Edward Purcell (1912-1997)

Yesterday, August 30, was the 100-year anniversary of the birth of physicist Edward Purcell (1912–1997). Purcell appears several times in the 4th edition of Intermediate Physics for Medicine and Biology. He first shows up in Chapter 1, when discussing fluid dynamics and the Reynolds number.

When the Reynolds number is small, viscous effects are important. The fluid is not accelerated, and external forces that cause the flow are balanced by viscous forces. Since viscosity is a form of internal friction in the fluid, work done on the system by the external forces is transformed into thermal energy. The low-Reynolds number regime is so different from our everyday experience that the effects often seem counterintuitive. They are nicely described by Purcell (1977).

The reference is to Purcell’s wonderful American Journal of Physics paper “Life at Low Reynolds Number” (Volume 45, Pages 3–11, 1977). It is a classic that I always hand out to my students when I teach PHY 325, Biological Physics (a class based on the textbook….you guessed it….Intermediate Physics for Medicine and Biology).

Purcell makes his second appearance in Chapter 4

The analysis [of diffusion] can also be applied to the problem of bacterial chemotaxis—the movement of bacteria along concentration gradients. This problem has been discussed in detail by Berg and Purcell (1977).

In this case, the reference is to his article with Howard Berg

Berg, H. C., and E. M. Purcell (1977). “Physics of Chemoreception,” Biophysical Journal, Volume 20, Pages 193–219.

Electricity and Magnetism,
Volume 2 of the Berkeley Physics Course,
by Edward Purcell.

In Chapter 8, Russ Hobbie and I often cite Purcell’s excellent textbook Electricity and Magnetism (1985), which is Volume 2 of the renowned Berkeley Physics Course. Our Figure 8.10 is a reproduction of one of his figures. Purcell’s book is unusual for an introductory text in that it develops magnetism as an implication of special relativity. Russ and I write

We now know that magnetism results from electric forces that moving charges exert on other moving charges and that the appearance of the magnetic force is a consequence of special relativity. An excellent development of magnetism from this perspective is found in Purcell (1985).

I’m not sure that this is the best way to teach magnetostatics to college freshman taking introductory physics, but it does provide exceptional insight into the ultimate origin of the magnetic force, especially when described in Purcell’s prose.

In Chapter 18 Russ and I describe the work that earned Purcell the Nobel Prize that he shared with Felix Bloch: nuclear magnetic resonance. We describe the Carr-Purcell pulse sequence, which is a set of radio-frequency magnetic pulses that result in a series of spin-echos, allowing the measurement of the NMR T2 relaxation time. We then consider the improved Carr-Purcell-Meiboom-Gill pulse sequence, which is like the Carr-Purcell sequence except that it avoids cumulative errors if the radio-frequency pulse does not have exactly the correct duration or amplitude.

I’m a loyal reader of Time Magazine, and to me it is impressive that Purcell has appeared on the cover of Time when the magazine selected 15 scientists—including Purcell—as men of the year for 1960.

You can learn more about Edward Purcell in an oral history transcript prepared by the Neils Bohr Library and Archives, part of the American Institute of Physics Center for History of Physics. Also, see his New York Times obituary here.

From Clocks to Chaos

From Clocks to Chaos:
The Rhythms of Life,
by Leon Glass and Michael Mackey.

In Chapter 10 of the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss nonlinear dynamics and chaos. Leon Glass and Michael Mackey are pioneers in applying nonlinear dynamics to biomedical problems. Their book From Clocks to Chaos: The Rhythms of Life discusses the idea of dynamical diseases, which are “characterized by sudden changes in the qualitative dynamics of physiological processes, leading to abnormal dynamics and disease.” I started working at the National Institutes of Health the year their book was published (1988), and a group of us would meet periodically to discuss potential applications of nonlinear dynamics to important biomedical questions.

Figure 10.34 of Intermediate Physics for Medicine and Biology is reproduced from a highly cited paper “Oscillation and Chaos in Physiological Control Systems” published in Science (Volume 197, Pages 287–289) by Mackey and Glass (over 1500 citations). It shows how changing one parameter in the system (the delay time) causes a transition from regular to chaotic behavior. In the new homework problem below, you are asked to reproduce this figure. The problem is rather advanced, because it requires you to solve a differential equation numerically using a computer program. But for those readers who are comfortable with computer programming, it provides a nice exercise in numerical analysis of a delay differential equation. And some of you who are familiar with software such at MATLAB or Mathematica might be able to reproduce the figure without knowing anything about numerical methods using their built-in differential equation solver routines. (I don’t approve of this kind of thing, being rather old-school about writing your own computer programs.)

Numerical Recipes:
The Art of Scientific Computing,
by Press et al.

For more background, I recommend the Scholarpedia article on the Mackey-Glass equation. Also, for those needing help with numerical methods, I suggest one of the versions of Numerical Recipes. (The copy on my bookshelf is Numerical Recipes in Fortran 77, but you may have a different favorite computer language).

Section 10.11

Problem 42 1/2 Write a computer program to reproduce the numerical results in Fig. 10.34b and c. The calculation was originally performed by Glass and Mackey using the delay differential equation

where x is the white blood cell count (equal to P/θ in the figure), and β_o=0.2, γ=0.1, and n=10. The initial condition for x is 0.1. Figure 10.34b uses τ = 6, and Fig. 10.34c uses τ = 20. (See Sec. 6.14 for some guidance on how to solve differential equations numerically.)

For additional fun, plot x(t-τ) versus x(t) for each case (a phase plane plot). For τ = 20, this plot contains a strange attractor. I believe it is the illustration that is on the cover of From Clocks to Chaos (however, I long ago lost or lent out my copy, so I can’t verify this).

For more about this differential equation, click here, here and here.

