procedure is entirely safe. Yes—in most cases the risks are small enough that the benefits outweigh the risks. In order to answer this question more precisely, a large scale study with nearly one million patients was conducted over three years. The conclusions were reported in the August 27 issue of the New England Journal of Medicine. The abstract of Fazel et al.’s paper “Exposure to Low-Dose Ionizing Radiation from Medical Imaging Procedures” (NEJM, Volume 361, Pages 849–857, 2009) is reproduced below.

Background: The growing use of imaging procedures in the United States has raised concerns about exposure to low-dose ionizing radiation in the general population.

Methods: We identified 952,420 nonelderly adults (between 18 and 64 years of age) in five health care markets across the United States between January 1, 2005, and December 31, 2007. Utilization data were used to estimate cumulative effective doses of radiation from imaging procedures and to calculate population-based rates of exposure, with annual effective doses defined as low (less than 3 mSv), high (greater than 20 to 50 mSv), or very high (greater than 50 mSv).

Results: During the study period, 655,613 enrollees (68.8%) underwent at least one imaging procedure associated with radiation exposure. The mean (±SD) cumulative effective dose from imaging procedures was 2.4±6.0 mSv per enrollee per year; however, a wide distribution was noted, with a median effective dose of 0.1 mSv per enrollee per year (interquartile range, 0.0 to 1.7). Overall, moderate effective doses of radiation were incurred in 193.8 enrollees per 1000 per year, whereas high and very high doses were incurred in 18.6 and 1.9 enrollees per 1000 per year, respectively. In general, cumulative effective doses of radiation from imaging procedures increased with advancing age and were higher in women than in men. Computed tomographic and nuclear imaging accounted for 75.4% of the cumulative effective dose, with 81.8% of the total administered in outpatient settings.

Conclusions: Imaging procedures are an important source of exposure to ionizing radiation in the United States and can result in high cumulative effective doses of radiation."

To help put this study in context, the NEJM published an accompanying editorial by Michael Lauer (“Elements of Danger—The Case of Medical Imaging,” Volume 361, Pages 841–843). Lauer writes that

Because the use of ionizing radiation carries “an element of danger in every . . . procedure,” we need to adopt a new paradigm for our approach to imaging. Instead of investing so many resources in performing so many procedures, we should take a step back and design and execute desperately needed large-scale, randomized trials to figure out which procedures yield net benefits. This approach would require leadership and courage on the part of our profession, our opinion leaders, and the research enterprise, but were we to insist that all, nearly all, procedures be studied in well-designed trials, we could answer many critical clinical questions within a short time. Because we will continue to be uncertain of the magnitude of harm, an accurate understanding of the magnitude of benefit is a moral imperative.

In Chapter 16 of the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the risk of radiation. While we do not provide a final answer regarding the safety of CT, we do outline many of the important issues one must examine in order to make an informed decision. The safety of computed tomography and other diagnostic imaging procedures will continue to be a crucial question of interest to readers of Intermediate Physics for Medicine and Biology. I will try to keep you posted as new information becomes available.

P.S. Thanks to Russ Hobbie for calling my attention to this paper. He reads the New England Journal of Medicine more than I do.

A New Homework Problem

While in Minneapolis last week, attending the 31st Annual International Conference of the IEEE Engineering in Medicine and Biology Society, I had the pleasure of co-chairing a session with Professor Michael Joy of the University of Toronto. Joy has done some fascinating work on measuring current and conductivity in biological tissue using magnetic resonance imaging. His research inspired me to write a new homework problem for Chapter 8 of the 4th edition of Intermediate Physics for Medicine and Biology.

Problem 21.5 The differential form of Ampere’s law, derived in Problem 21, provides a relationship between the current density J and the magnetic field B that allows you to measure biological current with magnetic resonance imaging [see, for example, Scott, G. C., M. L. G. Joy, R. L. Armstrong, and R. M. Henkelman (1991) “Measurement of Nonuniform Current Density by Magnetic Resonance,” IEEE Transactions on Medical Imaging, Volume 10, Pages 362–374]. Suppose you use MRI and find the distribution of magnetic field to be

B_x = C (y z² – y x²)
B_y = C (x z² – x y²)
B_z = C 4 x y z

where C is a constant with the units of T/m³. Determine the current density. Assume the current varies slowly enough that the displacement current can be neglected.

