Friday, June 15, 2018

Search Engine Optimization and Intermediate Physics for Medicine and Biology

Lately I've become fascinated by search engine optimization. My goal is to increase the visibility—and more specifically, the number of pageviews—of this blog. The gurus claim my pagerank will increase if I focus on well-chosen keywords or keyword phrases, so I selected the phrase “Intermediate Physics for Medicine and Biology.” I'm supposed to use my keyword phrase, Intermediate Physics for Medicine and Biology, often in each post, especially in the first paragraph. I've gotten into the habit of using the acronym IPMB for Intermediate Physics for Medicine and Biology, but now I realize this is killing my ranking! I'm a fan of good writing, and this repetition of Intermediate Physics for Medicine and Biology is annoying. So, dear readers, I will avoid repeating the phrase Intermediate Physics for Medicine and Biology too often.

Google helps you refine your selection of keywords. I typed “Intermediate Physics for Medicine and Biology” into the search bar and looked at the bottom of the page to see popular alternative keyword suggestions.

Google's alternative keywords when searchng for "Intermediate Physics for Medicine and Biology." The first suggestion adds the words "pdf free download"!
Popular alternative keywords related to the phrase "Intermediate Physics for Medicine and Biology."

Oh my; people are being naughty. I don’t condone illegal downloading, but it's nice to know somebody wants to read Intermediate Physics for Medicine and Biology.

Many searches are looking for Intermediate Physics for Medicine and Biology's solution manual. Russ Hobbie and I provide the solution manual only to instructors, and we try to keep it off the internet. I hope we have succeeded, but I’m not sure. It's like trying to stop the tide from coming in. Instructors should forget about Google and just send Russ or me an email. We may require you to jump through hoops to prove you aren't an imposter, but ultimately we'll send you the solution manual.

What other strategies have I adopted for search engine optimization? I’ve started using the “description” box in the Blogger software (thank you Mr. Google for letting me use this wonderful software for free!). I’m using “alt text” for images, which helps readers interpret an image if they can't see it (my real reason for using “alt text,” however, is to up my ranking). They say to compose identifying anchor text for your links, instead of writing "click here." I now give descriptive names to picture files rather than calling them “picture1.jpg.” I also heard that putting your keyword phrase in bold, italics, and underlining helps: Intermediate Physics for Medicine and Biology. I even read that you should use your keyword phrase as a heading.

Intermediate Physics for Medicine and Biology

Search engines value hyperlinks, so I'm trying to increase the number of links to hobbieroth.blogspot.com. External links are best, but I can't control them. I can control internal links from one blog post to another, which led to my April 13 creation of the Blog to IPMB Mapping, a shameless orgy of internal linking.

Blogger's analytics software lets me monitor pageviews. I've become addicted to checking these statistics. A few weeks ago a burst of views originated from inside Russia. Someone there read almost every post in one night, binging on Intermediate Physics for Medicine and Biology. My most viewed post is an article about Frank Netter, Medical Illustrator. I don't know why it's so popular, but I suspect Google ranking has something to do with it.

Experts recommend repeating your keyword phrase near the end of the post, so I'll leave you with these final words: Intermediate Physics for Medicine and Biology.

Friday, June 8, 2018

The Radium Girls

The Radium Girls by Kate Moore
I recently finished Kate Moore's The Radium Girls: The Dark Story of America’s Shining Women. I chose to read this book because of its relation to topics about radiation risk in Intermediate Physics for Medicine and Biology, but I soon discovered that it isn’t about medical physics. Rather, it focuses on the young women who suffered from occupational radiation exposure. After reviewing previous books about the radium girls, Moore writes:
“As a storyteller and a non-academic, I was struck by the fact that the books focused on the legal and scientific aspects of the women’s story, and not on the compelling lives of the girls themselves. In fact, I soon discovered that no book existed that put the radium girls center stage and told the story from their perspective. The individual women who had fought and died for justice had been eclipsed by their historic achievements; they were now known only by the anonymous moniker of ‘the Radium Girls.’ Their unique experiences—their losses and their loves; their triumphs and their terrors—had been forgotten, if ever charted in the first place.

I became determined to correct that omission.”
The job of a radium girl was to paint luminous dials on clocks and instruments, so you could see them in the dark. They used a radioluminescent paint containing radioactive radium mixed with a scintillator such as zinc-sulfide. Most worked for either the United States Radium Corporation in Orange, New Jersey, or the Radium Dial Company in Ottawa, Illinois. Their supervisors taught them to make a fine point on their paint brush by putting it in their mouth, a process called lip-pointing. Each time they lip-pointed, they ingested a bit of radium.

Radium girls lip-pointing in a dial factory: "Lip, Dip, Paint."
Radium girls lip-pointing in a dial factory: "Lip, Dip, Paint." From Wikipedia.
Moore examines the individual lives of these girls—many in their 20s, some in their teens—and explains their physical symptoms and health problems in excruciating detail. Don’t read the book if you're squeamish; for instance, one of the first symptoms was a tooth ache, but when a dentist extracted the tooth a chunk of the jaw would come out too. Radium—an alpha emitter in the same column of the periodic table as calcium—is taken up by bones. With a half-life of 1600 years, it irradiates the bones throughout the girl’s life.

