Blog to IPMB Mapping

One reason I write this blog is to help instructors who are teaching from Intermediate Physics for Medicine and Biology. The blog, however, is over ten years old, and there are more than 500 posts. Teachers may not be able to find what they need.

Help is here! I have prepared a mapping of the sections in IPMB to the weekly blog posts (see an excerpt below). You can find it here, or through the book website, or download the pdf (but the links might not work). Now an instructor teaching, say, Section 1.1 (Distances and Sizes) can find eight related posts. I will keep the file up-to-date as new posts appear.

Some posts, including many of my favorites, are not associated with a particular section; I did not include those. A few posts fit with two or three sections, and appear several times. The majority relate to a single section.

What do I write about most? Four sections in IPMB have ten or more related posts.

• Section 9.10, Possible Effects of Weak External Electric and Magnetic Fields, 11 posts. Many of these posts debunk myths about the dangers of weak low-frequency fields.
• Section 17.7, Radiopharmaceuticals and Tracers, 11 posts. Several posts discuss potential shortages of technetium.
• Section 16.2, The Risk of Radiation, 19 posts. These posts are about radiation accidents, the “risk” of very low doses of radiation, and the linear-no-threshold model.
• Section 7.10, Electrical Stimulation, 20 posts. This section reflects my research interests, with multiple posts describing pacemakers, defibrillators, and neural stimulation.

Which chapters have the most posts? In first place are Chapters 8 (Biomagnetism) and 16 (Medical Uses of X-Rays), each with 39. Tied for last are Chapters 3 (Systems of Many Particles) and 5 (Transport Through Neutral Membranes), each with only 11. I guess I don’t like to post about thermodynamics.

I hope this mapping from IPMB to the blog helps instructors use the textbook. Enjoy!

Used Math

Used Math,
by Clifford Swartz.

How much mathematics is needed when taking a class based on Intermediate Physics for Medicine and Biology? Students come to me all the time and say “I am interested in your class, but I don’t know if I have enough math background.” I wish I had a small book that reviewed the math needed for a class based on IPMB. Guess what? Used Math by Clifford Swartz is just what I need. In the preface, Swartz writes:

In this book, which is part reference and part reminder, we are concerned with how to use math. We concentrate on those features that are most needed in the first two years of college science courses. That range is not rigorously defined, of course. A sophomore physics major at M.I.T. or Cal. Tech. must use differential equations routinely, while a general science major at some other place may still be troubled by logarithms. It is possible that even the Tech student has never really understood certain things about simple math. What, for instance, is natural about the natural logs? We have tried to cover a broad range to topics—all the things that a science student might want to know about math but has never dared ask.

Students and instructors might benefit if I went through Used Math chapter by chapter, assessing what math is needed, and what is math not needed, when studying from IPMB. Also, what math is needed but is not included in Used Math.

Chapter 1: Reporting and Analyzing Uncertainty

Russ Hobbie and I assume our readers know about scientific notation and significant figures. The best time to teach significant figures is during laboratory. (Wait! Is there is a lab that goes along with IPMB? No. At least not that I know of. But perhaps there should be.) In my Biological Physics class, students often answer homework using too many significant figures. I don’t take off points, but I write annoying notes in red ink.

Chapter 2: Units and Dimensions

Russ and I do not review how to convert between units. My students usually don’t have trouble with this. Often, however, they will do algebra and derive an equation that is dimensionally wrong (for example, containing “a + a²” where a has units of length). I take off extra points for such mistakes, and I harp about them in class.

Chapter 3: Graphs

We assume students can plot a simple graph of y(x) versus x. In class, when we derive a result such as y(x) = x/(x² + a²), I ask the students what a sketch of this function looks like. Often they have trouble drawing it. Our homework problems routinely ask students to plot their result. I deduct points if these plots are not qualitatively correct. IPMB discusses semilog and log-log plots in Chapter 2.

Chapter 4: The Simple Functions of Applied Math

Students should be familiar with powers, roots, trigonometric functions, and the exponential function before taking a class based on IPMB. Chapter 2 is devoted to the exponential, and Appendix C lists properties of exponents and logarithms. We define the hyperbolic functions sinh and cosh upon first use (Eq. 6.98). I don’t give placement quizzes at the first class meeting, but if I did I would have the students sketch plots of x², √x, sin(x), cos(x), tan(x), e^x, log(x), sinh(x), cosh(x), and tanh(x). If you can’t do that, you will never be able to translate mathematical results into physical insight.

Chapter 5: Statistics

I discussed the statistics used in IPMB before in this blog. We analyze probability distributions in Chapter 3 on thermodynamics and Chapter 4 on diffusion, and go into more detail in Appendix G (mean and standard deviation), Appendix H (the binomial distribution), Appendix I (the Gaussian distribution), and Appendix J (the Poisson distribution). We don’t discuss analyzing data, such as testing a hypothesis using a student t-test. One topic missing from Used Math is simple concepts from probability; for example, when you role two dice what is the probability that they add to five? When I taught quantum mechanics (a subject in which probability is central), I spent an entire class calculating the odds of winning at craps. You will understand probability by the time you finish that calculation.

Chapter 6: Quadratic and Higher Power Equations

Russ and I use the quadratic equation without review. We don’t solve any higher order equations in IPMB, and we never ask the student to factor a polynomial using a procedure similar to long division (yuk!).

Chapter 7: Simultaneous Equations

Students should know how to solve systems of linear equations. I often solve small systems (two or three equations) in class. Sometimes when teaching I derive the equations and then say “the rest is just math” and state the solution. This happens often when doing a least-squares fit at the start of Chapter 11. I don’t ask students to solve a system of many (say, five) equations.

Chapter 8: Determinants

IPMB does not stress linear algebra and we never require that students calculate the determinant of a matrix. However, we do occasionally require the student to calculate a cross product using a method similar to taking a determinant (Eq. 1.9), so students need to know the rules for evaluating 2 × 2 and 3 × 3 determinants.

Chapter 9: Geometry

Used Math goes into more detail about analytical geometry (conic sections, orbits, and special curves like the catenary) than is needed in IPMB. The words ellipse and hyperbola never appear in our book (parabola does.) We discuss cylindrical and spherical coordinates in Appendix L. Students should know how to find the surface area and volume of simple objects like a cube, cylinder, or sphere.

Chapter 10: Vectors

Russ and I use vectors throughout IPMB. They are reviewed in Appendix B. We define the dot and cross product of two vectors when they are first encountered.

Chapter 11: Complex Numbers

We avoid complex numbers. I hate them. One exception: we introduce complex exponentials when discussing Fourier methods, where we present them as an alternative to sines and cosines that is harder to understand intuitively but easier to handle algebraically. You could easily skip the sections using complex exponentials, thereby banishing complex numbers from the class.

