The Solution Manual

Cover of the 6th edition of
Intermediate Physics for
Medicine and Biology. 

Gene Surdutovich and I have now submitted the sixth edition of Intermediate Physics for Medicine and Biology, corrected the page proofs, corrected the corrected page proofs, and then checked the corrections of the corrected-corrected page proofs. The book is now in the hands of our publisher, Springer Nature, and we await the arrival of our free copies. You would think that finally we were done and could now rest.

But Nooooo! There’s still the solution manual. We have a draft of the solution manual that I think is 99% complete, but it needs one more pass to check for errors. Today, I want to tell you a little more about the solution manual.

First, it’s almost a second book. We have over a thousand homework problems in the sixth edition, and the solution manual can fit about three solutions per page, so that means it has several hundred pages. IPMB is equation dense, but the solution manual is equation denser. IPMB was written in LaTeX, but for historical reasons the solution manual was written using MS Word. However, I lost access to MS Office about a year ago (long story…) so I use free software called LibreOffice. It’s almost identical to MS Word, except for the equation editor, which is completely different. The solution manual also has many figures and tables. It’s a big production.

Once the sixth edition of IPMB is published (Springer's website says February 2017), we’ll send the solution manual to instructors upon request, although we do check to make sure the instructor is really an instructor. I realize the solution manual would be valuable to students, and especially to students who are working through the book on their own. We have to balance their needs with the desire of most instructors to not have the solution manual widely distributed among students; Solving a homework assignment should not be merely copying from the solution manual. Russ and I solved this dilemma for previous editions by sending the solution manual, for free, to instructors on request, but asking them to pledge not to post it on the web. This has worked fairly well. 

Each solution to a homework problem starts with a preamble: a sentence or two in italics saying why we included the problem and how the student would gain from solving it. For instance, here’s the preamble to a problem in Chapter 1 of the sixth edition, about biomechanics.

1.10  This is the first of a series of problems about biomechanics. In this problem, students practice drawing a free-body diagram and analyzing static equilibrium for a person doing pushups.

Each problem can fit into three special categories: 

* = Higher difficulty 

§ = Complete a derivation from the text 

¶ = New in the sixth edition

The higher difficulty problems are often among my favorites, but they tend to be long or require advanced mathematics. Instructors will have to use their own judgement about if their students are up to the task. The problems that complete a derivation from the text are really meant to force the student to fill in missing steps in the textbook. Sometimes these problems resemble this example from Chapter 5: 

Problem 53 Substitute Eqs. 5.98 and 5.99 into Eq. 5.96 to derive Eq. 5.100. 

We also mark the new problems in the sixth edition. This way, if instructors are already familiar with the 5th edition of IPMB and its solution manual, they can identify the new stuff more easily. 

We try to include enough detail that instructors and students can easily follow the solution. It’s always a judgment call as to how much detail is necessary. We also try to stress the translation of physics to math and then back from math to physics, the plotting of results, and the examining of limiting cases, because we often urge the student to do just these things. We sometimes try to sum up why the calculation is important. And occasionally, we add a little commentary at the end of a problem, but not too often because the solution manual is already long enough.

If you really want to get the most out of IPMB, do the homework problems. That’s where much of the learning takes place. And for students who love biology but don’t like math, view these problems as a way to hone a new skill. Think of them as an opportunity, not a obstacle.

We keep adding more, more, more problems with each edition. I haven’t done the math, but I suspect that at the current rate by the 9th edition of IPMB the homework problems will take up more space than the text itself, and by the 15th edition the book will have become just a homework collection with no text! Who knows? I’ll be long gone by then.

One final warning. Gene and I are trying to eliminate any errors in the solution manual, but I don’t think we have checked it as thoroughly as we checked the textbook itself. If you get an answer that’s different than in the solution manual, it may be your mistake or it may be ours. Please let us know and we’ll try to correct any errors.

Enjoy!

Memories of the National Institutes of Health

These days, when I see the current state of the National Institutes of Health, I grieve for the NIH I once knew. I worked in the NIH intramural research program from 1988 to 1995. Professionally, these were the best, most productive years of my career. I’m feeling a little nostalgic today, and would like to share with you my description of NIH published in the memoirs I wrote for the American Institute of Physics in 2024, just before the present presidential administration took office. My experiences at NIH were the ideal preparation for being a coauthor on Intermediate Physics for Medicine and Biology.

