The Truth About Terahertz

In Chapter 14 of the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss Terahertz Radiation.

For many years, there were no good sources or sensitive detectors for radiation between microwaves and the near infrared (0.1-100 THz; 1 THz = 10¹² Hz). Developments in optoelectronics have solved both problems, and many investigators are exploring possible medical uses of THz radiation (“T rays”). Classical electromagnetic wave theory is needed to describe the interactions, and polarization (the orientation of the E vector of the propagating wave) is often important. The high attenuation of water to this frequency range means that studies are restricted to the skin or surface of organs such as the esophagus that can be examined endoscopically. Reviews are provided by Smye et al. (2001), Fitzgerald et al. (2002), and Zhang (2002).

(By the way, apologies to Dr. N. N. Zinovev, a coauthor on the Fitzgerald et al. paper, whose last name is spelled incorrectly in our book.) 

In the September 2012 issue of the magazine IEEE Spectrum, Carter Armstrong (a vice president of engineering at L-3 Communications, in San Francisco) reviews some of the challenges facing the development of Terahertz radiation. His article “The Truth About Terahertz” begins

Wirelessly transfer huge files in the blink of an eye! Detect bombs, poison gas clouds, and concealed weapons from afar! Peer through walls with T-ray vision! You can do it all with terahertz technology—or so you might believe after perusing popular accounts of the subject.

The truth is a bit more nuanced. The terahertz regime is that promising yet vexing slice of the electromagnetic spectrum that lies between the microwave and the optical, corresponding to frequencies of about 300 billion hertz to 10 trillion hertz (or if you prefer, wavelengths of 1 millimeter down to 30 micrometers). This radiation does have some uniquely attractive qualities: For example, it can yield extremely high-resolution images and move vast amounts of data quickly. And yet it is nonionizing, meaning its photons are not energetic enough to knock electrons off atoms and molecules in human tissue, which could trigger harmful chemical reactions. The waves also stimulate molecular and electronic motions in many materials—reflecting off some, propagating through others, and being absorbed by the rest. These features have been exploited in laboratory demonstrations to identify explosives, reveal hidden weapons, check for defects in tiles on the space shuttle, and screen for skin cancer and tooth decay.

But the goal of turning such laboratory phenomena into real-world applications has proved elusive. Legions of researchers have struggled with that challenge for decades.

Armstrong then explores the reasons for these struggles. The large attenuation coefficient of T-rays places severe limitations on imaging applications. He then turns specifically to medical imaging.

Before leaving the subject of imaging, let me add one last thought on terahertz for medical imaging. Some of the more creative potential uses I’ve heard include brain imaging, tumor detection, and full-body scanning that would yield much more detailed pictures than any existing technology and yet be completely safe. But the reality once again falls short of the dream. Frank De Lucia, a physicist at Ohio State University, in Columbus, has pointed out that a terahertz signal will decrease in power to 0.0000002 percent of its original strength after traveling just 1 mm in saline solution, which is a good approximation for body tissue. (Interestingly, the dielectric properties of water, not its conductive ones, are what causes water to absorb terahertz frequencies; in fact, you exploit dielectric heating, albeit at lower frequencies, whenever you zap food in your microwave oven.) For now at least, terahertz medical devices will be useful only for surface imaging of things like skin cancer and tooth decay and laboratory tests on thin tissue samples.

Following a detailed review of terahertz sources, Armstrong finishes on a slightly more optimistic note.

There is still a great deal that we don’t know about working at terahertz frequencies. I do think we should keep vigorously pursuing the basic science and technology. For starters, we need to develop accurate and robust computational models for analyzing device design and operation at terahertz frequencies. Such models will be key to future advances in the field. We also need a better understanding of material properties at terahertz frequencies, as well as general terahertz phenomenology.

Ultimately, we may need to apply out-of-the-box thinking to create designs and approaches that marry new device physics with unconventional techniques. In other areas of electronics, we’ve overcome enormous challenges and beat improbable odds, and countless past predictions have been subsequently shattered by continued technological evolution. Of course, as with any emerging pursuit, Darwinian selection will have its say on the ultimate survivors.

Terahertz radiation is such a big field that one year ago the IEEE introduced a new journal: IEEE Transactions on Terahertz Science and Technology. In the inaugural issue, Taylor et al. examine “THz Medical Imaging.”

Benedek and Villars, Volume 3

Physics With Illustrative Examples
From Medicine and Biology, Volume 3,
by Benedek and Villars.

