Insulin

A drawing of insulin by David Goodsell, from Wikipedia.

 
Chapter 10 of Intermediate Physics for Medicine and Biology discusses feedback. The homework problems of that chapter include an example of the classic feedback loop controlling the amount of glucose in the blood by the hormone insulin. 

A Short History of Biology,
by Isaac Asimov.

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.

 

To learn more about the discovery of insulin, see the University of Toronto website: https://insulin100.utoronto.ca.

Happy 100th birthday, insulin! 

New Heritage Minute: The Discovery of Insulin.

https://www.youtube.com/watch?v=amCeBhkNo50

Who is Banting?

https://www.youtube.com/watch?v=V0_9LzAYLRY 

 

Insulin 2021

https://www.youtube.com/watch?v=q0EdNC1Fq7k

 

Insulin Pump

https://www.youtube.com/watch?v=Crkyl9bqfC0 

Digital Subtraction Angiography

In Chapter 16 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss digital subtraction angiography.

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.

2016 IEEE Honors Ceremony - Medal for Innovations in Healthcare Technology — Charles Mistretta

https://www.youtube.com/watch?v=y55ZStb93II

A Bifurcation Diagram for the Heart

In Figure 10.26 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I plot a bifurcation diagram for the logistic map: x_j+1 = a x_j (1 − x_j).

A bifurcation diagram for the logistic map, showing 300 values of x_j for values of a between 1 and 4. Figure 10.26 in Intermediate Physics for Medicine and Biology.

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 APD_j 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 APD_j (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 period CL 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.

Servoanalysis of Carotid Sinus Reflex Effects on Peripheral Resistance

In Chapter 10 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss feedback and control. Homework Problem 12 analyzes the feedback circuit that controls blood pressure.

Problem 12 from Chapter 10 of Intermediate Physics for Medicine and Biology.

The reference to the article by Allen Scher and Allan Young is

Scher AM, Young AC (1963) “Servoanalysis of Carotid Sinus Reflex Effects on Peripheral Resistance,” Circulation Research, Volume 12, Pages 152–165.

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, p_art, in the homework problem) and the pressure in the carotid sinus (p_sinus). 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 (p_o in the drawing). The feedback circuit set p_sinus = p_o, 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 p_sinus to whatever value you want by varying p_o, wait several seconds for the system to come to a new equilibrium (so p_sinus and p_art have adjusted to a new constant value), and then measure p_art. Scher and Young obtained a plot of p_art versus p_sinus, 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 p_art with p_sinus 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 p_sinus. 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 p_art and p_sinus, 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 p_sinus = p_art.
• 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. 
• The experiments were performed at the University of Washington School of Medicine in Seattle. 
  
• Allen Scher was a World War II veteran, serving as a Marine in the Pacific. He contributed to our understanding of the electrocardiogram, and was a coauthor on the Textbook of Physiology, cited often as “Patton et al. 1989” in IPMB.
  
• 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!