Friday, July 26, 2013

Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields

A good textbook about bioelectricity and biomagnetism is Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields by Jaakko Malmivuo and Robert Plonsey (Oxford University Press, 1995). One of the best features of the book is that it is available for free online at www.bem.fi/book/index.htm. The book covers many of the topics Russ Hobbie and I discuss in Chapters 6-9 of the 4th edition of Intermediate Physics for Medicine and Biology: the cable equation, the Hodgkin and Huxley model, patch-clamp recordings, the electrocardiogram, biomagnetism, the bidomain model, and magnetic stimulation. The book’s Introduction outlines its eight parts:
Part I discusses the anatomical and physiological basis of bioelectromagnetism. From the anatomical perspective, for example, Part I considers bioelectric phenomena first on a cellular level (i.e., involving nerve and muscle cells) and then on an organ level (involving the nervous system (brain) and the heart).

Part II introduces the concepts of the volume source and volume conductor and the concept of modeling. It also introduces the concept of impressed current source and discusses general theoretical concepts of source-field models and the bidomain volume conductor. These discussions consider only electric concepts.

Part III explores theoretical methods and thus anatomical features are excluded from discussion. For practical (and historical) reasons, this discussion is first presented from an electric perspective in Chapter 11. Chapter 12 then relates most of these theoretical methods to magnetism and especially considers the difference between concepts in electricity and magnetism.

The rest of the book (i.e., Parts IV - IX) explores clinical applications. For this reason, bioelectromagnetism is first classified on an anatomical basis into bioelectric and bio(electro)magnetic constituents to point out the parallelism between them. Part IV describes electric and magnetic measurements of bioelectric sources of the nervous system, and Part V those of the heart.

In Part VI, Chapters 21 and 22 discuss electric and magnetic stimulation of neural and Part VII, Chapters 23 and 24, that of cardiac tissue. These subfields are also referred to as electrobiology and magnetobiology. Part VIII focuses on Subdivision III of bioelectromagnetism - that is, the measurement of the intrinsic electric properties of biological tissue. Chapters 25 and 26 examine the measurement and imaging of tissue impedance, and Chapter 27 the measurement of the electrodermal response.

In Part IX, Chapter 28 introduces the reader to a bioelectric signal that is not generated by excitable tissue: the electro-oculogram (EOG). The electroretinogram (ERG) also is discussed in this connection for anatomical reasons, although the signal is due to an excitable tissue, namely the retina.
Jaakko Malmivuo is a Professor in the School of Electrical Engineering at Aalto University in Helsinki, Finland. He is also the director of the Ragnar Granit Institute.

Robert Plonsey is the Pfizer-Pratt University Professor Emeritus of Biomedical Engineering at Duke University. This year, he received the IEEE Biomedical Engineering Award “for developing quantitative methods to characterize the electromagnetic fields in excitable tissue, leading to a better understanding of the electrophysiology of nerve, muscle, and brain.” Plonsey is cited on 16 pages of Intermediate Physics for Medicine and Biology, the most of any scientist or author.

Friday, July 19, 2013

Reinventing Physics For Life-Science Majors

The July issue of Physics Today contained an article by Dawn Meredith and Joe Redish titled Reinventing Physics for Life-Science Majors. Much in the article is relevant to the 4th edition of Intermediate Physics for Medicine and Biology. The main difference between the goals of their article and IPMB is that they discuss the introductory physics course, whereas Russ Hobbie and I wrote an intermediate-level text. Nevertheless, many of the aims remain the same. Meredith and Redish begin
“Physics departments have long been providing service courses for premedical students and biology majors. But in the past few decades, the life sciences have grown explosively as new techniques, new instruments, and a growing understanding of biological mechanisms have enabled biologists to better understand the physiochemical processes of life at all scales, from the molecular to the ecological. Quantitative measurements and modeling are emerging as key biological tools. As a result, biologists are demanding more effective and relevant undergraduate service classes in math, chemistry, and physics to help prepare students for the new, more quantitative life sciences.” 
Their section on what skills should students learn reads like a list of goals for IPMB:
  • Drawing inferences from equations…. 
  • Building simple quantitative models…. 
  • Connecting equations to physical meaning…. 
  • Integrating multiple representations…. 
  • Understanding the implications of scaling and functional dependence…. 
  • Estimating….”
Meredith and Redish realize the importance of developing appropriate homework problems for life-science students, which is something Russ and I have spent an enormous amount of time on when revising IPMB. “We have spent a good deal of time in conversation with our biology colleagues and have created problems of relevance to them that are also doable by students in an introductory biology course.” They then offer a delightful problem about calculating how big a worm can grow (see their Box 4). They also include a photo of a “spherical cow;” you need to see it to understand. And they propose the Gauss gun (see a video here) as a model for exothermic reactions. They conclude
“Teaching physics to biology students requires far more than watering down a course for engineers and adding in a few superficial biological applications. What is needed is for physicists to work closely with biologists to learn not only what physics topics and habits of mind are useful to biologists but also how the biologist’s work is fundamentally different from ours and how to bridge that gap. The problem is one of pedagogy, not just biology or physics, and solving it is essential to designing an IPLS [Introductory Physics for the Life Sciences] course that satisfies instructors and students in both disciplines.”