To solve this problem, you need the result of Problem 21 in Chapter 8, which asks the reader to derive the differential form of Ampere’s law from the integral form given in the book by Eq. 8.11. If I were teaching a class from the book, I would assign both Problems 21 and 21.5, and expect the student to solve them both. But for readers of this blog, I will tell you the answer to Problem 21 (ignoring displacement current), so you will have the relationship needed to solve the new Problem 21.5: curl B = μ₀ J. The curl is introduced in Section 8.6. If you don’t have the 4th edition of Intermediate Physics for Medicine and Biology handy, take a look in a math handbook for information about how to calculate the curl (or see Schey’s book Div, Grad, Curl, and All That).

The story of how you measure B using MRI is interesting, but a bit too complicated to describe in detail here. In brief, a magnetic resonance imaging device has a strong static magnetic field about which nuclear spins (such as those of hydrogen) precess. The magnetic field produced by the current density modifies the static magnetic field, causing a phase shift in this precession. This phase shift is detected, and the magnetic field can be deduced from it. Technically, this method allows one to determine the component of the magnetic field that is parallel to the static field. Obtaining the other components requires rotating the object and repeating the procedure. See Chapter 18 for more about MRI.

Send me an email (roth@oakland.edu) if you would like the answer to the new Problem 21.5.

Enjoy.

31st Annual International Conference of the IEEE Engineering in Medicine and Biology Society

I’m posting this blog from Minneapolis, Minnesota, where I am attending the 31^st Annual International Conference of the IEEE Engineering in Medicine and Biology Society. The theme of the conference is “Engineering the Future of Biomedicine,” and there are many fascinating talks and posters that would interest readers of the 4^th edition of Intermediate Physics for Medicine and Biology. Conference chair Bin He and his colleagues have put together a great meeting.

My friend Ranjith Wijesinghe and I have a poster later today about the “Effect of Peripheral Nerve Action Currents on Magnetic Resonance Imaging.” We analyzed if the magnetic field of action currents can be used to generate an artifact in an MRI, allowing direct imaging of biocurrents in the brain. There has been a lot of interest, and many publications, on this topic recently, but we conclude that the magnetic fields are just too small to have a measureable effect.

Last night, I got to hear Earl Bakken give a talk on “The History of Short-Term and Long-Term Pacing.” Bakken is a giant in the history of artificial pacemakers, and is the founder of Medtronic Corportion based in Minneapolis. He talked about the early years when Medtronic was a small electronics laboratory in a garage. He recommended a 10-minute video on YouTube, which he said told his story well. He also quoted one of my favorite books, Machines in our Hearts, a wonderful history of pacemakers and defibrillators. Tonight a social is being held at the Bakken Museum, “the only museum of its kind in the country, [where you can] learn about the history of electricity and magnetism and how it relates to medicine.” For a guy like me, this is great stuff.

Earl Bakken; Ready, Fire, Aim!

http://www.youtube.com/watch?v=XgEssNsMXoA

So far, the presentations are fascinating and inspirational. I must admit, the students who attend these conferences always stay the same age as I grow older. I don’t think these meetings used to be this exhausting for me. As that old Garth Brooks song says, “the competition’s getting younger.” They are also getting more diverse. The speaker who welcomed us to the Bakken talk said that in just a few years, Americans will be a minority within the IEEE Engineering in Medicine and Biology Society. This is not difficult to believe, after seeing researchers from so many countries attending this year.

As I survey all the research presented at this meeting, I am proud that so much of the underlying science is described in Intermediate Physics for Medicine and Biology. I am more convinced than ever that Russ Hobbie and I have written a book that will be of great value to future biomedical engineers.

Resource Letter MPRT-1: Medical Physics in Radiation Therapy

When Russ Hobbie and I were preparing the 4^th edition of Intermediate Physics for Medicine and Biology, we tried to update our book with the most recent references. But, inevitably, as time passes the book becomes increasingly out-of-date. How does one keep up with the literature? This blog is meant to help our readers stay current, but sometimes more drastic measures are required. Fortunately, the American Journal of Physics publishes “Resource Letters,” in which the author reviews important sources (mainly textbooks and research articles) on a particular topic. In the September 2009 issue of AJP, Steven Ratliff of Saint Cloud State University published “Resource Letter MPRT-1: Medical Physics in Radiation Therapy” (Volume 77, Pages 774–782, 2009). The abstract is reproduced below.

