Intermediate Physics for Medicine and Biology | |||||
Bradley J. Roth |
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| The list author says: “Books that are cited by the 4th edition of Intermediate Physics for Medicine and Biology. These are some of the best biological and medical physics books I know of, and are books that have been useful to me during my career.” | |||||
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![Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables [Applied Mathematics Series 55]](https://images-na.ssl-images-amazon.com/images/I/41gJxuCCKuL._SL110_.jpg) |
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| Radiobiology for the Radiologist, by Eric Hall and Amato Giaccia. |
This section provides a brief introduction to radiobiology, but it ignores many important details. For these details see Hall and Giaccia (2012).Radiobiology for the Radiologist, by Eric Hall and Amato Giaccia, is a leading graduate textbook in radiology and medical physics. It analyzes the “four Rs” of radiobiology:
A modest dose of x-rays to a mixed population of aerated and hypoxic cells results in significant killing of aerated cells but little killing of hypoxic cells. Consequently, the viable cell population immediately after irradiation is dominated by hypoxic cells. If sufficient time is allowed before the next radiation dose, the process of reoxygenation restores the proportion of hypoxic cells to about 15%. If this process is repeated many times, the tumor cell population is depleted, despite the intransigence to killing by x-rays of the cells deficient in oxygen.They later use the four Rs to summarize why fractions are important during radiotherapy.
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.I like the colorful figures in Hall and Giaccia's book. For instance, is that French ram wearing a beret?
The advantages of prolongation of treatment are to spare early reactions and to allow adequate reoxygenation in tumors. Excessive prolongation, however, allows surviving tumor cells to proliferate during treatment.
Section 17.12
Problem 57 1/2. Estimate the annual effective dose (in Sv yr-1) if the air contains a trace of radon. Use the data in Fig. 17.27, and assume the concentration of radon corresponds to an activity of 150 Bq m-3, which is the action level at which the Environmental Protection Agency suggests you start to take precautions. Make reasonable guesses for any parameters your need.Here is my solution (stop reading now if you first want to solve the problem yourself). In order to be accessible to a wide audience, I avoid jargon and unfamiliar units.
One bequerel is a decay per second, and a cubic meter is 1000 liters, so we start with 0.15 decays per second per liter. The volume of air in your lungs is about 6 liters, implying that approximately one atom of radon decays in your lungs every second.This all seems nice and logical, except the result is a factor of ten too low! It is probably even worse than that, because my initial radon concentration was higher than average and in Table 16.6 of IPMB Russ Hobbie and I report a value of 2.28 mSv for the average annual effective dose. My calculation here is an estimate, so I don’t expect the answer to be exact. But when I saw such a low value I was worried and started to read some of the literature about radon dose calculations. Here is what I learned:
Radon decays by emitting an alpha particle. You don’t, however, get just one. Radon-222 (the most common isotope of radon) alpha-decays to polonium-218, which alpha-decays to lead-214, which beta-decays twice to polonium-214, which alpha-decays to lead-210 (see Fig 17.27 in Intermediate Physics for Medicine and Biology). The half-life of lead-210 is so long (22 years) that we can treat it as stable. Each decay of radon therefore results in three alpha particles. An alpha particle is ejected with an energy of about 6 MeV. Therefore, roughly 18 MeV is deposited into your lungs each second. If we convert to SI units (1 MeV = 1.6 × 10-13 joule), we get about 3 × 10-12 joules per second.
Absorbed dose is expressed in grays, and one gray is a joule per kilogram. The mass of the lungs is about 1 kilogram. So, the dose rate for the lungs is 3 × 10-12 grays per second. To find the annual dose, multiply this dose rate by one year, or 3.2 × 107 seconds. The result is about 10-4 gray, or a tenth of a milligray per year.
If you want the equivalent dose in sieverts, multiply the absorbed dose in grays by 20, which is the radiation weighting factor for alpha particles. To get the effective dose, multiply by the tissue weighting factor for the lungs, 0.12. The final result is 0.24 mSv per year.
