Protons are also used to treat tumors (Khan 2010, Ch.
26; Goitein 2008). Their advantage is the increase of stopping power at low energies. It is possible to make them
come to rest in the tissue to be destroyed, with an enhanced
dose relative to intervening tissue and almost no dose distally
(“downstream”) as shown by the Bragg peak in Fig.16.47.
Energy loss versus depth for a 150 MeV proton beam in water, with and
without straggling (fluctuations in the range). The Bragg peak enhances
the energy deposition at the end of the proton range. Adapted from Fig.
16.47 in Intermediate Physics for Medicine and Biology.
In December 1904, William Henry Bragg, Professor of
Mathematics and Physics at the University of Adelaide and
his assistant Richard Kleeman published in the Philosophical
Magazine (London) novel observations on radioactivity.
Their paper “On the ionization of curves of radium,” gave
measurements of the ionization produced in air by alpha particles, at varying distances from a very thin source of
radium salt. The recorded ionization curves “brought to light
a fact, which we believe to have been hitherto unobserved. It
is, that the alpha particle is a more efficient ionizer towards the
extreme end of its course.” This was promptly followed
by further results in the Philosophical Magazine in 1905.
Their finding was contrary to the accepted wisdom of the
day, viz. that the ionizations produced by alpha particles
decrease exponentially with range. From theoretical considerations,
they concluded that an alpha particle possesses a
definite range in air, determined by its initial energy and
produces increasing ionization density near the end of its
range due to its diminishing speed.
Although Bragg discovered the Bragg peak for alpha particles, the same behavior is found for other heavy charged particles such as protons. It is the key concept underlying the development of proton therapy. Brown and Suit conclude
The first patient treatment by charged particle therapy
occurred within a decade of Wilson’s paper [the first use of protons in therapy, published in 1946]. Since then, the
radiation oncology community has been evaluating various
particle beams for clinical use. By December 2004, a
century after Bragg’s original publication, the approximate
number of patients treated by proton–neon beams is 47,000
(Personal communication, Janet Sisterson, Editor, Particles) [over 170,000 today].
There have been several clear clinical gains. None
of these would have been possible, were it not for the
demonstration that radically different depth dose curves
were feasible.
Let’s examine Magee’s fall using elementary physics. Homework Problem 29 in Chapter 2 of Intermediate Physics for Medicine and Biology explains how someone falling through the air reaches a steady-state, or terminal, speed. A typical terminal speed, v, when skydiving is about 50 m/s. This may be a little slower than average, but v decreases with mass and ball turret gunners like Magee were usually small. Skydivers will reach their terminal speed after about 20 seconds. Magee fell for much longer than that, so starting four miles up didn’t matter. He could have begun forty miles up and his terminal speed would have been the same (presumably he would have suffocated, but that’s another story).
When falling, what kills you is the sudden deceleration when you hit the ground. Suppose you’re traveling at v = 50 m/s and you hit a hard surface like cement. You come to a stop over a distance, h, of a few centimeters (a person isn’t rigid, so there would be some distance that corresponds to the body splatting). Let’s estimate 10 cm, or h = 0.1 m. If the acceleration, a, is uniform, we can use an equation from kinematics to calculate a from v and h: a = v2/(2h) = 502/0.2 = 12,500 m/s2. This is about 1250g, where g is the acceleration of gravity (approximately 10 m/s2).
How much acceleration can a person survive? It’s hard to say. Some roller coasters can accelerate at up to 3g and you feel a thrill. Astronauts in the Mercury space program experienced about 10g during reentry and they survived. Flight surgeon John Stapp withstood 46g on a rocket sled, but that is probably near the maximum. Clearly 1250g is well over the threshold of survivability. You would die.
So, how did Magee survive? He didn’t hit cement. Instead, he crashed through the glass ceiling of the St. Nazaire railroad station. Most sources I’ve read claim that shattering the glass helped break his fall. Maybe, but I have another idea. Some of the articles I’ve examined have German soldiers finding Magee alive on the station floor, but others say he was found tangled in steel girders. Below is a picture of the railroad station as it looked during World War II.