Chapter 12: Calculus—Differentiation

Students must know the definition of a derivative. In class I derive a differential equation for pressure by adding the forces acting on a small cube of fluid and then taking the limit as the size of the cube shrinks to zero. If students don’t realize that this process is equivalent to taking a derivative, they will be lost. Also, they should know that a derivative gives the slope of a curve or a rate of change. What functions should students be able to differentiate? Certainly powers, sines and cosines, exponentials, and logarithms. Plus, students must know the chain rule and the product rule. They should be able to maximize a function by setting its derivative to zero, and they should realize that a partial derivative is just a derivative with respect to one variable while the other variables are held constant (Appendix N).

Chapter 13: Integration

Students must be able to integrate simple functions like powers, sines and cosines, and exponentials. They should know the difference between a definite and indefinite integral, and they should understand that an integral corresponds to the area under a curve. Complicated integrals are provided to the student (for example, Appendix K explains how to evaluate integrals of e^-x2) or a student must consult a table of integrals. In my class, I always use the “guess and check” method for solving a differential equation: guess a solution containing some unknown parameters, plug it into the differential equation, and determine what parameters satisfy the equation; no integration is needed. One calculation that some students have problems with is integrating a function over a circle. In class, I carefully explain in how the area element becomes rdrdθ. At first the students look bewildered, but most eventually master it. I avoid integration by parts (which I dislike), but it is needed when calculating the electrical potential of a dipole. Perhaps you can devise a way to eliminate integration by parts altogether?

Chapter 14: Series and Approximations

Appendix D of IPMB is about Taylor series. If you remember only that e^x is approximately 1+x, you will know 90% of what you need. The expansions of sin(x) and cos(x) are handy, but not essential. When deriving the dipole approximation, I use the Taylor series of 1/(1-x). (The day I discuss the dipole is one of the most mathematical of the semester.) Student’s never need to derive a Taylor series, and they rarely require more than the first two terms of the expansion. The geometric series (1+x+x²+…) appears in Homework Problem 28 of Chapter 8, but the sum of the series is given. In IPMB, we never worry about convergence of an infinite series. Fourier series is central to imaging. In Medical Physics (PHY 3260), I spend a couple weeks discussing Fourier series and Fourier transforms, the most mathematically intensive part of IPMB. If students can handle Chapters 11 and 12, they can handle any math in the book.

Chapter 15: Some Common Differential Equations

I always tell my class “if you can solve only one differential equation, let it be dy/dx = by” (in case you are wondering, the solution is y = e^bx). As I mentioned earlier, I preferred to solve differential equations by guess and check. In IPMB, you can get away with guesses that involve powers, trig functions, and exponentials. Some students claim that a course in differential equations is needed before taking a class using IPMB. I disagree. We don’t need advanced methods (e.g., exact differential equations) and we never analyze existence and uniqueness of solutions. We just guess and check. Appendix F discusses differential equations in general, but my students rarely need to consult it. I emphasize understanding differential equations from a physical point-of-view. I expect my students to be able to translate a physical statement of a problem into a differential equation. Yes, I put such questions on my exams. To me, that is a crucial skill.

Chapter 16: Differential Operators

What Used Math calls differential operators, I call vector calculus: divergence, gradient, and curl. Russ and I use vector calculus occasionally. I expect students to be able to do homework problems using it, but I don’t expect them to do such calculations on exams. Mostly, vector calculus appears when talking about electricity and magnetism in Chapters 6-8. I think an instructor could easily design the class to avoid vector calculus altogether. Whenever Russ and I use vector calculus, we typically cite Div, Grad, Curl and All That, which is my favorite introduction to these concepts.


That sums up of the topics in Used Math. Is there any other math in IPMB? Special functions sometimes pop up, such as Bessel functions, the error function, and Legendre polynomials. Usually these appear in homework problems that you don’t have to assign. We occasionally ask students to solve differential equations numerically (see Sec. 6.14), usually in the homework. I skip these problems when I teach from IPMB; there is not enough time for everything. In some feedback problems in Chapter 10 (for example, Problems 10.12 and 10.17) the operating point must be evaluated numerically. I do assign these problems, and I tell students to find the solution by trial and error. We don’t spend time developing fancy methods for solving nonlinear equations, but I want students to realize they can solve equations such as xe^x = 1 numerically (the solution is approximately x = 0.57).

In summary, Used Math contains almost all the mathematics you need when taking a class from IPMB. It would be an excellent supplementary reference for students. From now on, when students ask me how much math they need to know for my Biological Physics or Medical Physics class, I will tell them all they need is in Used Math.

Everything's Up To Date in Kansas City

Union Station.

I posted the last two entries in this blog while on a trip to Kansas City to visit my parents. I didn’t grow up in the Kansas City area, but I did graduate from Shawnee Mission South High School in Overland Park Kansas, and I was a physics major at the University of Kansas in Lawrence. My dad is a native of Kansas City Missouri, while my mom moved to Kansas City Kansas when young and attended Wyandotte High School.

Kauffman Center
for the Performing Arts.

We had a great visit, including a ride on Kansas City’s new streetcar, which travels a route along Main Street from Union Station, past the Power and Light District, within a few blocks of the Kauffman Center, to the River Market. We also had a great pork sandwich at Pigwich in the East Bottoms. Kansas City is booming.

Liberty Memorial.

Is there any connection between Kansas City and medical physics? Yes, there is. Rockhurst University, a liberal arts college located a mile west of where my dad grew up on Swope Parkway, offers an undergraduate program in the physics of medicine, which is similar to the medical physics major we offer at Oakland University. I thought the readers of Intermediate Physics for Medicine and Biology might like to see how another school other than Oakland structures its undergraduate medical physics curriculum.

From their Physics of Medicine website:

POM Program Overview: To suit your interests and career goals the POM Program has three program choices:

• Medical Physics Major - Major Track designed for students wishing to enter graduate school in Medical Physics
• Physics of Medicine (POM) Pre-Professional Major - Major Track designed for students wishing to enter a Medical/Healthcare Graduate Program
• Physics of Medicine (POM) Minor— Minor designed to complement pre-healthcare or pre-medicine program

Advantages to students of the POM Program are:

1. Deeper understanding of physics principles and their applicability to a medical or health field career.
2. Stronger post-graduate application to competitive health field programs.
3. Undergraduate research opportunities – potential for capstone area or future graduate work. 
4. Value to students of interdisciplinary study, allowing them to tie together coursework in science/math with professional goals. 

All Physics of Medicine Coursework is designed to complement the Scientific Foundations for Future Physicians Report, Report of the AAMC-HHMI Committee (2009).