The heroes of this story are women like Grace Fryer and Catherine Donohue, who demanded justice for themselves and other victims. The villains are the leaders of the corporations. I had some sympathy for these companies at first, because the dangers from radiation were not well understood in the 1920s, so how could they know? But as time went by and the hazards became obvious, the executives denied the facts and covered up the risks. By the book's end, these men personify evil.

Sometimes I get frustrated when people believe conspiracy theories and fairy tales about the danger from low levels of radiation, but The Radium Girls helps me understand why it happens. When people in authority ignore the risk to others for their own profit and then lie about it, they undermine trust, until no one believes even the most solid science.

If you are driving through Illinois on I-80, stop in Ottawa and see the statue of a dial painter. Moore describes its creation:
“For a long time—too long—the legacy of the radium girls was recorded only in the law books and in scientific files. But in 2006, an eighth-grade Illinois student called Madeline Piller read a book on the dial-painters by Dr. Ross Mullner. ‘No monuments,’ he wrote, ‘have ever been erected in their memory.’

Madeline was determined to change that. ‘They deserve to be remembered,’ she said. ‘Their courage brought forth federal health standards. I want people to know [there] is a memorial to these brave women.’

When she began to champion her cause, she found that Ottawa, at last, was ready to honor its native heroines and their comrades-in-arms. The town held fish-fry fund-raisers and staged plays to secure the $80,000 needed. ‘The mayor was supportive,’ said Len Grossman. ‘It was a complete turnaround. That was wonderful to see.’

On September 2, 2011, the bronze statue for the dial-painters was unveiled by the governor in Ottawa, Illinois. It is a statue of a young woman from the 1920’s, with a paintbrush in one hand and a tulip in the other, standing on a clock face. Her skirt swishes, as though at any moment she might step down from her time-ticking pedestal and come to life."
The blog Backyard Tourist has excellent photos of the statue.

The Radium Girls doesn’t explain much of the physics behind radiation exposure, but it does remind us why we study medical physics. For a history lesson, a case study in occupational safety, an inspirational story, and a great read, I recommend The Radium Girls.

The Radium Girls discusses radiation risks that are covered in Section 16.12 of Intermediate Physics for Medicine and BIology
The Radium Girls discusses radiation risk, a topic covered in Section 16.12 of Intermediate Physics for Medicine and Biology.


A YouTube video of Kate Moore talking about her book The Radium Girls

Friday, June 1, 2018

Sepulveda, Roth and Wikswo (1989): How to Write a Scientific Paper

In 1989, Nestor Sepulveda, John Wikswo and I published “Current Injection into a Two-Dimensional Anisotropic Bidomain” (Biophysical Journal, 55:987-999).  Of my papers, this is one of my favorites.

When I teach my graduate Bioelectric Phenomena class here at Oakland University, we study the Sepulveda et al. (1989) article. The primary goal of the class is to introduce students to bioelectricity, but a secondary goal is to analyze how to write scientific papers. When we get to our paper, I let students learn the scientific content from the publication itself. Instead, I use class time to analyze scientific writing. The paper lends itself to this task: It is written well enough to serve as an example of technical writing, but it is written poorly enough to illustrate how writing can be improved. Critically tearing apart the writing of someone else’s paper in front of students would be rude, but because this writing is partly mine I don’t feel guilty.

Many readers of Intermediate Physics for Medicine and Biology will eventually write papers of their own, so in this post I share my analysis of scientific writing just as I present it in class. Students read Current Injection into a Two-Dimensional Anisotropic Bidomain in advance, and then during class we go through the writing page by page, and often line by line, using a powerpoint presentation that I have placed on the IPMB website. I use the “animation” feature of powerpoint so edits, revisions, and corrections can be considered one at a time. To see for yourself, download the powerpoint and click “slide show.” Then, start using the right arrow to analyze the paper.

The first page of a powerpoint to analyze the scientific writing in the paper Current Injection into a Two-Dimensional Anisotropic Bidomain, by Sepulveda, Roth and Wikswo
A screen shot of the first page of the powerpoint. It looks a mess, but the animation feature lets you consider all these suggestions one by one. You can download it and use it to teach your students.