Notice the structures below the glass ceiling. I wouldn’t call them girders or struts. To me they look like a web of steel cables or ties. My hypothesis is that this web functioned as a net. Suppose Magee landed on one of the ties and it deflected downward, perhaps dragging part of the ceiling with it, or pulling down other ties, or breaking at one end, or stretching like a bungee cord. All this pulling and breaking and stretching would reduce his deceleration. Let’s guess that he came to rest about three meters below where he first hit a tie. Now his acceleration (assuming it’s uniform) is a = 502/6 = 417 m/s2, or about 42g. That’s a big deceleration, but it may be survivable. You would expect him to be hurt, and he was; he suffered from several broken bones, damage to a lung and kidney, and a nearly severed arm.
If my hypothesis is correct, the shattering of glass had little or nothing to do with breaking Magee’s fall. I’m sure it made a loud noise, and must have given the accident a dramatic flair, but the glass ceiling may have been irrelevant to his survival.
I don’t think we can ever know for sure why Magee didn’t die, short of building a replica of the train station, dropping corpses (or, more hygienically, crash dummies) through the roof, and video recording their fall. Still, it’s fun to speculate.
After the crash, what happened to Magee? He was captured, became a prisoner of war, and was treated for his injuries. In May 1945 the war in Europe ended and he was freed. He returned to the United States and lived another 58 years. He was awarded the Air Medal and a well-earned Purple Heart. Alan Magee's survival represents a fascinating example of physics applied to medicine and biology.
Triumph of Victory. A reenactment of Alan Magee’s fall.
Russ Hobbie and I don’t discuss Cerenkov Luminescence Imaging in Intermediate Physics for Medicine and Biology, but you can learn a lot about it using the physics we do discuss. For example, can particles travel faster than the speed of light? They can’t travel faster than the speed of light in a vacuum, but they can travel faster than the speed of light in a material such as water or tissue where light is slowed and the medium has an index of refraction. Below is a new homework problem, in which we consider electrons emitted in tissue by beta decay of the isotopeiodine-131, used in many medical applications.
Problem 9 ¼. The end point kinetic energy (see Fig. 17.8) for beta decay of 131I is 606 keV, and tissue has an index of refraction of 1.4. Do any of the emitted electrons have a speed faster than the speed of light in the tissue? To determine this speed, use Eq. 14.1. Because the electrons move near the speed of light, to determine their speed as a function of their kinetic energy use a result from special relativity, Eq. 17.1.
For those who don’t have IPMB at your side (shame on you!), Eq. 14.1 is cn = c/n, where cn is the speed of light in the medium, c is the speed of light in a vacuum (3 × 108 m/s), and n is the index of refraction, and Eq. 17.1 is T + mc2 = mc2/√(1 − v2/c2), where v is the speed of the particle, T is its kinetic energy, and mc2 is the rest mass of an electron expressed as energy (511 keV).
If you solved this problem correctly, you found that some of the more energetic electrons emitted during beta decay of 131I do travel faster than the speed of light in tissue.
Cerenkov radiation is emitted at an angle θ with respect to the direction that the particle is moving. This distribution of light is characteristic of a shock wave, and is similar to the distribution of sound in a sonic boom made by a plane when it flies faster than the speed of sound. The new problem below requires the reader to calculate θ.
Problem 9 ½. The drawing below shows a particle moving to the right faster than the speed of light in the medium. The position of the particle at several instants is indicated by the purple dots. The location of light emitted by the particle at each position is shown by the black circles. The light adds to form a conical wave front, shown by the green lines.
(a) Use the red right triangle to calculate the angle θ as a function of the particle speed, v, and the index of refraction, n.
(b) Compute the value of θ for the fastest electrons emitted by beta decay of 131I in tissue.
The number of photons emitted tends to be greatest at short wavelengths, so Cerenkov radiation often has a blue tinge. However, readers of IPMB learned in Chapter 14 that the spectrum of radiation can look different when viewed as a function of frequency (or energy) rather than as a function of wavelength. Below is a new problem to explore this effect.
Problem 9 ¾. The number of photons dN emitted with a wavelength between λ and λ + dλ is approximately
dN = Cdλ/λ2, where C is a constant.
