Teaching Dynamics to Biology Undergraduates: the UCLA Experience

The goal of Intermediate Physics for Medicine and Biology, and the goal of this blog, is to explore the interface between physics, medicine, and biology. But understanding physics, and in particular the physics used in IPMB, requires calculus. In fact, Russ Hobbie and I state in the preface of IPMB that “calculus is used without apology.” Unfortunately, many biology and premed students don’t know much calculus. In fact, their general math skills are often weak; even algebra can challenge them. How can students learn enough calculus to make sense of IPMB?

A team from UCLA has developed a new way to teach calculus to students of the life sciences. The group is led by Alan Garfinkel, who appears in IPMB when Russ and I discuss the response of cardiac tissue to repetitive electrical stimulation (see Chapter 10, Section 12). An article describing the new class they’ve developed was published recently in the Bulletin of Mathematical Biology (Volume 84, Article Number 43, 2022).

There is a growing realization that traditional “Calculus for Life Sciences” courses do not show their applicability to the Life Sciences and discourage student interest. There have been calls from the AAAS, the Howard Hughes Medical Institute, the NSF, and the American Association of Medical Colleges for a new kind of math course for biology students, that would focus on dynamics and modeling, to understand positive and negative feedback relations, in the context of important biological applications, not incidental “examples.” We designed a new course, LS 30, based on the idea of modeling biological relations as dynamical systems, and then visualizing the dynamical system as a vector field, assigning “change vectors” to every point in a state space. The resulting course, now being given to approximately 1400 students/year at UCLA, has greatly improved student perceptions toward math in biology, reduced minority performance gaps, and increased students’ subsequent grades in physics and chemistry courses. This new course can be customized easily for a broad range of institutions. All course materials, including lecture plans, labs, homeworks and exams, are available from the authors; supporting videos are posted online.

Sharks and tuna, the predator-prey problem,
from Garfinkel et al.,
Bulletin of Mathematical Biology,
84:43, 2022.

This course approaches calculus from the point of view of modeling. Its first example develops a pair of coupled differential equations (only it doesn’t use such fancy words and concepts) to look at interacting populations of sharks and tuna; the classical predator-prey problem analyzed as a homework problem in Chapter 2 of IPMB. Instead of focusing on equations, this class makes liberal use of state space plots, vector field illustrations, and simple numerical analysis. The approach reminds me of that adopted by Abraham and Shaw in their delightful set of books Dynamics: The Geometry of Behavior, which I have discussed before in this blog. The UCLA course uses the textbook Modeling Life: The Mathematics of Biological Systems, which I haven’t read yet but is definitely on my list of books to read.

My favorite sentence from the article appears when it discusses how the derivative and integral are related through the fundamental theorem of calculus.

We are happy when our students can explain the relation between the COVID-19 “New Cases per day” graph and the “total cases” graph.

If you want to learn more, read the article. It’s published open access, so anyone can find it online. You can even steal its illustrations (like I did with its shark-tuna picture above).

I’ll end by quoting again from Garfinkel et al.’s article, when they discuss the difference between their course and a traditional calculus class. If you replace the words “calculus” and “math” by “physics” in this paragraph, you get a pretty good description of the approach Russ and I take in Intermediate Physics for Medicine and Biology.

The course that we developed has a number of key structural and pedagogical differences from the traditional “freshman calculus” or “calculus for life sciences” classes that have been offered at UCLA and at many other universities. For one, as described above, our class focuses heavily on biological themes that resonate deeply with life science students in the class. Topics like modeling ecological systems, the dynamics of pandemics like COVID-19, human physiology and cellular responses are of great interest to life science students. We should emphasize that these examples are not simply a form of window dressing meant to make a particular set of mathematical approaches palatable to students. Rather, the class is structured around the idea that, as biologists, we are naturally interested in understanding these kinds of systems. In order to do that, we need to develop a mathematical framework for making, simulating and analyzing dynamical models. Using these biological systems not purely as examples, but rather as the core motivation for studying mathematical concepts, provides an intellectual framework that deeply interests and engages life science students.

 

Introduction to state variables and state space. Video 1.1 featuring Alan Garfinkel.

https://www.youtube.com/watch?v=yZWG0ALL3mI

Defining vectors in higher dimensions. Video 1.2 featuring Alan Garfinkel.

https://www.youtube.com/watch?v=2Rjk0O3yWc8

Two-Semester Intermediate Course Sequence in Physics for the Life Sciences

This week I spoke at the American Association of Physics Teachers 2021 Summer Meeting. Getting to the meeting was easy; I just logged onto a website. Because of the Covid-19 pandemic, the entire conference was virtual and all the talks were prerecorded. A video of my talk—“Two-Semester Intermediate Course Sequence in Physics for the Life Sciences”—is posted below. If you want a powerpoint of the slides, you can find it here. As readers of this blog might suspect, the courses I describe are based on the textbook Intermediate Physics for Medicine and Biology. 

“Two-Semester Intermediate Course Sequence in Physics for the Life Sciences,” delivered at the AAPT 2021 Virtual Summer Meeting on August 2, 2021. https://www.youtube.com/watch?v=_1b9OdQktrI

Redish, E. F. (2021)
“Using Math in Physics: Overview,”
The Physics Teacher, 59:314–318.