When using this powerpoint, keep these points in mind:
  • One reason I use Sepulveda et al. (1989) as my example is that it has the classic format of a scientific paper: Introduction, Methods, Results, and Discussion. It also contains an Abstract, References, and other sections of a scientific publication. 
  • Often I highlight a sentence or two of text and ask students to revise and improve it. If you are leading a class using this powerpoint, stop and let the students struggle with the revision. Then compare their revised text to mine. The class should be interactive.
  • I have talked before in this blog about the importance of writing. In the powerpoint, I mention two publications that have helped me become a better writer. First is Strunk and White’s book Elements of Style. The powerpoint illustrates much of their advice—such as their famous admonition to “omit needless words"—with concrete examples. You can read Elements of Style online here. Second is N. David Mermin’s essay “What’s Wrong with These Equations” published in Physics Today (download it here). Mermin explains how to integrate math with prose, and introduces the “Good Samaritan Rule” (remind your reader what an equation is about when you refer to it, rather than just saying “Eq. 4”) and other concepts. 
  • Some of the points raised in my powerpoint are trivial, such as the difference between “there,” “their,” and “they’re.” Others are more substantial, such as sentence construction and clarity. I find it takes most of a 90 minute class to finish the whole thing. 
  • On the sixth page of the powerpoint I have a note reminding me to “Tell Story.” The story is one I wrote about in the original version of my paper Art Winfree and the Bidomain Model of Cardiac Tissue. “Nestor Sepulveda, a research assistant professor from Columbia who was working in John [Wikswo]'s lab, had written a finite element computer program that we modified to do bidomain calculations. One of the first simulations he performed was of the transmembrane potential induced in a two-dimensional sheet of cardiac tissue having 'unequal anisotropy ratios' (different degrees of anisotropy in the intracellular and extracellular spaces). Much to our surprise, Nestor found that when he stimulated the tissue through a small cathodal electrode, depolarization (a positive transmembrane potential) appeared under the electrode, but hyperpolarization (a negative transmembrane potential) appeared near the electrode along the fiber direction (Fig. 2). The depolarization was stronger in the direction perpendicular to the fibers, giving those voltage contour lines a shape that John named the 'dogbone.' Only Nestor understood the details of his finite element code, and I was a bit worried that his program might contain a bug that caused this weird result. So I quietly returned to my office and developed an entirely different numerical scheme, using Fourier Transforms, to do the same calculation. Of course, I got the same result Nestor did (there was no bug). Although I didn't realize it then, I would spend the next 15 years exploring the implications of Nestor's result.” During class, I often take off on tangents telling old "war stories" like this. I can't help myself.
  • John Wikswo, my coauthor and PhD dissertation advisor, is still active, and he and I continue to collaborate. I learned much about scientific writing from him, but our writing styles are different and he might not agree with all the suggestions in the powerpoint. Tragically, Nestor Sepulveda has passed away; a great loss for bioelectricity research. I miss him.
  • If you are teaching and want to discuss how to write a scientific paper, feel free to use this powerpoint. In fact, I encourage you to download it and modify it to suit your needs. Students could even use it for self study, although they would not see some essential hand waving.
Although the powerpoint suggests many changes to the Sepulveda et al. (1989) paper, I nevertheless consider that article to be a success. According to Google Scholar, it has been cited 379 times. I believe it had an impact on the field of pacing and defibrillation of the heart. Overall, I am proud of the writing.

Let me close by emphasizing that writing is an art. Your style might not be the same as mine. Take my suggestions in the powerpoint as just that: suggestions. Yet, whether or not you agree with my suggestions, I believe your students will benefit by going through the process of revising a scientific paper. It is the next best thing to assigning them to write their own paper. Enjoy!

Friday, May 25, 2018

The Constituents of Blood

Intermediate Physics for Medicine and Biology: The Constituents of BloodI'm a big supporter of blood donation. This week I gave another pint to the Red Cross, which brings my total to 8 gallons. As I lay there with a needle stuck in my arm, I began to wonder "what's in this blood they're squeezing out of me?"

Table 3.1 in Intermediate Physics for Medicine and Biology lists some constituents of blood. I reproduce the table below, with revisions.

Constituent Density in mg/cm3 Number in 1 μm3
Water 1000 33,000,000,000
Sodium 3 83,000,000
Glucose 1 3,300,000
Cholesterol 2 3,100,000
Hemoglobin 150 1,400,000
Albumin 45 390,000

This version of the table highlights several points. Water molecules outnumber all others by a factor of four hundred. Sodium ions are sixty times more common than hemoglobin molecules, but the mass density of hemoglobin is over fifty times that of sodium. In other words, if judged by number of molecules (and therefore the osmotic effect) sodium is most important, but if judged by mass or volume fraction, hemoglobin dominates. Glucose and cholesterol are intermediate cases. Albumin has a surprisingly small number of molecules, given that I thought it was one of the main contributors to osmotic pressure. It is a big molecule, however, so by mass it contributes nearly a third as much as hemoglobin.

Are other molecules in blood important? You can find a comprehensive list of blood constituents beautifully illustrated here. When judged by number, sodium is the most important small ion, but the chloride ion contributes nearly as much. Carbon dioxide and bicarbonate are also significant, and potassium has about the same number of molecules as glucose. If you drive drunk, you may have twice as many ethyl alcohol molecules as potassium ions (if the number of ethanol molecules reaches the level of sodium or chloride ions, you die). Urea has a similar number of molecules as hemoglobin.

Judged by mass, you get an entirely different picture. Large protein molecules dominate. Hemoglobin is by far the largest contributor to blood by mass (after water, of course), followed by albumin and another group of proteins called globulins. Next are glycoproteins such as the clotting factor fibrinogen and iron-binding transferrin.