This resource letter provides a guide to the literature on medical physics in the field of radiation therapy. Journal articles, books, and websites are cited for the following topics: radiological physics, particle accelerators, radiation dose measurements, protocols for radiation dose measurements, radiation shielding and radiation protection, neutron, proton, and heavy-ion therapies, imaging for radiation therapy, brachytherapy, quality assurance, treatment planning, dose calculations, and intensity-modulated and image-guided therapy.

I highly recommend this Resource Letter for anyone interested in radiation therapy. Particularly useful is Ratliff’s concluding section “Recommended Path Through the Literature.”

The best single reference for a newcomer to the field is Goitein (Ref. 14). It is clear, up to date, readable, complete, and gives a good explanation of what medical physicists do. For a person who does not want to enter the field but is just curious or needs to get some information and does not want to spend any money, a good place to start is the free on-line book by Podgorsak (Ref. 153). Van Dyk (Ref. 17) is a good place to start for those who want a clinical emphasis. The book by Turner (Ref. 91) has good problems (some with answers) and covers many aspects of the subject.

For those wanting to make a career of Medical Physics, a small but good starting library would consist of Goitein (Ref. 14), Hendee et al. (Ref. 30), Johns and Cunningham (Ref. 15), Khan (Ref. 16), Podgorsak (Ref. 153), Turner (Ref. 91), and van Dyk (Ref. 17). Khan is more useful once you have learned the material. If you have more money, you could add Attix (Ref. 19) and Podgorsak’s book on radiation physics (Ref. 26). Cember and Johnson (Ref. 92) is a good addition if you are interested in the health-physics aspects of radiotherapy.

If you were restricted to one book and wanted to learn as much as possible, then the handbook of Mayles et al. (Ref. 18) is worthy of serious consideration.

The references Ratliff cites in his conclusion (less than 10% of the 183 publications included in the entire Resource Letter) are listed below.

14. Radiation Oncology—A Physicist's Eye View, Michael Goitein (Springer Science+Business Media, LLC, New York, 2008).

15. The Physics of Radiology, Harold Elford Johns and John Robert Cunningham, 4^th ed. (Charles C. Thomas, Springfield, Illinois, 1983).

16. The Physics of Radiation Therapy, Faiz M. Khan, 3^rd ed. (Lippincott Williams and Wilkins, Philadelphia, PA, 2003).

17. The Modern Technology of Radiation Oncology—A Compendium for Medical Physicists and Radiation Oncologists, Vols. 1 and 2, edited by Jacob Van Dyk (Medical Physics, Madison, WI, 1999 and 2005).

18. Handbook of Radiotherapy Physics—Theory and Practice, edited by P. Mayles, A. Nahum, and J. C. Rosenwald (Taylor & Francis, New York, 2007).

19. Introduction to Radiological Physics and Radiation Dosimetry, Frank Herbert Attix (Wiley-VCH, Weinheim, Germany, 1986).

26. Radiation Physics for Medical Physicists, E. B. Podgorsak (Springer-Verlag, New York, 2006).

30. Radiation Therapy Physics, William R. Hendee, Geoffrey S. Ibbott, and Eric G. Hendee, 3^rd ed. (Wiley, Hoboken, NJ, 2005).

91. Atoms, Radiation, and Radiation Protection, James E. Turner, 2^nd ed. (Wiley, New York, 1995).

92. Introduction to Health Physics, Herman Cember and Thomas E. Johnson, 4^th ed. (McGraw-Hill Medical, New York, 2009).

153. Radiation Oncology Physics: A Handbook for Teachers and Students, edited by E. B. Podgorsak (International Atomic Energy Agency, Vienna, 2005). (www-naweb.iaea.org/nahu/dmrp/pdf_files/ToC.pdf)

By the way, if you look in the acknowledgments of Ratliff’s publication you will find the ubiquitous Russ Hobbie among those thanked for their helpful suggestions.