Energy: A Human History

In Chapter 2 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I have an end-of-chapter homework problem about consuming a finite resource.

Section 2.10 

Problem 37. The consumption of a finite resource is often modeled using the logistic equation. Let y(t) be the cumulative amount of a resource consumed and y_∞ be the total amount that was initially available at t = −∞. Model the rate of consumption [I wish Russ and I had written “amount consumed” instead of “rate of consumption”] using Eq. 2.29 over the range −∞ < t < ∞. 

(a) Set y₀ = y_∞/2, so that the zero of the time axis corresponds to when half the resource has been used. Show that this simplifies Eq. 2.29. 

(b) Differentiate y(t) to find an expression for the rate of consumption. Sketch plots of dy/dt versus t on linear and semilog graph paper. When does the peak rate of consumption occur? 

When this model is applied to world oil consumption, the maximum is called Hubbert’s peak (Deffeyes 2008).

The answer to this exercise can be found in the IPMB solution manual. (The solution manual is available free of charge to instructors. If you need a copy, email me at roth@oakland.edu.) All exercises in the solution manual have a brief preamble, explaining the goal of the exercise and why it’s important.

2.37¶ This is not a biological example, except in the sense that if we ignore this example we humans may all end up dead. Students use a variation of the logistic equation to analyze the consumption of a finite resource (e.g., oil).

I won’t solve the entire problem in this blog post, but I will show the semilog plot from the solution manual.

A semilog plot of amount consumed (solid) and the rate of consumption (dashed) for a finite resource modeled using the logistic equation. This plot is part of the solution to Problem 37b.

 

 

 

 

Energy: A Human History,
by Richard Rhodes.

The rate of consumption of the resource (dy/dt) first rises exponentially, reaches a peak, and then falls exponentially. (Remember, a straight line on a semilog plot corresponds to exponential growth or decay.) For the mathematically inclined, the dy/dt curve corresponds to a hyperbolic secant squared.

Why do I bring up this topic? Recently I read Energy: A Human History, by Richard Rhodes, a sweeping account of energy transitions that changed our world. Rhodes includes a figure that looks a little bit like this: 

My rendition of a figure from the final chapter of Energy: A Human History showing the historical evolution of the world energy mix.

What a wonderful plot! It both summarizes Rhodes’s book and illustrates the power and ubiquity of Hubbert’s peak. That semilog plot from Homework Problem 37 appears over and over as one finite resource replaces another.

I should add a few qualifiers.

• Historical data is noisy and the curves pictured above merely approximate a complicated behavior. 
• The plot begins at about the time of the industrial revolution. The population of humans was probably too small, and our technology too primitive, to apply this model before that time. 
• All future data (say, after 2016, the year Energy was published) is extrapolation or prediction. 
• I labeled the yellow curve on the right “Renewables” but it really represents whatever comes next, be it wind, solar, hydroelectric, geothermal, or even nuclear fusion. 
• Let’s hope that the Renewables curve corresponds to an infinite resource, not a finite one, so it will never reach a peak and then fall. Is that wishful thinking? I don’t know, but the figure encourages us to ask such questions. 
• Nuclear energy shot up much faster than would be expected right after World War II, but then the curve flattened prematurely because of fears about radiation. 
• Natural gas appears to be with us for the foreseeable future, unless we can wean ourselves off of it to address global warming. The use of coal is almost done (regardless of what a certain senator from West Virginia thinks), and the use of oil has reached its peak and is on its way down (now might be a good time to buy an electric car). 
• Climate change is the critical issue looming over the right side of the plot. We must leave many of those fossil fuels (coal, oil, gas) in the ground to prevent an environmental disaster.

Perhaps I need to add extra parts to that homework problem.

(c) Suppose at time t you discover that pollution from this finite resource is killing people, and you stop consuming it immediately. How would that change the plots you made in part (b)? 

(d) What would happen if the resource is killing people but people continue to consume it nevertheless?

 Richard Rhodes, The Light of New Fires: Energy Transitions Yesterday and Today, presented at the American Museum of Science and Energy, Oak Ridge, Tennessee, October 22, 2015.

Essential Concepts in MRI

Essential Concepts in MRI,
by Yang Xia.

