Friday, December 26, 2014

Excerpt from the Fifth Edition

Next month, Russ Hobbie and I will receive the page proofs for the 5th edition of Intermediate Physics for Medicine and Biology. I welcome their arrival because I enjoy working on the book with Russ, but also I dread their coming because they can take over your life for weeks. The page proofs are our last chance to rid the book of errors; we will do our best.

I thought that you, dear readers, might like a preview of the 5th edition. We did not add any new chapters, but we did include several new sections such as this one on color vision.
14.15 Color Vision

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. Color printers are based on the colors yellow, cyan and magenta, because when we view the printed page, we are looking at the reflection after some light has been absorbed by the ink. For instance, if white light is incident on a page containing ink that absorbs blue light, the reflected light will contain red and green and therefore appear yellow. Human vision is trichromate, but other animals (such as the dog) have only two types of cones (dichromate vision), and still others have more than three types.

Some people suffer from colorblindness. The most common case is when the cones responding to green light are defective, so that red, yellow and green light all activate only the red receptor. Such persons are said to be red-green color blind: they cannot distinguish red, yellow and green, but they can distinguish red from blue.

As with pitch perception, the sensation of color involves both physics and physiology. For instance, one can stare at a blue screen until the cones responding to blue become fatigued, and then immediately stare at a white screen and see a yellow afterimage. Many other optical illusions with color are possible.
You may recognize parts of this excerpt as coming from a previous entry to this blog. In fact, we used the blog as a source of material for the new edition.

I will leave you with another excerpt, this one from the conclusion of A Christmas Carol. Every Christmas I read Dickens’s classic story about how three spirits transformed the miser Ebenezer Scrooge. It is my favorite book; I like it better than even IPMB!

I wish you all the happiest of holidays.
Scrooge was better than his word. He did it all, and infinitely more; and to Tiny Tim, who did not die, he was a second father. He became as good a friend, as good a master, and as good a man, as the good old city knew, or any other good old city, town, or borough, in the good old world. Some people laughed to see the alteration in him, but he let them laugh, and little heeded them; for he was wise enough to know that nothing ever happened on this globe, for good, at which some people did not have their fill of laughter in the outset; and knowing that such as these would be blind anyway, he thought it quite as well that they should wrinkle up their eyes in grins, as have the malady in less attractive forms. His own heart laughed: and that was quite enough for him.

Friday, December 19, 2014

A Theoretical Physicist’s Journey into Biology

Many physicists have shifted their research to biology, but rarely do we learn how they make this transition or, more importantly, why. But the recent article “A theoretical physicist’s journey into biology: From quarks and strings to cells and whales” by Geoffrey West (Physical Biology, Volume 11, Article number 053013, 2014) lets us see what is involved when changing fields and the motivation for doing it. Readers of the 4th edition of Intermediate Physics for Medicine and Biology will remember West from Chapter 2, where Russ Hobbie and I discuss his work on Kleber’s law. West writes
“Biology will almost certainly be the predominant science of the twenty-first century but, for it to become successfully so, it will need to embrace some of the quantitative, analytic, predictive culture that has made physics so successful. This includes the search for underlying principles, systemic thinking at all scales, the development of coarse-grained models, and closer ongoing collaboration between theorists and experimentalists. This article presents a personal, slightly provocative, perspective of a theoretical physicist working in close collaboration with biologists at the interface between the physical and biological sciences.”
West describes his own path to biology, which included reading some classic texts such as D’Arcy Thompson’s On Growth and Form. He learned biology during intense free-for-all discussions with his collaborator James Brown and Brown’s student Brian Enquist.
“The collaboration, begun in 1995, has been enormously productive, extraordinarily exciting and tremendous fun. But, like all excellent and fulfilling relationships, it has also been a huge challenge, sometimes frustrating and sometimes maddening. Jim, Brian and I met every Friday beginning around 9:00 am and finishing around 3:00 pm with only short breaks for necessities. This was a huge commitment since we both ran large groups elsewhere. Once the ice was broken and some of the cultural barriers crossed, we created a refreshingly open atmosphere where all questions and comments, no matter how ‘elementary’, speculative or ‘stupid’, were encouraged, welcomed and treated with respect. There were lots of arguments, speculations and explanations, struggles with big questions and small details, lots of blind alleys and an occasional aha moment, all against a backdrop of a board covered with equations and hand-drawn graphs and illustrations. Jim and Brian generously and patiently acted as my biology tutors, exposing me to the conceptual world of natural selection, evolution and adaptation, fitness, physiology and anatomy, all of which were embarrassingly foreign to me. Like many physicists, however, I was horrified to learn that there were serious scientists who put Darwin on a pedestal above Newton and Einstein.”
West’s story reminds me of the collaboration between physicist Joe Redish and biologist Todd Cook that I discussed previously in this blog, or Jane Kondev’s transition from basic physics to biological physics when an Assistant Professor at Brandeis (an awkward time in your career to make such a dramatic change).

