Enhancement of Human Color Vision by Breaking the Binocular Redundancy

Russ Hobbie and I added a discussion of color vision to the 5th edition of Intermediate Physics for Medicine and Biology.

The eye can detect color because there are three types of cones in the retina, each of which responds to a different wavelength of light (trichromate vision): red, green, and blue, the primary colors. However, the response curve for each type of cone is broad, and there is overlap between them (particularly the green and red cones). The eye responds to yellow light by activating both the red and green cones. Exactly the same response occurs if the eye sees a mixture of red and green light. Thus, we can say that red plus green equals yellow. Similarly, the color cyan corresponds to activation of both the green and blue cones, caused either by a monochromatic beam of cyan light or a mixture of green and blue light. The eye perceives the color magenta when the red and blue cones are activated but the green is not. Interestingly, no single wavelength of light can do this, so there is no such thing as a monochromatic beam of magenta light; it can only be produced my mixing red and blue. Mixing all three colors, red and green and blue, gives white light.

I know that some animals have dichromate vision (only two color receptors), as do some color blind people. Also, a few animals have tetrachromate vision (four color receptors). But I never imagined that I could have enhanced color vision just by wearing a pair of fancy glasses. Could I become a tetrachromat?

Yes! A preprint appeared recently in the biological physics arXiv by Mikhail Kats and his colleagues at the University of Wisconsin about “Enhancement of Human Color Vision by Breaking the Binocular Redundancy” (arXiv:1703.04392). Graduate student and National Science Foundation Graduate Research Fellow Brad Gundlach is the lead author of this fascinating paper. The abstract is given below.

To see color, the human visual system combines the responses of three types of cone cells in the retina—a process that discards a significant amount of spectral information. We present an approach that can enhance human color vision by breaking the inherent redundancy in binocular vision, providing different spectral content to each eye. Using a psychophysical color model and thin-film optimization, we designed a wearable passive multispectral device that uses two distinct transmission filters, one for each eye, to enhance the user’s ability to perceive spectral information. We fabricated and tested a design that “splits” the response of the short-wavelength cone of individuals with typical trichromatic vision, effectively simulating the presence of four distinct cone types between the two eyes (“tetrachromacy”). Users of this device were able to differentiate metamers (distinct spectra that resolve to the same perceived color in typical observers) without apparent adverse effects to vision. The increase in the number of effective cones from the typical three reduces the number of possible metamers that can be encountered, enhancing the ability to discriminate objects based on their emission, reflection, or transmission spectra. This technique represents a significant enhancement of the spectral perception of typical humans, and may have applications ranging from camouflage detection and anti-counterfeiting to art and data visualization.

I’d love to try out a pair of these glasses! I wonder whether they provide merely a subtle change in vision or offer an entirely new visual experience? Also, what would it be like to have each eye receiving different color information? Does the brain need to be trained to handle the additional information, or does it adapt easily? If the enhancement of vision is dramatic, I could easily see these glasses becoming the hot new gadget people clamor for this Christmas. And it all comes from applying physics to medicine and biology.

Five Popular Misconceptions about Osmosis

In Chapter 5 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss osmotic pressure.

5.2 Osmotic Pressure in an Ideal Gas

The selective permeability of a membrane gives rise to some striking effects. The flow of water that occurs because solutes are present that cannot get through the membrane is called osmosis. This phenomenon seems strange when it is first encountered, and explanations are often fraught with misconceptions (Kramer and Myers 2012).

What are these misconceptions that explanations are often fraught with? The reference is to the paper “Five Popular Misconceptions About Osmosis” (American Journal of Physics, Volume 80, Pages 694–699, 2012). The paper raises five questions.

1. Is osmosis limited to mixtures in the liquid state? 
2. Does osmosis require an attractive interaction between solute and solvent? 
3. Can osmosis drive solvent from a compartment of lower to higher solvent concentration? 
4. Can the osmotic pressure be interpreted as the partial pressure of the solute? 
5. What exerts the force that drives solvent across the semipermeable membrane, overcoming both viscous resistance and an opposing hydrostatic pressure gradient?