Various radioisotopes, such as 99mTc (half-life 6.02 h [hours]), 201Tl [thallium-201] (half-life 3.04 d [days]), and 133Xe [xenon-133] (half-life 5.27 d), are used for single-photon emission computed tomography (SPECT) in medical diagnostic scans. In particular, 99mTc has become the most important medical radioisotope at present… Over 30 commonly used radiopharmaceuticals are based on 99mTc [for example, 99mTc–sestamibi, 99mTc–tetrofosmin, and 99mTc-exametazime]... The 99mTc radioisotopes are supplied by 99Mo/99mTc generators, which continuously generate 99mTc through the β-decay of the parent nucleus 99Mo [molybdenum-99 is trapped in alumina (Al2O3) where it decays to pertechnetate (TcO4-); eluting solution flowing through the alumina collects the 99mTc]... This supply method provides two excellent advantages. First, it is possible to transport 99Mo/99mTc generators from a production facility to any place in the world because the half-life of 99Mo is... 2.75 d. Second, when a 99Mo/99mTc generator is transported to a hospital, 99mTc can be produced fresh for up to 2 weeks by daily milking/elution from this 99Mo/99mTc generator. At present, the parent nucleus 99Mo is produced in nuclear reactors by the neutron-induced fission of 235U [uranium-235] in highly enriched uranium (HEU) targets, in which the fraction of 235U is approximately 90%. However, some nuclear reactors that have supplied 99Mo require major repairs or shutdown [for example, the Chalk River reactor in Ontario, Canada], which may lead to a 99mTc shortage. Thus, many alternative methods to produce 99Mo or 99mTc [such as in a cyclotron] without HEU have been proposed…
The September 11th terrorist attacks in Washington D.C. [these attacks actually took place in New York City, at the Pentagon in Arlington County Virginia, and near Shanksville, Pennsylvania] in 2001 also affected medical radioisotope production from the viewpoint of the safeguards of nuclear materials. The control of fissionable nuclides such as 235U and 239Pu [plutonium-239] is important for the safeguards of nuclear materials… The International Atomic Energy Agency (IAEA) hopes to discontinue 99mTc production using HEU targets, which can be transmuted into nuclear weapons... In the near future, 99mTc will be supplied by nuclear reactors using LEU [low-enriched uranium] targets in addition to HEU. The Nuclear Energy Agency (NEA) reported the prediction that the 99Mo/99mTc supply will be larger than the world demand when the scheduled nuclear reactors using LEU start 99Mo production…
Because the Tc [technitium] chemistry is the same, all the radiopharmaceuticals based on 99mTc can, in principle, be applied to other Tc isotopes. There are five Tc isotopes with half-lives in the range from hours to days: 94mTc (half-life 52 m [minutes]), 94gTc (half-life 4.88 h), 95mTc (half-life 60 d), 95gTc (half-life 20 h), and 96gTc (half-life 4.28 d) [superscript “g” stands for ground state, whereas superscript “m” stands for metastable excited state]… The half-life of 96gTc (4.28 d) is long enough for worldwide delivery from a production facility and lengthy use of up to 2 weeks in hospitals. 95gTc (20 h) can also be transported to a wide area and used for 3–5 days in hospitals. Thus, 95gTc and 96gTc are candidates for alternative γ-ray emitters. However, the decay rates of 95gTc and 96gTc are lower than that of 99mTc by a factor of 3.3 and 17, respectively, because the decay rate of a radioisotope is inversely proportional to its half-life. This fact leads to the question of whether these isotopes can work as 99mTc medical radioisotopes.
In the current study, we present the relative γ-ray flux of these isotopes with simple assumptions. We also estimate the patient radiation does [dose] per Tc-labeled tracer using… PHITS [Particle and Heavy Ion Transport code System, a general purpose Monte Carlo particle transport simulation code]... Various nuclear reactions that are production methods of Tc isotopes, such as (p, n) reactions [in which a proton enters the nucleus and a neutron leaves it]…, deuteron [hydrogen-2]-induced reactions…, and 96Ru [ruthenium-96] (n, p)96gTc reactions…, were studied. We consider the production by the (p, n) reaction on an enriched Mo isotope. We also calculate the production rate using a typical PET [positron emission tomography] medical cyclotron [If you must make 96gTc in a cyclotron, why not make 99mTc in the cyclotron instead?]. Because the energies of decay γ-rays of these Tc isotopes are typically higher than 200 keV, they are not suitable for the traditional SPECT cameras. Thus, we also discuss the property of possible ETCC [Electron-Tracking Compton Camera] for high energy γ-rays.
The developing human brain remains one of the few unsolved mysteries of science. Advancements in developmental biology, neuroscience, and medical imaging have brought us closer than ever to understand brain development in health and disease. However, the precise role of mechanics throughout this process remains underestimated and poorly understood. Here we show that mechanical stretch plays a crucial role in brain development. Using the nonlinear field theories of mechanics supplemented by the theory of finite growth, we model the human brain as a living system with a morphogenetically growing outer surface and a stretch-driven growing inner core. This approach seamlessly integrates the two popular but competing hypotheses for cortical folding: axonal tension and differential growth. We calibrate our model using magnetic resonance images from very preterm neonates. Our model predicts that deviations in cortical growth and thickness induce morphological abnormalities. Using the gyrification index, the ratio between the total and exposed surface area, we demonstrate that these abnormalities agree with the classical pathologies of lissencephaly and polymicrogyria. Understanding the mechanisms of cortical folding in the developing human brain has direct implications in the diagnostics and treatment of neurological disorders, including epilepsy, schizophrenia, and autism.I also enjoyed a physics colloquium about “Motifs in Morphogenesis” by Lakshminarayanan Mahadevan of Harvard University. I liked how he presented simple, toy models that illustrate development (my type of physics). Mahadevan is a MacArthur “Genius Grant” Fellow, and I can see why. Great talk.