Some courses specific to the program are:

PH 3200 Physics of the Body I: This course expands on the physics principles developed in introductory physics courses through an in-depth study of mechanics, fluids and thermodynamics as they are applied to the human body. Areas of study include the following: biomechanics (torque, force, motion and lever systems of the body; application of vector analysis of human movement to video), thermodynamics and heat transfer (food intake and mechanical efficiency) and the pulmonary system (pressure, volume and compliance relationships). Guest speakers from the medical community will be invited. [This course appears to cover the material in Chapters 1-3 in IPMB]

PH 3210 Physics of the Body II: This course is a continuation of Physics of the Body I with a concentration on the cardiovascular system, electricity and wave motion. Areas of study include the following: cardiovascular system (heart as a force pump, blood flow and pressure), electricity in the body (action potentials, resistance-capacitance circuit of nerve impulse propagation, EEG, EKG, EMG), and sound (hearing, voice production, sound transfer and impedance, ultrasound – transmission and reflection). In addition, students complete a guided, in-depth, individual investigation on a topic pertinent to Physics of the Body. Guest speakers from the medical community will be invited. [Approximately Chapters 6, 7, and 13 in IPMB. PH 3200 and 3210 together are similar to Oakland University’s PHY 325, Biological Physics]

PH 3240 Physics of Medical Imaging: This course focuses on an introduction to areas of modern physics required for an understanding of contemporary medical diagnostic and treatment procedures. Topics include a focus on the physics underlying modern medical imaging instruments: the EM Spectrum, X-Ray, CT, Gamma Camera, SPECT, PET, MRI and hybrid instrumentation. In this course, students learn about the physics involved in how these diagnostic and therapeutic instruments work as well as the numerous physics and patient factors that contribute to the choice of instrument for diagnosis. There will be field trips to local hospitals and medical imaging facilities and invited guest speakers. [Chapters 15-18 in IPMB; similar to OU’s PHY 326, Medical Physics]

PH 4400 Optics: This course covers both the geometric and physical properties of optical principles including optics of the eye, lasers, fiber optics, and use of endoscopy in medicine. Students will complete a final optics research project in which they relate content learned to an area of optics research. [Chapter 14 in IPMB. We have no comparable course at OU. We offer a standard optics class, but with no biomedical emphasis. This class intrigues me.]

PH 4900 Statistics for the Health Sciences: This course introduces the basic principles and methods of health statistics. Emphasis is on fundamental concepts and techniques of descriptive and inferential statistics with applications in health care, medicine and public health. Core content includes research design, statistical reasoning and methods. Emphasis will be on basic descriptive and inferential methods and practical applications. Data analysis tools will include descriptive statistics and graphing, confidence intervals, basic rules of probability, hypothesis testing for means and proportions, and regression analysis. Students will use specialized statistical software to conduct data analysis of health related data sets. [Nothing exactly like this in IPMB. At OU, we require all medical physics majors to take a statistics class, taught by the Department of Mathematics and Statistics.]

PH 4900 Research in Physics of Medicine: Independent student research on coursework from Physics of Medicine Program. Students will choose topic from Physics of Medicine Program coursework to investigate further and prepare for presentation submission. This course will serve as a capstone course for Medical Physics and Physics of Medicine Pre-Professional Majors. [I am a big supporter of undergraduate research. At OU, medical physics majors can satisfy their capstone requirement by either research or our seminar class.]

MT 3260 Mathematical Modeling in Medicine: Students will build mathematical models and use these models to answer questions in various areas of medicine. Topics may include: Epidemic modeling, genetics, drug treatment, bacterial population modeling, and neural systems/networks. [IPMB is focused on mathematical modeling. I teach PHY 325 and 326 as workshops on mathematical modeling in biology and medicine.]

The Rockhurst physics of medicine minor looks like an idea I am tempted to steal. Their requirements are:

To complete the Physics of Medicine Minor:

Prerequisites: one year of introductory/general physics and Calculus I (complete in first two years)

Upper Division Courses: complete 4 upper-division POM courses (12 hrs.total)

Required:

• PH 3200: Physics of the Body I (3 Hours, Offered Fall Semester Odd years) 
• PH 3210: Physics of the Body II (3 Hours, Offered Spring Semester even years)

Choose 2 from the following:

• PH 3240: Physics of Medical Imaging (3 Hours, Offered Spring Semester Odd Years) 
• PH 4400: Optics (3 hours, Offered Fall Semester Even Years) 
• MT 3260: Mathematical Modeling in Medicine (3 Hours, Offered Fall Semester Even years)
• PH 4900: Statistics for the Health Sciences (3 Hours, Offered Spring semesters)

An OU version might be Biological Physics (PHY 325) and Medical Physics (PHY 326), plus their prerequisites: two semesters of introductory physics and two semesters of calculus.

The Nelson Art Gallery.

I enjoy my trips to Kansas City because there is a lot to do and see there, from the Nelson Art Gallery to Crown Center to the Liberty Memorial and the National World War I Museum. I remember in high school attending shows at the Starlight Theater in Swope Park, and watching many Kansas City Royals baseball games at Kauffman Stadium (where I saw George Brett play in the World Series!). The Truman Library is in nearby Independence Missouri.

The Country Club Plaza.

I didn’t expect to find a hub of medical physics education in Kansas City, but there it is. In addition to the Rockhurst program, the Kansas University Medical Center has a CAMPEP-accredited clinical medical physics residency (while driving on I-35, I could see cranes putting up a new KU Med Center building), and the Stowers Institute, less than a mile north of Rockhurst and just east of the Country Club Plaza, has a strong biomedical research program. As the song says, Everything's Up To Date in Kansas City.

Kansas City celebrating the 2015 Royals World Series Championship.

PHY 325 and PHY 326

One reason I write this blog is to help instructors who adopt Intermediate Physics for Medicine and Biology as their textbook. I teach classes from IPMB myself; here at Oakland University we have a Biological Physics class (PHY 325) and a Medical Physics class (PHY 326). Instructors might benefit from seeing how I structure these classes, so below are my most recent syllabi.  

Syllabus, Biological Physics

Fall 2015

Class: Physics 325, MWF, 8:00–9:07, 378 MSC

Instructor: Brad Roth, Dept. Physics, 166 Hannah Hall, 370-4871, roth@oakland.edu, fax: 370-3408, office hours MWF, 9:15–10:00, https://files.oakland.edu/users/roth/web

Text: Intermediate Physics for Medicine and Biology, 5th Edition, by Hobbie and Roth (An electronic version of this book is available for free through the OU library)
Book Website: https://files.oakland.edu/users/roth/web/hobbie.htm (get the errata!).
Book Blog: http://hobbieroth.blogspot.com

Goal: To understand how physics influences and constrains biology

Grades

Point/Counterpoint		5 %
Exam 1	Feb 5	20 %	Chapters 1–3
Exam 2	March 18	20 %	Chapters 4–6
Exam 3	April 20	20 %	Chapter 7, 8, 10
Final Exam	April 20	10 %	Comprehensive
Homework		25 %

Schedule

Sept 4		Introduction
Sept 9, 11	Chapter 1	Mechanics, Fluid Dynamics
Sept 14–18	Chapter 2	Exponential, Scaling
Sept 21–25	Chapter 3	Thermodynamics
Sept 28–Oct 2		Exam 1
Oct 5–9	Chapter 4	Diffusion
Oct 12–16	Chapter 5	Osmotic Pressure
Oct 19–23	Chapter 6	Electricity and Nerves
Oct 26–30		Exam 2
Nov 2–6	Chapter 7	Extracellular Potentials
Nov 9–13	Chapter 8	Biomagnetism
Nov 16–20	Chapter 10	Heart Arrhythmias, Chaos
Nov 23, 25	Chapter 10	Feedback
Nov 30–Dec 4	Chapter 10	Feedback
Dec 7		Review
Dec 9		Final Exam