Electromagnetic Units

I have always found electromagnetic units confusing. There are just so many of them, and it is difficult to keep them all straight. Russ Hobbie and I introduce many of these units in the 4th edition of Intermediate Physics for Medicine and Biology. In mechanics, there are three fundamental units: the meter, second, and kilogram. Many other derived units can be expressed in terms of these three, such as: the unit of force, the newton  (after Isaac Newton), equal to a kilogram meter per second squared (N = kg m/s²); the unit of energy, the joule (after James Joule), equal to a kilogram meter squared per second squared (J = kg m²/s²); the unit of power, the watt (after James Watt), equal to a kilogram meter squared per second cubed (W = kg m²/s³); the pascal (after Blaise Pascal), the kilogram per meter per second squared (Pa = kg/(m s²); and (an easy one) the unit of frequency, the hertz (after Heinrich Hertz), which is the reciprocal of a second (Hz = 1/s).

Once electricity is introduced, a fourth unit is needed. Although purists use the ampere (after André-Marie Ampère) leading to the MKSA system of units, I prefer to take that fourth unit to be the unit of charge, the coulomb (after Charles-Augustin de Coulomb), introduced in Chapter 6 of Intermediate Physics for Medicine and Biology. Let’s call my nonstandard system of units the MKSC system. If you insist on using the ampere, just remember that an ampere is a coulomb per second (A = C/s) and you can easily do all the conversions.

Another important unit in electrostatics is the volt (after Alessandro Volta), which is defined in Chapter 6 as a joule per coulomb. Therefore, a volt is a kilogram meter squared per second squared per coulomb (V = kg m²/(s² C)). The units of electric field are then a volt per meter, but because the unit of force is a newton, equal to a kilogram meter per second squared, we find that a V/m is the same as a N/C. You see, things are already getting a bit complicated.

Next up is the ohm, Ω (after Georg Ohm), also introduced in Chapter 6. From Ohm’s law, a volt must equal an ampere times an ohm. Using the definitions for the volt and ampere given previously, we find that an ohm is actually a fancy way of saying kilogram meter squared per second per coulomb squared (Ω = kg m²/(s C²)). A siemens (after Werner Siemens) is the reciprocal of the ohm (S = s C²/(kg m²)). It used to be known as a “mho” (ohm spelled backwards). Be careful, because the symbol for the siemens, S, and the symbol for the second, s, are the same letter, one uppercase and one lowercase. It’s easy to confuse them.

Yet another electrostatics unit defined in Chapter 6 is the farad (after Michael Faraday), defined as coulomb per volt (F = C/V). The farad is therefore a second squared coulomb squared per kilogram per meter squared (F = s² C²/(kg m²)). You probably know that the time constant of a resistor-capacitor circuit is given by RC, implying that an ohm times a farad should be equal to second. You can easily verify, using our definition of ohm and farad in the MKSC units, that this is indeed the case.

So far, the units are a bit complicated, but not too bad. Things get worse when magnetism enters the picture. The magnetic field is measured in tesla (after Nikola Tesla), as introduced in Chapter 8. Can we write a tesla in terms of MKSC, or do we need some new unit for magnetism? Well, the force on a moving charge in a magnetic field is equal to the charge times the speed times the magnetic field strength. I will leave it to the reader to show that this equation implies that a tesla is simply shorthand for a kilogram per coulomb per second (T = kg/(C s)).

In Intermediate Physics for Medicine and Biology, we don’t discuss the unit for inductance, the henry (after Joseph Henry). Problem 38 in Chapter 8 implies that a volt is equal to a henry times an ampere per second. Again, I will leave it to the reader to show that the henry is therefore equal to an ohm second, or in other words a kilogram meter squared per coulomb squared (H = kg m²/C²). The time constant in a resistor-inductor circuit is L/R, implying that a henry per ohm should be a second. If we recall that a henry is equal to an ohm second, this result becomes obvious.

Another magnetic unit sometimes used for magnetic flux is the weber (after Wilhelm Weber), defined as a tesla times meter squared, implying that a weber is a kilogram meter squared per coulomb per second (Wb = kg m²/(C s)).

To summarize, below is a table listing all the units we have discussed.

N = kg m/s²
J = kg m²/s²
W = kg m²/s³
Pa = kg/(m s²)
Hz = 1/s
A = C/s
V = kg m²/(s² C)
Ω = kg m²/(s C²)
S = s C²/(kg m²)
F = s² C²/(kg m²)
T = kg/(C s)
H = kg m²/C²
Wb = kg m²/(C s)

Who’s Citing IPMB?

I’m obsessed with citations. I realize citation analysis has its limits, but it provides an objective way to measure the impact of a publication. Today I want to focus on several recent publications that have cited the textbook that Russ Hobbie and I wrote, the 4th edition of Intermediate Physics for Medicine and Biology (IPMB).

Most citations to IPMB appear in research articles published in scientific journals. Anna Longo, from the Università di Palermo in Italy, and her collaborators cite IPMB as reference 4 in their article “Discrimination of LINAC Photon and Sunlight Contributions in Watch Glass Analyzed by Means of Thermoluminescence” (Nuclear Instruments and Methods in Physics Research Section B-Beam Interactions with Materials and Atoms, Volume 281, Pages 89–96, 2012).

In the last decades the risk of accidental radiological exposure or overexposure of population has increased, because of both incidents related to industrial and medical applications of ionizing radiations and incidents related to the transport or to the dismission of radioactive sources, but also because of criminal activities with use of radioactive material [1], [2] and [3]. Biological effects produced by ionizing radiation on humans are strictly related to the absorbed dose [4].

De Wael et al., from the University of Antwerp in Belgium (“Use of Potentiometric Sensors To Study (Bio)molecular Interactions,” Analytical Chemistry, Volume 84, Pages 4921–4927, 2012), write

A Bolzmann (Gibbs) type of statistical mechanics reasoning will lead to the Nernst equation to calculate the developed potential.¹⁷

Reference 17 is to IPMB, but it is to…forgive me, Russ!…the vastly inferior 3rd edition. (I’m joking, of course. The 4th edition of IPMB is, to a first approximation, the 3rd edition with some extra homework problems and an additional chapter about ultrasound. I’ve loved every edition, but I’m only a coauthor on the 4th.)

