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!