Later in the paper, the authors answer these questions.

1. The phenomenology of osmosis is the same for gases, liquids, and supercritical fluids. The misconception is that osmosis is limited to liquids. 
2. Osmosis does not depend on an attractive force between solute and solvent. The misconception is that osmosis requires an attractive force. 
3. Osmosis can drive solvent from a lower to a higher solvent concentration compartment. The misconception is that osmosis always happens down a concentration gradient. 
4. The osmotic pressure cannot be interpreted as the partial pressure of the solute. The misconception is that it can. 
5. The semipermeable membrane exerts the force that drives solvent flow. The misconception is that no force is required to explain the flow.

So, how did Russ and I do?

1. We certainly get the first question correct, because our initial explanation is for an ideal gas. 
2. I think we get the second one right too, but it is not as clear, because we restrict our discussion to ideal solutions in which no heat is evolved or absorbed. 
3. We cast our discussion in terms of the chemical potential, and then relate the chemical potential to the hydrostatic pressure and the solute concentration. I don’t think we ever address the issue of solvent concentration. I’ll say we are silent on this one. 
4. We say “Except in an ideal gas, it [the chemical potential] is not the same as the partial pressure (a concept that is not normally used in a liquid).” So we get this one right, and I’m glad we put the not in italics. 
5. In Section 5.9.6 we have a nice discussion about the forces acting on the membrane. But we never really say what force explains the solvent flow. Again, I’ll say we are silent on this one.

Kramer and Myers have an illuminating discussion about the force causing the solvent to cross the membrane (I’ve removed all their references; you can find them in the original paper).

Consider an idealized semipermeable membrane as a force field that repels solute but has no effect on the solvent. The Brownian motion of the solute molecules bring them into occasional contact with this field, at which time they receive some momentum directed away from the membrane. Viscous interactions between solute and solvent then rapidly distribute this momentum to the solvent molecules in the neighborhood of the membrane. In this way, the membrane exerts a repulsive force on the solution as a whole. Since additional pure solvent can freely cross our idealized membrane, it flows into the solution compartment, gradually increasing the hydrostatic pressure in the solution. Thus, a pressure gradient builds up across the thickness of the membrane. This pressure gradient exerts a second force on the solution, capable of counteracting the membrane force. Quantitative treatments show that the pressure difference required to stop solvent flow into a dilute solution is exactly Π = k_BTc_B. Nelson has aptly called the mechanism by which the membrane drives fluid flow the rectification of Brownian motion.

Overall I would say Russ and I do okay. We don’t propagate any of the five misconceptions. We answer three of their questions correctly and are silent on two others. Most of the discussion about osmosis goes back to the 3^rd or earlier editions of IPMB, so Russ is the one who got it right. At least I didn’t screw it up.

My Honors College Class: The Making of the Atomic Bomb

The Making of the Atomic Bomb,
by Richard Rhodes.

This semester I am teaching a class in Oakland University’s Honors College called “The Making of the Atomic Bomb,” based on Richard Rhodes’s book by the same name. The class is a mixture of nuclear physics, a history of the Manhattan Project, and a discussion about World War II (today we discuss Pearl Harbor). I became interested in this topic from the writings of Cameron Reed of Alma College here in Michigan.

The Honors College students are outstanding, but they are from disciplines throughout the university and do not necessarily have strong math and science backgrounds. Therefore the mathematics in this class is minimal, but nevertheless we do a two or three quantitative examples. For instance, Chadwick’s discovery of the neutron in 1932 was based on conclusions drawn from collisions of particles, and relies primarily on conservation of energy and momentum. When we analyze Chadwick’s experiment in my Honors College class, we consider the head-on collision of two particles of mass M₁ and M₂. Before the collision, the incoming particle M₁ has kinetic energy T and the target particle M₂ is at rest. After the collision, M₁ has kinetic energy T₁ and M₂ has kinetic energy T₂.