Suppose you’ve read Chapter 18 of Intermediate Physics for Medicine and Biology covering magnetic resonance imaging and you want to learn more. What do you read next? I suggest the new textbook by Yang Xia, Essential Concepts in MRI: Physics, Instrumentation, Spectroscopy, and Imaging. Xia writes in the Preface

In the fall of 1994, I became a new assistant professor of physics at Oakland University, in the specialization of medical physics. After receiving my assignment to teach a graduate-level one-semester course in magnetic resonance imaging (MRI) for the next semester, I sat in my nearly empty office and wondered what and how to teach my students…

As I went over [the MRI books available at the time] for a possible adaptation for my course, I could not find any single book that contained what I had in mind as the four essential and inseparable components of MRI—theory, instrumentation, spectroscopy, and imaging… I eventually realized, painfully, that I would have to put together the materials myself… My lecture notes, evolved and revised substantially during the last 26 years, became the basis for this book…

The book is grouped into five parts. Part I introduces the essential comcepts in magnetic resonance, including the use of the classical description and a brief introduction of the quantum mechanical description. It also includes the description for a number of nuclear interactions that are fundamental to magnetic resonance. Part II covers the essential concepts in experimental magnetic resonance, which are common for both NMR spectroscopy and MRI. Part III describes the essential concepts in NMR spectroscopy, which should also be beneficial for MRI researchers. Part IV introduces the essential concepts in MRI. The final part is concerned with the quantitative and creative nature of MRI research…

IPMB covers some of the material in Essential Concepts, particularly that dealing with physics and imaging. Nuclear magnetic resonance spectroscopy is entirely absent in IPMB. I had not seen the material in Essential Concepts about spectroscopy since taking an organic chemistry course while an undergraduate at the University of Kansas, and even then I didn’t understand much of it. IPMB has little to say about instrumentation and I found these sections of Essential Concepts to be among the most useful for me.

Essential Concepts is full of excellent images and illustrations. Some images, such as a high-resolution picture of a pickle, I had seen before on the door to Xia’s laboratory at Oakland University. We both were members of the physics department at OU for over twenty years. In fact, if you look at the acknowledgment section of Essential Concepts, you’ll find my name—along with many others—listed as reading and commenting on a draft of the book. Of course, this was done virtually, as Xia sat in his house and I in mine during the COVID-19 pandemic. This book is one of the few good things that arose from that plague.

The Early Development of Q-Space NMR Microscopy — Yang Xia

https://www.youtube.com/watch?v=6X3XT_Nw2ZE

FLASH

In radiotherapy, a dose of radiation is usually not given all at once, but instead is applied in fractions. In Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss fractionation this way.

The central problem of radiation oncology is how much dose to give a patient, over what length of time, in order to have the greatest probability of killing the tumor while doing the least possible damage to surrounding normal tissue. While the dose is sometimes given all at once (over several minutes), it is usually given in fractions five days a week for four to six weeks.

Radiobiology for the Radiologist,
by Hall and Giaccia.

We can gain insight into why fractionation works from Eric Hall and Amato Giaccia’s book Radiobiology for the Radiologist.

The basis of fractionation in radiotherapy can be understood in simple terms. Dividing a dose into several fractions spares normal tissues because of repair of sublethal damage between dose fractions and repopulation of cells if the overall time is sufficiently long. At the same time, dividing a dose into several fractions increases damage to the tumor because of reoxygenation and reassortment of cells into radiosensitive phases of the cycle between dose fractions.

True Tales of Medical Physics,
by Jacob Van Dyk.

Despite the apparent advantages of delivering radiation in many fractions, recently a new technique has been proposed in which the radiation is applied very quickly all at once. In True Tales of Medical Physics (2022), Dr. Radhe Mohan writes

At the time of writing of this chapter, ultra-high dose rate radiotherapy, called FLASH radiotherapy, has become the rage. In contrast with the conventional low dose rate protracted radiotherapy, which requires a fractionated course of up to 40 (sometimes even more) treatments, with each daily fraction taking between 15 and 60 min, in FLASH radiotherapy, the entire treatment can be delivered in a fraction of a second. The question is whether FLASH is something real or just a flash in the pan. Around 2015, a medical physicist, Dr. Alejandro Mazal of Institut Curie, in Paris, France, presented results of a study conducted by Favaudon, et al. (https://www.ncbi.nlm.nih.gov/pubmed/25031268) at his institution showing sparing of normal tissues at ultrahigh dose rates. I was skeptical. Naively, I thought why should the dose rate matter? It is the dose deposited that determines the biological damage. Since Favaudon’s work, many experiments have been carried out all over the world confirming the normal tissue sparing effect of FLASH and, equally importantly, showing that the response of tumours to FLASH and conventional low dose rates is about the same. The number of researchers involved in FLASH as well as the number of publications is increasing exponentially. The underlying mechanisms are not yet understood; however, multiple hypotheses are being offered. It turns out that the sparing effect of ultra-high dose rates was discovered in the 1960s and 70s for electron beams. Research activities remained on the back burner until Favaudon’s efforts. The rekindling of interest in FLASH radiotherapy is being thought of as akin to “sleeping beauty awakened.”

