Nonlinear Dynamics

Nonlinear dynamics is discussed in several chapters in the 4th edition of Intermediate Physics for Medicine and Biology, and particularly in Chapter 10. Where can you go to get a more information about this topic? Several fine books are cited in our references.

Nonlinear Dynamics and Chaos,
by Steven Strogatz.

One book that Russ Hobbie cited in earlier editions of our text is Nonlinear Dynamics and Chaos, by Steven Strogatz. Even though we still cite the book in the 4th edition, I was not really familiar with it until last year, when my daughter Stephanie used it in a class on nonlinear dynamics at the University of Michigan. She loved the book, and recommended it to me. In the preface, Strogatz writes

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. It is based on a one-semester course I’ve taught for the past several years at MIT. My goal is to explain the mathematics as clearly as possible, and to show how it can be used to understand some of the wonders of the nonlinear world... A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory.

When Time Breaks Down,
by Art Winfree.

For anyone who reads Intermediate Physics for Medicine and Biology and wants to learn more about nonlinear dynamics, I recommend this delightful text. Strogatz, the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University, was a collaborator and student of one of my heroes, the late Art Winfree. Art’s book When Time Breaks Down had a tremendous influence on my early career. I have not yet read Strogatz’s newest book Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life, but reading it is on my list of things to do.

From Clocks to Chaos,
by Glass and Mackey.

A book that came out when I was working at the National Institutes of Health is Leon Glass and Michael Mackey’s From Clocks to Chaos. While this book may not present the math as elegantly as Strogatz’s book, it does focus specifically on biological and medical problems. In particular, it introduces the idea of a “dynamical diseases”: diseases characterized by abnormal temporal organization.

Dynamics:
The Geometry of Behavior,
by Abraham and Shaw.

When explained well, nonlinear dynamics is a very visual subject. An older book that makes much use of pictures is Dynamics: The Geometry of Behavior by Abraham and Shaw. In fact it could be called a “picture book,” but don’t let that description fool you. The math is presented at a high level, but in a primarily visual way. It was a great help to me when I was first learning the subject.

The Visual Display of Quantitative Information

The Visual Display
of Quantitative Information,
by Edward Tufte.

Early in my graduate school career (back when I used to have time to read widely), a fascinating book was published titled The Visual Display of Quantitative Information. Its author Edward Tufte describes the book as a “celebration of data graphics.” In the introduction, he writes

Modern data graphics can do much more than simply substitute for small statistical tables. At their best, graphics are instruments for reasoning about quantitative information. Often the most effective way to describe, explore, and summarize a set of numbers—even a very large set—is to look at pictures of those numbers. Furthermore, of all methods for analyzing and communicating statistical information, well-designed graphics are usually the simplest and at the same time the most powerful.

A page from The Visual Display
of Quantitative Information,
by Edward Tufte.

Tufte suggests ways to improve data graphics. For instance, Chapter 4 concludes by summarizing these five principles: 1) Above all else show the data, 2) Maximize the data-ink ratio, 3) Erase non-data-ink, 4) Erase redundant data-ink, and 5) Revise and edit. Chapter 9 offers this recommendation: “Graphical elegance is often found in simplicity of design and complexity of data.” Perhaps Tufte’s poem at the end of Chapter 8 summarizes these ideas more succinctly:

For non-data-ink, less is more.
For data-ink, less is a bore.

Of course, words can’t convey the lessons of this book. You need to see the graphics appearing on every page to appreciate his points.

Many of the readers of the 4th edition of Intermediate Physics for Medicine and Biology will go on to become research scientists, engineers, or medical doctors, and will publish papers full of interesting data. That data will be presented more clearly, simply, and elegantly by following the principles and techniques outlined in The Visual Display of Quantitative Information and Tufte’s other books. 

Listen to Edward Tufte talk about the Art of Visualization.
https://www.youtube.com/watch?v=AdSZJzb-aX8 

The Bends

Physics with Illustrative Examples
from Medicine and Biology,
by Benedek and Villars.

When I teach about hydrostatics from the 4th edition of Intermediate Physics for Medicine and Biology, I like to make a little digression and discuss a biomedical application of hydrostatic pressure: decompression sickness. Also known as “the bends,” this illness occurs after breathing high-pressure air, which causes nitrogen to be dissolved in the blood. If the pressure is then released suddenly the nitrogen can form bubbles that block circulation. This effect is not unlike the formation of foam—made from bubbles of carbon dioxide—when you open a bottle of pop. You can find a nice discussion of the physiological effects of increased fluid pressure in Physics With Illustrative Examples from Medicine and Biology: Mechanics, by George Benedek and Felix Villars.