Intermediate Physics for Medicine and Biology examines an identical situation in Section 15.11 on Charged-Particle Stopping Power.

The maximum possible energy transfer W_max can be calculated using conservation of energy and momentum. For a collision of a projectile of mass M₁ and kinetic energy T with a target particle of mass M₂ which is initially at rest, a nonrelativistic calculation gives

One important skill I teach my Honors College students is how to extract a physical story from a mathematical expression. One way to begin is to introduce some dimensionless parameters. Let t be the ratio of kinetic energy picked up by M₂ after the collision to the incoming kinetic energy T, so t = T₂/T or, using the notation in IPMB, t = W_max/T (the subscript “max” arises because this maximum value of T₂ corresponds to a head-on collision; a glancing blow will result in a smaller T₂). Also, let m be the ratio of M₁ to M₂, so m = M₁/M₂. A little algebra results in the simpler-looking equation

The goal is to unmask the physical behavior hidden in this equation. The best way to proceed is to examine limiting cases. There are three that are of particular interest.

m much less than 1. When m is small (think of a fast-moving proton colliding with a stationary lead nucleus) the denominator is approximately one, so t = 4m. Because m is small, so is t. This means the proton merely bounces back elastically as if striking a brick wall. Little energy is transferred to the lead nucleus.

 m much greater than 1. When m is large (think of a fast-moving lead nucleus smashing into a stationary proton) the denominator is approximately m², so t = 4/m. Because m is large, t is small. This means the lead continues on as if the proton were not even there, with little loss of energy. The proton flies off at a high speed, but because of its small mass it carries off negligible energy.

m equal to 1. When m is one (think of a neutron colliding with a proton, which was the situation examined by Chadwick), the denominator becomes 4, and t = 1. All of the energy of the neutron is transferred to the proton. The neutron stops and the proton flies off at the same speed the neutron flew in.

A mantra I emphasize to my students is that equations are not just things you put numbers into to get other numbers. Equations tell a physical story. Being able to extract this story from an equation is one of the most important abilities a student must learn. Never pass up a chance to reinforce this skill.

Glucose, Mannitol, Sucrose, and Raffinose

The structure of glucose.

You would think by now I would know everything in Introductory Physics for Medicine and Biology; after all, I’m one of the authors. So when thumbing through the book the other day (doesn’t everyone thumb through IPMB when they have a spare moment?) I came across Figure 4.11, showing a log-log plot of the diffusion constant as a function of molecular radius. Four data points stand out—glucose, mannitol, sucrose, and raffinose—because they are plotted as open rather than solid circles. This figure was drawn originally by Russ Hobbie and has appeared in every edition of IPMB. I got to wondering “why did Russ choose to plot those four molecules out of the thousands available?” And then, more specifically, I found myself asking “just what is raffinose anyways?”

To figure all this out, I grabbed the textbook I read in graduate school while auditing the biochemistry class taken by Vanderbilt medical students (Biochemistry, by the late Geoffrey Zubay). These molecules are carbohydrates or, more simply, sugars. Glucose is the canonical example; this six-carbon molecule C₆H₁₂O₆ is “the single most important substrate for energy metabolism” and in humans it is “the single most important sugar in the blood”. It usually exists in a ring conformation. It is a monosaccharide because it consists of a single ring. Other monosaccharides are fructose and galactose, which all have the same formula, C₆H₁₂O₆, but the arrangement of the atoms is slightly different.

Mannitol differs from glucose by having an extra two hydrogen atoms: C₆H₁₄O₆. Technically it’s a sugar alcohol rather than a sugar. You’d think it would act similarly to glucose, but it doesn’t. Mannitol is relatively inert in humans. It doesn’t cross the blood-brain barrier (I discussed the implications of this previously in this blog) and it is not reabsorbed by the kidney like glucose is so it acts as an osmotic diuretic. In Fig. 4.11, the mannitol and glucose data almost overlap, and it is hard to tell which data point is which. According to a paper by Bashkatov et al. (2003), glucose has a larger diffusion coefficient than mannitol, so glucose must be the data point above and to the left, and mannitol below and to the right.