What is the mechanism by which FLASH preferentially kills tumor cells while sparing normal cells? Mohan offers some speculation.

The more we learn about FLASH, the more questions arise. Our team is contributing to understanding the basic mechanisms, to designing and conducting experiments to acquire in vivo and in vitro data, and to interpreting the results. The current dominant hypothesis for FLASH seems to be that, at extremely high dose rates, oxygen is depleted, making normal tissues hypoxic (i.e., low in oxygen content) and, therefore, resistant to radiationdamage. Tumours are not spared, possibly because they are already low in oxygen. I have a different hypothesis: FLASH also spares cells of the immune system (T-lymphocytes) that infiltrate the tumour and kill tumour cells. Another hypothesis, that seems to be appropriate at least for radiationtherapy with carbon ions, is that FLASH may actually generate oxygen within the tumour, which sensitizes tumours. The FLASH effect overall may be a combination of all of these factors.

So, should we dribble radiation out in fractions over many weeks, or give it all in one big burst? I don’t know. I do know that if FLASH pans out, we textbook writers need to update our textbooks. I’m rooting for FLASH, because it will certainly be easier on the patient to have only one treatment instead of daily hospital visits over a month. But beware: you'd better aim your radiation beam accurately, because you only have one chance. Don’t throw away your shot!

 

The Emerging Story of FLASH Radiotherapy, presented by Marie-Catherine Vozenin.

https://www.youtube.com/watch?v=bP6Eve6OUJk

 

My Shot, from Hamilton, by Lin-Manuel Miranda.

Medical Physics for World Benefit

Screenshot of the website
Medical Physics for World Benefit,
www.mpwb.org.

In the last two blog posts (here and here), I discussed the book True Tales of Medical Physics, edited by Jacob Van Dyk. Today, I want to bring to your attention something else I learned about when reading True Tales: the group Medical Physics for World Benefit.

[Jacob (Jake) Van Dyk] was the main founder of Medical Physics for World Benefit (www.MPWB.org), an organization devoted to supporting medical physics activities, largely by training and mentoring, especially for lower income settings.

The vision of this organization is to create

A world with access to effective and safe applications of physics and technology in medicine 

and its mission is

To support activities which will yield effective and safe use of physics and technologies in medicine through advising, training, demonstrating, and/or participating in medical physics-related activities, especially in low to middle income countries.

What’s there not to like? 

You can join or donate to the organization on its website.

We are physicists who work in medicine. If you are a medical physicist and care about global health and access to quality health care, consider joining us.

We help low to middle income countries with training, education, and other methods of support. We are registered charities in the USA and Canada. Learn more about donating to MPWB.

Too cheap to give? At least follow Medical Physics for World Benefit on Facebook or Twitter (@medphyswb).

Finally, I’m gonna give ya a tip. Many academic libraries subscribe to a package from Springer Publishing that lets institutional library members download pdf’s of Springer books for free. So, you can download Intermediate Physics for Medicine and Biology, True Tales of Medical Physics, and my recently published Are Electromagnetic Fields Making Me Ill? all at no charge. Then, take the money you saved and donate it to Medical Physics for World Benefit. 

Deal or no deal?

The Physics of Radiology

The Physics of Radiology,
by Johns and Cunningham.

In last week’s blog post, I reviewed the recently published book True Tales of Medical Physics. A point I didn’t mention in my review was the central role of one textbook in the education of many of the authors who described their life story in True Tales. The Physics of Radiology was written by Harold Johns and John Cunningham. The first edition was published in 1953, but I have access through the Oakland University library to the fourth edition from 1983. This iconic book defined the field of medical physics and radiology in the second half of the twentieth century. Chapters 15–17 in Intermediate Physics for Medicine and Biology summarize material covered in more detail in The Physics of Radiology.

In True Tales, Jacob Van Dyk wrote

In 1971, I was hired by Professor Harold Elford Johns to work as a medical physicist at the Princess Margaret Hospital (PMH) in Toronto. Professor Jack Cunningham was my immediate boss. Professor Johns was considered the guru of Medical Physics with a world-renowned reputation for being a great scientist, a feared graduate student supervisor, and humanitarian. Over the years, he received multiple awards including five honorary doctorate degrees, and Officer of the Order of Canada. He was the first medical physicist to be inducted into the Canadian Medical Hall of Fame. Jack Cunningham also received the Officer of the Order of Canada along with multiple other awards, largely for his work on software development for computerized radiation treatment planning systems. Johns and Cunningham were the authors of The Physics of Radiology, the textbook which gave me my medical physics grounding as it did for all other young, aspiring medical physicists at that time….