(a) Sketch a plot of dN/dλ versus λ. Don’t worry about the scale of the axes (in other words, don't worry about the value of C); just make the plot qualitatively correct.
(b) Use methods similar to those introduced in Section 14.8 to determine the number of photons emitted with an energy between E and E + dE. Don’t worry about constant factors, just determine how dN/dE varies with E.
(c) Sketch a plot of dN/dE versus E. Again, just make the plot qualitatively correct.
If you solved part (c) correctly, you should have drawn a plot with a flat line, because dN/dE is independent of E. Of course, there must be some limits to this result, otherwise the particle would emit an infinite amount of energy when integrated over all photon energies. See Ciarrocchi and Belcari’s review for an explanation.
Perhaps the most interesting part of Ciarrocchi and Belcari’s article is their discussion of biomedical applications. You can use Cerenkov radiation to image beta emitters like 131I, positron emitters like 18F used in positron emission tomography, and high-energy protons required for proton therapy.
To learn more about Cerenkov radiation, watch this video by Don Lincoln. Enjoy!
Science-Based Medicine is dedicated to evaluating medical treatments and products of interest to the public in a scientific light, and promoting the highest standards and traditions of science in health care. Online information about alternative medicine is overwhelmingly credulous and uncritical, and even mainstream media and some medical schools have bought into the hype and failed to ask the hard questions.
We provide a much needed “alternative” perspective—the scientific perspective.
Good science is the best and only way to determine which treatments and products are truly safe and effective. That idea is already formalized in a movement known as evidence-based medicine (EBM). EBM is a vital and positive influence on the practice of medicine, but it has limitations and problems in practice: it often overemphasizes the value of evidence from clinical trials alone, with some unintended consequences, such as taxpayer dollars spent on “more research” of questionable value. The idea of SBM is not to compete with EBM, but a call to enhance it with a broader view: to answer the question “what works?” we must give more importance to our cumulative scientific knowledge from all relevant disciplines.
How do we separate the wheat from the chaff? It’s not easy. Reading Intermediate Physics for Medicine and Biology is a good place to start. Many of these readers would benefit from a short course about science-based medicine. Does such a course exist? Yes! Harriet Hall (the SkepDoc, who I discussed previously in this blog) has recorded a series of ten videos about science-based medicine. She debunks much of the nonsense out there. Below, I link to the videos. Your homework assignment is to watch them.
If the coronavirus pandemic has taught us anything, it’s that we must base medicine on science.
Lecture 1: Science-based medicine versus evidence-based medicine
Like the cardiac pacemaker, the Inspire device is implanted in the upper chest. Instead of monitoring the electrocardiogram, the device monitors breathing; instead of stimulating the heart, it stimulates the hypoglossal nerve controlling muscles in the tongue.
A patient with obstructive sleep apnea has their airway blocked while sleeping, causing the body to crave oxygen. This results in a brief reawakening as the person opens their airway for better airflow. Once oxygen is restored, the patient goes back to sleep. Then, the entire process starts again, so sleep is frequently and repeatedly interrupted.
One way to treat obstructive sleep apnea is using continuous positive airway pressure (CPAP), which requires wearing a mask attached by a hose to a pump. Some people can’t or won’t tolerate CPAP, and it’s hard to imagine that anyone likes it.
When Inspire detects that you’re taking a breath it stimulates the tongue to contract, opening the airway. You only need it when sleeping, so it has a button you can push to turn it on before bed and turn it off when you wake up.
Inspire is yet one more example of how physics can be applied to medicine, and in particular how electrical stimulation can be used to treat patients. I’m into it.
“The Bidomain Model of Cardiac Tissue: Predictions and Experimental Verification” was submitted to the editors in January, 1993. Alas, the book was never published. However, I still have a copy of the chapter, and you can download it here. Now—after nearly thirty years—it’s obsolete, but provides a glimpse into the pressing issues of that time.
I was a impudent young buck back in those days. Three times in the chapter I recast the arguments of other scientists (my competitors) as syllogisms. Then, I asserted that their premise was false, so their conclusion was invalid (I'm sure this endeared me to them). All three syllogisms dealt with whether or not cardiac tissue could be treated as a continuous tissue, as opposed to a discrete collection of cells.