This is the third and final entry in a series of blog entries about Benedek and Villars’ textbook Physics With Illustrative Examples From Medicine and Biology. Today I discuss Volume 3, about electricity and magnetism. In the preface to the first edition of Volume 3, Benedek and Villars write

With this volume on Electricity and Magnetism, we complete the third and final volume of our textbooks on Physics, with Illustrative Examples from Medicine and Biology. We believe that this volume is as unique as our previous books on Classical Mechanics (Vol. 1) and Statistical Physics (Vol. 2). Here, we continue our program of interweaving into the rigorous development of classical physics, an analysis and clarification of a wide variety of important phenomena in physical chemistry, biology, physiology, and medicine.

All three volumes of
Physics With Illustrative Examples
From Medicine and Biology,
by Benedek and Villars.

The topics covered in Volume 3 are similar to those Russ Hobbie and I discuss in Chapters 6-9 in the 4th edition of Intermediate Physics for Medicine and Biology. Because I do research in the fields of bioelectricity and biomagnetism, you might expect that this would be my favorite volume of the three, but it’s not. I don’t find that it contains as many rich and interesting biological examples. Yet it is a solid book, and contains much useful electricity and magnetism.

Physics With Illustrative Examples
From Medicine and Biology,
by Benedek and Villars.

Before leaving this topic, I should say a few words about George Benedek and Felix Villars. Benedek is currently the Alfred H. Caspary Professor of Physics and Biological Physics in the Department of Physics in the Harvard-MIT Division of Health Sciences and Technology. His group’s research program “centers on phase transitions, self-assembly and aggregation of biological molecules. These phenomena are of biological and medical interest because phase separation, self-assembly and aggregation of biological molecules are known to play a central role in several human diseases such as cataract, Alzheimer's disease, and cholesterol gallstone formation.” Villars was born in Switzerland. In the late 1940s, he collaborated with Wolfgang Pauli, and developed Pauli-Villars regularization. He began work at the MIT in 1950, where he collaborated with Herman Feshbach and Victor Weisskopf. He became interested in the applications of physics to biology and medicine, and helped establish the Harvard-MIT Division of Health Sciences and Technology. He died in 2002 at the age of 81.

Benedek and Villars, Volume 2

Physics With Illustrative Examples
From Medicine and Biology, Volume 2,
by Benedek and Villars.

Last week I discussed volume 1 of Benedek and Villars’ three-volume textbook Physics With Illustrative Examples From Medicine and Biology, which dealt with mechanics. The second volume discusses statistical physics. The preface to their first edition of Volume 2 states

In the present volume we develop and present the ideas of statistical physics, of which statistical mechanics and thermodynamics are but one part. We seek to demonstrate to students, early in their career, the power, the broad range, and the astonishing usefulness of a probabilistic, non-deterministic view of the origin of a wide range of physical phenomena. By applying this approach analytically and quantitatively to problems such as: the size of random coil polymers; the diffusive flow of solutes across permeable membranes; the survival of bacteria after viral attack; the attachment of oxygen to the binding sites on the hemoglobin molecule; and the effect of solutes on the boiling point and vapor pressure of volatile solvents; we demonstrate that the probabilistic analysis of statistical physics provides a satisfying understanding of important phenomena in fields as diverse as physics, biology, medicine, physiology, and physical chemistry.

Many of the topics in Volume 2 of Benedek and Villars are similar to Chapters 3–5 in the 4th edition of Intermediate Physics for Medicine and Biology: the Boltzmann factor, diffusion, and osmotic pressure. As I said last week, I’m most interested in those topics Benedek and Villars discuss that are not covered in Intermediate Physics for Medicine and Biology, such as their fascinating description of the use of Poisson statistics by Luria and Delbruck.

If a bacterial culture is brought into contact with bacteriophage virus particles, the viruses will attack the bacteria and kill them in a matter of hours. However, a small number of bacteria do survive the attack. These survivors will reproduce and pass on to their descendants their resistance to the virus. The form of resistance of the offspring of the surviving bacteria is that their surface does not adsorb the attacking virus. Bacterial strains can also be resistant to metabolic inhibitors, such as streptomycin, penicillin, and sulphonamide. If a bacterial culture is subjected to attack by these antibiotics, the resistant strain will emerge just as in the case of the phage resistant bacteria.