[When Van Dyk was studying for his medical physics certification exams], Professors Johns and Cunningham were working on a draft of the fourth edition of their book, The Physics of Radiology. In January, I asked Jack Cunningham if I could review the available draft of this fourth edition. Considering that they would be contributors to the certification examination questions, my guess was that some, if not all, of the questions could be answered if I knew everything in this new edition. So, I went through this draft of the book from cover to cover and I solved (at least I worked on) every problem that was posed at the end of each chapter. As part of this process, I provided Jack with some comments on some questionable things that I found in the draft. As a result, my name was listed, along with others, in the acknowledgments when the book was published in 1983.

In his chapter of True Tales, Terry Peters wrote

During my early years at McGill, I became involved in the activities of the newly formed Canadian College of Physicists in Medicine (CCPM), which had begun the process of credentialling Medical Physicists in Canada. While I had Engineering, rather than Physics, training, I felt that my background had prepared me well for the roles I was playing in Diagnostic Radiology at the Neuro. Nevertheless, I felt it would do no harm to formally study radiation physics and its practical implementation in medicine, so in 1983 I embarked on a mission to devour The Physics of Radiology, by Johns and Cunningham, in preparation for the CCPM Fellowship exams in 1984. The examination process had evolved into an oral session, and a closed book examination—where three questions were selected from a previously published catalogue of questions covering all aspects of Medical Physics. Every Friday afternoon for almost a year I studied “Johns and Cunningham” with Gino Fallone, then a physicist at the Montreal General Hospital, who had also decided to take the certification examination. A gruelling process, but finally successful—we both became CCPM fellows that year.

Martin Yaffe's contribution to True Tales described a bit about Johns background and career.

Dr. Johns had been born in Chengdu, China to Canadian church missionary parents and he had spent his early years there, roaming about small communities in the mountains of Szechuan province with his father, a no-nonsense disciplinarian who believed strongly in devotion to duty and hard work. He learned to be focussed and driven to succeed at whatever was his mission. When the family eventually returned to Canada, he brought that to his graduate work in physics and later to the University of Saskatchewan where he built a strong medical physics research group, concentrating on developing and refining radiation therapy. There he developed the first (or possibly the second—there is some debate as his unit and a competitor, built by Eldorado Mining and Refining Ltd., were used to treat patients within a week or two of each other) cobalt-60 radiation treatment system and carried out pioneering work on radiation dosimetry and treatment planning. Dr. Johns and his work in Saskatchewan were actually mentioned in the film First Man, about the astronaut Neil Armstrong whose daughter had suffered from a brain tumour. Later, he began work on The Physics of Radiology, a textbook which he referred to jokingly (I think) as “The Bible”. This book truly became a guide to those working in radiation oncology all over the world and was published in multiple languages. While the book and its various editions consumed many of his evenings after a hard day at the lab, Johns reverse bragged that he earned about two cents per hour on his textbook writing efforts.

I once estimated that I make about ten cents an hour for my work on IPMB. I guess the difference represents inflation.

Yaffe also reminisced on Johns’ personality and mentoring technique.

Johns had an abrupt nature, not hesitating to poke you emphatically when he felt that you needed to think harder. Often, he would read your carefully written document, hold it up between you and slowly rip it to shreds before filing it in the trash bin. If it was late in the day, he would tell you to meet him the next morning at eight to re-write.

What I learned in those sessions was how to sharply focus your thinking on a problem and how to persist until you had a workable solution. Dr. Johns had two more senior students at the time—Aaron Fenster… and Don Plewes. These two and the lab technician, Dan Ostler, more or less adopted me and provided mentoring to prepare me for my sessions with Johns. Also, Johns used to invite me into his office when he was working on a paper with Aaron or Don and let me watch. While he was more respectful toward them, it was not uncommon for him to fix one of them with his laser-like glare which he held on them for what seemed like minutes and then say something like: “Plews” (he never pronounced the “e” that made it rhyme with Lewis; instead he made it rhyme with “news”), “If you sent that to a journal, they’d crap all over you”. Or, as he slowly ripped up a piece of writing that Aaron had proudly submitted, he’d say at a similar slow pace, “well (rrrrip) Fenster (rrrrip), your (rrrrip) writing (rrrrip) is improving.” So, rather than feel discriminated against, I simply realized that the standards were high, and I’d have to present my best game at all times.