Many trace constituents hardly affect the osmotic pressure or density of blood, but are excellent biomarkers for diagnosing diseases.

If you're starting to think that blood is awfully crowded, you're right. The picture below is by David Goodsell. No scale bar is included, but each candy-apple-red hemoglobin molecule in the lower left has a diameter of about 6 nm. The water, ions, and other small molecules such as glucose are not shown; if they had been they would produce a fine granular appearance (water has diameter of about 0.3 nm) filling in the spaces between the larger macromolecules.

Blood. Illustration by David S. Goodsell, the Scripps Research Institute.
Blood. Serum is in the upper right and a red blood cell is in the lower left. In the serum, the Y-shaped molecules are antibodies (an immunoglobulin), the long thin light-red molecules are fibrinogen (a glycoprotein), and the numerous potato-like yellow proteins are albumin. The red blood cell is filled with red hemoglobin molecules. The cell membrane is in purple. The illustration is by David S. Goodsell of the Scripps Research Institute.

In another eight weeks I will get free juice and cookies be eligible to give blood again. It doesn't hurt (much) or take (too) long. If you want to donate, contact the American Red Cross. Give the gift of life.

Friday, May 18, 2018

A Biological Constant

Intermediate Physics for Medicine and Biology: A Biological Constant
Membranes, Ions and Impulses, by Kenneth Cole
Physics has many famous constants: Planck’s constant, the speed of light, and the gravitational constant, to name a few. Biology has few such constants. Life is so full of variety that almost any parameter can vary between species or tissues. In fact, physicists differ from biologists by their focus on the unity rather than the diversity of life.

There is, however, one parameter that comes close to being a biological constant. All cells are surrounded by a membrane whose thickness and composition varies little among species. Therefore, the capacitance per unit area, Cm, of a membrane is as close to being a biological constant as you are likely to find.

In Section 6.16 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I calculate the capacitance of a lipid bilayer, and find that Cm is about 0.01 farads per square meter. Many of the key papers during the “golden age” of classical biophysics didn’t use standard SI units. Instead of measuring distance in meters, they used centimeters. If you express Cm as per square centimeter, and if you use microfarads instead of farads, you get the easy-to-remember value of Cm = 1 μF/cm2. Kenneth Cole wrote in his book Membranes, Ions and Impulses:
“This figure of about 1 μF/cm2 has been so confirmed and refined, extended and approximated for membranes of red cells and almost all other living cells, as to become a biophysical constant.”
Are there other biological constants? I suppose some constants governing the structure of key biological molecules, such as the distance between adjacent base pairs of the DNA double helix (0.34 nm), are conserved throughout biology. But these parameters belong more to the realm of biochemistry than biophysics. If you restrict your selection to parameters discussed in IPMB, Cm is one of the few biological constants.

Membranes, Ions and Impuses: A Chapter of Classical Biophysics, by Kenneth Cole

Membrane Capacitance, as discussed in Membranes, Ions and Impulses


 
Table of Contents for Membranes, Ions and Impulses, by Kenneth Cole

Friday, May 11, 2018

The Curie Temperature

Intermediate Physics for Medicine and Biology: The Curie Temperature In Chapter 8 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss magnetic materials, including ferromagnets (permanent magnets in which electron spins are aligned even in the absence of an external magnetic field). We write
“If the temperature of the sample is raised above a critical temperature called the Curie temperature, the magnetism is destroyed.”
When seeing such a sentence, my first inclination is to write a homework problem that uses a toy model to illustrate the physics behind the concept. Unfortunately, analyzing the Curie temperature is difficult, so no new homework problem appears in this post (readers are encouraged to try their hand at writing one).

Solid State Physics by Ashcroft and Mermin
When faced with a difficult concept in material physics, I reach for a copy of Solid State Physics by Neil Ashcroft and N. David Mermin. Regular readers of this blog may recall that I am a big fan of Mermin (for instance, see here and here). Everything I know about solid state physics (which isn't much) I learned from Solid State Physics. When Ashcroft and Mermin describe magnetic ordering of spins, they explain that
“Quantitative theories of magnetic ordering have proved most difficult to construct near the critical temperature Tc at which ordering disappears. The difficulty is not peculiar to the problem of magnetism. The critical points of liquid-vapor transitions, superconducting transitions (Chapter 34), the superfluid transition in liquid He4, and order-disorder transitions in alloys, to name just a few, present quite strong analogies and give rise to quite similar theoretical difficulties.”
They settle for a phenomenological description of the Curie temperature.
“The critical temperature Tc above which magnetic ordering vanishes is known as the Curie temperature in ferromagnets… As the critical temperature is approached from below, the spontaneous magnetization…drops continuously to zero. The observed magnetization just below Tc is well described by a power law.