Some authors are citing even earlier editions. The German team of Burkhard et al. (“Spatial Heterogeneity of Autoinducer Regulation Systems,” Sensors, Volume 12, Pages 4156–4171, 2012) cite the second edition of IPMB, which came out in 1988.

The diffusion coefficients for AHL are well known; [33] gives 4.9 × 10¹⁰ m²/s, the relation between molecular mass and diffusion coefficient given in [34] yields for 3OC6HSL a diffusion coefficient of 9 × 10¹⁰ m²/s. We choose the latter value.

IPMB is reference 34, and I am guessing they refer to Fig. 4.12 (using the 4th edition figure numbers), which plots the diffusion constant as a function of molecular weight. I’m glad they chose the latter value.

According to the Web of Science, an Indian team led by Sunny Nagpal cited IPMB in “A Review on Need and Importance of Impurity Profiling” (Current Pharmaceutical Analysis, Volume 7, Pages 62–70, 2011). Unfortunately, the Oakland University library does not have access to this article, and I haven’t gone to the extreme of ordering these articles through interlibrary loan (obsessions have their limits). I found several other articles I couldn’t access, some in foreign languages, that I will not mention here.

An Italian team led by Alberto Rainer cited our analysis of biomechanics in their Annals of Biomedical Engineering article “Load-Adaptive Scaffold Architecturing: A Bioinspired Approach to the Design of Porous Additively Manufactured Scaffolds with Optimized Mechanical Properties” (Volume 40, Pages 966–975, 2012). IPMB is reference 11.

The line of action of the force was defined as the line joining the center of the head of the femur to the center of gravity of the lower end of this bone. Further studies have demonstrated the importance of taking into account forces exerted by muscles on the femur head, especially for describing single-limb stand.¹¹

Some citations to IPMB aren’t what I would expect. For instance, in his paper “Within Subject Matter Eligibility-A Disease and a Cure” (Southern California Law Review, Volume 84, Pages 387–466, 2011) Allen Yu writes

In general, natural laws can be written in many forms. The relation F = m X a can also be written in the form of conservation of momentum p = m X v, for example. E.g., Lasaga, supra note 63, at 232. See also Russell K. Hobbie and Bradley J. Roth, Intermediate Physics for Medicine and Biology 83–84 (4th ed. 2007) (discussing, as another example, how continuity equations in general can be written in both integral and differential forms).

They say that all publicity is good publicity, so I am happy for the citation, but I am not sure what motivated Mr. Yu to choose IPMB rather than one of the other thousands of books he could have cited to make this very general point.

Sometimes citations can be a little annoying. For instance, Hsu and Hsu discuss the 4th edition of IPMB in “Physics Teaching in the Medical Schools of Taiwan” (Kaohsiung Journal of Medical Sciences, Volume 28, Pages S33–S35, 2012).

The credit hours would determine the textbooks and the scope and depth of teaching. Moreover, because of the distinction between the medical education system in Taiwan and those in other countries like the USA, a suitable physics textbook for medical students in Taiwan has also been a long-term problem. For instance, Physics by Kane and Sternheim [2] with a broad introduction to physical applications in medicine could be too simple in content because of the lack of calculus. Intermediate Physics for Medicine and Biology by Hobbie [1] apparently contains a lot of material beyond the level of general physics. Other physics textbooks can also fail to include physical application in medicine, be at a level too basic or advanced in physical principles or compound factors, and might not be suitable for use in Taiwan.

I guess they consider us to be too advanced for Taiwanese medical students, which is surprising given that I consider our book to the at an intermediate level. I’ll ignore their omission of the second author in “Hobbie [1]”, but the use of the word “apparently” suggests that Hsu and Hsu haven’t actually looked at our book.

Vaz and Griffiths, from the University of West England (“Parathyroid Imaging and Localization Using SPECT/CT: Initial Results,” Journal of Nuclear Medicine and Technology, Volume 39, Pages 1–6, 2011), cite IPMB multiple times, but it seems that we are just one of a group of texts they use to cover their bases. The 3rd edition of IPMB is reference 25.

99mTc-sestamibi has yielded sensitivity rates of about 90% in primary hyperparathyroidism (1–3,15–28). With this method, 900 MBq are administered intravenously, and planar images are acquired at 15 min and at 1.0–3 h after injection. (1–3,15–28)…

Especially when combined with CT, SPECT becomes particularly helpful for preoperative localization of eutopic and ectopic parathyroid adenomas (1–3,15–28)...

Many surgeons routinely use ultrasound, radionuclide parathyroid imaging, or both before surgery, and scintigraphy is also useful for locating the adenoma during surgery (1–3,15–28)…

Although the superior or inferior origin of a parathyroid gland often can be determined by its location, an enlarged gland may migrate and be seen in scintigraphic images at the level of the thyroid gland (1–3,15–28).

The internet is changing the way physicists publish articles. The 2nd edition of IPMB is cited in the paper “Peculiarities of Brain’s Blood Flow: Role of Carbon Dioxide” by Alexander Gersten, which appeared in the preprint collection arXiv, submitted in March 2011.

It seems however that the physical and mathematical aspects of the global cerebral blood flow (CBF), or average rCBF, were not sufficiently explored. Our main interest is use of physical principles (Hobbie, 1988), physical and mathematical reasoning as well as means to describe the main features of CBF in a simple way.

My collaborator and former PhD advisor, John Wikswo, and his colleagues cited IPMB as reference 3 in their recent review “How Do Control-Based Approaches Enter into Biology?” (Annual Reviews of Biomedical Engineering, Volume 13, Pages 369–396, 2011). Reference 1 is Guyton and Hall’s Textbook of Medical Physiology; that’s pretty good company.