The Spach Experiment
The first example had to do with the claim by Madison Spach that the rate of rise of the cardiac action potential, and time constant of the action potential foot, varied with direction.
Continuous cable theory predicts that the time course of the action potential does not depend on differences in axial resistance with direction.
The rate of rise of the cardiac wave front is observed experimentally to depend on the direction of propagation.
Therefore, cardiac tissue does not behave like a continuous tissue.
I then argued that their first premise is incorrect. In one-dimensional cable theory, the time course of the action potential doesn’t depend on axial resistance, as Spach claimed. But in a three-dimensional slab of tissue superfused by a bath, the time course of the action potential depends on the direction of propagation. Therefore, I contended, their conclusion didn’t hold; their experiment did not prove that cardiac tissue isn’t continuous. To this day the issue is unresolved.
Defibrillation
A second example considered the question of defibrillation. When a large shock is applied to the heart, can its response be predicted using a continuous model, or are discrete effects essential for describing the behavior?
An applied current depolarizes or hyperpolarizes the membrane only in a small region near the ends of a continuous fiber.
For successful defibrillation, a large fraction of the heart must be influenced by the stimulus.
Therefore, defibrillation cannot be explained by a continuous model.
I argued that the problem is again with the first premise, which is true for tissue having “equal anisotropy ratios” (the same ratio of conductivity parallel and perpendicular to the fibers, in both the intracellular and extracellular spaces), but is not true for “unequal anisotropy ratios.” (Homework Problem 50 in Chapter 7 of IPMB examines unequal anisotropy ratios in more detail). If the premise is false, the conclusion is not proven. This issue is not definitively resolved even today, although the sophisticated simulations of realistically shaped hearts with their curving fiber geometry, performed by Natalia Trayanova and others, suggest that I was right.
Reentry Induction
The final example deals with the induction of reentry by successive stimulation through a point electrode. As usual, I condensed the existing dogma to a syllogism.
In a continuous tissue, the anisotropy can be removed by a coordinate transformation, so reentry caused by successive stimulation through a single point electrode cannot occur, since there is no mechanism to break the directional symmetry.
Reentry has been produced experimentally by successive stimulation through a single point electrode.
Therefore, cardiac tissue is not continuous.
Once again, that pesky first premise is the problem. In tissue with equal anisotropy ratios you can remove anisotropy by a coordinate transformation, so reentry is impossible. However, if the tissue has unequal anisotropy ratios the symmetry is broken, and reentry is possible. Therefore, you can’t conclude that the observed induction of reentry by successive stimulation through a point electrode implies the tissue is discrete.
I always liked this book chapter, in part because of the syllogisms, in part because of its emphasis on predictions and experiments, but mainly because it provides a devastating counterargument to claims that cardiac tissue acts discretely. Although it was never published, I did send preprints around to some of my friends, and the chapter took on a life of its own. This unpublished manuscript has been cited 13 times!
Winfree AT (1997) “Rotors, fibrillation, and dimensionality,” In: Holden AV, Panfilov AV (eds): Computational Biology of the Heart, Chichester, Wiley, Pages 101–135.
I’ll end with the closing paragraph of the chapter.
The bidomain model ignores the discrete nature of cardiac cells, representing the tissue as a continuum instead. Experimental evidence is often cited to support the hypothesis that the discrete nature of the cells plays a key role in cardiac electrophysiology. In each case, the bidomain model offers an alternative explanation for the phenomena. It seems wise at this point to reconsider the evidence that indicates the significance of discrete effects in healthy cardiac tissue. The continuous bidomain model explains the data, recorded by Spach and his colleagues, showing different rates of rise during propagation parallel and perpendicular to the fibers, anodal stimulation, arrhythmia development by successive stimulation from a point source, and possibly defibrillation. Of course, these alternative explanations do not imply that discrete effects are not responsible for these phenomena, but only that two possible mechanisms exist rather than one. Experiments must be found that differentiate unambiguously between alternative models. In addition, discrete junctional resistance must be incorporated into the bidomain model. Only when such experiments are performed and the models are further developed will we be able to say with any certainty that cardiac tissue can be described as a continuum.