Sucrose is a disaccharide, which means it is two monosaccharides bound together through a “glycosidic linkage”. It’s common table sugar, and consists of a molecule of glucose bound to a molecule of fructose. Russ probably chose to plot sucrose as a typical disaccharide. Two other  disaccharides he could have chosen are lactose (glucose + galactose) and maltose (glucose + glucose).

Raffinose is a trisaccharide, consisting of galactose + glucose + fructose. Therefore, Russ’s choice of plotting glucose, sucrose, and raffinose makes sense: the most important monosaccharide, disaccharide, and trisaccharide. A fun fact about raffinose is that the human digestive tract does not have the enzyme needed to digest it. However, certain gas-producing bacteria in our gut can digest it, resulting in flatulence. You probably won’t be surprised to learn that beans often contain a lot of raffinose.

So, Russ is a clever fellow. He hid a short review of carbohydrate biochemistry in Fig. 4.11. Who knew?

Benefits and Barriers of Accommodating Intraocular Lenses

In Chapter 14 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss vision. In particular, we analyze the refraction of light by the lens of the eye, and examine different disorders such as hyperopia, and myopia. We then write

This ability of the lens to change shape and provide additional converging power is called accommodation…. As we age, the accommodation of the eye decreases... A normal viewing distance of 25 cm or less requires 4 diopters or more of accommodation... This limit is usually reached in the early 40s. To make up for the lack of accommodation, one can place a converging lens in front of the eye when viewing nearby objects (reading glasses).

When a patient has a cataract, their lens becomes cloudy. A common surgical procedure is to remove the opaque lens and replace it with an artificial intraocular lens. A conventional IOL is designed to supply the correct power to provide clear distance vision, but it cannot accommodate. Reading glasses provide one option for close vision, but many patients find them to be an inconvenient nuisance.

Researchers are now racing to create accommodating IOLs. A recent review by Jay Pepose, Joshua Burke, and Mujtaba Qazi discusses the “Benefits and Barriers of Accommodating Intraocular Lenses” (Current Opinion in Ophthalmology, Volume 28, Pages 3–8, 2017).

Presbyopia [the loss of accommodation] and cataract development are changes that ubiquitously affect the aging population. Considerable effort has been made in the development of intraocular lenses (IOLs) that allow correction of presbyopia postoperatively. The purpose of this review is to examine the benefits and barriers of accommodating IOLs, with a focus on emerging technologies.

Apparently the current accommodating intraocular lenses don’t function by changing their focal length, but rather by being pushed forward when the eye muscles responsible for accommodation contract. They only provide about 1 diopter of accommodation, which is not enough to avoid reading glasses. The review concludes

Such limitations [of the presently available accommodating IOLs] may be circumvented in the future by accommodative design strategies that rely more on shape-related changes in the surfaces of the IOLs or in refractive index than by forward translation alone. Fibrosis and contraction of the capsular bag, which can alter the position of the IOL optic or the performance of an accommodating IOL represent other challenges, and at least one accommodating IOL … has been designed for implantation in the ciliary sulcus. Approval of accommodating IOLs capable of delivering three or more diopters of accommodation would allow a full range of intermediate and near vision without the compromise of photic phenomenon or loss of contrast inherent to other optical strategies, and perhaps also allow refractive targeting that could minimize hyperopic surprises by taking advantage of this expanded amplitude of accommodation.

Some “accommodating” IOLs are multifocal, providing two focal lengths and therefore two images simultaneously, one for distance vision and one for reading. The brain then sorts out the mess. Apparently this is not as difficult as is sounds.

I predict that accommodating intraocular lenses will soon become very sophisticated. Cataract surgery is performed on millions of people each year; it is common in the elderly population, which is growing dramatically as baby boomers age; in principle the problem is not complex, you just need to make a lens that can adjust its focal length by about ten percent; compared to other medical devices like pacemakers and defibrillators, accommodating IOLs should be cheap; and new nanotechnologies plus knowledge gained from the miniaturization of other medical devices may pave the way to rapid advances. Accommodating intraocular lenses may soon become an example of how to successfully apply physics to solve a problem in medicine.