For example, in whole-organ physiology, control has been modeled in detail to provide a clear understanding of a multitude of phenomena such as the control of blood oxygenation, pH and pressure, body temperature, heart rate, hormone and glucose levels, neurohumeral feedback, pain adaptation, skeletal muscle contraction, and visual object tracking (1–3).

Of course, I cite my own book (Roth, B. J., “The Role of Magnetic Forces in Biology and Medicine,” Experimental Biology and Medicine, Volume 236, Pages 132–137, 2011). In fact, I cite it in the opening paragraph of the paper (IPMB is reference 1).

Over the last 20 years, several research groups have developed imaging methods that take advantage of the force acting on biocurrents when a magnetic field is present. The underlying mechanism is familiar to anyone who has taken an introductory physics class¹: a wire carrying a current I, having a length L and lying perpendicular to a magnetic field B experiences a magnetic force F = ILB, often called the “Lorentz force.”

Feel free to ignore this one, since self-citations really shouldn’t count. By the way, I discussed this paper in a blog entry last year.

Not all citations are from journal articles. IPMB is cited in Xiaogai Li’s doctoral thesis “Finite Element and Neuroimaging Techniques to Improve Decision-Making in Clinical Neuroscience,” completed in 2012 at the Royal Institute of Technology in Stockholm.

The scalar proportionality constant D is known as the diffusion coefficient and depends on the medium viscosity, the particle size and the temperature [68].

Reference 68 is IPMB, and I expect the author refers to Eq. 4.23 in the 4th edition. A lot of these citations are to IPMB’s discussion of diffusion. My guess is that there are few good books on this topic.

Bonginkosi Vincent Kheswa cited the very first edition of IPMB in his masters thesis “Deflection of Ag-atoms in an Inhomogeneous Magnetic Field” (Stellenbosch University, South Africa, 2011)

The γ-rays are high-energy photons that originate from transitions between the energy levels within the atomic nucleus [Ho78].

An odd reference to IPMB appears in the journal Computing in Science and Engineering (Volume 13, Pages 6–10, 2011), in Peter Jung's review of the textbook Introductory Biophysics by Claycomb and Tran (2010).

Furthermore, this book [Claycomb and Tran] assumes that the reader has already taken a course in calculus based introductory physics; in that respect, it’s unlike Russell K. Hobbie and Bradley J. Roth’s Intermediate Physics for Medicine and Biology,³ which assumes no knowledge of basic physics.

The preface of our book states that “The reader is assumed to have taken physics and to know the basic vocabulary.” I expect a reader of IPMB who had “no knowledge of basic physics” would struggle. But it’s nice to know that Jung believes our book is so clear that one could study from it with no prior exposure to physics.

Citations also appear in patents. Sawhney et al. cite IPMB in US patent 8,003,705 (“Biocompatible Hydrogels Made With Small Molecule Precursors,” 2011).

Visually observable visualization agents are preferred. Wavelengths of light from about 400 to 750 nm are observable to the human as colors (R. K. Hobbie, Intermediate Physics for Medicine and Biology, 2nd Ed., pages 371–373).

Other books sometimes cite IPMB, such as The SQUID as Diagnostic Tool in Medicine and its Use With Other Experimental Stimulation and Theoretical Methods for Evaluation and Treatment of Various Diseases by Photios Anninos of the Democritus University of Thrace in Alexandroupolis, Greece. IPMB is reference 20, and refers to our analysis of Fourier series in Chapter 11.

In this Fourier statistical analysis each MEG record it was stored for off-line statistical analysis in which it was trying to find the best fit of one trigonometric mathematical function [20] as it is seen in the following equation:...

Another place to find citations are conference proceedings. Stiles et al. cite IPMB at in the proceedings of the American Institute of Aeronautics and Astronautics (AIAA) Gossamer Systems Forum, held April 4–7, 2011 in Denver, Colorado. Their paper “Voltage Requirements for Electrostatic Inflation of Gossamer Space Structures” refers to Eq. 6.10 and Fig. 6.10 in Section 6.3 about Gauss’s Law.

An approximation of the field at a distance from a charged membrane can be made using the equation for the field due to a finite rectangular plate.³⁰

Another example is “Ascorbic Acid Encapsulation in Hydrophobic Silica Xerogel,” (Castro et al., Food Technology and Biotechnology, Volume 49, Pages 347–351, 2011) contained in the Selected Papers Presented at the International Congress on Bioprocesses in Food Industries 2010, held October 5–8 in Curitiba, Brazil. IPMB is reference 12. I’m guessing that the authors are referring to Section 5.9, A Continuum Model for Volume and Solute Transport in a Pore.

Taking into account the combined effect of xerogel porous radius r and of porous wall drag on the diffusion process (12), and using ~0.24 nm for the AA molecule mean radius and r~0.58 nm (from XRD results), another estimation of D_eff is performed: D_eff~6.2 × 10^-7 cm²/s, which is 3.4 larger than the previous value.

What can we learn from all this? IPMB shows up in all sorts of publications, often unexpectedly, and the citations are from scientists throughout the world. It is very gratifying that researchers choose to cite Intermediate Physics for Medicine and Biology. Russ and I believe that our book makes a contribution to science and education, and it is good to know that others occasionally agree with us.

The Physics of the Olympics

The 4th edition of Intermediate Physics for Medicine and Biology begins in Chapter 1 with a discussion of biomechanics. Of course, biomechanics is essential for understanding the physics of sports, but Russ Hobbie and I barely even begin to consider this vast topic. With the Olympic games going on in London, I decided to provide references to several papers from my favorite journal, the American Journal of Physics, about the physics of the Olympics. Most of these, and many others, can be found in Cliff Frohlich’s excellent resource letter, which leads off the list.