In my lecture, I emphasize the role of toy models in developing insight, and the importance of connecting math to physics and biology. After the talk, I had a chat with Ed Redish (who I’ve mentioned in this blog before), and he referred me to a series of articles he’s publishing in The Physics Teacher. The first is titled “Using Math in Physics: Overview” (Volume 59, Pages 314–318, 2021). Redish and I seem to be singing the same song, although his lyrics are better. What he says about math in physics describes what Russ Hobbie and I try to do in IPMB. Redish begins

The key difference between math as math and math in science is that in science we blend our physical knowledge with our knowledge of math. This blending changes the way we put meaning to math and even the way we interpret mathematical equations. Learning to think about physics with math instead of just calculating involves a number of general scientific thinking skills that are often taken for granted [my italics] (and rarely taught) in physics classes. In this paper, I give an overview of my analysis of these additional skills. I propose specific tools for helping students develop these skills in subsequent papers.

He makes other good points, such as

• Math in math classes tends to be about numbers. Math in science is not. Math in science blends physics conceptual knowledge with mathematical symbols

and my favorite

• In introductory math, equations are almost always about solving and calculating. In physics [they’re] often about explaining! [his italics, my exclamation point].

The Art of Insight
in Science and Engineering
by Sanjoy Mahajan.

I like to paraphrase Richard Hamming and say “the purpose of equations is insight, not numbers.” Redish’s article reminds me of Sanjoy Mahajan’s book The Art of Insight in Science and Engineering. Both are superb.

In subsequent articles in The Physics Teacher (some already published, some in the works), Redish discusses skills every student needs to master.

• Dimensional Analysis 
• Estimation 
• Anchor Equations 
• Toy Models 
• Functional Dependence 
• Reading the Physics in a Graph 
• Telling the Story
  

I like to think that IPMB reinforces these skills. They certainly are ones that I try to emphasize in my “Biological Physics” and “Medical Physics” classes, and that Russ and I attempt to reinforce in our homework problems.

Screenshot of the
Living Physics Portal.

Finally, a valuable resource for teachers of physics-for-the-life-sciences was noted during the Q&A: the Living Physics Portal.

The Living Physics Portal is an online environment for physics faculty to share and discuss free curricular resources for teaching introductory physics for life sciences (IPLS). The objective of the Portal is to improve the education of the next generation of medical professionals and biologists by making physics classes more relevant for life sciences students. We do this by supporting physics instructors in finding and creating curricular materials and engaging in community discussions with other instructors to improve their courses.

Although IPMB is not intended to be used in an introductory course, I believe many materials on the Living Physics Portal would be useful to instructors teaching from IPMB. Conversely, much of the information you find in IPMB, and on this blog, could be helpful to introductory teachers. 

 

If you’re preparing to teach a class based on Intermediate Physics for Medicine and Biology, I suggest first looking at the materials on the book’s website, then scanning through the book’s blog (especially those posts marked “useful for instructors”), next reading Redish’s The Physics Teacher articles, and finally browsing the Living Physics Portal. Then you’ll be ready to teach physics for the life sciences at any level.

Qualifying Exams

First page of the 2020 Physics
Qualifying Exam.

I have discussed the Oakland University Medical Physics PhD Qualifying Exam previously in this blog. It’s a series of three written exams over math, physics, and biology, plus an oral exam.

I’ve collected the written qualifying exams over the last ten years (2011-2020) in a single file that you’re welcome to download. These exams are broad but not deep. They cover material at a level similar to, or somewhat higher than, Intermediate Physics for Medicine and Biology. Anyone working at the intersection of physics with biology should master these topics. The exams allow you to hone your problem solving skills. If you’re a student interested in applying physics to physiology, or math to medicine, but are stuck at home and not able to attend classes because of the covid-19 pandemic, you might want to try solving the 300 problems in this collection. (Slightly less than 300, because there wasn’t a math exam in 2014 and because we sometimes repeated questions from previous years.) If you want to try some of the exams from 2010 or earlier, you can find them at https://sites.google.com/view/bradroth/home/medical-physics-graduate-program/qualifying-exams?authuser=0.

Sorry, but I don’t have written solutions for these exams. You can always email me (roth@oakland.edu) if you’re stuck.

Enjoy!

An Advanced Undergraduate Laboratory in Living State Physics

One weakness of Intermediate Physics for Medicine and Biology is that it doesn’t have an associated laboratory. Students need to learn how to perform experiments and use instruments.

An Advanced Undergraduate Laboratory
In Living State Physics,
by Wikswo, Vickery, and Venable.

Fortunately, instructors wanting to develop a lab don’t need to start from scratch. My PhD advisor, John Wikswo, and his colleagues Barbara Vickery and John Venable created An Advanced Undergraduate Laboratory in Living State Physics at Vanderbilt University around 1980. I didn’t take this lab class, but my wife Shirley did (she obtained a masters degree in physics from Vanderbilt), and she still has the lab manual. 

Wikswo obtained a grant from the National Science Foundation to support the development of the lab. He collaborated with John Venable, a biologist on the Vanderbilt faculty. When I was a graduate student, Venable was the Associate Dean of the College of Arts and Sciences. Barbara Vickery was a Vanderbilt undergraduate biomedical engineering major.