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| On Growth and Form, by D'Arcy Wentworth Thompson. |
Morphogenesis, the study of how forms arise in biology, has attracted scientists for aeons. A century ago, D'Arcy Wentworth Thompson crystallized this question in his opus On Growth and Form (Thompson, 1917) using a series of biological examples and geometric and physical analogies to ask how biological forms arise during development and across evolution. In light of the advances in molecular and cellular biology since then, a succinct modern view of the question states: how do genes encode geometry?...I had never been to Princeton University, so during lunch breaks I snuck out to look around the campus. It is beautiful (even in February), with many historical buildings. I particularly liked the gorgeous chapel, shown below.
On Growth and Form raised the question of the origin of biological shape in a physical framework. Since then, advances in our understanding of the biochemical basis of the laws of heredity have provided the modern conceptual understanding for how shapes develop anew at each generation, from a single cell – thus surviving the death of an individual through its offspring. As this Special Issue illustrates, we are now beginning to understand how genes encode geometry. As morphology both enables and constrains function, a natural next question is how biology creates functional (and plastic) shape that begins to link morphology to physiology and behaviour. As you mull this question, we would like to thank all the authors and referees of the articles in this Special Issue for their contributions, and we hope you enjoy reading it!
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| Princeton University Chapel |
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| Pyne Hall |
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| Alexander Hall |
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| Joseph Henry electromagnet displayed in Jadwin Hall. |
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| My poster with Debabrata Auddya. |
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| My poster with graduate student Kharananda Sharma. |
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| Molecular Biology of the Cell, by Bruce Alberts et al. |
Cellular DNA is organized into chromosomes.… Figure 16.30 shows, at different magnifications, a strand of DNA, various intermediate structures that we will not discuss, and a chromosome as seen during the M phase of the cell cycle. The size goes from 2 nm for the DNA double helix to 1400 nm for the chromosome.Figure 16.30 in IPMB is an illustration from the book Molecular Biology of the Cell by Bruce Alberts and his coauthors. This acclaimed textbook is currently in its 6th edition (2014). The Oakland University library has the 5th edition (2008), which I quote in this blog post.
Figure 4-72 Chromatin packing. This model shows some of the many levels of chromatin packing postulated to give rise to the highly condensed mitotic chromosome.Alberts et al. state at the start of their Chapter 4
In this chapter we begin by describing the structure of DNA. We see how, despite its chemical simplicity, the structure and chemical properties of DNA make it ideally suited as the raw material of genes. We then consider how the many proteins in chromosomes arrange and package this DNA. The packing has to be done in an orderly fashion so that the chromosomes can be replicated and apportioned correctly between the two daughter cells at each cell division. It must also allow access to chromosomal DNA for the enzymes that repair it when it is damaged and for the specialized proteins that direct the expression of its many genes. We shall also see how the packaging of DNA differs along the length of each chromosome in eucaryotes, and how it can store a valuable record of the cell’s developmental history.One of the most interesting feature of this figure is the “beads-on-a-string” appearance of chromatin. Alberts et al. write
The proteins that bind to DNA to form eukaryotic chromosomes are traditionally divided into two general classes: the histones and the nonhistone chromosomal proteins. The complex of both classes of protein with the nuclear DNA of eukaryotic cells is known as chromatin. Histones are present in such enormous quantities in the cell (about 60 million molecules of each type per human cell) that their total mass in chromatin is about equal to that of the DNA.For those who prefer videos over text and illustrations, below are two movies about how DNA is packaged in a cell.
Histones are responsible for the first and most basic level of chromosome packing, the nucleosome, a protein-DNA complex discovered in 1974. When interphase nuclei are broken open very gently and their contents examined under the electron microscope, most of the chromatin is in the form of a fiber with a diameter of about 30 nm (Figure 4-22A). If this chromatin is subjected to treatments that cause it to unfold partially, it can be seen under the electron microscope as a series of “beads on a string” (Figure 4-22B). The string is DNA, and each bead is a “nucleosome core particle” that consists of DNA wound around a protein core formed from histones.
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| Physics Today article about the Digital Library of Mathematical Functions. |
One classic scientific reference that the revolution [in online information] has radically affected is the Handbook of Mathematical Functions, familiarly known as A+S, edited by Milton Abramowitz and Irene Stegun. In this article we discuss how A+S was transformed into an online 21st-century resource known as the Digital Library of Mathematical Functions, or DLMF, and how that new, modern resource makes far more information available to users in ways that are quite different from the past. The DLMF also contains far more material—in many cases updated—than does A+S.
We invite readers to explore the library: Hover the mouse over intriguing objects, symbols, and graphics to see behind the scenes. Open the info boxes to see what other possibly useful data may be available. We believe that the library will prove as useful to scientists and engineers of today and tomorrow as A+S has been since 1964.I’m a scientist of the past, so I’m keeping my paper copy of Abramowitz and Stegun; I love the feel of the pages as I thumb through then, and I even like the smell of it. But readers of IPMB are scientists of the future, and for them I recommend NIST’s Digital Library of Mathematical Functions.