• Forhlich, C. (2011) “Resource Letter PS-2: Physics of Sports,” American Journal of Physics, Volume 79, Pages 565–574.
• Tan, A. and G. Miller (1981) “Kinematics of the Free Throw in Basketball,” American Journal of Physics, Volume 49, Pages 542–544.
• Brancazio, P. J., (1981) “Physics of Basketball,” American Journal of Physics, Volume 49, Pages 356–365.
• Frohlich, C. (1979) “Do Springboard Divers Violate Angular Momentum Conservation?” American Journal of Physics, Volume 47, Pages 583–592.
• Frohlich, C. (1985) “Effect of Wind and Altitude on Record Performance in Foot Races, Pole Vault, and Long Jump,” American Journal of Physics, Volume 53, Pages 726–730.
• Eriksen, H. K., J. R. Kristiansen, O. Langangen, and I. K. Wehus (2009) “How Fast Could Usain Bolt Have Run? A Dynamical Study,” American Journal of Physics, Volume 77, Pages 224–228. 
• Helene, O. and M. T. Yamashita (2010) “The Force, Power, and Energy of the 100 Meter Sprint,” American Journal of Physics, Volume 78, Pages 307–309.
• Heck, A. and T. Ellermeijer (2009) “Giving Students the Run of Sprinting Models,” American Journal of Physics, Volume 77, Pages 1028–1038.
• Helene, O. and M. T. Yamashita (2005) “A Unified Model for the Long and High Jump,” American Journal of Physics, Volume 73, Pages 906–908.
• Frohlich, C. (1981) “Aerodynamic Effects on Discus Flight.,”American Journal of Physics, Volume 49, Pages 1125–1132.
• Lichtenberg, D. B. and J. G. Wills (1978) “Maximizing the Range of the Shot Put,” American Journal of Physics, Volume 46, Pages 546–549.
• Barrow, J. D. (2010) “Rowing and the Same-Sum Problem Have Their Moments,” American Journal of Physics, Volume 78, Pages 728–732. 

For those readers who don’t have access to the American Journal of Physics, here is a website from NBC news, developed with help from the National Science Foundation, about the science of the summer Olympics.

I saw a review of The Science of Sports: Winning in the Olympics this week from The Scientist.

Here is a nice explanation with video of the physics of the high jump on the Science Friday website.

Finally, for all of you who—like me—fell asleep last night before Gabby Douglas (the “flying squirrel”) won her individual all-around gold medal in women’s gymnastics, here is a video of her winning floor routine.

Gabrielle Douglas, London 2012 Olympics.

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

Frank Netter, Medical Illustrator

The CIBA Collection
of Medical Illustrations,
by Frank Netter.

When I started graduate school at Vanderbilt University, I had a strong background in physics but was weak in biology and medicine. One of the sources I used to learn some anatomy was the eight-volume CIBA Collection of Medical Illustrations by Frank Netter. I dearly loved browsing through his illustrations. Because of my interest in cardiac electrophysiology, I was particularly fond of Volume 5 about the heart. Some of his illustrations can be seen online here, here, here, here, and here.

At http://www.netterimages.com you can learn much about Netter and his work. Some of Netter’s books have recently been updated and reissued. A video (below) about this reissue includes an interview with Netter, showing him at work on his drawings. Netter’s Atlas of Neuroscience was updated by David Felten, the Associate Dean for Research at the Oakland University William Beaumont School of Medicine. I often see students walking around the OU campus carrying Netter’s Atlas of Human Anatomy. You can even buy Netter flash cards.

The Netter Collection of Medical Illustrations.

The CIBA “green books” relaunched. 

https://www.youtube.com/embed/24d1XG948kg

The Society of Illustrators Hall of Fame contains an entry about Netter.

Frank H. Netter (1906–1991) was born in New York and grew up during the Golden Age of Illustration. He studied at the National Academy of Design, and later at the Art Students League. But his mother wanted him to be a doctor, and when she died suddenly, he resolved to give up art, and study medicine as she had wished. He graduated from City College of New York, BS 1927, and New York University Medical College, MD 1931. But the demand for his pictures far exceeded the demand for his surgery.

More about Netter’s life is described in his New York Times obituary. Also, see the article “Frank H Netter, Medicine's Michelangelo: An Editorial Perspective,” by Rita Washko (Science Editor, Volume 29, Pages 16–18, 2006).

Readers of the 4th edition of Intermediate Physics for Medicine and Biology who need to brush up on the anatomy should take a look at Netter’s books.

Finally, listen to his daughter talk about Frank Netter's life and work.

Medicine’s Michelangelo: The Life and Art of Frank H. Netter, M.D. 

https://www.youtube.com/embed/Dpn5AgHBqyI

A Mechanism for Anisotropic Reentry in Electrically Active Tissue

1992 was a good year for me. My wife and I, who had been married for seven years, had two young daughters, and we had just bought a house in Kensington, Maryland. While working at the National Institutes of Health I published eight papers in 1992, mostly about magnetic stimulation of nerves. My favorite paper from that year, however, was one about the heart: “A Mechanism for Anisotropic Reentry in Electrically Active Tissue” (Journal of Cardiovascular Electrophysiology, Volume 3, Pages 558–566). The lead author was Joshua Saypol, an engineering undergraduate at Brown University who would come home to Maryland each summer and work at NIH. Josh was a big, strong fellow, and handy to have around when we had heavy things to move. But he was also smart and hard-working, and we ended up publishing three papers together. The cardiac paper was the last of these, and the least cited (indeed, according to the Web of Science the paper has not been cited by anyone other than me for the last ten years). You can get the gist of it from the abstract.

Introduction: Numerical simulations of wavefront propagation were performed using a two-dimensional sheet of tissue with different anisotropy ratios in the intracellular and extracellular spaces.
Methods and Results: The tissue was represented by the bidomain model, and the active properties of the membrane were described by the Hodgkin-Huxley equations. Two successive stimuli, delivered through a single point electrode, resulted in the formation of a reentrant wavefront when the second stimulus was delivered during the vulnerable period of the first wavefront.
Conclusion: The mechanism for the development of reentry was that the bidomain tissue responded to point cathodal stimulation by depolarizing the tissue under the electrode in the direction perpendicular to the fiber axis, and hyperpolarizing the tissue in the direction parallel to the fiber axis. Such a distribution of depolarization and hyperpolarization modifies the refractory period of the action potential differently in each direction, resulting in block in the direction perpendicular to the fiber axis and leading to reentry and the formation of stable, rotating wavefronts.