Sir Peter Mansfield (1933-2017)

MRI pioneer Peter Mansfield died last week. Russ Hobbie and I mention Mansfield in Chapter 18 of Intermediate Physics for Medicine and Biology

Many more techniques are available for imaging with magnetic resonance than for x-ray computed tomography. They are described by Brown et al. (1994), by Cho et al. (1993), by Vlaardingerbroek and den Boer (2004), and by Liang and Lauterbur (2000). One of these authors, Paul C. Lauterbur, shared with Sir Peter Mansfield the 2003 Nobel Prize in physiology or medicine for the invention of magnetic resonance imaging.

Mansfield made many contributions to the development of MRI, including the invention of echo-planar imaging. Russ and I write

Echo-planar imaging (EPI) eliminates the π pulses [normally used to rotate the spins in the x-y plane to form a spin echo]. It requires a magnet with a very uniform magnetic field, so that T₂ [the transverse relaxation time, that is determined in part by dephasing of the spins in the x-y plane] (in the absence of a gradient) is only slightly greater than T₂^* [the experimentally observed transverse relaxation time]. The gradient fields are larger, and the gradient pulse durations shorter, than in conventional imaging. The goal is to complete all the k-space [all the points k_x-k_y in the spatial frequency domain] measurements in a time comparable to T₂^*. In EPI the echoes are not created using π pulses. Instead, they are created by dephasing the spins at different positions along the x axis using a G_x gradient, and then reversing that gradient to rephrase the spins, as shown in Fig. 18.32.

A MRI pulse sequence for echo planar imaging,
from Intermediate Physics for Medicine and Biology.

Mansfield tells about his first presentation on echo-planar imaging in his autobiography, The Long Road to Stockholm.

It was during the course of 1976 that Raymond Andrew convened a meeting in Nottingham of interested people in imaging…Most attendees brought us up to date with their images and gave us short talks on the goals that they were pursuing. Although my group had made considerable headway in a whole range of topics, I chose to speak about an entirely new imaging method that I had worked out theoretically but for which I had really no experimental results. The technique was called echo planar imaging (EPI), a condensation of planar imaging using spin echoes. I spoke for something like half an hour, talking in great detail, and at the end of the talk the audience seemed to be left in stunned silence. There were no questions, there was no discussion at all, and it was almost as though I had never spoken. In fact I had given a detailed talk about how one could produce very rapid images in a typically one shot process lasting, conservatively, for something like 40 or 50 milliseconds.

You can learn more about Mansfield in obituaries in the New York Times, in The Scientist, and from the BBC. Also, the Nobel Prize website has much information including a biography and his Nobel Prize address. Below, watch and listen to Mansfield talk about MRI.

Good, Fast, Cheap: Pick Any Two

When I worked at the National Institutes of Health, one of my coworkers had a sign in his office that read “Good, Fast, Cheap: Pick Any Two.” A recent video about “Building tomorrow's MRI--faster, smaller, and cheaper” reminded me of that saying. The video is part of a series called Science Happens! by Carl Zimmer.

Russ Hobbie and I describe magnetic resonance imaging in Chapter 18 of Intermediate Physics for Medicine and Biology. However, we don’t discuss the possibilities related to low-field MRI. The Science Happens! website says

Matthew Rosen and his colleagues at the Martinos Center for Biomedical Imaging in Boston want liberate the MRI. They’re hacking a new kind of scanner that’s fast, small, and cheap. Using clever algorithms, they can use a weak magnetic field to get good images of our brains and other organs. Someday, people may not have to go to hospital for an MRI. The scanners may show up in sports arenas, battlefields, and even the backs of ambulances.

A longer, more technical video of Rosen describing his work is given below.

For more details, see Rosen’s open access article “Low-Cost High-Performance MRI” (Scientific Reports, 5:15177, 2015).