Building 1

The National Institutes of Health is the best place in the world to do biomedical research. I worked in the intramural program where scientists and medical doctors perform their studies on the NIH campus in Bethesda, Maryland. About 15% of NIH’s funding goes to the intramural program. The rest is for the extramural program, which awards grants to faculty at universities across the USA. NIH consists of an alphabet soup of disease-oriented institutes, such as the National Heart, Lung, and Blood Institute (NHLBI), the National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK), and the biggest of all, the National Cancer Institute (NCI). When I was at NIH, Tony Fauci was the head of the National Institute of Allergy and Infectious Diseases (NIAID) and was already acclaimed for his investigations of HIV and AIDS. During part of my stay, Harold Varmus—known for his work on cancer-causing genes—was the NIH director. He would ride his bike to work at NIH’s impressive James Shannon Building (also known as Building 1). We all loved him.

Bethesda is just inside the Capital beltway. It’s lovely but expensive. We couldn’t afford to live there, so first we rented an apartment in Wheaton and later bought a fixer-upper house in Kensington. [While living there] our second daughter, Kathy, was born in April 1991.

NIH has its own subway stop on the red line, with an extraordinarily deep escalator. Once Wikswo [my PhD advisor] visited me at NIH. I was escorting him there on the subway and when we reached the NIH stop I mentioned that he was about to ride on the longest escalator he ever saw. Wikswo is always up for a challenge and chose to climb the stairs instead (I rode up). He did fine initially, but as he approached the top even he was exhausted.

Tens of thousands of people were employed at NIH. It was far bigger than Morrison where I grew up. It had tenured investigators like at a university and many post doc trainees, but no students. It even had its own newspaper: the NIH Record. NIH is a federal lab. In 1990 when the federal government shut down I had to stay home.

Building 10

The heart of the intramural campus is NIH’s unique Clinical Center (Building 10). This state-of-the-art hospital is entirely dedicated to clinical research. Patients who are treated at the Clinical Center must fit into one of the ongoing research protocols, but if they do they receive medical treatment at no cost. Many clinical trials require normal volunteers who are paid to serve as healthy controls. I remember a guy who was a normal volunteer in so many studies that it became his full-time job.

Building 16

Another landmark on the NIH campus is the beautiful Stone House (Building 16), located near the entrance from Rockville Pike. The Stone House is part of the Fogarty International Center, which focuses on supporting biomedical researchers who come to NIH from around the globe. I had the privilege to work with international scientists from all over the world.

When I was at NIH, most of its research was focused on genetics. The Human Genome Project began in 1990, with James Watson (of DNA fame) and Francis Collins (future director of NIH during Covid) leading the effort to sequence the human genome while Craig Venter competed with them from his private company, the Institute of Genomic Research. I wasn’t interested in genomics, but NIH was so large that there were still plenty of people for me to interact with.

I worked in the Biomedical Engineering and Instrumentation Program (BEIP). The National Institute of Biomedical Imaging and Bioengineering (NIBIB) didn’t exist yet and BEIP was part of the National Center for Research Resources (NCRR). The purpose of BEIP was to supply engineers, physicists, and mathematicians to collaborate with the biologists and medical doctors in the disease institutes. Our program was funded by a “tax” on the other institutes and we were expected to focus on collaboration and limit the time we spent on our own research. We didn’t have to apply for grants, like faculty at a university had to, which was a one of the best features of the intramural program.

Within BEIP I was part of the Mechanical Engineering Section led by Seth Goldstein. I wasn’t a mechanical engineer but Seth wanted his section to contain a broad mix of scientists. He was a great boss. When I needed help overcoming some administrative obstacle or assistance with an engineering issue he was always there for me. Otherwise, he left me alone to follow my own path. Some of the other members of my section were Ron Levin, an expert in magnetic resonance imaging and computers; Richard Chadwick, whose mathematical models of heart biomechanics would later influence my work on mechanotransduction; Steve Leighton, an excellent design engineer who spent his summers at the Woods Hole Oceanographic Institute building a ultramicrotome for use in a scanning electron microscope (Leighton had a sign in his office that read “Good, Fast, Cheap: Pick any two”); and Peter Basser, my best friend at NIH who arrived a year before I did. He was an expert on tissue mechanics and porous media. All the guys in the Mechanical Engineering Section used Apple Macintosh computers instead of PCs, so I did that too and have been a loyal Mac user ever since.