The paper arises from two previous lines of research. First is the calculation of the transmembrane potential induced by a point stimulus, performed by Nestor Sepulveda, John Wikswo and me (“Current Injection Into a Two Dimensional Bidomain,” Biophysical Journal, Volume 55, Pages 987–999, 1989), which I discussed in a previous blog entry. We found that cardiac tissue is depolarized (positive transmembrane potential) under a cathode, but hyperpolarized (negative transmembrane potential) a millimeter or two from the cathode in each direction along the cardiac fibers (at what are nowadays called “virtual anodes”). That paper used a passive steady-state membrane, but in a subsequent paper I derived an algorithm to solve the bidomain equations including time dependence and an active model for the membrane kinetics (“Action Potential Propagation in a Thick Strand of Cardiac Muscle,” Circulation Research, Volume 68, Pages 162–173, 1991). Having this algorithm, I decided to investigate what effect the virtual anodes had on propagation following an extracellular stimulus. Both of these papers were based on the bidomain model, which is a mathematical model of the electrical properties of cardiac tissue that Russ Hobbie and I describe in Chapter 7 of the 4th edition of Intermediate Physics for Medicine and Biology.

Another reason I like the paper with Josh so much is that we collaborated with Arthur Winfree while writing it. I’ve written about our work with Winfree previously in this blog. Art had made a prediction about the induction of “reentry” (a cardiac arrhythmia) following a premature stimulus (a stimulus applied to tissue near the end of its refractory period). It provided the ideal hypothesis to test with our model. I remember vividly Josh coming to me with plots of the transmembrane potential showing the first signs of reentry, and how even after our discussions with Art we didn’t quite believe what we were seeing. Winfree helped Josh and I publish a preliminary letter about our calculation in the International Journal of Bifurcation and Chaos (Volume 1, Pages 927–928, 1991), which was just starting up. It has been almost ten years now since Art passed away, and I still miss him.

Astute readers (and I’m sure ALL readers of this blog are astute) will notice something odd in the abstract quoted above: “the active properties of the membrane were described by the Hodgkin-Huxley equations” (my italics). What are the Hodgkin-Huxley equations—which describe a squid nerve axon action potential (see Chapter 6 of Intermediate Physics for Medicine and Biology)—doing in a paper about cardiac tissue? This is a legitimate criticism, and one the reviewers raised, but surprisingly it didn’t prove fatal for publication of the article (although I was asked to change the title to the generic “...Electrically Active Tissue,” and you won’t find the word “cardiac” in the abstract). I used the Hodgkin-Huxley model because I didn’t know any better at the time. (In the paper, we claimed that “we used the Hodgkin-Huxley model instead of a myocardial membrane model because of a limitation of computer resources,” and that might be part of the reason too.) Models more appropriate for cardiac tissue (such as the Beeler-Reuter model that I used in later publications) were more complicated, and I wasn’t familiar with them. Besides, Josh and I were most interested in generic properties of reentry induction that would probably not be too sensitive to the membrane model (or so we told ourselves). I wonder now why we didn’t use the generic FitzHugh-Nagumo model, but we didn’t. Never again would reviewers let me get away with using the Hodgkin-Huxley model for cardiac tissue (and rightly so), and I suspect it is one of the reasons the paper is rarely cited anymore.

Nevertheless, the paper did make an important contribution to our understanding of the induction of reentry, which is why I like it so much. It was the first paper to present the idea of regions of hyperpolarization shortening the refractory period, and thereby creating regions of excitable tissue through which wave fronts can propagate. We state this clearly in the discussion.

The crucial point is that a premature stimulus causes an unusually-shaped transmembrane potential distribution that produces a directionally-dependent change of the refractory period, thereby creating a necessary condition for conduction block in one direction.

We go into more detail in the results

The depolarization wavefront is followed by a front of refractoriness. During the refractory period, the sodium channel inactivation gate (the h gate) opens slowly, while the potassium channel [activation gate] (the n gate) closes slowly; the tissue remains refractory until these two gates have recovered sufficiently. If a hyperpolarizing current is applied to the tissue during the refractory period, it will cause the h gate to open and the n gate to close more quickly than they normally would, thereby shortening the refractory period. Thus, when the tissue is stimulated, the refractory period is shortened in the area of hyperpolarization along the x axis [parallel to the fibers]. In the area along the y axis [perpendicular to the fibers] that is depolarized by the stimulus, on the other hand, the h and n gates move away from their resting values, and therefore the refractory period is lengthened. If the second stimulus is timed just right, it can take the tissue along the x direction out of the refractory period, while along the y direction the tissue remains unexcitable. Thus, the action potential elicited by the large depolarization directly below the electrode can propagate only in the x direction.

This idea influenced subsequent work by myself (“Nonsustained Reentry Following Successive Stimulation of Cardiac tissue Through a Unipolar Electrode,” Journal of Cardiovascular Electrophysiology, Volume 8, Pages 768–778, 1997) and others (Efimov et al., “Virtual Electrode-Induced Phase Singularity: A Basic Mechanism of Defibrillation Failure,” Circulation Research, Volume 82, Pages 918–925, 1998), and now, twenty years later, lies at the heart of the concept of “virtual electrodes” and their role during defibrillation (see, for instance: Efimov, Gray, and Roth, “Virtual Electrodes and Deexcitation: New Insights into Fibrillation Induction and Defibrillation,” Journal of Cardiovascular Electrophysiology, Volume 11, Pages 339–353, 2000). After I left NIH, Marc Lin, Wikswo and I confirmed experimentally this mechanism of reentry induction (“Quatrefoil Reentry in Myocardium: An Optical Imaging Study of the Induction Mechanisms,” Journal of Cardiovascular Electrophysiology, Volume 10, Pages 574–586, 1999).