I made my own shift from physics to biology much earlier in my career--in graduate school. Changing fields is not such a big deal when you are young, but I think all of us who make this transition have to cross that cultural barrier and make that huge commitment to learning a new field. I remember spending much of my first summer at Vanderbilt University reading papers by Hodgkin, Huxley, Rushton, and others, slowly learning how nerves work. Certainly my years at the National Institutes of Health provided a liberal education in biology.

I will give West the last word. He concludes by writing
“Many of us recognize that there is a cultural divide between biology and physics, sometimes even extending to what constitutes a scientific explanation as encapsulated, for example, in the hegemony of statistical regression analyses in biology versus quantitative mechanistic explanations characteristic of physics. Nevertheless, we are witnessing an enormously exciting period as the two fields become more closely integrated, leading to new inter-disciplinary sub-fields such as biological physics and systems biology. The time seems right for revisiting D’Arcy Thompson’s challenge: ‘How far even then mathematics will suffice to describe, and physics to explain, the fabric of the body, no man can foresee. It may be that all the laws of energy, and all the properties of matter, all…..chemistry…. are as powerless to explain the body as they are impotent to comprehend the soul. For my part, I think it is not so’. Many would agree with the spirit of this remark, though new tools and concepts including closer collaboration may well be needed to accomplish his lofty goal.”

Friday, December 12, 2014

In Vitro Evaluation of a 4-leaf Coil Design for Magnetic Stimulation of Peripheral Nerve

In the comments to last week’s blog entry, Frankie asks if there is a way to “safely, reversibly block nerve conduction (first in the lab, then in the clinic) with an exogenously applied E&M signal?” This is a fascinating question, and I may have an answer.

When working at the National Institutes of Health in the early 1990’s, Peter Basser and I analyzed magnetic stimulation of a peripheral nerve. The mechanism of excitation is similar to the one Frank Rattay developed for stimulating a nerve axon with an extracellular electrode. You can find Rattay’s method described in Problems 38-41 of Chapter 7 in the 4th edition of Intermediate Physics for Medicine and Biology. The bottom line is that excitation occurs where the spatial derivative of the electric field is largest. I have already recounted how Peter and I derived and tested our model, so I won’t repeat it today.

If you accept the hypothesis that excitation occurs where the electric field derivative is large, then the traditional coil design for magnetic stimulation--a figure-of-eight coil--has a problem: the axon is not excited directly under the center of the coil (where the electric field is largest), but a few centimeters from the center (where the electric field gradient is largest). What a nuisance. Doctors want a simple design like a crosshair: excitation should occur under the center. X marks the spot.

As I pondered this problem, I realized that we could build a coil just like the doctor ordered. It wouldn’t have a figure-of-eight design. Rather, it would be two figure-of-eights side by side. I called this the four leaf coil. With this design, excitation occurs directly under the center.

John Cadwell of Cadwell Labs built a prototype of this coil; an x ray of it is shown above. We wanted to test the coil in a well-controlled animal experiment, so we sent it to Paul Maccabee at the State University of New York Health Science Center in Brooklyn. Paul did the experiments, and we published the results in the journal Electroencephalography and clinical Neurophysiology (Volume 93, Pages 68-74, 1994). The paper begins
Magnetic stimulation is used extensively for non-invasive activation of human brain, but is not used as widely for exciting limb peripheral nerves because of both the uncertainty about the site of stimulation and the difficulty in obtaining maximal responses. Recently, however, mathematical models have provided insight into one mechanism of peripheral nerve stimulation: peak depolarization occurs where the negative derivative of the component of the induced electric field parallel to nerve fibers is largest (Durand et al. 1989; Roth and Basser 1990). Both in vitro (Maccabee et al. 1993) and in vivo (Nilsson et al. 1992) experiments support this hypothesis for uniform, straight nerves. Based on these results, a 4-leaf magnetic coil (MC) design has been suggested that would provide a well defined site of stimulation directly under the center of the coil (Roth et al. 1990). In this note, we perform in vitro studies which test the performance of this new coil design during magnetic stimulation of a mammalian peripheral nerve.”
Maccabee’s experiments showed that the coil worked as advertised. In the Discussion of the paper we concluded that “the 4-leaf coil design provides a well defined stimulus site directly below the center of the coil”.