Engineers of Dreams:
Great Bridge Builders and the
Spanning of America,
by Henry Petroski.

Often you can teach best by telling a story, and when discussing decompression sickness I like to tell the story of the Eads Bridge. James Eads built the first bridge over the Mississippi River at St Louis. It is a beautiful arch bridge that opened in 1874. When building the supports for the bridge under the river, Eads used “caissons,” watertight structures sunk under the river and filled with compressed air. The high air pressure prevented water from filling the caisson, allowing workers to excavate the river bottom. In his book Engineers of Dreams: Great Bridge Builders and the Spanning of America, Henry Petroski has described decompression sickness experienced by men working in Eads’ caissons.

When the caisson reached a depth of seventy feet, the workmen began to experience some difficulty climbing the stairs to the surface. As the caisson was sunk deeper, men suffered increasing attacks of cramps and paralysis, which were thought to be due to insufficient clothing or poor nutrition. In March 1870, when the caisson had reached ninety-three feet, the air pressure inside it was about four times what it was in the open air, and workmen began dying upon emerging from the caisson, or after being hospitalized for an ailment that came then to be called "caisson disease" but today is known as “the bends.” Eads asked his family physician, Dr. Alphonse Jaminet, to look after the workmen, but Jaminet himself became paralyzed one day, having spent time down in the caisson and come up after only a few minutes in the air lock.

Perhaps somewhat to his own surprise, Jaminet recovered, and began to conduct research into these mysterious attacks. He shortly concluded that the major cause was too-rapid decompression in the face of a drastic difference in air pressure between the submerged caisson and the outer air above. Thereupon he placed restrictions on the amount of time the men could work inside the caisson, and on the speed with which the pressure in the air lock could be reduced.

Incidentally, Petroski has written many fascinating books about engineering, including To Engineer Is Human: The Role of Failure in Successful Design and The Evolution of Useful Things. He also has a monthly essay on engineering in American Scientist, the magazine of Sigma Xi, the Scientific Research Society. Although there’s not much medicine or biology in Petroski’s work, certainly a biomedical engineer studying from Intermediate Physics for Medicine and Biology will find many important lessons about engineering design. I give Petroski’s books two thumbs up.

Inside Story: Physics in Medicine

The Institute of Physics has an excellent website called “Inside Story: Physics in Medicine,” which contains some fascinating animations with colorful images. It is at a significantly more elementary level than the 4th edition of Intermediate Physics for Medicine and Biology, but might be used as a fun “extra” in a medical physics class based on that book. MRI Scans, Colonoscopy, PET Scans, and Radiotherapy are the featured topics.

When you first link to the webpage, you have two choices. If your computer has Macromedia Flash Plugin 7, then definitely enter the “flash” site, as it is much more interesting than the “html” site.“Inside Story” was produced by the Institute of Physics and the Medical Research Council, a English organization that “promotes the balanced development of medical and related biological research in the UK.” It was developed as part of the 2005 Einstein Year, a worldwide celebration of the one hundredth anniversary of Einstein’s miraculous year, when Albert Einstein, at age 26, published his theories of Brownian motion, special relativity and the photoelectric effect.

Virtual Colonoscopy

Ever had a colonoscopy? It’s not pleasant. A paper published this week in the New England Journal of Medicine (Volume 359, pages 1207—1217), titled “Accuracy of CT Colonography for Detection of Large Adenomas and Cancers” suggests an alternative to the traditional procedure for detecting colorectal cancer: a “virtual colonoscopy.” This X-ray technology uses Computed Tomography (CT), which Russ Hobbie and I discuss in Chapter 12 of the 4th edition of Intermediate Physics for Medicine and Biology. The NEJM article concludes that “in this study of asymptomatic adults, CT colonographic screening identified 90% of subjects with adenomas or cancers measuring 10 mm or more in diameter. These findings augment published data on the role of CT colonography in screening patients with an average risk of colorectal cancer.” To learn more about this study, see the Associated Press article by Mike Strobbe, and an article in US News and World Report.

Any X-ray procedure does have a risk associated with the radiation dose. A typical virtual colonsocopy has a dose of 5 to 10 mSv. By comparison, the yearly dose from the natural background radiation is about 3 mSv. (The sievert is a unit of dose equal to a Joule per kilogram, adjusted for its biological effectiveness. A mSv is one thousandth of a sievert.) See my December 7, 2007 entry in this blog, or Chapter 16 of the 4th edition of Intermediate Physics for Medicine and Biology, for more information about radiation safety and CT scans. Of course, any risk of radiation must be weighed against risks involved with traditional colonoscopy procedures.