Insulin was isolated and first used to treat diabetes in 1921, one hundred years ago. To celebrate this landmark, I will quote a few paragraphs from the section on blood hormones in Isaac Asimov’s A Short History of Biology.
The most spectacular early result of hormone work… was in connection with the disease, diabetes mellitus. This involved a disorder in the manner in which the body broke down sugar for energy, so that a diabetic accumulated sugar in his blood to abnormally high levels. Eventually, the body was forced to get rid of the excess sugar through the urine, and the appearance of sugar in the urine was symptomatic of an advanced stage of the disease. Until the twentieth century, the disease was certain death.
Suspicion arose that the pancreas was somehow connected with the disease, for in 1893, two German physiologists, Joseph von Mering (1849–1908) and Oscar Minkowski (1858–1931), had excised the pancreas of experimental animals and found that severe diabetes developed quickly. Once the hormone concept had been propounded by Starling and Bayliss, it seemed logical to suppose that the pancreas produced a hormone which controlled the manner in which the body broke down sugar.
Attempts to isolate the hormone from the pancreas… failed, however. Of course, the chief function of the pancreas was to produce digestive juices, so that it had a large content of protein-splitting enzymes. If the hormone were itself a protein (as, eventually, it was found to be) it would break down in the very process of extraction.
In 1920, a young Canadian physician, Frederick Grant Banting (1891–1941), conceived the notion of tying off the duct of the pancreas in the living animal and then leaving the gland in position for some time. The digestive-juice apparatus of the gland would degenerate, since no juice could be delivered, while those portions secreting the hormone directly into the blood stream would (he hoped) remain effective. In 1921, he obtained some laboratory space at the University of Toronto and with an assistant, Charles Herbert Best (1899–[1978]), he put his notion into practice. He succeeded famously and isolated the hormone “insulin.” The use of insulin has brought diabetes under control, and while a diabetic cannot be truly cured even so and must needs submit to tedious treatment for all his life, that life is at least a reasonably normal and prolonged one.
Charles Best and Frederick Banting, circa 1924, University of Toronto Library, from Wikipedia.
Where does physics, engineering, and technology enter this story? Consider the insulin pump. This modern medical device includes a battery-powered pump, an insulin reservoir, and a cannula and tubing for delivery of the insulin under the skin. It is controlled by a computer the size of a cell phone.
16.6 Angiography and Digital Subtraction Angiography
One important problem in diagnostic radiology is to image
portions of the vascular tree. Angiography can confirm the
existence of and locate narrowing (stenosis), weakening and
bulging of the vessel wall (aneurysm), congenital malformations
of vessels, and the like. This is done by injecting a contrast material containing iodine into an artery. If the
images are recorded digitally, it is possible to subtract one
without the contrast medium from one with contrast and see
the vessels more clearly (Fig. 16.23).
Figure 16.23 in Intermediate Physics for Medicine and Biology. Digital
subtraction angiography. (a) Brain image with contrast material. (b)
Image without contrast material. (c) The difference image. Anterior view
of the right internal carotid artery. Photograph courtesy of Richard Geise, Department of Radiology, University of Minnesota.
One of the pioneers of digital subtraction angiography was Charles Mistretta. The first two paragraphs in the introduction of his article “Digital Angiography: A Perspective” (Radiology, Volume 139, Pages 273-276, 1981) puts his work into perspective (references removed).
Within weeks of Roentgen’s discovery of the x-ray in 1895, Haschek and Lindenthal performed post-mortem arteriography in a hand. For the next 60 years, radiology in general and angiography in particular were largely limited to using film as a means for permanent recording of x-ray images. Recently, new technical developments in television, digital electronics, and image intensifier design have improved the electronic recording of images, and have caused renewed interest in the techniques of intravenous angiocardiography and arteriography originally described by Castellanos et al. [and] Robb and Steinberg.