This is a nice story, but it’s all about exciting an action potential. What does it have to do with Frankie’s goal of blocking an action potential? Well, if you flip the polarity of the coil current, instead of depolarizing the nerve under the coil center, you hyperpolarize it. A strong enough hyperpolarization should block propagation. We wrote
“In a final type of experiment, performed on 3 nerves, the action potential was elicited electrically, and a hyperpolarizing magnetic stimulus was applied between the stimulus and recording sites at various times. The goal was to determine if a precisely timed stimulus could affect action potential propagation. Using induced hyperpolarizing current at the coil center, with a strength that was approximately 3 times greater than that needed to excite by depolarization at that location, we never observed a block of the action potential. Moreover, no significant effect on the latency of the action potential propagating to the recording site was observed….Our magnetic stimulator was able to deliver stimuli with strengths up to only 2 or 3 times the threshold strength, and therefore the magnetic stimuli were probably too weak to block propagation. It is possible that such phenomena might be observed using a more powerful stimulator.”
Frankie, I have good news and bad news. The good news is that you should be able to reversibly block nerve conduction with magnetic stimulation using a four-leaf coil. The bad news is that it didn’t work with Paul’s stimulator; perhaps a stronger stimulator would do the trick. Give it a try.

Friday, December 5, 2014

The Bubble Experiment

When I was a graduate student, my mentor John Wikswo assigned to me the job of measuring the magnetic field of a nerve axon. This experiment required me to dissect the ventral nerve cord out of a crayfish, thread it through a wire-wound ferrite-core toroid, immerse the nerve and toroid in saline, stimulate one end of the nerve, and record the magnetic field produced by the propagating action currents. One day as I was lowering the instrument into the saline bath, a bubble got stuck in the gap between the nerve and the inner surface of the toroid. “Drat” I thought as I searched for a needle to remove it. But before I could poke it out I wondered “how will the bubble affect the magnetic signal?”

To answer this question, we need to review some magnetism. Ampere's law states that the line integral of the magnetic field around a closed path is proportional to the net current passing through a surface bounded by that path. For my experiment, that meant the magnetic signal depended on the net current passing through the toroid. The net current is the sum of the current inside the nerve axon and that fraction of the current in the saline bath that threads the toroid--the return current. In general, these currents flow in opposite directions and partially cancel. One of the difficulties I faced when interpreting my data was determining how much of the signal was from intracellular current and how much was from return current.

I struggled with this question for months. I calculated the return current with a mathematical model involving Fourier transforms and Bessel functions, but the calculation was based on many assumptions and required values for several parameters. Could I trust it? I wanted a simpler way to find the return current.

Then along came the bubble, plugging the toroid like Pooh stuck in Rabbit's front door. The bubble blocked the return current, so the magnetic signal arose from only the intracellular current. I recorded the magnetic signal with the bubble, and then--as gently as possible--I removed the bubble and recorded the signal again. This was not easy, because surface tension makes a small bubble in water sticky, so it stuck to the toroid as if glued in place. But I eventually got rid of it without stabbing the nerve and ending the experiment.

To my delight, the magnetic field with the bubble was much larger than when it was absent. The problem of estimating the return current was solved; it is the difference of the signal with and without the bubble. I reported this result in one of my first publications (Roth, B. J., J. K. Woosley and J. P. Wikswo, Jr., 1985, An experimental and theoretical analysis of the magnetic field of a single axon. In: Biomagnetism: Applications and Theory, Weinberg, Stroink and Katila, Eds., Pergamon Press, New York, pp. 78-82.).
“When taking data from a crayfish nerve, the toroid and axon were lifted out of the bath for a short time. […] When again placed in the bath an air bubble was trapped in the center of the toroid, filling the space between the axon and the toroid inner surface. […] Taking advantage of this fortunate occurrence, data were taken with and without the bubble present. […] The magnetic field with the bubble present […] is narrower and larger than the field with the toroid filled with saline.”

On the day of the bubble experiment I was lucky. I didn't plan the experiment. I wasn't wise enough or thoughtful enough to realize in advance that a bubble was the ideal way to eliminate the return current. But when I looked through the dissecting microscope and saw the bubble stuck there, I was bright enough to appreciate my opportunity. “Chance favors the prepared mind.”

I have a habit of turning all my stories into homework problems. You will find the bubble story in the 4th edition of Intermediate Physics for Medicine and Biology, Problem 39 of Chapter 8. Focus on part (b).
Problem 39 A coil on a magnetic toroid as in Problem 38 is being used to measure the magnetic field of a nerve axon.
(a) If the axon is suspended in air, with only a thin layer of extracellular fluid clinging to its surface, use Ampere's law to determine the magnetic field, B, recorded by the toroid.
(b) If the axon is immersed in a large conductor such as a saline bath, B is proportional to the sum of the intracellular current plus that fraction of the extracellular current that passes through the toroid (see Problem 13). Suppose that during an experiment an air bubble is trapped between the axon and the inner radius of the toroid? How is the magnetic signal affected by the bubble? See Roth et al. (1985).