Homework

Chapter 1:	6, 7, 8, 16, 17, 33, 40, 42	due Wed, Sept 16
Chapter 2:	3, 5, 10, 29, 42, 46, 47, 48	due Wed, Sept 23
Chapter 3:	29, 30, 32, 33, 34, 40, 47, 48	due Wed, Sept 30
Chapter 4:	7, 8, 12, 20, 22, 23, 24, 41	due Wed, Oct 14
Chapter 5:	1, 3, 5, 6, 7, 8, 10, 16	due Wed, Oct 21
Chapter 6:	1, 2, 22, 28, 37, 41, 43, 61	due Wed, Oct 28
Chapter 7:	1, 10, 15, 24, 25, 36, 42, 47	due Wed, Nov 11
Chapter 8:	3, 10, 24, 25, 27, 28, 29, 32	due Wed, Nov 18
Chapter 10:	12, 16, 17, 18, 40, 41, 42, 43	due Wed, Dec 2

Syllabus, Medical Physics

Winter 2016 

Class: Physics 326, MWF, 10:40–11:47, 204 DH

Instructor: Brad Roth, Department of Physics, 166 HHS, (248) 370-4871, roth@oakland.edu, fax: (248) 370-3408, office hours MWF 9:30–10:30, https://files.oakland.edu/users/roth/web.

Text: Intermediate Physics for Medicine and Biology, 5th Edition, by Hobbie and Roth. An electronic version of the textbook is available through the OU library.
Book Website: https://files.oakland.edu/users/roth/web/hobbie.htm (get the errata!).
Book Blog: http://hobbieroth.blogspot.com

Goal: To understand how physics contributes to medicine

Grades

Point/Counterpoint		5 %
Exam 1	Feb 5	20 %	Chapters 13–15
Exam 2	March 18	20 %	Chapters 16, 11–12
Exam 3	April 20	20 %	Chapter 17, 18
Final Exam	April 20	10 %
Homework		25 %

Schedule

Jan 6, 8		Introduction
Jan 11, 13, 15	Chpt 13	Sound and Ultrasound
Jan 20, 22	Chpt 14	Atoms and Light
Jan 25, 27, 29	Chpt 15	Interaction of Photons and Matter
Feb 1, 3, 5		Exam 1
Feb 8, 10, 12	Chpt 16	Medical Uses of X rays
Feb 15, 17, 19	Chpt 11	Least Squares and Signal Analysis
Feb 22, 24, 26		Winter Recess
Feb 29, March 2, 4	Chpt 12	Images
March 7, 9, 11	Chpt 12	Images
March 14, 16, 18		Exam 2
March 21, 23, 25	Chpt 17	Nuclear Medicine
March 28, 30, Apr 1	Chpt 17	Nuclear Medicine
April 4, 6, 8	Chpt 18	Magnetic Resonance Imaging
April 11, 13, 15	Chpt 18	Magnetic Resonance Imaging
April 18		Conclusion
April 20		Final Exam

Homework

Chapter 13:	7, 10, 12, 21, 22, 27, 30, 36	due Fri, Jan 22
Chapter 14:	4, 5, 16, 21, 22, 47, 48, 49	due Wed, Jan 27
Chapter 15:	2, 4, 5, 10, 12, 14, 15, 16	due Wed, Feb 3
Chapter 16:	4, 5, 7, 16, 19, 20, 22, 31	due Wed, Feb 17
Chapter 11:	9, 11, 15, 20, 21, 36, 37, 41	due Wed, Mar 2
Chapter 12:	7, 9, 10, 23	due Wed, Mar 9
Chapter 12:	25, 32, 34, 35, and 27 (extra credit)	due Wed, Mar 16
Chapter 17:	1, 2, 7, 9, 14, 17, 20, 22	due Wed, Mar 30
Chapter 17:	29, 30, 40, 54, 57, 58, 59, 60	due Wed, Apr 6
Chapter 18:	9, 10, 13, 14, 15, 18, 35, 49	due Wed, Apr 13

Point/Counterpoint articles

Jan 8: The 2014 initiative is not only unnecessary but it constitutes a threat to the future of medical physics. Med Phys, 38:5267–5269, 2011.

Jan 15: Ultrasonography is soon likely to become a viable alternative to x-ray mammography for breast cancer screening. Med Phys, 37:4526–4529, 2010.

Jan 22: High intensity focused ultrasound may be superior to radiation therapy for the treatment of early stage prostate cancer. Med Phys, 38:3909–3912, 2011.

Jan 29: The more important heavy charged particle radiotherapy of the future is more likely to be with heavy ions rather than protons. Med Phys, 40:090601, 2013.

Feb 12: The disadvantages of a multileaf collimator for proton radiotherapy outweigh its advantages. Med Phys, 41:020601, 2014.

Feb 19: Low-dose radiation is beneficial, not harmful. Med Phys, 41:070601, 2014.

March 4: Recent data show that mammographic screening of asymptomatic women is effective and essential. Med Phys, 39:4047–4050, 2012.

March 11: PDT is better than alternative therapies such as brachytherapy, electron beams, or low-energy x rays for the treatment of skin cancers. Med Phys, 38:1133–1135, 2011.

March 25: Submillimeter accuracy in radiosurgery is not possible. Med Phys, 40:050601, 2013.

April 1: Within the next ten years treatment planning will become fully automated without the need for human intervention. Med Phys, 41:120601, 2014.

April 8: Medical use of all high activity sources should be eliminated for security concerns. Med Phys, 42:6773, 2015.

April 15: MRI/CT is the future of radiotherapy treatment planning. Med Phys, 41:110601, 2014.

Notes:

• The OU library has an electronic version of IPMB that students can download. If they are willing to read pdfs, they have no textbook expense in either class.
• I skip Chapter 9. I have nothing against it. There just isn’t time for everything.
• I cover Chapters 13-16 before the highly mathematical Chapters 11-12.  I don’t like to start the semester with a week or two of math.
• In Medical Physics, we spend the last 15 minutes of class each Friday discussing a point/counterpoint article from the journal Medical Physics. The students seem to really enjoy this.
• I let the students work together on the homework, but they cannot simply copy someone else’s work. They must turn in their own assignment.
• Both PHY 325 and PHY 326 are aimed at upper-level undergraduates. The prerequisites are a year of introductory physics and a year of introductory calculus. The students tend to be physics majors, medical physics majors, bioengineering majors, plus a few biology, chemistry, math, and mechanical engineering majors. The typical enrollment is about ten.
• I encourage premed students to take these classes. Occasionally one does, but not too often. I wish more would, because I believe it provides an excellent preparation for the MCAT. Unfortunately, they have little room in their busy schedule for two extra physics classes.
• OU offers a medical physics major. It consists of many traditional physics classes, these two specialty classes (PHY 325 and PHY 326), plus some introductory and intermediate biology.
• I am a morning person, so I often teach at 8 A.M. The students hate it, but I love it. Sometimes, however, I can’t control the time of day for the class and I teach at a later time.

Trivial Pursuit IPMB

Trivial Pursuit.