The acknowledgments section of the paper brings back many memories.

Acknowledgments: We thank Art Winfree for his many ideas and suggestions, Peter Basser for his careful reading of the manuscript and Barry Bowman for his editorial assistance. The calculations were performed on the NIH Convex C240 computer. We thank the staff of the NIH computer center for their support.

First, of course, we mentioned Art’s contributions. Peter Basser, the inventor of MRI Diffusion Tensor Imaging, was a friend of mine at NIH, and we used to read each other’s papers before submission to a journal. Barry Bowman also worked at NIH. He was a former high school English teacher, and I’d always give him drafts of my papers for polishing. Much of what I know about writing English well I learned from him. I suspect my current laptop computer can calculate faster than the Convex C240 supercomputer could, but it was fairly powerful for the time. In 1992, Josh and I did our programming in FORTRAN. Some things never change.

Magnetic Characterization of Isolated Candidate Vertebrate Magnetoreceptor Cells

Big news this week in the field of magnetoreception. A paper titled “Magnetic Characterization of Isolated Candidate Vertebrate Magnetoreceptor Cells” by Stephan Eder and his colleagues was published online (“early edition”) in the Proceedings of the National Academy of Sciences. One commentator went so far as to suggest that these magnetoreceptors are “the biological equivalent of the elusive Higgs boson” (an exaggeration, but a catchy quote with a grain of truth). The abstract to the paper is given below.

Over the past 50 y, behavioral experiments have produced a large body of evidence for the existence of a magnetic sense in a wide range of animals. However, the underlying sensory physiology remains poorly understood due to the elusiveness of the magnetosensory structures. Here we present an effective method for isolating and characterizing potential magnetite-based magnetoreceptor cells. In essence, a rotating magnetic field is employed to visually identify, within a dissociated tissue preparation, cells that contain magnetic material by their rotational behavior. As a tissue of choice, we selected trout olfactory epithelium that has been previously suggested to host candidate magnetoreceptor cells. We were able to reproducibly detect magnetic cells and to determine their magnetic dipole moment. The obtained values (4 to 100 fA m²) greatly exceed previous estimates (0.5 fA m²). The magnetism of the cells is due to a μm-sized intracellular structure of iron-rich crystals, most likely single-domain magnetite. In confocal reflectance imaging, these produce bright reflective spots close to the cell membrane. The magnetic inclusions are found to be firmly coupled to the cell membrane, enabling a direct transduction of mechanical stress produced by magnetic torque acting on the cellular dipole in situ. Our results show that the magnetically identified cells clearly meet the physical requirements for a magnetoreceptor capable of rapidly detecting small changes in the external magnetic field. This would also explain interference of ac powerline magnetic fields with magnetoreception, as reported in cattle.

The PNAS published a highlight about the article.

Identification of cells that sense Earth’s magnetic field

Researchers have isolated magnetic cells thought to underlie certain animals’ ability to navigate by Earth’s magnetic field. Behavioral studies have long provided evidence for the existence of a magnetic sense, but the identity of the specialized cells that comprise this internal compass has remained elusive. Stephan Eder and colleagues isolated the putative magnetic field-sensing cells that line the trout’s nasal cavity, and which contain iron-rich deposits of the magnetic material called magnetite. The authors placed a suspension of trout nasal tissue under a light microscope, and identified magnetic cells by their rotational motion in the presence of a slowly rotating external magnetic field. After siphoning off the rotating cells to characterize them in greater detail, the authors discovered that each cell contained reflective, iron-rich magnetic particles that were anchored to the cell membrane. The authors also determined that the cells are about 100 times more sensitive to magnetic fields than previously estimated. The findings suggest that the cells are capable of detecting magnetic north as well as small changes in the external magnetic field, and could form the basis of an accurate magnetic sensory system, according to the authors.

Russ Hobbie and I discuss the role of magnetic materials in biology in our chapter about biomagnetism in the 4th edition of Intermediate Physics for Medicine and Biology. We included in our book a photograph of magnetosomes (intracellular magnetite particles) in magnetotactic bacteria. In the photo, the magnetosomes are each about 0.05 μm on a side, and about 20 particles form a line roughly 1 μm long. Eder et al., on the other hand, find magnetic inclusions that are more spherical, and roughly 1–2 μm across. A trout cell has a really big magnetic moment when it contains such a large inclusion, but less than one cell in a thousand responds to the magnetic field and therefore presumably contains one. For a magnetotactic bacterium to have the same magnetic moment, it would need to be packed solid with magnetite.

I find the PNAS paper to be fascinating, and the method to detect individual cells using a rotating magnetic field is clever. However, in my opinion the last sentence of the abstract is a bit speculative, given that typical residential 60 Hz magnetic fields are 10,000 times smaller than the 2 mT fields used by Eder et al., and the frequency is almost 200 times higher. Granted the large magnetic moment makes the idea of powerline field detection intriguing, but that hypothesis is far from proven and I remain skeptical.

One of the coauthors on the PNAS paper is Joseph Kirschvink, whose work we discuss extensively in Section 9.10, Possible Effects of Weak External Electric and Magnetic Fields. Kirschvink is the Nico and Marilyn Van Wingen Professor of Geobiology at Caltech. He has developed several fascinating and controversial hypotheses, such as the Snowball Earth concept and the idea that a meteor found in 1984 contains evidence of life on Mars (he collaborated with my PhD advisor, John Wikswo, to make magnetic field measurements on that meteor). Kirschvink received the William Gilbert Award from the American Geophysical Union in 2011 for his work on geomagnetism. In the citation for this award, Benjamin Weiss of MIT wrote that “Joe represents everything we are looking for in a William Gilbert awardee. He is an ‘ideas man,’ a gadfly, working at the edge of the crowd while the crowd chases after him!” Kirschvink has also won Caltech’s Feynman Prize for Excellence in Teaching.