Friday, July 12, 2013

The Bohr Model

One hundred years ago this month, Niels Bohr published his model of the atom (On the Constitution of Atoms and Molecules, Philosophical Magazine, Volume 26 July 1913, p. 1-25). In the May 2013 issue of Physics Today, Helge Kragh writes
“Published in a series of three papers in the summer and fall of 1913, Niels Bohr’s seminal atomic theory revolutionized physicists’ conception of matter; to this day it is presented in high school and undergraduate-level textbooks.” 
I find Bohr’s model fascinating for several reasons: 1) it was the first application of quantum ideas to atom structure, 2) it predicts the size of the atom, 3) it implies discrete atomic energy levels, 4) it explains the hydrogen spectrum in terms of transitions between energy levels, and 5) it provides an expression for the Rydberg constant in terms of fundamental parameters. In his book The Making of the Atomic Bomb, Richard Rhodes discusses the background leading to Bohr’s discovery.
Johann Balmer, a nineteenth-century Swiss mathematical physicist, identified in 1885 … a formula for calculating the wavelengths of the spectral lines of hydrogen…A Swedish spectroscopist, Johannes Rydberg, went Balmer one better and published in 1890 a general formula valid for a great many different line spectra. The Balmer formula then became a special case of the more general Rydberg equation, which was built around a number called the Rydberg constant [R]. That number, subsequently derived by experiment and one of the most accurately known of all universal constants, takes the precise modern value of 109,677 cm-1.

Bohr would have known these formulae and numbers from undergraduate physics, especially since Christensen [Bohr’s doctorate advisor] was an admirer of Rydberg and had thoroughly studied his work. But spectroscopy was far from Bohr’s field and he presumably had forgotten them. He sought out his old friend and classmate, Hans Haansen, a physicist and student of spectroscopy just returned from Gottingen. Hansen reviewed the regularity of the line spectra with him. Bohr looked up the numbers. ‘As soon as I saw Balmer’s formula,’ he said afterward, ‘the whole thing was immediately clear to me.’

What was immediately clear was the relationship between his orbiting electrons and the lines of spectral light….The lines of the Balmer series turn out to be exactly the energies of the photons that the hydrogen electron emits when it jumps down from orbit to orbit to its ground state. Then, sensationally, with the simple formula R=2π2me4/h3 (where m is the mass of the electron, e the electron charge and h Planck’s constant—all fundamental numbers, not arbitrary numbers Bohr made up) Bohr produced Rydberg’s constant, calculating it within 7 percent of its experimentally measured value!...”
In chapter 14 of the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the Bohr model, but interestingly we do not attribute the model to Bohr. However, at other locations in the book, we casually refer to Bohr’s model by name: see Problem 33 of Chapter 15 where we mention “Bohr orbits,” and Sections 15.9 and 16.1.1 where we refer to the “Bohr formula.” I guess we assumed that everyone knows what the Bohr model is (a pretty safe assumption for readers of IPMB). In Problem 4 of Chapter 14 (one of the new homework problems in the 4th edition), the reader is asked to derive the expression for the Rydberg constant in terms of fundamental parameters (you don't get exactly the same answer as in the quote above; presumably Rhodes didn't use SI units).

Bohr would become one the principle figures in the development of modern quantum mechanics. He also made fundamental contributions to nuclear physics, and contributed to the Manhattan project. He was awarded the Nobel Prize in Physics in 1922 “for his services in the investigation of the structure of atoms and of the radiation emanating from them.” He is Denmark’s most famous scientist, and for years he led the Institute of Theoretical Physics at the University of Copenhagen. A famous play, titled “Copenhagen” is about his meeting with former collaborator Werner Heisenberg in then-Nazi-controlled Denmark in 1941. Watch the BBC production of this play on youtube here.