Prior to 1970, applications involving the subtraction of unprocessed video information stored on analog discs or tape were common. These methods were adequate for augmentation of arterial injection techniques but were not sensitive enough to be used in conjunction with intravenous injection of contrast media. However, techniques capable of imaging the small contrast levels produced after an intravenous injection of contrast media were reported by Ort et al. and Kelcz et al. In combination with analog storage devices, these investigators used both time and K-edge energy subtraction methods for iodine imaging. In spite of their greater sensitivity, the poor reliability of those analog systems made them unsuitable for clinical use and lead to the design of the University of Wisconsin digital video image processor. Over the next five years, this processor was used by a number of investigators for a variety of energy and time subtraction studies both in animals and humans…
Mistretta is now professor emeritus in the Department of Radiology at the University of Wisconsin, where he has been doing medical imaging research since 1971.
Students will benefit from his advice for young medical physicists presented in a spotlight article from the University of Wisconsin.
Choose a career and position that you enjoy and that you are eager to go to every day. Pick a career that makes a difference in the world and hopefully helps people. When you get old some day and start becoming aware of your mortality, it really helps to look back and say “I did my best and I helped make the world a little better place”. As medical physicists we have an excellent chance of making this come true.
The bifurcation diagram summarizes the behavior of the map as a function of the parameter a. Some values of a correspond to a steady state, others represent period doubling, and still others lead to chaos.
When I teach Biological Physics, I don’t introduce chaos using the logistic map. Instead, I solve IPMB’s Homework Problem 41, about cardiac restitution and the onset of fibrillation.
While Problem 41 provides insight into chaos and its relation to cardiac arrhythmias, Russ and I don’t draw a bifurcation diagram that summarizes how the action potential duration, APD, depends on the cycle length, CL (the time between stimuli, it’s the parameter analogous to a in the logistic map). In this post I present such a diagram.
A bifurcation diagram associated with Homework Problem 41 in Intermediate Physics for Medicine and Biology. The plot shows 20 values of APDj for values of CL between 100 and 400 ms.
I don’t have the software to create a beautiful diagram like in Fig. 10.26, so I made one using MATLAB. It doesn’t have as much detail as does the diagram for the logistic map, but it’s still helpful.
The region marked 1:1 (for CL = 310 to 400 ms) implies steady-state behavior: Each stimulus excites an action potential with a fixed duration. Transients existed before the system settled down to a steady state, so I discarded the first 10,000 iterations before I plotted 20 values of APDj (j = 10,001 to 10,020).
Between CL = 283 and 309 ms the system predicts alternans: the response to the stimulus alternates between two APDs (long, short, long, short, etc.). Sometimes this is called a 2:2 response. Alternans are occasionally seen in the heart, and are usually a sign of trouble.
From CL = 154 to 282 ms the response is 2:1, meaning that after a first stimulus excites an action potential the second stimulus occurs during the refractory period and therefore has no effect. The third stimulus excites another action potential with the same duration as the first (once the transients die away). This is a type of period doubling; the stimulus has periodCL but the response has period 2CL.
In cardiac electrophysiology, this behavior resembles second-degree heart block.
For a CL of 153 ms or shorter, the system is chaotic. I didn’t explore the diagram in enough detail to tell if self-similar regions of steady-state behavior exist within the chaotic region, as occurs for the logistic map (see Fig. 10.27 in IPMB).
A bifurcation diagram is a useful way to summarize the behavior of a nonlinear system, and provides insight into deadly heart arrhythmias such as ventricular fibrillation.
I downloaded this paper to learn more about their experiment. Below are excerpts from their introduction.
The baroceptors of the carotid sinus (and
artery) and the aortic arch are the major
sense organs which reflexly control the systemic
blood pressure. Since the demonstration
of the reflex function of these receptors…
there has been much work on the responses
of the blood pressure, heart, and peripheral
vessels to changes in pressure in the carotid
arteries and the aorta…. In our study, we subjected the isolated perfused
carotid sinus to maintained pressures
at different levels… and measured the resultant
systemic pressures and pressure changes.
Two variables were measured: the systemic pressure (Russ and I call this the arterial pressure, part, in the homework problem) and the pressure in the carotid sinus (psinus). Let’s consider them one at a time.