M(T) ∼ (TcT)β,

where β is typically between 0.33 and 0.37.”
Below I plot of the spontaneous magnetization M versus the absolute temperature T for β=1/3.

magnetization versus temperature

The Curie temperature is interesting for two reasons. First, it is not named after Marie Curie, who plays such a big role in medical physics for isolating some of the first radioactive elements including radium and polonium. Instead, it is named after her husband Pierre Curie, who did important research on magnetism. Second, the ferromagnetic material that Russ and I discuss most in IPMB is magnetite (Fe3O4), which is found in magnetosomes, small magnetic particles that cause magnetotactic bacteria to align with the earth's magnetic field. The Curie temperature for magnetite is 585 °C, or 858 K, which is too hot to support life. Perhaps other substances exist for which the Curie temperature plays a role in biology and medicine, but I don’t know what they are.

I conclude with a quote from Mermin’s delightful essay “Writing Physics” in which he talks about writing Solid State Physics with Ashcroft. Enjoy!
“The striking exception to my inability to write collaboratively is my eight-year collaboration with Neil Ashcroft on our 800 page book on solid state physics. We have very different prose styles. Yet the book has a clear and distinctive uniform tone, which can't be identified as belonging to either of us. I think the reason this worked was that Neil knows solid state physics much better than I do. So he would produce the first drafts. Characteristically, I would not understand them. So I would try to make sense of what he was saying, and then produce my typical kind of irritating second draft. Neil, however, would now have to correct all my mistakes in a massively rewritten third draft. I would then have to root out any new obscurities he had introduced in a fourth draft. By this kind of tennis-playing, we would go through five or six drafts, and emerge with something that was clear, correct, and sounded like a human voice. That voice, however, was neither of ours.”

Friday, May 4, 2018

Strange Glow

Intermediate Physics for Medicine and Biology: Strange Glow
Strange Glow by Timothy Jorgensen
I recently read Strange Glow: The Story of Radiation, by Timothy Jorgensen. This book overlaps many of the topics Russ Hobbie and I discuss in Intermediate Physics for Medicine and Biology, particularly in Section 16.12 (The Risk of Radiation). Jorgensen writes
"The common denominator of most radiation exposure scenarios is fear. Just mention the word radiation, and you instill fear—a perfectly understandable response given the images of mushroom clouds and cancerous tumors that immediately come to mind. Those images would justifiably cause anyone to be anxious. Nevertheless, some people have also become highly afraid of diagnostic x-rays, luggage scanners, cell phones, and microwave ovens. This extreme level of anxiety is unwarranted, and potentially dangerous.

When people are fearful, they tend to exaggerate risk. Research has shown that people’s perception of risk is tightly linked to their fear level. They tend to overestimate the risk of hazards that they fear, while underestimating the risk of hazards they identify as being less scary. Often their risk perception has little to do with the facts, and the facts might not even be of interest to them. For example, many Americans are terrified of black widow spiders, which are found throughout the United States. They are uninterested in the reality that fewer than two people die from black widow bites each year, while over 1,000 people suffer serious illness and death annually from mosquito bites. Mosquitoes are just too commonplace to worry about. Likewise, the risk of commercial airplane crashes is tiny compared to motorcycle crashes, but many a biker is afraid to fly.

The point is that risk perception drives our decision making, and these perceptions often do not correspond to the real risk levels, because irrational fear is taking our brains hostage. When irrational fear enters the picture, it is difficult to objectively weigh risks. Ironically, health decisions driven by fear may actually cause us to make choices that increase, rather than decrease, our risks."
Strange Glow is written for a general audience. Those who have studied from IPMB will already have a stronger quantitative background in math and physics than is needed for Strange Glow’s qualitative discussion. However, as Jorgensen writes in the preface, “These highly quantitative approaches have proved to be largely ineffective in communicating the essence of risk to the public.” I can’t argue with that. I recommend IPMB for a technical background, but Strange Glow for appreciating the broader impact of radiation on society.

Like Gaul, Strange Glow is divided into three parts. Part 1 describes how radiation was discovered, Part 2 discusses the effects of radiation on human health, and Part 3 focuses on risk assessment. I liked the third part best. Jorgensen emphasizes the human stories behind the science. For instance, he begins the chapter about radon by telling the tale of the Watras house.
“On December 2, 1984, Stanley J. Watras, an engineer working on construction of the new Limerick nuclear power plant near Portstown, Pennsylvania, arrived at work. The plant, just seven miles from his home in Boyertown, was scheduled to begin generating power within three weeks, and the construction crew had just installed radiation detectors at the plant doors—a standard safeguard to ensure that nuclear workers don’t exit the plant with any radioactive contamination on their bodies. When Watras arrived that day, he set off the alarms on the detectors as he walked into the plant. Over the following two weeks he would set off the alarms every morning. Further investigation revealed that his clothes were contaminated with radioactivity that he had picked up at his home!