The lab wasn’t designed for any particular textbook, but Wikswo was an early adopter of Russ Hobbie’s Intermediate Physics for Medicine and Biology, and I think I can see its influence. I don’t have an electronic copy of the 250-page lab manual; you would have to contact Wikswo for that. Below I quote parts of it.

1.1 An Introduction to the Living State Physics Laboratory

The undergraduate physics curriculum at a typical university might include an introductory class in biophysics or medical physics in addition to the more traditional curriculum of mechanics, electricity and magnetism, light and sound, thermodynamics, and modern physics. While introductory and advanced laboratory classes cover these standard fields of physics, generally there has been little opportunity for an undergraduate student to gain laboratory experience in biophysics or medical physics. The need for such experience is particularly acute today for preprofessional and scientifically oriented students. Of these students, physics majors are not being exposed to an important area of experimental physics, and pre-medical students and majors in other departments such as Molecular Biology, Chemistry, and Biomedical Engineering are presently receiving only a minimal exposure to modern biophysical techniques and instrumentation. Thus by introducing an advanced undergraduate laboratory in physics applied to living systems, we expect to broaden the experience in experimental physics for physics majors and non-majors alike.

Several options were available to us in designing this laboratory. We could, for example, have structured the laboratory to emphasize applications of physics to certain living systems such as the nervous system, the cardiovascular system, and the special senses. Rather than take this system-oriented approach, we have chosen to organize the course by areas of physics. The course will draw on techniques and ideas from the whole breadth of physics (mechanics, electricity, thermodynamics, optics, etc.) and apply these to topics of biophysical interest [the same approach as IPMB]. Since we will study intact living systems such as people and frogs, as well as isolated living preparations and inanimate molecules and models, this laboratory will use physics to study topics conventionally identified with both biophysics and medical physics, as well as with electrophysiology, physical chemistry, biomedical engineering and molecular biology. Because of the intended breadth of the planned experiments and their organization by area of physics rather than by biological system, we have chosen to title this laboratory “An Advanced Undergraduate Laboratory in Living State Physics”. The generality of the term “Living State Physics” is intended to parallel the generality of the term “solid state physics”, which as an experimental discipline utilizes the complete spectrum of physical concepts and techniques...

1.2 Summary of Experiments

a. Introduction to Bioelectric Phenomena. The first of the three experiments in this section is an exercise with an oscilloscope and an electronic stimulator which will allow the student to obtain a familiarity with the use of these instruments. In the second and third experiments, the Thornton Modular Plug-In System is used to provide familiarity with the basic physics describing the electromyogram and the electroencephalogram…

b. The Heart Experiments. This section should enable the student to gain an understanding of the basic principles of cardiac physiology. In the laboratory, the student will measure the frog and the human electrocardiogram…

c. Nerve Action Potential… [Students perform an] in-depth study of the properties of nerve propagation in the isolated sciatic nerve of a frog. In both experiments, from extracellular recordings of the nerve action potential it will be possible to demonstrate the graded response of the nerve bundle, the strength-duration relationship of stimuli producing a threshold response, bi-directional conduction, and the monophasic response…

d. Nerve Modeling. In the first experiment, the passive cable properties of the nerve are studied by using a resistor-capacitor network that represents a section of a nerve axon… The active properties of the nerve are investigated in the second experiment. An electronic nerve model which has a design based on a system of equations similar to those developed by Hodgkin and Huxley is used…

e. Skeletal Muscle. The first of the two experiments in this section is an introduction to the active and passive mechanical properties of skeletal muscle using the frog gastrocnemius muscle. The experiment includes measurement of the muscle twitch, the ability of the muscle to do work, and the maximum tension developed by the muscle at different lengths, as well as demonstration of the phenomena of temporal summation and the graded response of muscle. The second experiment involves characterization of the mechanical properties of muscle in its resting and contractile states…

f. Diffusion. In this experiment, a Cenco model is used for qualitative demonstration of the transport phenomenon of diffusion, showing the exponential approach to equilibrium and how the relative sizes of molecules and pores affect diffusion rates.

g. Compartmental Modeling. The usefulness of compartmental modeling in analysis of some systems is demonstrated by constructing one- and two-compartment models for several open and closed thermal systems. The theoretical models are analyzed mathematically…

h. The Physical Aspects of Vision. The minimum number of photons that the human eye can detect in a single detectable flash is the minimum number of photons whose absorption by photoreceptor cells in the eye leads to the firing of an impulse in the brain. This threshold value is determined by recording the fraction of detected flashes as a function of relative intensity of the flashes… by utilizing Poisson statistics.

i. Ultrasound… The experiments introduce the physics of mechanical waves by using ultrasound transducers, a two-dimensional ultrasound target, and an existing ultrasound scanner and transient analyzer to demonstrate wave propagation, attenuation, reflection, refraction, pulse-echo principles, piezoelectric crystals and the concepts of cross-section and spatial resolution.

The first time I ever saw my wife was when she was in Wikswo's office asking a question about one of the lab exercises. I needed to talk to him about some very important issue related to my research, and she was in the way! Well, one thing led to another and....

I recall how Shirley and my friend Ranjith Wijesinghe were lab partners doing the vision experiment. It required sitting in a small, dark enclosure for about half an hour while their eyes became adapted to the dark. I had only recently met Shirley, and I recall being jealous of Ranjith for getting to spend such a private time with her! 