The Physics of Radiology is one of those landmark textbooks (like Jackson’s Classical Electrodynamics in physics) that is a rite of passage for a student in that a field of study. As a coauthor on IPMB, I know what an honor it would be for your book to make that sort of impact. Johns and Cunningham was cited in the second edition of IPMB, but not in earlier or later editions.

The fourth edition is the last that Johns and Cunningham published. However, just last year an updated fifth edition was prepared by a team of five authors.

True Tales of Medical Physics: Insights into a Life-Saving Specialty

True Tales of Medical Physics:
Insights into a Live-Saving Specialty,
by Jacob Van Dyk.

I’ve found the perfect book for readers of Intermediate Physics for Medicine and Biology who are fascinated by medical physics but who don’t want a lot of technical details and math. Jacob Van Dyk recently published True Tales of Medical Physics: Insights into a Life-Saving Specialty. The book consists of 22 chapters written by leading medical physicists, in which they each discuss their career, focusing on interesting anecdotes and life lessons. If I were a young student pondering what career to pursue, this is a book I’d want to read.

Van Dyk’s instructions to the contributors were

to communicate what medical physics is and what medical physicists do to a broad audience including science students, graduate students and residents, experienced medical physicists and their family members, and the general public who are wondering about medical physics. The book will consist of a series of short stories written by award-winning medical physicists—stories that are of personal interest as it relates to their careers. Each story will be unique to the author and could serve any one or more of the following purposes:

1. Be an inspiration to young people searching for career directions, as well as more experienced physicists who are seeking direction on leadership development. 
2. Provide an overview of what medical physicists do with a level of description that is understandable by the non-medical physicist.
3. Provide lessons on life’s experiences from high-profile medical physicists who have significant experience and who are clearly at the top of the field as shown by the awards that they have won. 
4. Be entertaining for those working in the field as well as others.

You can look at this book as a Plutarchian collection of comparative biographies, or you can focus on cross-cutting lessons that appear again and again in the various chapters. Here are some of the lessons I noticed.

• The critical role of mentoring. All the authors stressed the importance of having supportive, inspirational mentors early in their career, and the satisfaction of mentoring their own students.
• Crucial advances grow out of discussions at scientific meetings. Clearly the opportunity to travel and attend meetings is a part of a scientist’s career that’s highly valued, and often leads to new research directions and collaborations.
• The division of their duties into three parts: research, teaching, and clinical work. The variety that arises from having these three different tasks keeps a medical physicist’s job from ever becoming dull or routine.
• Leading scientific societies. The American Association of Physicists in Medicine (AAPM), the American Society for Radiation Oncology (ASTRO), the International Organization for Medical Physics (IOMP), and others professional groups are mentioned over and over by these authors.
• The challenge of the American Board of Radiology (ABR) exams. Today, these certification exams act as a gateway to a career in clinical medical physics.
• The interdisciplinary nature of medical physics. Many of these authors brought expertise from one field (say, computer programming) and integrated that knowledge with other fields (say, anatomy or medical imaging). 
• Failures are opportunities. These scientists had their share of setbacks, but managed to overcome them and use them as springboards to success. They persisted.
  
• The role of industry in medical physics research. Many authors tell stories of interacting with for-profit companies making imaging or therapy devices. Working with industry can be complicated and aggravating, but when successful the resulting products can have a huge impact on medical practice.
• Science is an international activity. Many authors had collaborators and students from all over the world, leading to lifelong friendships.
  

True Tales of Medical Physics illustrates what a career in medical physics is like better than any textbook can (even IPMB!). Some of the authors worked on old, now obsolete devices—colbalt-60 radiation therapy, the betatron, film/screen cassettes—but they also helped develop today’s cutting edge technologies: computed tomography (CT), intensity-modulated radiation therapy (IMRT), magnetic resonance imaging (MRI), and medical ultrasound (US). These authors worked at leading medical institutions, such as the Memorial Sloan Kettering Cancer Center and the MD Anderson Cancer Center. Many were included in the IOMP’s 50th anniversary list of 50 medical physicists who have made an outstanding contribution to the advancement of medical physics over the last 50 years (I can’t help but compare this to the list of the 50 greatest basketball players prepared by the National Basketball Association on their 50th anniversary).