Magnetic Resonance Imaging (MRI) is unparalleled in its ability to visualize anatomical structure and function non-invasively with high spatial and temporal resolution. Yet to overcome the low sensitivity inherent in inductive detection of weakly polarized nuclear spins, the vast majority of clinical MRI scanners employ superconducting magnets producing very high magnetic fields. Commonly found at 1.5–3 tesla (T), these powerful magnets are massive and have very strict infrastructure demands that preclude operation in many environments. MRI scanners are costly to purchase, site, and maintain, with the purchase price approaching $1 M per tesla (T) of magnetic field. We present here a remarkably simple, non-cryogenic approach to high-performance human MRI at ultra-low magnetic field, whereby modern under-sampling strategies are combined with fully-refocused dynamic spin control using steady-state free precession techniques. At 6.5 mT (more than 450 times lower than clinical MRI scanners) we demonstrate (2.5 × 3.5 × 8.5) mm³ imaging resolution in the living human brain using a simple, open-geometry electromagnet, with 3D image acquisition over the entire brain in 6 minutes. We contend that these practical ultra-low magnetic field implementations of MRI (less than 10 mT) will complement traditional MRI, providing clinically relevant images and setting new standards for affordable (less than $50,000) and robust portable devices.

$50,000 is expensive by Manu Prakash's standards, but for an MRI device $50k is darn cheap! Recalling my friend’s motto, I think that Rosen has picked Fast and Cheap, but he’s gotten Pretty Good too, which is not a bad trade-off (all of engineering is trade-offs). If you want Super Good, spend the million bucks.

Finally, Rosen isn’t the only one interested in reinventing magnetic resonance imaging. Michael Garwood at Russ’s own University of Minnesota is also working on smaller, lighter, cheaper MRI.

Let the race begin. Humanity will be the winner.

Enjoy!

Alan Perelson wins the 2017 Max Delbruck Prize in Biological Physics

Alan Perelson, of Los Alamos National Laboratory, has been named the winner of the 2017 Max Delbruck Prize in Biological Physics by the American Physical Society. His award was “for profound contributions to theoretical immunology, which bring insight and save lives.”

One skill Russ Hobbie and I try to develop in students using Intermediate Physics for Medicine and Biology is the ability to translate words into mathematics. Below I present a new homework problem based on one of Perelson’s most highly cited papers (Perelson et al., 1996, Science, 271:1582–1586), which provides practice in this important technique. This exercise asks the student to make a mathematical model of the immune system that explains how T-cells—a type of white blood cell—respond to HIV infection.

Section 10.8

Problem 37 1/2. A model of HIV infection includes the concentration of uninfected T-cells, T, the concentration of infected T-cells, T*, and the concentration of virions, V.

(a) Write a pair of coupled differential equations for T* and V based on the following assumptions

• If no virions are present, the immune system removes infected T-cells with rate δ,
• If no infected T-cells are present, the immune system removes virions with rate c, 
• Infected T-cells are produced at a rate proportional to the product of the concentrations of uninfected T-cells and virions; let the constant of proportionality be k, 
• Virions are produced at a rate proportional to the concentration of infected T-cells with a constant of proportionality Nδ, where N is the number of virions per infected T-cell. 

(b) In steady state, determine the concentration of uninfected T-cells.

One of Perelson’s coauthors on the 1996 paper was David Ho. Yes, the David Ho who was Time Magazine’s Man of the Year in 1996.

For those who prefer video, watch Perelson discuss immunology for physicists.

The Genetic Effects of Radiation

The Genetic Effects of Radiation,
by Isaac Asimov.

My local public library had their quarterly used book sale last weekend, and as usual I went to search for Isaac Asimov books. I collect Asimov’s books in part to pay homage to the huge influence he had on me as a teenager. He was the main reason I became a scientist. No luck this time; I came back from the sale empty handed. It’s difficult for me to find Asimov books that I don’t have, because I have so many (most bought second-hand for a pittance). Nevertheless, he wrote over 500 books, and I own far fewer than that, so I always have a chance.