Trivial Pursuit is a popular and fun board game invented in the 1980s. While playing it, you learn many obscure facts (trivial, really).

When my daughter Kathy was in high school, she would sometimes test out of a subject by studying over the summer and then taking an exam. Occasionally I would help her study by skimming through her textbook and creating Trivial Pursuit-like questions. We would then play Trivial Pursuit using my questions instead of those from the game. I don’t know if it helped her learn, but she always passed those exams.

Readers of Intermediate Physics for Medicine and Biology may want a similar study aid to help them learn about biological and medical physics. Now they have it! At the book website you can download 100 game cards for Trivial Pursuit: IPMB. To play, you will need the game board, game pieces, and instructions of the original Trivial Pursuit, but you replace the game cards by the ones I wrote.

The game pieces for Trivial Pursuit.

In case you have never played, here are the rules in a nutshell. The board has a circle with spots of six colors. You roll a die and move your game piece around the circle, landing on the spots. Your opponent asks you a question about a topic determined by the color. If you answer correctly you roll again; if you are wrong your opponent rolls. There are special larger spots where a correct answer gets you get a little colored wedge. The first person to get all six colored wedges wins.

The original version of Trivial Pursuit had topics such as sports or literature. The Trivial Pursuit: IPMB topics are

• Numbers and Units (blue)
• People (pink)
• Anatomy and Physiology (yellow)
• Biological Physics (brown)
• Medical Physics (green)
• Mathematics (orange).

One challenge of an interdisciplinary subject like medical and biological physics is that you need a broad range of knowledge. I suspect mathematicians will find the math questions to be simple, but the biologists may find them difficult. Physicists may be unfamiliar with anatomy and physiology, and chemists may find all the topics hard. The beauty of the game is that it rewards a broad knowledge across disciplines.

A game card for Trivial Pursuit.

Many may find the People section most challenging. I suggest you only require the player to know the person’s last name, although the first name is also given on my game card. In Units and Numbers I generally only require numbers to be known approximately. The goal is to have an order-of-magnitude knowledge of biological parameters and physical constants. Many questions ask you to estimate the size of an object, like in Section 1.1 of IPMB. For the math and physics questions you may need a pencil and paper handy, because some of the questions contain equations. You can’t simply show your opponent the equation on the game card, because both the questions and answers are together. This is unlike the real Trivial Pursuit game cards, which had the answers on the back. Unfortunately, such two-sided cards are difficult to make.

I know the game is not perfect. Some questions are truly trivial and others ask for some esoteric fact that no one would be expected to remember. Some questions may have multiple answers of which only one is on the card. You can either print out the game cards (requiring 100 pieces of paper) or use a laptop or mobile device to view the pdf. I try to avoid repetitions, but with 100 game cards some may have slipped in inadvertently.

Trivial Pursuit.

I may try using Trivial Pursuit: IPMB next time I teach Biological Physics (PHY 325) or Medical Physics (PHY 326) here at Oakland University. It would be excellent for, say, the last day of class, or perhaps a day when I know many students will be absent (such as the Wednesday before Thanksgiving). It doesn’t teach important high-level skills, such as learning to use mathematical models to describe biology, or understanding how physics constrains the way organisms evolve. You can’t teach a complex and beautiful subject like tomography using Trivial Pursuit. But for learning a bunch of facts, the game is useful.

Enjoy!

The Mystery of the Flawed Homework Problem

When teaching PHY 325 (Biological Physics) this fall, I assigned my students homework from the 5th edition of Intermediate Physics for Medicine and Biology. One problem comes from Section 7.10 about Electrical Stimulation.

Problem 36. If the medium has a constant resistance, find the energy required for stimulation as a function of pulse duration.

The odd thing is, when I looked in the solution manual to review how to solve this problem, it contained answers to parts (a) and (b), and (b) is the most useful part. Where are (a) and (b)? Somehow when preparing the 5th edition, part (b) was left out (it is missing from the 4th edition too). Nevertheless, part (b) ended up in the solution manual (don’t ask me how). This is what Problem 36 should look like:

Problem 36. The longevity of a pacemaker battery is related to the energy required for stimulation.

(a) Find an expression for the energy U expended by a pacemaker to stimulate the heart as a function of the pulse duration t. Use the Lapicque strength-duration curve (Eq. 7.45), and assume the body and electrodes have a constant resistance R. Sketch a plot of energy versus duration.

(b) In general you want to stimulate using the least energy. Determine what duration minimizes the energy expended per pulse.

I don’t usually solve homework problems from the book in this blog, but because the interesting part of this problem was left out of IPMB I don’t think it will hurt in this case. Also, it provides readers with a sneak peak at the solution manual. Remember that Russ Hobbie and I will only send the solution manual to instructors, not students. So if you are teaching from IPMB and want the solution manual, by all means contact us. If you are a student, however, you had better talk to your instructor.

7.36 Issues such as pacemaker battery life are related to the energy required for electrical stimulation. This problem relates the energy to the strength-duration curve, and provides additional insight into the physical significance of the chronaxie.

(a) Let the resistance seen by the electrode due to the medium be R. The power is i²R. Therefore the total energy is

 (b) The duration corresponding to minimum energy is found by setting dU/dt = 0. We get

which reduces to t = t_C. The minimum energy corresponds to a duration equal to the chronaxie.

In the 5th edition’s solution manual, each problem has a brief preamble (in italics) explaining the topic and describing what the student is supposed to learn. We also mark problems that are higher difficulty (*), that complete a derivation from the text (§), and that are new in the fifth edition (¶). Problem 7.36 didn’t fall into any of these categories. We typically outline the solution, but don’t always show all the intermediate steps. I hope we include enough of the solution that the reader or instructor can easily fill in anything missing.

One thing not in the solution manual is the plot of energy, U, versus duration, t. Below I include such a plot. The energy depends on the rheobase current i_R, the chronaxie t_C, and the resistance R.

The energy of a stimulus pulse as a function of pulse duration.

I wonder if this change to Problem 7.36 should go into the IPMB errata? It is not really an error, but more of an omission. After some thought, I have decided to include it, since it was supposed to be there originally. You can find the errata at the book's website: https://sites.google.com/view/hobbieroth. I urge you to download it and mark the corrections in your copy of IPMB.

I hope this blog post has cleared up the mystery behind Problem 7.36. Yet, the curious reader may have one last question: why did I assign a homework problem to my students that is obviously flawed? The truth is, I chose which homework problems to assign by browsing through the solution manual rather than the book (yes, the solution manual is that useful). Problem 7.36 sure looked like a good one based on the solution manual!

The MCAT and IPMB

The Medical College Admission Test, famously known as the MCAT, is an exam taken by students applying to medical school. The Association of American Medical Colleges will introduce a new version of the MCAT next year, focusing on competencies rather than on prerequisite classes. How well does the 4th edition of Intermediate Physics for Medicine and Biology prepare premed students for the MCAT?

The new MCAT will be divided into four sections, and the one most closely related to IPMB deals with the chemical and physical foundations of biological systems. Within that section are two foundational concepts, of which one is about how “complex living organisms transport materials, sense their environment, process signals, and respond to changes that can be understood in terms of physical principles.” This concept is further subdivided into five categories. Below, I review the topics included in these categories and indicate what chapter in IPMB addresses each.