In the early 1940s, Luria and Delbruck were working on ‘mixed infection’ experiments in which the bacteriophage resistant strain of E. coli bacteria were used as indicators in studies they were making on T1 and T2 virus particles. Starting in the Fall of 1942, they began to put aside the mixed infection experiment and asked themselves: What is the origin of those resistant bacterial strains that they were using as indicators?

They go on to give a detailed description of how Poisson statistics were used by Luria and Delbruck to study mutations.

Russ Hobbie and I discuss the Poisson distribution in our Appendix J. The Poisson distribution is an approximation of the more familiar binomial distribution, applicable for large numbers and small probabilities. One can see how this distribution would be appropriate for Luria and Delbruick, who had large numbers of viruses and a small probability of a mutation.

Russ and I cite Volume 1 of Benedek and Villars’ text in our Chapter 1 on biomechanics. We draw the data for our Fig. 4.12 from Benedek and Villars’ Volume 2. We never cite their Volume 3, about electricity and magnetism, which I’ll discuss next week.

Benedek and Villars, Volume 1

Physics With Illustrative Examples
From Medicine and Biology, Volume 1,
by Benedek and Villars.

One early textbook that served as a precursor to Introductory Physics for Medicine and Biology is the 3-volume Physics With Illustrative Examples From Medicine and Biology, by George Benedek and Felix Villars. The first edition, published in 1973, was just bound photocopies of a typewritten manuscript, but a nicely printed second edition appeared in 2000. The preface to Volume 1 of the first edition states

This is a unique book. It is an introductory textbook of physics in which the development of the principles of physics is interwoven with the quantitative analysis of a wide range of biological and medical phenomena. Conversely, the biological and medical examples serve to vitalize and motivate the learning of physics. By its very nature, this book not only teaches physics, but also exposes the student to topics in fields such as anatomy, orthodedic medicine, physiology, and the principles of hemostatic control.

This book, and its follow-up, Volumes II and III, grew out of an introductory physics course which we have offered to freshmen and sophomores at MIT since 1970. The stimulus for this course came from Professor Irving M. London, MD, Director of the Harvard-MIT Program in Health Sciences and Technology. He convinced us that continued advances in the biological and medical sciences demand that students, researchers, and physicians should be capable of applying the quantitative methods of the physical sciences to problems in the life sciences. We have written this book in the hope that students of the life sciences will come to appreciate the value of training in physics in helping them to formulate, analyze, and solve problems in their own fields.

This quote applies almost without change (except for replacing MIT with Russ Hobbie’s University of Minnesota) to Intermediate Physics for Medicine and Biology. Clearly the goals and objectives of the two works are the same.

Many of the topics in Volume 1 of Benedek and Villars are similar to those found in Chapters 1 and 10 of Intermediate Physics for Medicine and Biology: biomechanics, fluid dynamics, and feedback. Particularly interesting to me are the topics that Russ Hobbie and I don’t discuss, such as the physiological effects of underwater diving.

On ascent and descent the diver must arrange to have the pressure of gas in his lungs be the same as that of the surrounding water. He can do this either by breathing out on ascent or by adjusting the output pressure of his compressed air tanks. Second to drowning, the most serious underwater diving accident is produced by taking a full breath of air at depth, and holding this breath as the diver rises to the surface quickly. For example, if the diver did this at 99 ft he would have gas at 4 atm in his lungs. This if fine at 99 ft, but if he holds this total volume of gas on ascending, then at the surface the surrounding water is at 1 atm, and his lungs are holding air at 3 atm. This can do two things. His lungs can rupture, thereby allowing gas to flow into the space between lungs and ribs. This is called pneumothorax. Also the great pressure of air in the lungs can force air bubbles into the blood stream. These air embolisms can then occlude blood vessels in the brain or the coronary circulation, and this can lead to death. Of course, the obvious necessity of balancing pressure in the ears, sinuses, and intestines must be realized.

Benedek and Villars also have a delightful description of the physiological effects of low air pressure experienced by balloonists. It is too long to reproduce here, but well worth reading.

In the coming weeks, I will discuss Benedek and Villars’ second and third volumes.

Are Backscatter x-ray machines at airports safe?

Two competing devices are used in airports to obtain full-body images of passengers: backscatter x-ray scanners and millimeter wave scanners. Today I want to examine those scanners that use x-rays.