Physicists around the world are celebrating this 100-year anniversary; for instance here, here, here and here.

I end with Bohr’s own words: an excerpt from the introduction of his first 1913 paper (references removed).
“In order to explain the results of experiments on scattering of α rays by matter Prof. Rutherford has given a theory of the structure of atoms. According to this theory, the atoms consist of a positively charged nucleus surrounded by a system of electrons kept together by attractive forces from the nucleus; the total negative charge of the electrons is equal to the positive charge of the nucleus. Further, the nucleus is assumed to be the seat of the essential part of the mass of the atom, and to have linear dimensions exceedingly small compared with the linear dimensions of the whole atom. The number of electrons in an atom is deduced to be approximately equal to half the atomic weight. Great interest is to be attributed to this atom-model; for, as Rutherford has shown, the assumption of the existence of nuclei, as those in question, seems to be necessary in order to account for the results of the experiments on large angle scattering of the α rays.

In an attempt to explain some of the properties of matter on the basis of this atom-model we meet however, with difficulties of a serious nature arising from the apparent instability of the system of electrons: difficulties purposely avoided in atom-models previously considered, for instance, in the one proposed by Sir J. J. Thomson. According to the theory of the latter the atom consists of a sphere of uniform positive electrification, inside which the electrons move in circular orbits. The principal difference between the atom-models proposed by Thomson and Rutherford consists in the circumstance the forces acting on the electrons in the atom-model of Thomson allow of certain configurations and motions of the electrons for which the system is in a stable equilibrium; such configurations, however, apparently do not exist for the second atom-model. The nature of the difference in question will perhaps be most clearly seen by noticing that among the quantities characterizing the first atom a quantity appears -- the radius of the positive sphere -- of dimensions of a length and of the same order of magnitude as the linear extension of the atom, while such a length does not appear among the quantities characterizing the second atom, viz. the charges and masses of the electrons and the positive nucleus; nor can it be determined solely by help of the latter quantities.

The way of considering a problem of this kind has, however, undergone essential alterations in recent years owing to the development of the theory of the energy radiation, and the direct affirmation of the new assumptions introduced in this theory, found by experiments on very different phenomena such as specific heats, photoelectric effect, Röntgen [etc]. The result of the discussion of these questions seems to be a general acknowledgment of the inadequacy of the classical electrodynamics in describing the behaviour of systems of atomic size. Whatever the alteration in the laws of motion of the electrons may be, it seems necessary to introduce in the laws in question a quantity foreign to the classical electrodynamics, i. e. Planck's constant, or as it often is called the elementary quantum of action. By the introduction of this quantity the question of the stable configuration of the electrons in the atoms is essentially changed as this constant is of such dimensions and magnitude that it, together with the mass and charge of the particles, can determine a length of the order of magnitude required. This paper is an attempt to show that the application of the above ideas to Rutherford's atom-model affords a basis for a theory of the constitution of atoms. It will further be shown that from this theory we are led to a theory of the constitution of molecules.

In the present first part of the paper the mechanism of the binding of electrons by a positive nucleus is discussed in relation to Planck's theory. It will be shown that it is possible from the point of view taken to account in a simple way for the law of the line spectrum of hydrogen. Further, reasons are given for a principal hypothesis on which the considerations contained in the following parts are based.

I wish here to express my thanks to Prof. Rutherford his kind and encouraging interest in this work.”