The PNAS paper has triggered an avalanche of press reports, including those in Science News,  the International Science Times, Science Daily, Phys.org, Live Science, and Discover Magazine.

Women in Medical Physics

Last week in this blog, I discussed the medical physicist Rosalyn Yalow, who was the second female to win the Nobel Prize in Physiology or Medicine (The first was biochemist Gerty Cori), and who developed, with Solomon Berson, the radioimmunoassay technique. Her story reminds us of the important contributions of females to medical physics. I am particularly interested in this topic because Oakland University recently was awarded an ADVANCE grant from the National Science Foundation, with the goal of increasing the participation and advancement of women in academic science and engineering careers. I am on the leadership team of this project, and we are working hard to improve the environment for female STEM (science, technology, engineering, and math) faculty.

Of course the real reason I support increasing opportunities for women in the sciences is that I am certain many of the readers of the 4th edition of Intermediate Physics for Medicine and Biology are female. Medical physics provides several role models for women. For instance, Aminollah Sabzevari published an article in the Science Creative Quarterly titled “Women in Medical Physics.” Sabzevari begins

Traditionally, physics has been a male-dominated occupation. However, throughout history there have been exceptional women who have risen above society’s restrictions and contributed greatly to the advancement of physics. Women have played an important role in the creation, advancement and application of medical physics. As a frontier science, medical physics is less likely to be bound by society’s norms and less subject to the inherent glass ceiling limiting female participation. Women such as Marie Curie, Harriet Brooks, and Rosalind Franklin helped break through that ceiling, and their contributions are worth observing.

Another notable female medical physicist is Edith Hinkley Quimby, who established the first measurements of safe levels of radiation. The American Association of Physicists in Medicine named the Edith H. Quimby Lifetime Achievement Award in her honor.

On a related note (though having little to do with medical or biological physics), I recently read a fascinating biography of Sophie Germain (1776–1831), who did fundamental work in number theory and elasticity.

Finally, in my mind the greatest female physicist of all time (yes, greater than Marie Curie) is Lise Meitner, who first discovered nuclear fission. A great place to learn more about her life and work is Richard Rhodes’ masterpiece The Making of the Atomic Bomb.

One characteristic these women have in common is that they overcame great obstacles in order to become scientists. Their tenacity and determination inspires us all.

Rosalyn Yalow and the Radioimmunoassay

The radioimmunoassay is a sensitive technique for measuring tiny amounts of biologically important molecules, such as the hormone insulin in the blood. The basic idea is to tag insulin with a radioisotope such as I-125, and mix it with antibodies for insulin. Then, add to this mix the patient’s blood. The insulin in the blood competes with the tagged insulin for binding to the antibodies. Next, remove the antibodies and their bound insulin, leaving just the free insulin in the supernatant. The radioactivity of the supernatant provides a way to determine the concentration of insulin in the blood.

Russ Hobbie and I describe the basics of a radioimmunoassay in Chapter 17 of the 4th edition of Intermediate Physics for Medicine and Biology.

Four kinds of radioactivity measurements have proven useful in medicine. The first involves no administration of a radioactive substance to the patient. Rather, a sample from the patient (usually blood) is mixed with a radioactive substance in the laboratory, and the resulting chemical compounds are separated and counted. This is the basis of various competitive binding assays, such as those for measuring thyroid hormone and the availability of iron-binding sites. The most common competitive binding technique is called radioimmunoassay. A wide range of proteins are measured in this manner.

The radioimmunoassay was developed by Rosalyn Yalow and Solomon Berson. Yalow received the Nobel Prize in Physiology or Medicine for this work in 1977 (Berson had died by then, and the Nobel committee never gives a prize posthumously). For readers of Intermediate Physics for Medicine and Biology, Yalow is interesting because she started out as a physics major, getting her bachelor’s degree in physics from Hunter College, part of the City University of New York (CUNY) system. In 1945 she obtained a PhD in nuclear physics from the University of Illinois at Urbana-Champaign. Building on this physics background, and collaborating with Berson, in the 1950s she developed the radioimmunoassay. Interestingly she and Berson refused to patent the method, wanting it to be freely available for use in medicine. Yalow died just over one year ago, at age 89.

You can learn more about Rosalyn Yalow and her inspiring life from her Nobel autobiography, her Physics Today obituary, her New York Times obituary, and the Jewish Woman’s Archive. For those who prefer a video, click here. I have not read Eugene Straus’s book Rosalyn Yalow: Nobel Laureate: Her Life and Work in Science, but I am putting it on my list of things to do.

Television interview with Rosalyn Yalow.

https://www.youtube.com/watch?v=wDH1nFMnELs 

I often like to finish a blog entry about a noteworthy scientist with their own words. Below are the opening paragraphs of Yalow’s Nobel Prize Lecture.

To primitive man the sky was wonderful, mysterious and awesome but he could not even dream of what was within the golden disk or silver points of light so far beyond his reach. The telescope, the spectroscope, the radiotelescope—all the tools and paraphernalia of modern science have acted as detailed probes to enable man to discover, to analyze and hence better to understand the inner contents and fine structure of these celestial objects.

Man himself is a mysterious object and the tools to probe his physiologic nature and function have developed only slowly through the millenia. Becquerel, the Curies and the Joliot-Curies with their discovery of natural and artificial radioactivity and Hevesy, who pioneered in the application of radioisotopes to the study of chemical processes, were the scientific progenitors of my career. For the past 30 years I have been committed to the development and application of radioisotopic methodology to analyze the fine structure of biologic systems.

From 1950 until his untimely death in 1972, Dr. Solomon Berson was joined with me in this scientific adventure and together we gave birth to and nurtured through its infancy radioimmunoassay, a powerful tool for determination of virtually any substance of biologic interest. Would that he were here to share this moment.