One of the most memorable parts of the lab was the pithing of the frog. None of the students liked doing that. Wikswo had a fun way of demonstrating the fight-of-flight response during the electrocardiogram lab. He would measure the ECG on one of the students, and then take out a giant syringe and say something like “now watch what happens to her heart rate when I inject her with this adrenaline.” Of course no one ever got injected, but the student was always so startled that her heart rate would jump dramatically.

If you are considering developing you own laboratory for Intermediate Physics for Medicine and Biology, you could start with Wikswo’s lab, and then add some of the experiments discussed in these American Journal of Physics papers. Good luck!

J. D. Prentice and K. G. McNeill (1962) “Measurement of the Beta Spectrum of I¹²⁸ in an Undergraduate Laboratory,” American Journal of Physics, Volume 30, Pages 66–67.  

Peter J. Limon and Robert H. Webb (1964) “A Magnetic Resonance Experiment for the Undergraduate Laboratory,” American Journal of Physics, Volume 32, Pages 361–364.    

L. J. Bruner (1979) “Cardiovascular Simulator for the Undergraduate Physics Laboratory,” American Journal of Physics, Volume 47, Pages 608–611.  

H. W. White, P. E. Chumbley, R. L. Berney, and V. H. Barredo (1982) “Undergraduate Laboratory Experiment to Measure the Threshold of Vision,” American Journal of Physics, Volume 50, Pages 448–450. 

Colin Delaney and Juan Rodriguez (2002) “A Simple Medical Physics Experiment Based on a Laser Pointer,” American Journal of Physics, Volume 70, Pages 1068–1070. 

Danny G. Miles Jr. and David W. Bushman (2005) “Protein Gel Electrophoresis in the Undergraduate Physics Laboratory,” American Journal of Physics, Volume 73, Pages 1186–1189. 

Luis Peralta (2006) “A Simple Electron-Positron Pair Production Experiment,” American Journal of Physics, Volume 74, Pages 457–461.  

Joseph Peidle, Chris Stokes, Robert Hart, Melissa Franklin, Ronald Newburgh, Joon Pahk, Wolfgang Rueckner, and Aravi Samuel (2009) “Inexpensive Microscopy for Introductory Laboratory Courses,” American Journal of Physics, Volume 77, Pages 931–938. 

Timothy A. Stiles (2014) “Ultrasound Imaging as an Undergraduate Physics Laboratory Exercise,” American Journal of Physics, Volume 82, Pages 490–501.  

Elliot Mylotta, Ellynne Kutschera, and Ralf Widenhorn (2014) “Bioelectrical Impedance Analysis as a Laboratory Activity: At the Interface of Physics and the Body,” American Journal of Physics, Volume 82, Pages 521–528.    

Alexander Hydea and Oleg Batishchevb (2015) “Undergraduate Physics Laboratory: Electrophoresis in Chromatography Paper,” American Journal of Physics, Volume 83, Pages 1003–1011.

Owen Paetkau, Zachary Parsons, and Mark Paetkau (2017) “Computerized Tomography Platform Using Beta Rays,” American Journal of Physics, Volume 85, Pages 896–900. 

Physics Girl

Because of the coronavirus, I had to transform my introductory physics course from in-person to online (in two days!). I thought: If I’m going to teach remotely, I might as well use some of the excellent resources that are available on the internet. This led me to Physics Girl.

Dianna Cowern produces funny and informative videos about physics. Some even deal with medical and biological physics. Below I have embedded a few about biomechanics, sound perception, sun screen, color vision, magnetic resonant imaging, and bioelectricity.

If you’re studying from Intermediate Physics for Medicine and Biology, consider these videos as supplementary material. If you like them, plenty more are at the Physics Girl YouTube channel.

Happy Physicsing!

Testing what exercise actually does to your butt.

https://www.youtube.com/watch?v=Dh8Yd0mQnB8

What stretching actually does to your body.

https://www.youtube.com/watch?v=1JgBp7dX4AU

Can you guess this note? Perfect pitch and physics.

https://www.youtube.com/watch?v=-65FMJTKGLs

Sunscreen in the UV.

https://www.youtube.com/watch?v=GRD-xvlhGMc

Does this look like white to you?

https://www.youtube.com/watch?v=uNOKWoDtbSk&t=5s

The projector illusion.

https://www.youtube.com/watch?v=Xp6bxCh_p7c

Are MRIs safe?
https://www.youtube.com/watch?v=hlRpl_GMPPc

My dad was struck by lightening (TWICE!)
https://www.youtube.com/watch?v=9-E7koihWF4

Videos for PHY 3250, Biological Physics

Last fall, I recorded my lectures for my PHY 3250 (Biological Physics) class, and posted them on YouTube. The videos are not great; they are nowhere near professional quality, and often the chalkboard is difficult to read. I originally recorded them as a backup for my students, in case they missed a class or wanted to review something they heard me say in a lecture. Nevertheless, I think that students and instructors may find these videos useful.

My Biological Physics class covers the first ten chapters in Intermediate Physics for Medicine and Biology. Topics include biomechanics, fluid dynamics, the exponential function, biothermodynamics, diffusion, osmotic pressure, bioelectricity, biomagnetism, and feedback.

Some videos are missing: Monday, September 30 was Exam 1; Wednesday, October 30 was Exam 2; Wednesday, November 27 the class played Trivial Pursuit IPMB; and Friday, November 29 was the day after Thanksgiving.