MCAT: Translational motion, forces, work, energy, and equilibrium in living systems

IPMB: Chapter 1 discusses mechanics, including forces and torques, with applications to biomechanics. Work and energy are introduced in Chapter 1, and analyzed in more detail in Chapter 3 on statistical mechanics and thermodynamics (parts of thermodynamics are included under another foundational concept dealing mostly with chemistry). Periodic motion is covered in Chapter 11, which discusses the amplitude, frequency and phase of an oscillator. Waves are analyzed in Chapter 13 about sound and ultrasound.

MCAT: Importance of fluids for the circulation of blood, gas movement, and gas exchange

IPMB: Chapter 1 analyzes fluids, including buoyancy, hydrostatic pressure, viscosity, Poiseuille flow, turbulence, and the circulatory system. Much of this material is not covered in a typical introductory physics class. Chapter 3 introduces absolute temperature, the ideal gas law, heat capacity, and Boltzmann’s constant.

MCAT: Electrochemistry and electrical circuits and their elements

IPMB: Chapters 6 and 7 cover electrostatics, including charge, the electric field, current, voltage, Ohm’s law, resistors, capacitors, and nerve conduction. Chapter 8 discusses the magnetic field and magnetic forces.

MCAT: How light and sound interact with matter

IPMB: Sound is analyzed in Chapter 13, including the speed of sound, the decibel, attenuation, reflection, the Doppler effect, ultrasound, and the ear. Chapter 14 covers light, photon energy, color, interference, and the eye. This chapter also describes absorption of light in the infrared, visible, and ultraviolet. Chapter 18 analyzes nuclear magnetic resonance.

MCAT: Atoms, nuclear decay, electronic structure, and atomic chemical behavior

IPMB: Chapter 17 is about nuclear physics and nuclear medicine, covering isotopes, radioactive decay, and half life. Atoms and atomic energy levels are explained in Chapter 14.

MCAT: General mathematical concepts and techniques

IPMB: Chapter 1 and many other chapters require students to estimate numerically. Chapter 2 covers linear, semilog, and log-log plots, and exponential growth. Metric units and dimensional analysis are used everywhere. Probability concepts are discussed in Chapter 3 and other chapters. Basic math skills such as exponentials, logarithms, scientific notation, trigonometry, and vectors are reinforced throughout the book and in the homework problems, and are reviewed in the Appendices.

The MCAT section about biological and biochemical foundations of living systems includes diffusion and osmosis (discussed in Chapters 4 and 5 of IPMB), membrane ion channels (covered in Chapter 9), and feedback regulation (analyzed in Chapter 10).

Overall, Intermediate Physics for Medicine and Biology covers many of the topics tested on the MCAT. A biological or medical physics class based on IPMB would prepare a student for the exam, and would reinforce problem solving skills and teach the physical principles underlying medicine, resulting in better physicians.

I’m a realist, however. I know premed students take lots of classes, and they don’t want to take more physics beyond a two-semester introduction, especially if the class might lower their grade point average. I have tried to recruit premed students into my Biological Physics (PHY 325) and Medical Physics (PHY 326) classes here at Oakland University, with little success. Perhaps if they realized how closely the topics and skills required for the MCAT correspond to those covered by Intermediate Physics for Medicine and Biology they would reconsider.

To learn more about how to prepare for the physics competencies on the MCAT, see Robert Hilborn’s article “Physics and the Revised Medical College Admission Test,” published in the American Journal of Physics last summer (Volume 82, Pages 428–433, 2014).

Update on the 5th edition of IPMB

A few weeks ago, Russ Hobbie and I submitted the 5th edition of Intermediate Physics for Medicine and Biology to our publisher. We are not done yet; page proofs should arrive in a few months. The publisher is predicting a March publication date. I suppose whether we meet that target will depend on how fast Russ and I can edit the page proofs, but I am nearly certain that the 5th edition will be available for fall 2015 classes (for summer 2015, I am hopeful but not so sure). In the meantime, use the 4th edition of IPMB.

What is in store for the 5th edition? No new chapters; the table of contents will look similar to the 4th edition. But there are hundreds—no, thousands—of small changes, additions, improvements, and upgrades. We’ve included many new up-to-date references, and lots of new homework problems. Regular readers of this blog may see some familiar additions, which were introduced here first. We tried to cut as well as add material to keep the book the same length. We won’t know for sure until we see the page proofs, but we think we did a good job keeping the size about constant.

We found several errors in the 4th edition when preparing the 5th. This week I updated the errata for the 4th edition, to include these mistakes. You can find the errata at the book website, https://sites.google.com/view/hobbieroth. I won’t list here the many small typos we uncovered, and all the misspellings of names are just too embarrassing to mention in this blog. You can see the errata for those. But let me provide some important corrections that readers will want to know about, especially if using the book for a class this fall or next winter (here in Michigan we call the January–April semester "winter"; those in warmer climates often call it spring).

• Page 78: In Problem 61, we dropped a key minus sign: “90 mV” should be “−90 mV”. This was correct in the 3rd edition (Hobbie), but somehow the error crept into the 4th (Hobbie and Roth). I can’t figure out what was different between the 3rd and 4th editions that could cause such mistakes to occur.

• Page 137: The 4th edition claimed that at a synapse the neurotransmitter crosses the synaptic cleft and “enters the next cell.” Generally a neurotransmitter doesn’t “enter” the downstream cell, but is sensed by a receptor in the membrane that triggers some response.

• Page 338: I have already told you about the mistake in the Bessel function identity in Problem 10 of Chapter 12. For me, this was THE MOST ANNOYING of all the errors we have found. 

• Page 355: In Problem 12 about sound and hearing, I used an unrealistic value for the threshold of pain, 10⁻⁴ W m⁻². Table 13.1 had it about right, 1 W m⁻². The value varies between people, and sometimes I see it quoted as high as 10 W m⁻². I suggest we use 1 W m⁻² in the homework problem. Warning: the solution manual (available to instructors who contact Russ or me) is based on the problem as written in the 4th edition, not on what it would be with the corrected value.

• Page 355: Same page, another screw up. Problem 16 is supposed to show how during ultrasound imaging a coupling medium between the transducer and the tissue can improve transmission. Unfortunately, in the problem I used a value for the acoustic impedance that is about a factor of a thousand lower than is typical for tissue. I should have used Z_tissue = 1.5 × 10⁶ Pa s m⁻¹. This should have been obvious from the very low transmission coefficient that results from the impedance mismatch caused by my error. Somehow, the mistake didn’t sink in until recently. Again, the solution manual is based on the problem as written in the 4th edition.

• Page 433: Problem 30 in Chapter 15 is messed up. It contains two problems, one about the Thomson scattering cross section, and another (parts a and b) about the fraction of energy due to the photoelectric effect. Really, the second problem should be Problem 31. But making that change would require renumbering all subsequent problems, which would be a nuisance. I suggest calling the second part of Problem 30 as Problem “30 ½.” 