When radiation safety personnel from the plant visited Watras’s home, they discovered what they didn’t think possible. There was more radon gas in the Watras split-level house than was found in a typical uranium mine . . . about 20 times as much! Surprised, the radiation safety technicians checked the radon levels in the neighboring houses. “Our house,” Watras remarked in consternation, “had perhaps the highest contamination level in the world, but our next door neighbors had none.” How could this be?”
Jorgensen then describes how the Environmental Protection Agency publicized--and perhaps exaggerated--the risks of radon. But by trying to err on the side of safety, their efforts became a case study in the challenges of risk assessment.
“This is one of the trade-offs of using multiple, highly conservative assumptions in risk assessment. It may seem prudent to inflate the risk in order not to underestimate it. Nevertheless, by adopting high-end estimates for every uncertain risk parameter, the cascade of high-end risk assumptions can compound to the point where the final predicted risk levels become incredulous and may even defy common sense.”
I find Jorgensen’s evidence-based, unemotional discussion of risk assessment to be a breath of fresh air. Far too often public fears are driven by emotions and ignorance, rather than a balancing of risks and benefits. I highly recommend Strange Glow to anyone wondering or worrying about the danger of radiation. Sometimes the danger is real and sometimes it is not, and you need to know which is which.

Below are some videos about the book and its author. Enjoy!



Friday, April 27, 2018

Frequency Encoding and Phase Encoding

Intermediate Physics for Medicine and Biology: Frequency Encoding and Phase Encoding


I'm always searching for ways to illustrate concepts using “simple” analytical examples (I’ll let you decide whether or not this example is simple). Today, I present analytical examples of frequency and phase encoding during magnetic resonance imaging. Russ Hobbie and I discuss MRI in Chapter 18 of Intermediate Physics for Medicine and Biology.

1. Introduction

Our goal is to understand how the measured MRI signal changes when magnetic field gradients are present. These gradients are essential for "encoding" information about the spatial distribution of spins in the frequency and phase of the signal. To simplify our discussion, we make several assumptions:
  • The radio-frequency π/2 and π pulses, used to rotate the spins into the x-y plane and then create an echo, are so brief that the spins rotate instantaneously compared to all other time scales. Similarly, any slice selection gradient Gz = dBz/dz exists only during the radio-frequency pulses. We won’t include Gz in our drawings of pulse sequences. 
  • We ignore relaxation, so the longitudinal and transverse time constants T1 and T2 are infinite.
  • Despite ignoring relaxation, the spins do dephase leading to a free induction decay with time constant T2*. Dephasing is caused by a distribution of spin frequencies, corresponding to small-scale static heterogeneities of the magnetic field. We assume that the spin frequencies ω have the distribution
    The peak frequency ωo is the Larmor frequency equal to γBo, where γ is the gyromagnetic ratio and Bo is the main magnetic field. The time constant τ indicates the width of the frequency distribution.

  • The spins are distributed uniformly along the x axis from -Δx to +Δx.

2. Spin-Echo

The spin-echo pulse sequence, with no gradients and no frequency or phase encoding, is similar to Fig. 18.24 in IPMB. Our pulse sequences consist of three functions of time. The radio-frequency (RF) pulses are shown on the first line; the time between the π/2 and π pulses is TE/2. The magnetic field gradient in the x direction, Gx = dBz/dx, is indicated in the second line; for this first example Gx is zero. The recorded signal, Mx, is in the third line.
MRI Spin-echo pulse sequence
Our goal is to calculate Mx(t). During the time between the two radio frequency pulses, we calculate the signal by integrating the precessing spins over x and ω


In this case the x integral is trivial: the integrand does not depend on x. We can solve the ω integral analytically using the u-substitution u=τ(ω-ωo), the cosine addition formula cos(A+B) = cosA cosB – sinA sinB, and the definite integral
The resulting free induction decay (FID) is

where τ corresponds to T2*. The exponential shape of the free induction decay arises from the particular form of our spin distribution. The wider the distribution of frequencies, the faster the decay.

The spins accumulate phase relative to those precessing at the Larmor frequency. Just before the π pulse the extra phase is (ω-ωo)TE/2. The π pulse changes the sign of this phase, or in other words adds an additional phase -(ω-ωo)TE. After the π pulse the signal is


The x integral is again trivial and the ω integral produces an echo


which peaks at t = TE and decays with time constant τ.

3. Phase Encoding

Phase encoding adds a gradient field Gx of duration T between the radio-frequency π/2 and π pulses. It shifts the phase of the spins by different amounts at different x locations (thus, position information is encoded in the phase of the signal). This phase shift is then reversed by the π pulse.
MRI phase encoding pulse sequence
The trickiest part of calculating Mx(t) is keeping track of the phase shifts: (ω-ωo)t is the phase shift up to time t because of the distribution of frequencies, -(ω-ωo)TE arises because the spins are flipped by the π pulse, γGxxT is caused by the phase-encoding gradient, and -2γGxxT is again from flipping by the π pulse. During the echo the signal simplifies to


We can solve both the x and ω integrals by repeatedly using the cosine addition formula (it is tedious but not difficult; I leave the details to you), and find


The amplitude of the echo depends on the factor sin(γGxΔxT)/ (γGxΔxT). For a Gx of zero this factor is one and the result is the same as for the spin-echo. If we repeat this pulse sequence with different values of Gx and measure the amplitude of each echo, we can trace out the function sin(γGxΔxT)/ (γGxΔxT), which is the Fourier transform of the spin distribution as a function of position.