At NIH you could spend all your time listening to science talks. Each week the “yellow sheet” was published listing about a dozen lectures each day. I can remember a speaker who gave a talk about a recent invention called the “world wide web.” All of us from the Mechanical Engineering Section attended. As we walked back to our offices after the seminar, we shook our heads and asked each other “but what good is it?” We would soon learn.

Building 13

Before 9/11 the security at NIH was lax. I generally rode the bus to work because we owned only one car (suburban Maryland had the best public transportation of anywhere I’ve lived). Sometimes [my wife] Shirley, [my oldest daughter] Stephanie, and Kathy would come pick me up to go home. They would simply drive onto the NIH campus, park in a visitor’s spot, and take the elevator up to my office in Building 13. Nowadays you can’t even enter the campus without the proper ID and permission.

If you want to learn more about the current state of NIH—the good, the bad, and the ugly—I suggest you read the NIH Vigils newsletter each week: an underground publication by current and former NIH employees, and definitely not an official mouthpiece of the administration. Assuming the NIH someday returns to its former glory, I encourage young people to search for summer internships and other opportunities to work there. I hope that someday I can again say that NIH is the best place in the world to do biomedical research.

 https://www.youtube.com/watch?v=ezpi8J1UQA0&t=43s

Biophysics at Kalamazoo

I’m always curious how colleges and universities structure undergraduate biological physics and medical physics programs. At Oakland University in Rochester, Michigan (where I worked until I retired in 2020) we have a Medical Physics major. As a Michigander, I want to introduce you to another program in our state: the Biological Physics concentration at Kalamazoo College.

To reach Kalamazoo from where I live in Rochester Hills, which is just north of Detroit, get on I-94 and drive west about three fourths of the way across the state, until you’re roughly 40 miles from Lake Michigan. There you’ll find a small, private liberal arts college founded by Baptist ministers in 1833. Kalamazoo College is known for its flexible curriculum, with an emphasis on study abroad, internships, undergraduate research, civic engagement, and a senior capstone project (they call it the “K-plan”). I’m a fan of a liberal arts education, so their program sounds attractive to me.

All students have a major, but many also focus on a concentration, which is an interdisciplinary set of courses centered on a theme (to me, it seems like a beefed up minor). One concentration is Biological Physics. It consists of six prerequisite courses: two semesters each of physics, chemistry, and calculus. Then the required courses are two semesters of biology, organic and physical chemistry, and two specialty courses on topics such as biophysics, neuroscience, complex systems, or chaos.

The biological physics concentration is light on physics compared to OU’s medical physics program, but that’s probably because it’s a concentration and not a major. A combination of a Kalamazoo physics major with the biophysics concentration would provide the strong base in physics I would want. But the biological physics concentration might also be appealing to students who seek a deeper math and physics background than a biology major would supply. Also, the concentration has a lot of overlap with the curriculum required to get into medical school. I would guess it attracts premed students (at least the ones who are not afraid of math, which is just a handful).

At Oakland we have a two-semester course sequence of Biological Physics and Medical Physics that’s based on Intermediate Physics for Medicine and Biology. The course at Kalamazoo most similar to these appears to be the Biophysics course (PHYS 205). The catalog description is given below. I put in italics the parts covered in IPMB.

PHYS 205 Biophysics 

How can we observe and comprehend the size and scale of living systems? How can we use physics to aid our understanding of biology? How large are bacteria and viruses? What size of torque can molecular motors develop? How does the flexibility of a molecule contribute to its biological function? What is the scale of membrane potentials? How efficient are different organisms at encoding their genes? Which animal can jump the highest per its size? How can we make sense of vast amounts of complex and sometimes "messy" biological data? This course is an introduction to the advantages and limitations of using physical techniques and models to address biological questions. We will focus on molecular-scale systems and dynamics, with topics to include modeling dynamic molecules and systems, optics and microscopy, physical properties of biomolecules and gaining numerical literacy. We will explore current biophysical research and help you develop the interdisciplinary toolset to engage with it.

I see a lot of overlap with IPMB, but clearly there is more of a molecular emphasis in PHYS 205.

What’s the perfect preparation for graduate study and a career in biological physics? I suggest students follow Kalamazoo’s Biological Physics concentration, but during the first summer after they complete the required prerequisite courses in physics and math, they rent an isolated cabin along Lake Michigan and spend three months reading and working the homework problems in the 6th edition of Intermediate Physics for Medicine and Biology, taking an hour off each evening to watch the sun set over the lake. Now that would be a great program!