If you are sitting at home self-quarantining with nothing to do, feel free to binge.

Enjoy!

Wednesday, September 4, 2019. Introduction.

https://www.youtube.com/watch?v=BpZO44XlKps&t=2915s

Friday, September 6, 2019. Biomechanics.

https://www.youtube.com/watch?v=z2-_ynK7mC4&t=28s

Monday, September 9, 2019. Hydrostatics.

https://www.youtube.com/watch?v=JIzzxaT8GUs&t=3420s

Wednesday, September 11, 2019. Fluid Dynamics.

https://www.youtube.com/watch?v=epBEt4IrAog

Friday, September 13, 2019.  The exponential function.

https://www.youtube.com/watch?v=PqoDQMIn2Z8

Monday, September 16, 2019. Scaling.

https://www.youtube.com/watch?v=8HapJ_irxb8

Wednesday, September 18, 2019. Boltzmann factor.

https://www.youtube.com/watch?v=4Yh9D4-X2cI

Friday, September 20, 2019. Heat capacity.

https://www.youtube.com/watch?v=7KNYTSKfqDE

Monday, September 23, 2019. Heat transfer.

https://www.youtube.com/watch?v=8zHLDM_rzK8

Wednesday, September 25, 2019. Review for Exam 1.

https://www.youtube.com/watch?v=vJ0mlt4zAJY

Friday, September 27, 2019. Review for Exam 1 (cont.).

https://www.youtube.com/watch?v=m-e04OyfExQ

Wednesday, October 2, 2019. Heat conduction.

https://www.youtube.com/watch?v=eOvRKLR5Uvk

Friday, October 4, 2019. Diffusion.

https://www.youtube.com/watch?v=qO1rNWI0l6I

Monday, October 7, 2019. Diffusion and convection.

https://www.youtube.com/watch?v=ChJs5D7stA8

Wednesday, October 9, 2019. Osmotic pressure.

https://www.youtube.com/watch?v=wdUli6XsSkY

Friday, October 11, 2019. Countercurrent exchange.

https://www.youtube.com/watch?v=ObwElQROX8s

Monday, October 14, 2019. Bioelectricity.

https://www.youtube.com/watch?v=x6Voj3puTks

Wednesday, October 16, 2019. Hodgkin & Huxley model.

https://www.youtube.com/watch?v=kZVN14rrzLg

Friday, October 18, 2019. Hodgkin & Huxley model (cont.).

https://www.youtube.com/watch?v=fg34n0ShzFc

Monday, October 21, 2019. The cable equation.

https://www.youtube.com/watch?v=alUujlzUPQ8

Wednesday, October 23, 2019. Action potential propagation.

https://www.youtube.com/watch?v=ZmmDQLvT0sI

Friday, October 25, 2019. Review for Exam 2.

https://www.youtube.com/watch?v=7_WNLgDPydY

Monday, October 28, 2019. Review for Exam 2 (cont.).

https://www.youtube.com/watch?v=onPXPYwedlg

Friday, November 1, 2019. Extracellular stimulation of nerves.

https://www.youtube.com/watch?v=fj6v7xvFwus

Monday, November 4, 2019. Extracellular potentials and the dipole.

https://www.youtube.com/watch?v=gcXAlrJPxCE

Wednesday, November 6, 2019. The heart.

https://www.youtube.com/watch?v=oalxSQ0YN-w

Friday, November 8, 2019. The electrocardiogram.

https://www.youtube.com/watch?v=lxYbFaNfVYQ

Monday, November 11, 2019. Pacemakers and defibrillators.

https://www.youtube.com/watch?v=49T0eNyKxHY

Wednesday, November 13, 2019. The electroencephalogram.

https://www.youtube.com/watch?v=UP-twf7MK3Y

Friday, November 15, 2019. Biomagnetism.

https://www.youtube.com/watch?v=5ghPyovl9VM

Monday, November 18, 2019. Transcranial magnetic stimulation.

https://www.youtube.com/watch?v=4XQD0viWpy4

Wednesday, November 20, 2019. Cardiac restitution.

https://www.youtube.com/watch?v=oef4la5psq4

Friday, November 22, 2019. Cellular automata.

https://www.youtube.com/watch?v=e0GiDcBlem0

Monday, November 25, 2019. Feedback.

https://www.youtube.com/watch?v=1n1DMCq-2TM

Monday, December 2, 2019. Feedback (cont.).

https://www.youtube.com/watch?v=r7RoUdMH7Ds

Monday, December 4, 2019. Review for Exam 3.

https://www.youtube.com/watch?v=QT2SVuZKOkM

 Wednesday, December 6, 2019. Review for Exam 3 (cont.).

https://www.youtube.com/watch?v=LgADeCoy_c8

The American Physical Society March Meeting: A Victim of the Coronavirus

I planned to devote this blog post to a discussion of the American Physical Society March Meeting, which was to be held in Denver this week. Unfortunately, the APS cancelled the meeting because of concerns about the coronavirus.

Email from the American Physical Society cancelling the March Meeting.

I learned of the cancellation eight hours before I was to leave for the airport. I’m not angry with the APS; I understand the difficult situation the organizers faced. Frankly, I was worried about contracting the virus at the meeting, and then carrying it back to southeast Michigan. Nevertheless, the last minute cancellation was frustrating.