4. Frequency Encoding

To do frequency encoding, we add a readout gradient Gx that is on during the echo and lasts a time T, like in Fig. 18.26 of IPMB. In addition, we include a prepulse of opposite polarity and half duration just before the readout, to cancel any extra phase shift accumulated during the echo. (Russ and I discuss this extra lobe of the Gx pulse when analyzing Fig. 18.29c, but we get its sign wrong).
MRI frequency encoding pulse sequence

The free induction decay and the phase reversal caused by the π-pulse are the same as in the spin-echo example. Once Gx begins the result differs. The frequency again depends on x. The phase shifts are: (ω-ωo)t because of the distribution of frequencies, -(ω-ωo)TE from the π pulse, -γGxxT/2 caused by the prepulse, and γGxx(t-(TE -T/2)) during readout. The recorded signal simplifies to


The echo during the readout gradient is (you really must fill in the missing steps yourself to benefit from this post)
The envelope of the echo is the product of two terms, which are both functions of time: An exponential e-|t-TE|/τ that has the shape of the echo with no gradient, and a factor sin(γGxΔx(t-TE))/ (γGxΔx(t-TE)). The amplitude of the echo at t=TE is the same as if Gx were zero, but the shape of the echo has changed because of the time-dependent factor containing the gradient. The function containing the sine is the Fourier transform of the spin distribution. Therefore, the extra time-dependent modulation of the echo by Gx contains information about the spatial distribution of spins.

5. Conclusion

What do we learn from this example? A phase-encoding gradient changes the amplitude of the echo but not its shape. A frequency-encoding gradient, on the other hand, changes the shape but not the amplitude. Both can be written as a modulated Larmor-frequency signal. In the pulse sequences shown above, the Larmor frequency is drawn too low in order to make the figure clearer. In fact, the Larmor frequencies in MRI are many megahertz, and thousands of oscillations occur during the free induction decay and echo.

I analyzed both phase encoding and frequency encoding in the x direction and considered each individually, because I wanted to compare and contrast their behavior. In practice, frequency encoding is performed using a Gx gradient in the x direction and phase encoding with a Gy gradient in the y direction, mapping out the two-dimensional Fourier transform of the spin distribution (see IPMB for more). 

Until I did this calculation I never completely understood what the shape of the echo looks like during readout. I hope it helps you as much as it helped me. Enjoy!

Friday, April 20, 2018

Listmania! IPMB

Intermediate Physics for Medicine and Biology: Listmania! IPMB

Amazon used to have a feature called Listmania! You could make a list of up to 40 books that was visible at Amazon's website. Ten years ago I created a Listmania! list related to Intermediate Physics for Medicine and Biology, reproduced below. Because the list is old, it does not include recent books (such as The Optics of Life) or books that I have discovered recently (such as The First Steps in Seeing). To learn about newer books, search this blog for posts labeled "book review." Amazon has discontinued Listmania!, but you can still find the lists if you look hard. I miss it.

If you are interested in what I read for pleasure, look here.

Enjoy!

**********************************************************

Intermediate Physics for Medicine and Biology

 

 