• Page 523: When discussing a model for the T1 relaxation time in magnetic resonance imaging, we write “At long correlation times T1 is proportional to the Larmor frequency, as can be seen from Eq. 18.34.” Well, a simple inspection of Eq. 18.34 reveals that T1 is proportional to the SQUARE of the Larmor frequency in that limit. This is also obvious from Fig. 18.12, where a change in Larmor frequency of about a factor of three results in a change in T1 of nearly a factor of ten. 

• Page 535: In Chapter 18 we discuss how the blood flow speed v, the repetition time T_R, and the slice thickness Δz give rise to flow effects in MRI. Following Eq. 18.56, we take the limit when v is much greater than "T_R/Δz". I always stress to my students that units are their friends. They can spot errors by analyzing if their equation is dimensionally correct. CHECK IF THE UNITS WORK! Clearly, I didn’t take my own advice in this case.

For all these errors, I humbly apologize. Russ and I redoubled our effort to remove mistakes from the 5th edition, and we will redouble again when the page proofs arrive. In the meantime, if you find still more errors in the 4th edition, please let us know. If the mistake is in the 4th edition, it could well carry over to the 5th edition if we don’t root it out immediately.

Physics Research & Education: The Complex Intersection of Biology and Physics

This morning, I am heading home after a productive week at a Gordon Research Conference about “Physics Research and Education: The Complex Intersection of Biology and Physics.” I wish I could tell you more about it, but Gordon Conferences have this policy…

To encourage open communication, each member of a Conference agrees that any information presented at a Gordon Research Conference, whether in a formal talk, poster session, or discussion, is a private communication from the individual making the contribution and is presented with the restriction that such information is not for public use….

So, there is little I can say, other than to point you to the meeting schedule published on the GRC website. I suspect that future blog entries will be influenced by what I learned this week, but I will only write about items that have also been published elsewhere.

 I can say a bit about Gordon Conferences in general. The GRC website states

The Gordon Research Conferences were initiated by Dr. Neil E. Gordon, of the Johns Hopkins University, who recognized in the late 1920s the difficulty in establishing good, direct communication between scientists, whether working in the same subject area or in interdisciplinary research. The Gordon Research Conferences promote discussions and the free exchange of ideas at the research frontiers of the biological, chemical and physical sciences. Scientists with common professional interests come together for a full week of intense discussion and examination of the most advanced aspects of their field. These Conferences provide a valuable means of disseminating information and ideas in a way that cannot be achieved through the usual channels of communication—publications and presentations at large scientific meetings.

Before this, the only Gordon Conference I ever attended was one at which I was the trailing spouse. My wife studied the interaction of lasers with tissue in graduate school, and she attended a Gordon Conference on that topic in the 1980s; I tagged along. I don’t remember that conference being as intense as this one, but maybe that’s because I’m getting older.

The conference was at Mount Holyoke College, a small liberal arts college in South Hadley, Massachusetts, about 90 minutes west of Boston. It is a lovely venue, and we were treated well. I hadn’t lived in a dormitory since college, but I managed to get used to it.

For those of you interested in education at the intersection of physics and biology—a topic of interest for readers of the 4th edition of Intermediate Physics for Medicine and Biology—I suggest you take a look at the recent special issue of the American Journal of Physics about “Research and Education at the Crossroads of Biology and Physics,” discussed in this blog before. In addition, see the website set up based on the “Conference on Introductory Physics for the Life Sciences,” held March 14–16, 2014 in Arlington, Virginia. I’ve also discussed the movement to improve introductory physics classes for students in the life sciences previously in this blog here, here, here, and here.

Now, I need to run so I can catch my plane….

Research and Education at the Crossroads of Biology and Physics

The May issue of the American Journal of Physics (my favorite journal) is a “theme issue” devoted to Research and Education at the Crossroads of Biology and Physics. In their introductory editorial, guest editors Mel Sabella and Matthew Lang outline their goals, which are similar to the objectives Russ Hobbie and I have for the 4th edition of Intermediate Physics for Medicine and Biology.

…there is often a disconnect between biology and physics. This disconnect often manifests itself in high school and college physics instruction as our students rarely come to understand how physics influences biology and how biology influences physics. In recent years, both biologists and physicists have begun to recognize the importance of cultivating stronger connections in these fields, leading to instructional innovations. One call to action comes from the National Research Council’s report, BIO2010, which stresses the importance of quantitative and computational training for future biologists and cites that sufficient expertise in physics is crucial to addressing complex issues in the life sciences. In addition, physicists who are now exploring biological contexts in instruction need the expertise of biologists. It is clear that biologists and physicists both have a great deal to offer each other and need to develop interdisciplinary workspaces…

This theme issue on the intersection of biology and physics includes papers on new advances in the fields of biological physics, new advances in the teaching of biological physics, and new advances in education research that inform and guide instruction. By presenting these strands in parallel, in a single issue, we hope to support the reader in making connections, not only at the intersection of biology and physics but also at the intersection of research, education, and education research. Understanding these connections puts us, as researchers and physics educators, in a better position to understand the central questions we face…

The infusion of Biology into Physics and Physics into Biology provides exciting new avenues of study that can inspire and motivate students, educators, and researchers at all levels. The papers in this issue are, in many ways, a call to biologists and physicists to explore this intersection, learn about the challenges and obstacles, and become excited about new areas of physics and physics education. We invite you to read through these articles, reflect, and discuss this complex intersection, and then continue the conversation at the June 2014 Gordon Research Conference titled, “Physics Research and Education: The Complex Intersection of Biology and Physics.”

And guess who has an article in this special issue? Yup, Russ and I have a paper titled “A Collection of Homework Problems About the Application of Electricity and Magnetism to Medicine and Biology.”

This article contains a collection of homework problems to help students learn how concepts from electricity and magnetism can be applied to topics in medicine and biology. The problems are at a level typical of an undergraduate electricity and magnetism class, covering topics such as nerve electrophysiology, transcranial magnetic stimulation, and magnetic resonance imaging. The goal of these problems is to train biology and medical students to use quantitative methods, and also to introduce physics and engineering students to biological phenomena.

Regular readers of this blog know that a “hobby” of mine (pun intended, Russ) is to write new homework problems to go along with our book. Some of the problems in our American Journal of Physics paper debuted in this blog. I believe that a well-crafted collection of homework problems is essential for learning biological and medical physics (remember, for them to be useful you have to do your homework). I hope you will find the problems we present in our paper to be “well-crafted”. We certainly had fun writing them. My biggest concern with our AJP paper is that the problems may be too difficult for an introductory class. The “I” in IPMB stands for “intermediate”, not “introductory”. However, most of the AJP theme issue is about the introductory physics class. Oh well; one needs to learn biological and medical physics at many levels, and the intermediate level is our specialty. If only our premed students would reach the intermediate level (sigh)….

Russ and I are hard at work on the 5th edition of our book, where many of the problems from our paper, along with additional new ones, will appear (as they say, You Ain’t Seen Nothing Yet!).