While I enjoyed all the chapters in True Tales, my favorite was by Marcel van Herk, a Steve Wozniak-like Dutch electronics guru. He started out as a 12-year-old hobbyist who built his own computer. Van Herk writes “One of the first things I did was to design and build a completely functional relay-based full adder (a circuit that can add two 4-bit binary numbers), soldered together while listening to Black Sabbath’s Iron Man in the living room, not totally to my mother’s liking due to the music and the spilled solder on the carpet. The parts I used were small electromechanical relays from 1950 punched card sorting machines, acquired cheaply.” He ended up developing software for the Elekta cone-beam CT imaging guidance system integrated with a medical linear accelerator. While his story is fascinating, it’s not uncommon; many of these scientists traveled individual, meandering paths into medical physics, taking them from a clueless neophyte to a giant in their field. A key lesson for students is that there’s no single route to success in science, and certainly not in medical physics.

If you are considering possible careers, I urge you to read True Tale of Medical Physics. It may change your life. You may change medicine.

Specific Heat Capacity

One of the most important parameters in thermodynamics is the specific heat capacity. In Chapter 3 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I define the specific heat capacity in this way:

Consider a system into which a small amount of heat Q flows. In many cases the temperature of the system rises [by an amount ΔT]… The heat capacity C of the system is defined as

                                        C = Q/ΔT .                 (3.39)

Heat capacity has units of J K^-1. It depends on the size of the object and the substance it is made of. The specific heat capacity, c, is the heat capacity per unit mass (J K⁻¹ kg⁻¹).

Air and Water,
by Mark Denny.

In Air and Water: The Biology and Physics of Life's Media, Mark Denny compares the specific heat capacity of life’s two most important substances.

The specific heat of air is 1006 J kg⁻¹ K⁻¹, a typical value for a gas… Water, however, … has a very high specific heat for a liquid… about 4200 J kg⁻¹ K⁻¹… It thus takes about four times as much heat to raise the temperature of a kilogram of water one degree as it does to raise the temperature of an equal mass of air.

A factor of four is significant, but frankly I would have expected an even bigger difference. The reason for the somewhat similar values of the specific heat capacity for air and water is that we are comparing heat capacity per unit mass. It may be more intuitive to compare heat capacity per unit volume. To convert from per kilogram to per cubic meter you must multiply the specific heat capacity per unit mass by the mass per unit volume, which is just the density, ρ. The density of air and water are very different. Air has a density of about 1.2 kg m⁻³, whereas water has a density of 1000 kg m⁻³.

We can express the specific heat capacity per unit volume as the product c times ρ. For air cρ is 1207 J K⁻¹ m⁻³ but for water cρ is 4,200,000 J K⁻¹ m⁻³. So water has a vastly higher specific heat capacity compared to air when expressed as per unit volume.

Denny says the same thing this way:

The relative similarity of specific heat between air and water can be misleading, however, because specific heat is measured on per-mass basis. One cubic meter of air weighs only about 1.2 kg, while a cubic meter of water weighs 1000 kg. It thus takes about 3500 times as much heat to raise the temperature of a given volume of water one degree as it does to raise the temperature of the same volume of air.

For similar volumes of air and water in thermal equilibrium, the heat stored in the air is negligible compared to that stored in the water. Biological tissue is mostly water, so that means air holds a lot less heat than tissue, per unit volume. This has implications for biological processes, such as heat exchange between air and tissue in the lungs.

Limping

In Chapter 1 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss biomechanics. One of our most important examples is the force on the hip.

The forces in the hip joint can be several times a person’s weight, and the use of a cane can be very effective in reducing them.

Indeed, a cane is very useful, as Russ and I show in Section 1.8 of IPMB. But what if you don’t have a cane handy, or if you prefer not to use one? You limp. In this post, we examine the biomechanics of limping.

When you limp, you lean toward the injured side to reduce the forces on the hip. The reader can analyze limping in this new homework problem.

Section 1.8

Problem 11 ½. The left side of the illustration below analyzes normal walking and reproduces Figures 1.11 and 1.12. The right side shows what happens when you walk with a limp. By leaning toward the injured side you reduce the distance between the hip joint and the body’s center of gravity, and your leg is more vertical than in the normal case.

Pertinent features of the anatomy of the leg: normal (left) and limping (right).

(a) Reproduce the analysis of Section 1.7 to calculate of the forces on the hip during normal walking using the illustration on the left. Begin by making a free-body diagram of the forces acting on the leg like in Figure 1.13. Then solve the three equations for equilibrium: one for the vertical forces, one for the horizontal forces, and one for the torques. Verify that the magnitude of the force on the hip joint is 2.4 times the weight of the body. 