Bradley J. Roth
The list author says: "Books that are cited by the 4th Edition of Intermediate Physics for Medicine and Biology. These are some of the best biological and medical physics books I know of, and are books that have been useful to me during my career."
Intermediate Physics for Medicine and Biology, 4th Edition (Biological and Medical Physics, Biomedical Engineering)
Intermediate Physics for Medicine and Biology, 4th Edition (Biological and Medical Physics, Biomedical Engineering)
"All the books listed below are cited in the 4th Edition of Intermediate Physics for Medicine and Biology, written by Russ Hobbie and me." 
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables [Applied Mathematics Series 55]
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables [Applied Mathematics Series 55]
"A math handbook that has everything you'll ever need to know."
The 2nd Law: Energy, Chaos, and Form (Scientific American Library Paperback)
The 2nd Law: Energy, Chaos, and Form (Scientific American Library Paperback)
"I love this coffee table book about the second law of thermodynamics.  A painless way to introduce yourself to the subject."
Introduction to Radiological Physics and Radiation Dosimetry
Introduction to Radiological Physics and Radiation Dosimetry
"Classic in the Medical Physics field."
The Essential Exponential! (For the Future of Our Planet)
The Essential Exponential! (For the Future of Our Planet)
"This book explains why we devoted an entire chapter of Intermediate Physics for Medicine and Biology to the exponential function."
Physics With Illustrative Examples From Medicine and Biology: Mechanics (Biological and Medical Physics, Biomedical Engineering)
Physics With Illustrative Examples From Medicine and Biology: Mechanics (Biological and Medical Physics, Biomedical Engineering)
"A classic textbook."
Physics With Illustrative Examples From Medicine and Biology: Electricity and Magnetism (Biological and Medical Physics, Biomedical Engineering)
Physics With Illustrative Examples From Medicine and Biology: Electricity and Magnetism (Biological and Medical Physics, Biomedical Engineering)
"The second edition of the book has much the same content as the first, but the quality of the printing and illustrations is vastly improved."
Physics With Illustrative Examples From Medicine and Biology: Statistical Physics (Biological and Medical Physics, Biomedical Engineering)
Physics With Illustrative Examples From Medicine and Biology: Statistical Physics (Biological and Medical Physics, Biomedical Engineering)
"Benedek and Villars were pioneers in biological and medical physics textbooks."
Random Walks in Biology
Random Walks in Biology
"The best book about the role of diffusion in biology that I know of."
Foundations of Medical Imaging
Foundations of Medical Imaging
"Fine book to study imaging algorithms."
Introduction to Membrane Noise
Introduction to Membrane Noise
"Great book on a little-known topic."
Air and Water
Air and Water
"One of my favorites. Written by a physiologist with an interest in physics (as opposed to Hobbie and I, who are physicists interested in physiology)."
Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles
Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles
"My favorite modern physics textbook."
The Feynman Lectures on Physics (3 Volume Set) (Set v)
The Feynman Lectures on Physics (3 Volume Set) (Set v)
"What physics list could be complete without Feynman?"
From Clocks to Chaos
From Clocks to Chaos
"Excellent book to learn the biological and medical applications of chaos."
The Machinery of Life
The Machinery of Life
"Wonderful picture book.  Great way to visualize the relative sizes of biological objects."
Bioelectricity and Biomagnetism
Bioelectricity and Biomagnetism
"Good, thick tome on bioelectricity."
Textbook of Medical Physiology
Textbook of Medical Physiology
"The classic physiology textbook."
Radiobiology for the Radiologist
Radiobiology for the Radiologist
"Great place to learn about the biological effects of radiation."
Medical Imaging Physics
Medical Imaging Physics
"Standard textbook in medical physics. Hendee is a pioneer in the field."
Ion Channels of Excitable Membranes, Third Edition
Ion Channels of Excitable Membranes, Third Edition
"The bible for information about ion channels."
Machines in Our Hearts: The Cardiac Pacemaker, the Implantable Defibrillator, and American Health Care
Machines in Our Hearts: The Cardiac Pacemaker, the Implantable Defibrillator, and American Health Care
"Learn about the history of pacemakers and defibrillators."
The Physics of Radiation Therapy
The Physics of Radiation Therapy
"The place to go to learn about radiation therapy."
Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields
Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields
"Fine textbook on bioelectricity."
Powers of Ten (Revised) (Scientific American Library Paperback)
Powers of Ten (Revised) (Scientific American Library Paperback)
"Classic work describing how the world looks at different length scales. Required reading by anyone interested in science."
Electric Fields of the Brain: The Neurophysics of EEG,  2nd Edition
Electric Fields of the Brain: The Neurophysics of EEG, 2nd Edition
"Great way to learn about the physics of the electroencephalogram."
Bioelectricity: A Quantitative Approach
Bioelectricity: A Quantitative Approach
"Standard textbook for a class in bioelectricity."
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
"My go-to book on numerical methods."
Electricity and Magnetism (Berkeley Physics Course, Vol. 2)
Electricity and Magnetism (Berkeley Physics Course, Vol. 2)
"Best introduction to electricity and magnetism I know. Part of the great Berkeley Physics Course."
Statistical Physics: Berkeley Physics Course, Vol. 5
Statistical Physics: Berkeley Physics Course, Vol. 5
"Great intuitive introduction to statistical mechanics.  Part of the Berkeley Physics Course."
Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (Fourth Edition)
Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (Fourth Edition)
"Need a little review of vector calculus? This is the place to find it."
Scaling: Why is Animal Size so Important?
Scaling: Why is Animal Size so Important?
"Great book on biological scaling."
How Animals Work
How Animals Work
"Great physiology book. Quirky, but fun."
Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity)
Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity)
"Best book for a first course in nonlinear dynamics."
Life in Moving Fluids: The Physical Biology of Flow (Princeton Paperbacks)
Life in Moving Fluids: The Physical Biology of Flow (Princeton Paperbacks)
"Best book I know of on biological fluid dynamics. Not too mathematical, but full of insight. I recommend all of Vogel's books."
Vital Circuits: On Pumps, Pipes, and the Workings of Circulatory Systems
Vital Circuits: On Pumps, Pipes, and the Workings of Circulatory Systems
"Great for understanding the fluid dynamics of the circulatory system."
Lady Luck: The Theory of Probability (Dover Books on Mathematics)
Lady Luck: The Theory of Probability (Dover Books on Mathematics)
"I often find probability theory boring, but not this book. An oldie but goodie."
The Geometry of Biological Time (Interdisciplinary Applied Mathematics)
The Geometry of Biological Time (Interdisciplinary Applied Mathematics)
"Classic by Art Winfree, who was a leading mathematical biologists.  Be sure to get the 2nd edition."
When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias
When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias
"Winfree's classic on the nonlinear dynamics of the heart."
Cardiac Electrophysiology: From Cell to Bedside, 4e
Cardiac Electrophysiology: From Cell to Bedside, 4e
"Comprehensive reference on cardiac electrophysiology."