You would think that I would at least know about all his books, even if I don’t own a copy. Yet somehow, I was unaware of (or had forgotten about) his book The Genetic Effects of Radiation, although it is a topic closely related to Intermediate Physics for Medicine and Biology. If interested, you can download a pdf of the book free (and I think legally) here. Below I present an excerpt about natural background radiation.

Background Radiation

Ionizing radiation in low intensities is part of our natural environment. Such natural radiation is referred to as background radiation. Part of it arises from certain constituents of the soil. Atoms of the heavy metals, uranium and thorium, are constantly, though very slowly, breaking down and in the process giving off alpha rays, beta rays, and gamma rays. These elements, while not among the most common, are very widely spread; minerals containing small quantities of uranium and thorium are to be found nearly everywhere.

In addition, all the earth is bombarded with cosmic rays from outer space and with streams of high-energy particles from the sun.

Various units can be used to measure the intensity of this background radiation. The roentgen, abbreviated r, and named in honor of the discoverer of X rays, Wilhelm Roentgen, is a unit based on the number of ions produced by radiation. Rather more convenient is another unit that has come more recently into prominence. This is the rad (an abbreviation for “radiation absorbed dose”) that is a measure of the amount of energy delivered to the body upon the absorption of a particular dose of ionizing radiation. One rad is very nearly equal to one roentgen.

Since background radiation is undoubtedly one of the factors in producing spontaneous mutations, it is of interest to try to determine how much radiation a man or woman will have absorbed from the time he is first conceived to the time he conceives his own children. The average length of time between generations is taken to be about 30 years, so we can best express absorption of background radiation in units of rads per 30 years.

The intensity of background radiation varies from place to place on the earth for several reasons. Cosmic rays are deflected somewhat toward the magnetic poles by the earth’s magnetic field. They are also absorbed by the atmosphere to some extent. For this reason, people living in equatorial regions are less exposed to cosmic rays than those in polar regions; and those in the plains, with a greater thickness of atmosphere above them, are less exposed than those on high plateaus.

Then, too, radioactive minerals may be spread widely, but they are not spread evenly. Where they are concentrated to a greater extent than usual, background radiation is abnormally high.

Thus, an inhabitant of Harrisburg, Pennsylvania, may absorb 2.64 rads per 30 years, while one of Denver, Colorado, a mile high at the foot of the Rockies, may absorb 5.04 rads per 30 years. Greater extremes are encountered at such places as Kerala, India, where nearby soil, rich in thorium minerals, so increases the intensity of background radiation that as much as 84 rads may be absorbed in 30 years.

In addition to high-energy radiation from the outside, there are sources within the body itself. Some of the potassium and carbon atoms of our body are inevitably radioactive. As much as 0.5 rad per 30 years arises from this source.

Rads and roentgens are not completely satisfactory units in estimating the biological effects of radiation. Some types of radiation—those made up of comparatively large particles, for instance—are more effective in producing ions and bring about molecular changes with greater ease than do electromagnetic radiations delivering equal energy to the body. Thus if 1 rad of alpha particles is absorbed by the body, 10 to 20 times as much biological effect is produced as there would be in the absorption of 1 rad of X rays, gamma rays, or beta particles.

Sometimes, then, one speaks of the relative biological effectiveness (RBE) of radiation, or the roentgen equivalent, man (rem). A rad of X rays, gamma rays, or beta particles has a rem of 1, while a rad of alpha particles has a rem of 10 to 20.

If we allow for the effect of the larger particles (which are not very common under ordinary conditions) we can estimate that the gonads of the average human being receive a total dose of natural radiation of about 3 rems per 30 years. This is just about an irreducible minimum.

This is typical Asimov. Let me add a few observations.