On the bright side, this blog offers me an opportunity to share what I was going to say at my presentation. The talk was, in fact, closely related to Intermediate Physics for Medicine and Biology. Phil Nelson—author of the trilogy Biological Physics, Physical Models of Living Systems, and From Photon to Neuron—organized a session about “Bringing Together Biology, Medicine, and Physics in Education,” and invited me to speak.

The session “Bringing Together Biology, Medicine, and Physics in Education”
that was supposed to be held at the American Physical Society March Meeting.

Below is my abstract.

The Purpose of Homework Problems is Insight, Not Numbers:
Crafting Exercises for an Intermediate Biological Physics Class

Bradley Roth 

Oakland University 

Richard Hamming famously said “The purpose of computing is insight, not numbers.” This view is true also for homework problems in an intermediate-level physics class. I constantly tell my students “an equation is not something you plug numbers into to get other numbers; it tells a story.” I will use examples from courses in Biological Physics and Medical Physics to illustrate this idea. A well-formed homework problem must balance brevity with storytelling. Often the problem is constructed by creating a “toy model” of an important biological system, and analysis of the toy model reveals some important idea or insight. A collection of such problems becomes a short-course in mathematical modeling as applied to medicine and biology, which is a skill that needs to be cultivated in biology majors, pre-med students, and anyone interested in using physical and mathematical tools to study biology and medicine.

If you want to hear more, download the powerpoint presentation at the book’s website: https://sites.google.com/view/hobbieroth/home.

Russ Hobbie and I are proud of the homework problems in Intermediate Physics for Medicine and Biology. We hope you will gain much insight from them.

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

The pile of books that I used as props
during my online talk.

That’s how the post ended when I wrote it Sunday evening. Then a miracle happened. Physicists began spontaneously organizing an online version of the APS March Meeting! By Tuesday I was listening to Leon Glass give a wonderful talk about cardiac dynamics. On Wednesday I heard Harry McNamara give a fascinating lecture about stimulating and recording electrical activity using light. On Thursday afternoon all the speakers (including myself) in the “Bringing Together Biology, Medicine, and Physics in Education” session presented our talks remotely. I greatly enjoyed it. Over 35 people listened online; I wonder if we would have had that many in Denver? Because I was sitting in my office, I was able to use many of the textbooks that I mentioned in my powerpoint as props. A video was made of each talk, and I’ll post a link to it in the comments when it’s available.

Phil Nelson is a hero of this story. He led the effort in the APS Division of Biological Physics, exhorting us that

Although we are all reeling from the abrupt cancellation of the March Meeting, it’s time for resilience. Science continues despite big bumps in the road, because science is important and it’s what we do.

 Amen!

Significant Advances in Computed Tomography

The journal Medical Physics recently published a virtual issue about “Significant Advances in Computed Tomography.” It’s accessible to all for free and is a wonderful resource for an instructor teaching a class based on Intermediate Physics for Medicine and Biology. Marc Kachelrieß, curator of the virtual issue, writes

It is now 40 years since Allan M. Cormack and Godfrey N. Hounsfield were jointly awarded the Nobel Prize in Physiology or Medicine for the development of computer assisted tomography, today known as computed tomography or simply as CT. Since its introduction in 1972 CT has become the most widespread and the most important tomographic medical imaging modality.

This inaugural virtual issue of the journal Medical Physics was created in honor of the 40^th anniversary of Cormack and Hounsfield’s 1979 Nobel Prize. It is a compilation of the most significant original scientific papers on advances in CT that have been published in our journal. These papers have been selected among the most cited CT articles published in our journal so far, with a focus on clinical relevance. CAD [coronary artery disease] papers were not considered. If there were two or more papers on a similar topic that met all selection criteria the one that was published first was chosen.

This compilation reflects many important CT developments starting with Hounsfield’s Nobel award address on “Computed Medical Imaging” [cited in IPMB]. Some of the topics that are covered include basic image reconstruction technologies, spiral CT, cardiac CT, CBCT [cone beam CT], tube current modulation, 4D respiratory CT, dual-source dual-energy CT, and new technologies such as iterative image reconstruction as well as the future technology of photon counting detector CT.

Thus, this virtual issue provides the reader with an opportunity to reflect on the historical developments of CT and also to gain insights into the hot CT topics of today and of the near future.

Table of Contents:

• “Computed Medical Imaging” by Godfrey N. Hounsfield
• “Optimal Short Scan Convolution Reconstruction for Fan Beam CT” by Dennis L. Parker 
• “Fast Calculation of the Exact Radiological Path for a Three-Dimensional CT Array” by Robert L. Siddon
• “Physical Performance Characteristics of Spiral CT Scanning” by Willi A. Kalender and Arkadiusz Polacin
• “Three‐Dimensional Computed Tomographic Reconstruction Using a C-Arm Mounted XRII: Correction of Image Intensifier Distortion” by Rebecca Fahrig, Michel Moreau, and David Wayne Holdsworth 
• “Electrocardiogram-Correlated Image Reconstruction from Subsecond Spiral Computed Tomography Scans of the Heart” by Marc Kachelriess and Willi A. Kalender 
• “Performance Evaluation of a Multi-Slice CT System” by Cynthia H. McCollough and Frank E. Zink 
• “Dose Reduction in CT by Anatomically Adapted Tube Current Modulation. II. Phantom Measurements” by Willi A. Kalender, Heiko Wolf, and Christoph Suess 
• “Cone-Beam Computed Tomography with a Flat-Panel Imager: Initial Performance Characterization” by David A. Jaffray and Jeff H. Siewerdsen 
• “Calculation of Effective Dose” by Cynthia H. McCollough and Beth A. Schueler 
• “Cone-Beam Volume CT Breast Imaging: Feasibility Study” by Biao Chen and Ruola Ning 
• “4D-CT Imaging of a Volume Influenced by Respiratory Motion on Multi-Slice CT” by Tinsu Pan, Ting-Yim Lee, Eike Rietzel, and George T. Y. Chen 
• “Volume CT with a Flat-Panel Detector on a Mobile, Isocentric C-Arm: Pre-Clinical Investigation in Guidance of Minimally Invasive Surgery” by Jeff H. Siewerdsen, Douglas J. Moseley, Shane Burch, Stuart K. Bisland, Arjan Bogaards, Brian C. Wilson, and David A. Jaffray 
• “A Three-Dimensional Statistical Approach to Improved Image Quality for Multislice Helical CT” by Jean‐Baptiste Thibault, Ken D. Sauer, Charles A. Bouman, and Jiang Hsieh 
• “Prior Image Constrained Compressed Sensing (PICCS): A Method to Accurately Reconstruct Dynamic CT Images from Highly Undersampled Projection Data Sets” by Guang‐Hong Chen, Jie Tang, and Shuai Leng 
• “Improved Dual-Energy Material Discrimination for Dual-Source CT by Means of Additional Spectral Filtration” by Andrew N. Primak, Juan C. Ramirez Giraldo, Xin Liu, Lifeng Yu, and Cynthia H. McCollough 
• “Dual-Source Spiral CT with Pitch up to 3.2 and 75 ms Temporal Resolution: Image Reconstruction and Assessment of Image Quality” by Thomas G. Flohr, Shuai Leng, Lifeng Yu, Tmas Allmendinger, Herbert Bruder, Martin Petersilka, Christian D. Eusemann, Karl Stierstorfer, Bernhard Schmidt, and Cynthia H. McCollough 
• “Vision 20/20: Single Photon Counting X-Ray Detectors in Medical Imaging” by Katsuyuki Taguchi and Jan S. Iwanczyk
• “Photon-Counting CT for Simultaneous Imaging of Multiple Contrast Agents in the Abdomen: An In Vivo Study” by Rolf Symons, Bernhard Krauss, Pooyan Sahbaee, Tyler E. Cork, Manu N. Lakshmanan, David A. Bluemke, and Amir Pourmorteza

These papers support and expand the discussion of computed tomography in Section 16.8 of Intermediate Physics for Medicine and Biology.

To learn more about this virtual issue, and about the history of computed tomography, listen to two videos by Cynthia McCollough, the president of the American Association of Physicists in Medicine. 

Cynthia McCollough introduces the virtual issue about 

“Significant Advances in Computed Tomography,”

published by the journal Medical Physics. 

https://www.youtube.com/watch?v=b_NB-EGmzc4

A video about the history of CT technology.

https://www.youtube.com/watch?v=RSyR8BlEz60

Intermediate Physics for Medicine and Biology has a New Website

A New Website

This summer I received an email from University Technology Services saying that faculty websites, like the one I maintain about Intermediate Physics for Medicine and Biology, would no longer be supported at Oakland University. In other words, IPMB needed a new online home. So today I announce our new website: https://sites.google.com/view/hobbieroth. If you try to access the old website listed in IPMB, www.oakland.edu/~roth/hobbie, it’ll link you to the new site, but I don’t know how long that will last.

What can you find at our new website? Lots of stuff, including

• Errata. The errata is a list of errors in IPMB. 
• Blog. Information about this book blog, including the mapping of blog posts to sections in IPMB, which is useful if you want additional information about a particular topic. 
• Links. Links to sites such as the IPMB Facebook group and the publisher webpage. 
• Trivial Pursuit IPMB. Game cards for the board game that’s all the rage: Trivial Pursuit IPMB. 
• MacDose. Links to MacDose, the computer program Russ Hobbie wrote to teach the interaction of radiation with matter.

If you’re looking for my website, it’s changed too, to https://sites.google.com/view/bradroth.

Class Videos

This semester I’m teaching PHY 3250, Biological Physics. I am recording each class, and I’ll upload the videos to YouTube. Anyone can watch the lectures for free, as if it were an online class. I still use the blackboard, and sometimes it’s difficult to read in the video. I hope you can follow most of the lectures.

PHY 3250 class on September 6, 2019, covering biomechanics.

https://www.youtube.com/watch?v=z2-_ynK7mC4&t=10s

 

Useful for Instructors

If you scroll down to the box on the right of hobbieroth.blogspot.com you will find a list of labels. Click the one called “Useful for Instructors” and you can find several posts that are….er….useful for instructors. If you’re teaching from IPMB, you might find these posts particularly helpful.

Google Scholar

Below is a screenshot of IPMB’s Google Scholar citation statistics. We’ve averaged 26 citations a year over the last ten years, or one every two weeks. We thank all of you who’ve referenced IPMB. We’re delighted you found it important enough to cite.