(b) Reanalyze the forces on the hip when limping. Use the geometry and data shown in the illustration on the right. Assume that any information missing from the diagram is the same as for the case of normal walking; For example, the abductor muscle makes an angle of 70° with the horizontal for both the normal and limping cases. Draw a free-body diagram and determine the magnitude of the force on the hip joint in terms of the weight of the body.

I won’t solve the entire problem for you, but I’ll tell you this: limping reduces the force on the hip from 2.4 times the body weight in the normal case to 1.2 times the body weight in the case of limping. No wonder we limp! 

The main reason for the lower force when limping is the smaller moment arm. If we calculate torques about the head of the femur, then in the normal case the moment arm for the force that the ground exerts on the foot is 18 – 7 = 11 cm. When limping, this moment arm reduces to 9 – 7 = 2 cm. The moment arm for the abductor muscles (the gluteus minimus and gluteus medius) is the same in the two cases. Therefore, rotational equilibrium can be satisfied with a small muscle force when limping, although a large muscle force is required normally. The torque is a critical concept for understanding biomechanics.

What do you do if both hips are injured? When walking, you first lean to one side and then the other; you waddle. This reduces the forces on the hip, but results in a lot of swinging from side to side as you walk.

If you are having trouble solving this new homework problem, contact me and I’ll send you the solution. 

Enjoy!

The Genetics of Cystic Fibrosis

In Appendix H of Intermediate Physics for Medicine and Biology, Russ Hobbie and I briefly mention the severe lung disease cystic fibrosis. Analyzing this disease provides an opportunity to examine the prevalence of a genetic disorder. I’ll do this by creating a new homework problem.

Appendix H

Problem 5 ½. About 1 in every 2500 people is born with cystic fibrosis, an autosomal recessive disorder. What is the probability of the gene responsible for cystic fibrosis in the population? What fraction of the population are carriers of the disease?

To answer these questions, first we must know that an “autosomal recessive disorder” is one in which you only get the disease if you have two copies of a recessive gene. To a first approximation, there are often two variants (or alleles) of a gene governing a particular protein: dominant (A) and recessive (a). In order to have cystic fibrosis, you must have two copies of the recessive allele (aa). If you have only one copy (Aa), you are healthy but are a carrier for the disease: your children could potentially get the disease if your mate is also a carrier. If you have no copies of the recessive allele (AA) then you’re healthy and your children will also be healthy.

Let’s assume the probability of the dominant allele is p, and the probability of the recessive allele is q. Since we assume there are only two possibilities, we know that p + q = 1. Our goal is to find q, the probability of the gene responsible for cystic fibrosis in the population.

When two people mate, they each pass on to their offspring one of their two copies of the gene. The probability that both parents are dominant (AA), so the child is normal, is p². The probability that both parents are recessive (aa), so the child has the disease, is q². There are two ways for the child to be a carrier: A from dad and a from mom, or a from dad and A from mom. So, the probability of a child being a carrier (Aa) is 2pq. There are only three possibilities or genotypes: AA, Aa, and aa. The sum of their probabilities must equal one: p² + 2pq + q² = 1. But this expression is equivalent to (p + q)² = 1, and we already knew that p + q = 1, so the result isn’t surprising.

The only people that suffer from cystic fibrosis have the genotype aa, so q² is equal to the fraction of people with the disease. The problem states that this fraction is 1/2500 (0.04%). So, q is the square root of 1/2500, or 1/50 (2%; wasn’t that nice of me to make the fraction be the reciprocal of a perfect square?). One out of every fifty copies of the gene governing cystic fibrosis is defective (that is, it is the recessive version that can potentially lead to the disease). If q is 1/50, then p is 49/50 (98%). The fraction of carriers is 2pq, or 3.92%. The only reason this result is not exactly 4% is that we don’t count someone with the disease (aa) as a carrier, even though they could pass the disease to their children (a carrier by definition has the genotype Aa). If we are rounding off our result to the nearest percent, then 1 out of every 25 people (4% of the population) are carriers.

This calculation is based on several assumptions: no natural selection, no inbreeding, and no selection of embryos based on genetic testing. Cystic fibrosis is such a severe disease that often victims don’t survive long enough to have children (modern medicine is making this less true). The untreated disease is so lethal that one wonders why natural selection didn’t eliminate it from our gene pool long ago. One possible reason is that carriers of cystic fibrosis might be better able to resist other diseases—such as cholera, typhoid fever, or tuberculosis—than are normal people. 