Now for the bad news: You still need to “clean out your bowels” before the procedure, regardless of which method you use: traditional or virtual.

Particle Physics Rap

Today’s post (a rare non-Friday message) has nothing to do with the 4th edition of Intermediate Physics for Medicine and Biology, and nothing to do with medicine and biology at all. But if you are a physics fan, you must check out the particle physics rap at www.physicscentral.com (see the video highlight). This rap celebrates the Large Hadron Collider (LHC), which was turned on September 10, beginning what may be some of the greatest particle physics experiments ever. The rap is too delightful to miss. Enjoy.

Note added October 26: Physics central took the blog off their site, but you can still find it at youtube: http://www.youtube.com/watch?v=j50ZssEojtM. 

 Listen to a physics rap celebrating the Large Hadron Collider.
http://www.youtube.com/watch?v=j50ZssEojtM 

Switching from Physics to Biology

Physicists studying from the 4th edition of Intermediate Physics for Medicine and Biology may be interested in entering the field of biological physics. If so, I suggest reading “Switching From Physics to Biology: Physicists in Transition Help Shape Biological Theory” by Jennifer Ouellette (The Industrial Physicist, Volume 9, Pages 20–23, 2003). The article, which can be found online, begins

Many in physics chafe at the oft-quoted maxim that the 21st century is the “age of biology.” Others see the biological boom as offering unique opportunities for physicists—and not just in the traditional area of building instrumentation for experimental research. Physicists are well positioned by their training to contribute to the development of a theoretical framework in biology, a field that has matured to the point where sufficient quantitative data and sophisticated experimental tools exist to test biological theories.

For other physics-to-biology stories, see Yuh-Nung Jan’s interview in Current Biology and Chris Sander’s story told on the Sloan-Kettering Institute website. Also, here is some advice from the “Grant Doctor” published in Science. 

 Listen to Jennifer Ouellette talk about change.
https://www.youtube.com/watch?v=tGZn0IdFHp4 

Biocurious

While surfing the internet one evening, I stumbled upon a fascinating website that will interest readers of the 4th edition of Intermediate Physics for Medicine and Biology. It is called “Biocurious, a biophysics blog.”

Biocurious is a weblog about biology (and physics, grad school, and miscellenaeous other things!) through the eyes of physicists.

As best I can tell, Biocurious is maintained entirely by two graduate students, Andre Brown of the University of Pennsylvania and Philip Johnson of the University of Toronto. The blog is interesting, well-written, and provides insight into the interface between physics and biology, as well as the lifestyle of biological physics grad students. One enjoyable feature of this site is the “molecule of the month” (from the protein data bank), and another is the extended list of other related blogs, which I have only begun to explore. I particularly like their header image, a picture by David Goodsell of a macrophage and bacterium at a magnification of 2,000,000.

Nice blog, Andre and Philip.

PHY 325

This fall, I am teaching PHY 325, Biological Physics, at Oakland University. Of course, the textbook is the 4th edition of Intermediate Physics for Medicine and Biology. You can follow along on the class website, which includes the syllabus, homework assignments, exams, interesting links, and a section called “hot news” that keeps track of up-to-date news for the class, including homework due dates, exam information, etc. We’ll cover the first ten chapters of the book.

Class starts on Wednesday, September 3, at 8 A.M. sharp (I’I'mm a morning person, and I guess the students will have to put up with waking early this semester, too). Welcome to all my PHY 325 students, including premed students, physics majors, and students in the new Engineering Biology program at Oakland.

Still More From The Preface

From the Preface.

The Fourth Edition [of Intermediate Physics for Medicine and Biology] follows the tradition of earlier editions. The book now has a second author: Bradley J. Roth of Oakland University. Both of us have enjoyed this collaboration immensely. We have added a chapter on sound and ultrasound, deleting or shortening topics elsewhere, in order to keep the book only slightly longer than the Third Edition. Some of the deleted material is available at the book’s website: https://sites.google.com/view/hobbieroth.

The Fourth Edition has 44% more end-of-chapter problems than the Third Edition; most highlight biological applications of the physical principles. Many of the problems extend the material in the text. A solutions manual is available to those teaching the course. Instructors can use it as a reference or provide selected solutions to their students. The solutions manual makes it much easier for an instructor to guide an independent-study student. Information about the Solutions Manual is available at the book’s website...

Biophysics is a very broad subject. Nearly every branch of physics has something to contribute, and the boundaries between physics and engineering are blurred. Each chapter could be much longer; we have attempted to provide the essential physical tools. Molecular biophysics has been almost completely ignored: excellent texts already exist, and this is not our area of expertise. This book has become long enough.

We would appreciate receiving any corrections or suggestions for improving the book.