Friday, July 5, 2013

The Spark of Life

This week I finished the book The Spark of Life: Electricity in the Human Body, by Frances Ashcroft. In the introduction, Ashcroft explains the goal of her book.
“In essence, this book is a detective story about a special kind of protein—the ion channel—that takes us from Ancient Greece to the forefront of scientific research today. It is very much a tale for today, as although the effects of static electricity and lightning on the body have been known for centuries, it is only in the last few decades that ion channels have been discovered, their functions unravelled and their beautiful, delicate, intricate structures seen by scientists for the first time. It is also a personal panegyric for my favourite proteins, which captured me as a young scientist and never let me go; they have been a consuming passion throughout my life. In Walt Whitman’s wonderful words, my aim is to ‘sing the body electric’.”
The book examines much of the history behind topics that Russ Hobbie and I discuss in the 4th edition of Intermediate Physics for Medicine and Biology, such as the work of Hodgkin and Huxley on the squid nerve axon, the electrocardiogram, and modern medical devices such as the pacemaker and cochlear implants. The book is definitely aimed at a general audience; having worked in the field of bioelectricity, I sometimes wish for more depth in the discussion. For instance, anyone wanting to know the history of pacemakers and defibrillators would probably prefer something like Machines in our Hearts, by Kirk Jeffrey. Nevertheless, it was useful to find the entire field of bioelectricity described in one relatively short and easily readable book. With its focus on ion channels, I consider this book as a popularization of Bertil Hille’s text Ion Channels of Excitable Membranes. Her book was also useful to me as a review of various drugs and neurotransmitters, which I don’t know nearly as much about as I should.

Here is a sample of Ashcroft’s writing, in which she tells about Rod MacKinnon’s determination of the structure of a potassium channel. Russ and I discuss MacKinnon’s work in Chapter 9 (Electricity and Magnetism at the Cellular Level) of IPMB.
“A slight figure with an elfin face, MacKinnon is one of the most talented scientists I know. He was determined to solve the problem of how channels worked and he appreciated much earlier than others that the only way to do so was to look at the channel structure directly, atom by atom. This was not a project for the faint-hearted, for nobody had ever done it before, no one really knew how to do it and most people did not even believe it could be done in the near future. The technical challenges were almost insurmountable and at that time he was not even a crystallographer. But MacKinnon is not only a brilliant scientist; he is also fearless, highly focused and extraordinarily hard-working (he is famed for working around the clock, snatching just a few hours’ sleep between experiments). Undeterred by the difficulties, he simultaneously switched both his scientific field and his job, resigning his post at Harvard and moving to Rockefeller University because he felt the environment there was better. Some people in the field wondered if he was losing his mind. In retrospect, it was a wise decision. A mere two years later, MacKinnon received a standing ovation—an unprecedented event at a scientific meeting—when he revealed the first structure of a potassium channel. And ion channels went to Stockholm all over again.”
Ashcroft is particularly good at telling the human interest stories behind the discoveries described in the book. There were several interesting tales about neurotoxins; not only the well-known tetrodotoxin, but also others such as saxitoxin, aconite, batrachotoxin, and grayanotoxin. The myotonic goats, who because of an ion channel disease fall over stiff whenever startled, are amazing. Von Humboldt’s description of natives using horses to capture electric eels is incredible. The debate in Parliament about August Waller’s demonstration of the electrocardiogram, using his dog Jimmie as the subject, was funny. If, like me, you enjoy such stories, read The Spark of Life.

I will end with Ashcroft’s description of how Hodgkin and Huxley developed their mathematical model of the action potential in the squid giant axon, a topic covered in detail in Chapter 6 of IPMB.
“Having measured the amplitude and time course of the sodium and potassium currents, Hodgkin and Huxley needed to show that they were sufficient to generate the nerve impulse. They decided to do so by theoretically calculating the expected time course of the action potential, surmising that if it were possible to mathematically simulate the nerve impulse it was a fair bet that only the currents they had recorded were involved. Huxley had to solve the complex mathematical equations involved using a hand-cranked calculator because the Cambridge University computer was ‘off the air’ for six months. Strange as it now seems, the university had only one computer at that time (indeed it was the first electronic one Cambridge had). It took Huxley about three weeks to compute an action potential: times have moved on—it takes my current computer just a few seconds to run the same simulation. What is perhaps equally remarkable is that we often still use the equations Hodgkin and Huxley formulated to describe the nerve impulse.

Three years after finishing their experiments, in 1952, Hodgkin and Huxley published their studies in a landmark series of five papers that transformed forever our ideas about how nerves work. The long time between completing their experiments and publication seems extraordinary to present-day scientists, who would be terrified of being scooped by their rivals. Not so in the 1950s—Huxley told me, ‘It never even entered my head.’ In 1963, Hodgkin and Huxley were awarded the Nobel Prize. Deservedly so, for they got such beautiful results and analysed them so precisely that they revolutionized the field and provided the foundations for modern neuroscience.”
For more about the Spark of life, see here, here, here, and here. Listen to and watch Ashcroft being interviewed by Denis Noble here, and giving the Croonian Lecture here.