Anyone interested in teaching biological and medical physics should have a look at this AJP theme issue. And regarding that Gordon Research Conference that Sabella and Lang mention, I’m registered and have purchased my airline tickets! It should be fun. If you are interested in attending, the registration deadline is May 11 (register here). You better act fast.

From Vision to Change: Educational Initiatives and Research at the Intersection of Physics and Biology

A few months ago, the journal CBE—Life Sciences Education published a special issue about education at the intersection of physics and biology. This topic is of great interest to readers of the 4th edition of Intermediate Physics for Medicine and Biology. The special issue was motivated by the American Association for the Advancement of Science report Vision and Change in Undergraduate Biology Education. While there were many interesting articles in this issue, my favorite was the essay “Learning Each Other’s Ropes: Negotiating Interdisciplinary Authenticity” (Volume 12, Pages 175–186, 2013), by Edward Redish and Todd Cooke, both from the University of Maryland. They describe their goals in the paper’s abstract.

A common feature of the recent calls for reform of the undergraduate biology curriculum has been for better coordination between biology and the courses from the allied disciplines of mathematics, chemistry, and physics. Physics has lagged behind math and chemistry in creating new, biologically oriented curricula, although much activity is now taking place, and significant progress is being made. In this essay, we consider a case study: a multiyear conversation between a physicist interested in adapting his physics course for biologists (E.F.R.) and a biologist interested in including more physics in his biology course (T.J.C.). These extended discussions have led us both to a deeper understanding of each other’s discipline and to significant changes in the way we each think about and present our classes. We discuss two examples in detail: the creation of a physics problem on fluid flow for a biology class and the creation of a biologically authentic physics problem on scaling and dimensional analysis. In each case, we see differences in how the two disciplines frame and see value in the tasks. We conclude with some generalizations about how biology and physics look at the world differently that help us navigate the minefield of counterproductive stereotypical responses.

I found this paper to be fascinating, and it will be helpful as Russ Hobbie and I prepare the 5th edition of IPMB. It is interesting that the authors use the word “negotiating” in the title, because I felt that Redish and Cooke were involved in an extended negotiation about how much physics to include in an introductory biology class. This process is not restricted to instruction; I go through an often painful negotiation regarding the emphasis of biology versus physics with the reviewers of almost every research article I’ve ever published. I like the conversational tone of Redish and Cooke’s paper, and how it describes the growth of a close collaboration between a biologist and a physicist, each with a different worldview. Probably the most important contribution of the article is the story of how they uncovered and dealt with their hidden biases (they use the term epistemologies, which is one of those words from the science education literature that I dislike). Readers of this blog may remember Redish; one of my blog entries earlier this year discussed his article in Physics Today about “Reinventing Physics for Life Science Majors.” At first, I was annoyed by Redish and Cooke’s habit of referring to themselves collectively in the first person and individually in the third person (as in, “our physicist” and “our biologist”), but as I read on this technique began to grow on me and in the end I found it endearing. I particularly enjoyed their discussion about the role of problem solving in physics and biology, and what makes a good homework problem.

In our interdisciplinary discussions, we also learned that biologists and physicists had dramatically different views of what makes a good biological example in physics… We came to understand that what would be of value in a physics class is biological authenticity—examples in which solving a physics problem in a biological context gives the student a deeper understanding of why the biological system behaves the way it does.

Russ and I strive to achieve authenticity in our end-of-chapter homework problems. Our book is aimed at an intermediate level--we assume the student is comfortable with calculus--so we may have an easier time constructing nontrivial physics exercises applied to biology than an introductory instructor would, but I sometimes wonder if the biologists and medical doctors find them as useful as we think they are.

Redish and Cooke present a list of “cultural components” of both physics and biology that are illuminating.

Physics: Common Cultural Components

• Introductory physics classes often stress reasoning from a few fundamental (usually mathematically formulated) principles. 

• Physicists often stress building a complete understanding of the simplest possible (often highly abstract) examples— “toy models”—and often do not go beyond them at the introductory level.
 
• Physicists quantify their view of the physical world, model with math, and think with equations, qualitatively as well as quantitatively.
 
• Physicists concern themselves with constraints that hold no matter what the internal details (conservation laws, center of mass, etc.).

Biology: Common Cultural Components

• Biology is often incredibly complex. Many biological processes involve the interactions of component parts leading to emergent phenomena, which include the property of life itself. 

• Most introductory biology does not emphasize quantitative reasoning and problem solving to the extent these are emphasized in introductory physics.
 
• Biology contains a critical historical constraint in that natural selection can only act on pre-existing molecules, cells, and organisms for generating new solutions.
 
• Much of introductory biology is descriptive (and introduces a large vocabulary).
 
• However, biology—even at the introductory level—looks for mechanism and often considers micro–macro connections between the molecules involved and the larger phenomenon.
 
• Biologists (both professionals and students) focus on and value real examples and structure–function relationships.

As I read these lists, it is clear to me that I am definitely in the physics camp. It would not be an exaggeration to say that a primary goal of IPMB is to force introduce the physicist’s culture, as described above, to students interested in biology and medicine.

I do have one minor criticism. Initially I was impressed by Redish’s analysis of the relationship of flow to pressure in a blood vessel (Hagen-Poiseuille flow), with the appearance of the fourth power of the radius, using simple arguments involving no calculus. Upon further reflection, however, I’m not totally comfortable with the derivation. Here it is in brief:

F_pressure = ΔP A

F_drag = b L v

Q = A v

where ΔP is the pressure drop, A is the cross-sectional area of the vessel, L is the vessel length, v is the speed (assumed uniform, or plug flow), b is a frictional proportionality constant, and Q is the volume flow. If you set the two forces equal, and eliminate v in favor of Q, you get

ΔP = (b L/A²) Q

The 1/A² dependence implies that the flow increases as the fourth power of the radius. My concern is this: suppose a student approaches Redish and says “I follow your derivation, but shouldn’t the drag force be proportional to the surface area where the flow contacts the vessel wall? In other words, shouldn’t the drag force be given by F_drag = c (2πrL) v?” (I use c for the proportionality constant because it now has different units that b.) Of course, if you do the calculation using this expression for the drag force, you get the wrong answer (a 1/r³ dependence)! I wonder if any of his students ever brought this up, and how he responded? The complete derivation is given in Chapter 1 of IPMB, and the central point is that the frictional force depends on dv/dr rather than v, but the analysis uses some rather advanced calculus that would be inappropriate in the introductory biology class that Redish and Cooke consider. The trade-off between simplifying a concept so it is accessible versus being as accurate as possible is always difficult. I don’t know what the best approach would be in this case. (I can always make one recommendation: buy a copy of IPMB!)

Despite this one reservation, I enjoyed Redish and Cooke’s paper very much. Let me give them the last word.

We conclude that the process [of interdisciplinary collaboration aimed at revising the biology introductory course] is significantly more complex than many reformers working largely within their discipline often assume. But the process of learning each other’s ropes—at least to the extent that we can understand each other’s goals and ask each other challenging questions—can be both enlightening and enjoyable. And much to our surprise, we each feel that we have developed a deeper understanding of our own discipline as a result of our discussions.