Below I have drawn a schematic diagram of the circulatory system, consisting of the pulmonary circulation (blood flow through the lungs, pumped by the right side of the heart) and the systemic circulation (blood flow to the various organs such as the liver, kidneys, and brain, pumped by the left side of the heart). Scher and Young measured the arterial pressure in the systemic circulation. Most of the pressure drop occurs in the arterioles, capillaries, and venules, so you can measure the arterial pressure in any large artery (such a the femoral artery in the leg) and it is nearly equal to the pressure produced by the left side of the heart. Arterial pressure is pulsatile, but Scher and Young used blood reservoirs to even out the variation in pressure throughout the cardiac cycle, providing a mean pressure.
The circulatory system.
My second drawing shows the carotid sinus, a region near the base of the carotid artery (the artery that feeds the brain) that contains baroceptors (nowadays commonly called baroreceptors; pressure sensors that send information about the arterial pressure to the brain so it can maintain the proper blood pressure). Scher and Young isolated the carotid sinus. They didn’t remove it completely from the animal—after all, they still needed to supply blood to the brain to keep it alive—but it was effectively removed from the circulatory system. In the drawing below I show it as being separate from the body. However, the nerves connecting the baroreceptors to the brain remain intact, so changes in the carotid sinus pressure still signal the brain to do whatever’s necessary to adjust the systemic pressure.
The carotid sinus was attached to a feedback circuit, similar to the voltage clamp used by Hodgkin and Huxley to study the electrical behavior of a nerve axon (see Sec. 6.13 of IPMB). I drew the feedback circuit as an operational amplifier (the green triangle), but this is metaphor for the real instrument. An operational amplifier will produce whatever output is required to keep the two inputs equal. In an electrical circuit, the output would be current and the inputs would be voltage. In Scher and Young’s experiment, the output was flow and the inputs were pressure. Specifically, one of the inputs was the pressure measured in the carotid sinus, and the other was a user-specified constant pressure (po in the drawing). The feedback circuit set psinus = po, allowing the sinus pressure to be specified by the experimenter.
A schematic diagram to represent the feedback circuit that controlled the sinus pressure.
Once this elaborate instrumentation was perfected, the experiment itself was simple: Adjust psinus to whatever value you want by varying po, wait several seconds for the system to come to a new equilibrium (so psinus and part have adjusted to a new constant value), and then measure part. Scher and Young obtained a plot of part versus psinus, similar to that given in our homework problem.
As always, details affect the results.
Any contribution from pressure sensors in the aortic arch was eliminated by cutting the vagus nerve. Only baroreceptors in the carotid sinus contributed to controlling blood pressure.
Scher and Young performed experiments on both dogs and cats. The data in Homework Problem 12 is from a cat.
The blood reservoirs acted like capacitors in an electrical circuit, smoothing changes with time.
In some experiments, a dog was given a large enough dose of anesthetic that the nerves sending information from the sinus baroreceptors to the brain were blocked. In other experiments, the nerve from the baroreceptors to the brain was cut. In both cases, the change in part with psinus disappeared.
Many of Scher and Young’s experiments examined how the feedback circuit varied with time in response to either a step change or a sinusoidal variation in psinus. All of these experiments were ignored in the homework problem, which considers steady state.
Often my students are confused by Problem 12. They think there is only one equation relating part and psinus, but to solve a feedback problem they need two. To resolve this conundrum, realize that when the carotid sinus is not isolated but instead is just one of many large arteries in the body, its pressure is simply the arterial pressure and the second equation is psinus = part.
The study provided hints about how the brain adjusted arterial pressure—by changing heart rate, stroke volume, or systemic resistance—but didn’t resolve this issue.
Scher was born on April 17, 1921 and died May 12, 2011 at the age of ninety. Recently we celebrated the the hundred-year anniversary of his birth. Happy birthday, Dr. Scher!
I am an emeritus professor of physics at Oakland University, and coauthor of the textbook Intermediate Physics for Medicine and Biology. The purpose of this blog is specifically to support and promote my textbook, and in general to illustrate applications of physics to medicine and biology.