1. Asimov rarely wrote specifically about medical physics, although he wrote much about related topics. I think The Genetic Effects of Radiation is closer to IPMB than his other books.
2. The Genetic Effects is over 50 years old; it is out of date. For example, it uses the archaic units of rad and rem instead of gray and sievert (100 rem = 1 Sv). Moreover, radon gas is now known to make the largest contribution to background radiation, but the word “radon” never appeared in The Genetic Effects. Yet, I was surprised how much has not changed. I think a reader of IPMB would still find much useful information in Asimov’s book.
3. The text is aimed at a general audience, rather than an expert. The book is not a replacement for, say, Radiobiology for the Radiologist, or even IPMB. Yet, for a 16-year old kid (as I was when devouring Asimov’s books about science), the level is just right.
4. The discussion is not mathematical. At times Asimov writes about mathematical results, but he rarely presents equations. Certainly Asimov’s writing has vastly fewer equations than IPMB.
5. Asimov doesn’t use a lot of figures. The Genetic Effects contains more pictures than most of his books.
6. This excerpt illustrates the "clear, cool voice of Asimov." I admire the clarity of his writing. No one explains things better.

And now I have to return to my search for more Asimov books. I am particularly a fan of his science essay collections originally published in Fantasy and Science Fiction. I have most of them, but somehow missed the very first: Fact and Fancy (1962). Garage sale season will be here in a few months. Hope springs eternal.

Manu Prakash and the Paperfuge

Three years ago I wrote a blog post about a crazy Stanford engineer, Manu Prakash, who developed a paper origami microscope called “foldscope” costing less than a dollar. LESS THAN A DOLLAR!

Well, he’s done it again. Now his team has invented a hand-held, lightweight centrifuge called “paperfuge” costing under 20 cents. UNDER 20 CENTS!!!

I’m thinking of buying one if I can scrape up the cash. Buddy, can you spare a dime?

Excuse me if you have already heard about paperfuge on social media; its been popping up a lot on Facebook and Twitter. I hate to jump on a bandwagon, but this is so amazing I have to tell you about it.

The physics of the centrifuge is described in a series of homework problems in the first chapter of Intermediate Physics for Medicine and Biology. Please, don’t think that topics relegated to the end-of-the-chapter exercises are less important than subjects discussed in the text. Sometimes key issues such as the centrifuge lend themselves to the homework, and you learn more by actively doing the problems then by passively reading prose (even mine!).

But let me get back to Prakash. His team recently published a paper in Nature Biomedical Engineering titled “Hand-Powered Ultralow-Cost Paper Centrifuge” (read it online here). The abstract says:

In a global-health context, commercial centrifuges are expensive, bulky and electricity-powered, and thus constitute a critical bottleneck in the development of decentralized, battery-free point-of-care diagnostic devices. Here, we report an ultralow-cost (20 cents), lightweight (2 g), human-powered paper centrifuge (which we name “paperfuge”) designed on the basis of a theoretical model inspired by the fundamental mechanics of an ancient whirligig (or buzzer toy; 3,300 BC). The paperfuge achieves speeds of 125,000 r.p.m. (and equivalent centrifugal forces of 30,000 g), with theoretical limits predicting 1,000,000 r.p.m. We demonstrate that the paperfuge can separate pure plasma from whole blood in less than 1.5 min, and isolate malaria parasites in 15 min. We also show that paperfuge-like centrifugal microfluidic devices can be made of polydimethylsiloxane, plastic and 3D-printed polymeric materials. Ultracheap, power-free centrifuges should open up opportunities for point-of-care diagnostics in resource-poor settings and for applications in science education and field ecology.

I’m telling you, the paperfuge is huge. My gosh, Prakash; this whirligig may make it big. I’m a fan of can-do Manu and his breakthrough; it’s a real coup.

You also might like the “News and Views” editorial that accompanies their paper. Plus, articles lauding the paperfuge are all over the internet, such as this one in PhysicsWorld and this one on the National Public Radio website.

For those of you who prefer video, check out this great clip put out by Stanford University. 

To learn more about foldscope, watch Prakash’s TED talk.

Finally, here is a video about his MacArthur genius grant.

Enjoy!