A Trick to Generate Exam Problems

Intermediate Physics for Medicine and Biology.

When teaching a class based on Intermediate Physics for Medicine and Biology, instructors need to write problems for their exams. My goal in this post is to explain a trick for creating good exam problems. 

One of my favorite homework problems in IPMB is from Chapter 4.

Problem 37. The goal of this problem is to estimate how large a cell living in an oxygenated medium can be before it is limited by oxygen transport. Assume the extracellular space is well stirred with uniform oxygen concentration C₀. The cell is a sphere of radius R. Inside the cell oxygen is consumed at a rate Q molecule m⁻³ s⁻¹. The diffusion constant for oxygen in the cell is D.

(a) Calculate the concentration of oxygen in the cell in the steady state.

(b) Assume that if the cell is to survive the oxygen concentration at the center of the cell cannot become negative. Use this constraint to estimate the maximum size of the cell.

(c) Calculate the maximum size of a cell for C₀ = 8 mol m⁻³, D = 2 x 10⁻⁹ m² s⁻¹, Q = 0.1 mol m⁻³ s⁻¹. (This value of Q is typical of protozoa; the value of C₀ is for air and is roughly the same as the oxygen concentration in blood.)

Homework problems for Chapter 4 in
Intermediate Physics for Medicine and Biology.

I usually work this problem in class. Not only do students practice solving the steady-state diffusion equation, but also they estimate the maximum size of a cell from some basic properties of oxygen. In the Solution Manual—available to instructors only (email us)—we explain the purpose of each problem in a preamble. Here is what the solution manual says about Problem 37:

This important “toy model” considers the maximum size of a spherical cell before its core dies from lack of oxygen. One goal of biological physics is to show how physics constrains evolution. In this case, the physics of diffusion limits how large an animal can be before needing a circulatory system to move oxygen around.

How do you create an exam problem on this subject? Here's the trick: Do Problem 37 in class and then put a question on the exam identical to Problem 37 except “sphere” is replaced by “cylinder”. The problem is only slightly changed; just enough to determine if the student is solving the problem from first principles or merely memorizing. In addition, nerve and muscle fibers are cylindrical, so the revised problem may provide an even better model for those cells. Depending on the mathematical abilities of your students, you may need to provide students with the Laplacian in cylindrical coordinates. (If the exam is open book then they can find the Laplacian in Appendix L).

Here’s a second example: Chapter 1 considers viscous flow in a tube; Poiseuille flow. On the exam, ask the student to analyze viscous flow between two stationary plates.

Section 1.17

Problem 36 ½. Consider fluid flow between two stationary plates driven by a pressure gradient. The pressure varies in the x direction with constant gradient dp/dx, the plates are located at y = +L and y = -L, and the system is uniform in the z direction with width H. The fluid has viscosity η.

(a) Draw a picture the geometry.

(b) Consider a rectangular box of fluid centered at the origin and derive a differential equation like Eq. 1.35 governing the velocity v_x(y).

(c) Solve this differential equation to determine v_x(y), analogous to Eq. 1.37. Assume a no-slip boundary condition at the surface of each plate. Plot v_x(y) versus y.

(d) Integrate the volume fluence and find the total flow i. How does i depend on the plate separation, 2L? How does this compare with the case of flow in a tube?

An interesting feature of this example is that i depends on the third power of L, whereas for a tube it depends on the fourth power of the radius. Encourage the student to wonder why.

Third example: A problem in Chapter 7 compares three different functions describing the strength-duration curve for electrical stimulation. On your exam, have the students analyze a fourth case.

Section 7.10

Problem 46 ½. Problem 46 analyzes three possible functions that could describe the strength-duration curve, relating the threshold current strength required for neural excitation, i, to the stimulus pulse duration, t. Consider the function i = A/tan^-1(t/B). Derive expressions for the rheobase i_R and chronaxie t_C in terms of A and B. Write the function in the form used in Problem 46. Plot i versus t.

And still more: Problem 32 in Chapter 8 examines magnetic stimulation of a nerve axon using an applied electric field E_i(x) = E₀ a²/(x² + a²). Give a similar problem on your exam but use a different electric field, such as E_i(x) = E₀ exp(-x²/a²).

And yet another: Chapter 10 examines the onset of cardiac fibrillation and chaos. The action potential duration APD is related to the diastolic interval (time from the end of the previous action potential to the start of the following one) DI by the restitution curve. Have the student repeat Problem 41 but using a different restitution curve: APD_i+1 = 300 DI_i/(DI_i + 100).

Final example: Problem 36 in Chapter 9 asks the student to calculate the electrical potential inside and outside a spherical cell in the presence of a uniform electric field (Figure 9.19). On your exam, make the sphere into a cylinder.

I think you get the point. On an exam, repeat one the of homework problems in IPMB, but with a twist. Change the problem slightly, using a new function or a modified geometry. You will be able to test the knowledge and understanding of the student without springing any big surprises on the exam. Many problems in IPMB that could be modified in this way.

Warning: This trick doesn’t always work. For instance, in Chapter 1 if you try to analyze fluid flow perpendicular to a stationary object, you run into difficulties when you change the sphere of Problem 46 into a cylinder. The cylindrical version of this problem has no solution! The lack of a solution for low Reynolds number flow around a cylinder is known as Stokes’ Paradox. In that case, you’re just going to have to think up your own exam question.