Backscatter x-ray scanners work by a different mechanism than ordinary x-ray images used in medicine. Chapter 16 of the 4th edition of Intermediate Physics for Medicine and Biology discusses traditional medical imaging (see Fig. 16.14). X-rays are passed through the body, and the attenuation of the beam provides the signal that produces the image. Backscatter x-ray scanners are different. They record the x-rays scattered backwards toward the incident beam via Compton scattering. This allows the use of very weak x-ray beams, resulting in a lower dose.

The dose (or, more accurately the equivalent dose) from one backscatter x-ray scan is about 0.05 μSv. The unit of a sievert is defined in Chapter 16 of Intermediate Physics for Medicine and Biology as a joule per kilogram (the definition includes a weighting factor for different types of radiation; for x-rays this factor is equal to one). The average annual background dose that we are all exposed to is about 3 mSv, or 3000 μSv, arising mainly from inhalation of the radioactive gas radon. Clearly the dose from a backscatter x-ray scanner is very low, being 60,000 times less than the average yearly background dose.

Nevertheless, the use of x-rays for airport security remains controversial because of our uncertainly about the effect of low doses of radiation. Russ Hobbie and I address this issue in Section 16.13 about the Risk of Radiation.

In dealing with radiation to the population at large, or to populations of radiation workers, the policy of the various regulatory agencies has been to adopt the linear-nonthreshold (LNT) model to extrapolate from what is known about the excess risk of cancer at moderately high doses and high dose rates, to low doses, including those below natural background.

If the excess probability of acquiring a particular disease is αH [where H is the equivalent dose in sieverts] in a population N, the average number of extra persons with the disease is

m = α N H.

The product NH, expressed in person-Sv, is called the collective dose. It is widely used in radiation protection, but it is meaningful only if the LNT assumption is correct [emphasis added].

So, are backscatter x-ray scanners safe? This question was debated in a Point/Counterpoint article appearing in the August issue of Medical Physics, a leading journal published by the American Association of Physicists in Medicine. A Point/Counterpoint article is included in each issue of Medical Physics, providing insight into medical physics topics at a level just right for readers of Intermediate Physics for Medicine and Biology. The format is always the same: two leading medical physicists each defend one side or the other of a controversial proposition. In August, the proposition is “Backscatter X-ray Machines at Airports are Safe.” Elif Hindie of the University of Bordeaux, France argues for the proposition, and David Brenner of Columbia University argues against it.

Now let us see what Drs. Hindie and Brenner have to say about this idea. Hindie writes (references removed)

The LNT model postulates that every dose of radiation, no matter how small, increases the probability of getting cancer. This highly speculative hypothesis was introduced on the basis of flimsy scientific evidence more than 50 years ago, at a time when cellular biology was a largely unexplored field. Over the past decades, an ever-increasing number of scientific studies have consistently shown that the LNT model is incompatible with radiobiological and experimental data, especially for very low doses.

The LNT model was mainly intended as a tool to facilitate radioprotection regulations and, despite its biological implausibility, this may remain its raison d’être. However, the LNT model is now used in a misguided way. Investigators multiply infinitesimal doses by huge numbers of individuals in order to obtain the total number of hypothetical cancers induced in a population. This practice is explicitly condemned as “incorrect” and “not reasonable” by the International Commission on Radiological Protection, among others.

Brenner counters

Of course this individual risk estimate is exceedingly uncertain. Some have argued that the risk at very low doses is zero. Others have argued that phenomena such as tissue/organ microenvironment effects, bystander effects, and “sneaking through” immune surveillance, imply that low-dose radiation risks could be higher than anticipated. The bottom line is that individual risk estimates at very low doses are extremely uncertain.

But when extremely large populations are involved, with up to 10⁹ scans per year in this case, risk should also be viewed from the perspective of the entire exposed population. Population risk quantifies the number of adverse events expected in the exposed population as a result of a proposed practice, and so depends on both the individual risk and on the number of people exposed. Population risk is described by ICRP as “one input to . . . a broad judgment of what is reasonable,” and by NCRP as “one of the means for assessing the acceptability of a facility or practice.” Population risk is considered in many other policy areas where large populations are exposed to very small risks, such as nuclear waste disposal or vaccination.

The debate about the LNT model and the validity of the concept of collective dose is not merely of academic interest. It gets to the heart of how we perceive, assess, and defend ourselves against the risk of radiation. Low doses of radiation are risky to a large population only if there is no threshold below which the risk falls to zero. Until the validity of the linear non-threshold model is confirmed, I suspect we will continue to witness passionate debates—and future point/counterpoint articles—about the safety of ionizing radiation.

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