A nice discussion of cystic fibrosis.
https://www.youtube.com/watch?v=QfjIGXNey3g

 

 

This video from the Cystic Fibrosis Foundation suggests that gene editing may cure cystic fibrosis. https://www.youtube.com/watch?v=nWj7Be6PSS4

Roger Bacon, Biological Physicist

The Story of Civilization,
by Will and Ariel Durant.

About a year ago I began reading the eleven-volume series The Story of Civilization by Will and Ariel Durant. I just finished Volume 4, The Age of Faith. A History of Medieval Civilization—Christian, Islamic, and Judaic—from Constantine to Dante: A.D. 325–1300. Of course, I’m always on the lookout for how a book overlaps with Intermediate Physics for Medicine and Biology. In The Age of Faith I found a scholar from the Middle Ages who might qualify as a biological physicist: Roger Bacon. Durant writes (citations removed)

VII. ROGER BACON: c. 1214–92

The most famous of medieval scientists was born in Somerset about 1214. We know that he lived till 1292, and that in 1267 he called himself an old man. He studied at Oxford under Grosseteste, and caught from the great polymath a fascination for science; already in that circle of Oxford Franciscans the English spirit of empiricism and utilitarianism was taking form. He went to Paris about 1240, but did not find there the stimulation that Oxford had given him…

Bacon is known for his support of the role of experiment in science. So much of medieval thought was based on religion and mysticism, and an emphasis on science and experiment is refreshing.

We must not think of him [Bacon] as a lone originator, a scientific voice crying out in the scholastic wilderness. In every field he was indebted to his predecessors, and his originality was the forceful summation of a long development. Alexander Neckham, Bartholomew the Englishman, Robert Grosseteste, and Adam Marsh had established a scientific tradition at Oxford; Bacon inherited it, and proclaimed it to the world. He acknowledged his indebtedness, and gave his predecessors unmeasured praise. He recognized also his debt—and the debt of Christendom—to Islamic science and philosophy, and through these to the Greeks…

Like Russ Hobbie and I, Bacon appreciated the role of math in science. Durant summarized Bacon’s view as “though science must use experiment as its method, it does not become fully scientific until it can reduce its conclusions to mathematical form.”

Bacon’s work on optics and vision overlaps with topics in IPMB. Durant notes that “one result of these studies in optics [performed by Bacon and others] was the invention of spectacles.” I can hardly think of a better example of physics interacting with physiology than eyeglasses. Durant concludes:

Experimenting with lenses and mirrors, Bacon sought to formulate the laws of refraction, reflection, magnification, and microscopy. Recalling the power of a convex lens to concentrate many rays of the sun at one burning point, and to spread the rays beyond that point to form a magnified image, he wrote:

We can so shape transparent bodies [lenses], and arrange them in such a way with respect to our sight and the objects of vision, that the rays will be refracted and bent in any direction we desire; and under any angle we wish we shall see the object near or at a distance. Thus from an incredible distance we might read the smallest letters…

These are brilliant passages. Almost every element in their theory can be found before Bacon, and above all in al-Haitham [an Arab scientist also known as Alhazen]; but the material was brought together in a practical and revolutionary vision that in time transformed the world. It was these passages that led Leonard Digges (d. c. 1571) to formulate the theory of which the telescope was invented.

I enjoy reading the Durants’ books. They contain not only the usual political and military history of the world, but also the history of science, art history, music history, comparative religion, linguistics, the history of medicine, philosophy, and literature. While The Story of Civilization may not be the definitive source on any of these topics, it is the best integration of all of them into one work that I am aware of. Had the Durants lived longer, future volumes (which they tentatively titled The Age of Darwin and The Age of Einstein) might have focused even more on the role of science in civilization. 

I won’t finish The Story of Civilization anytime soon; I still have seven volumes to go. The series runs to over ten thousand pages, single-spaced, small font (I had to buy more powerful reading glasses for this project). I’ll continue to search for discussions of medical physics and biological physics throughout.

Now, on to The Renaissance. 

The Story of Civilization. 1. Our Oriental Heritage, 2. The Life of Greece, 3. Caesar and Christ, 4. The Age of Faith, 5. The Renaissance, 6. The Reformation, 7. The Age of Reason Begins, 8. The Age of Louis XIV, 9. The Age of Voltaire, 10. Rousseau and Revolution, and 11. The Age of Napoleon.

 

In Our Time: Season 19/Episode 30, Roger Bacon (April 20, 2017)

https://www.youtube.com/watch?v=i3riF-F7hGY

 

The Durants—Will & Ariel Durant: The Story of Civilization Documentary.

https://www.youtube.com/watch?v=Jc8aFTuCAu0