From Neuron to Brain

From Neuron to Brain,
by Stephen Kuffler and John Nicholls.

In 1982, when I was accepted into graduate school at Vanderbilt University, I already knew that I wanted to study with John Wikswo, who was measuring the magnetic field of nerve axons. There was just one problem: I didn’t know how nerves worked. So I asked John to recommend some books that would get me up-to-speed before I arrived in Nashville. One text he suggested was From Neuron to Brain, by Stephen Kuffler and John Nicholls. The book taught me the basics of nerve electrophysiology, and allowed me to be (more-or-less) ready to go when I showed up at Vanderbilt.

From Neuron to Brain is now in its 5th edition. I obtained a copy through interlibrary loan, and I’m delighted to say that it still looks to be a great neuroscience textbook. One change is that the authors are different. Kuffler died in 1980, but Nicholls has carried on, now with 5 coauthors (don’t you just hate it when a fine textbook adds additional “coauthors” in later editions!). The Preface to the 5th edition begins

When the First Edition of our book appeared in 1976, its preface stated that our aim was “…to describe how nerve cells go about their business of transmitting signals, how the signals are put together, and how out of this integration higher functions emerge. The book is directed to the reader who is curious about the workings of the nervous system but does not necessarily have a specialized background in biological sciences. We illustrate the main points by selected examples…”

This new, Fifth Edition has been written with the same aim in mind but in a very different context. When the First Edition appeared there were hardly any books, and only a few journals devoted to the nervous system. The extraordinary advances in molecular biology, genetics, and immunology had not been applied to the study of nerve cells or the brain, and the internet was not available for searching the literature. The explosion of knowledge since 1976 means that even though we still want to produce a readable narrative, the topics that have to be addressed and the number of pages have increased. Inevitably, descriptions of certain older experiments have had to be jettisoned, even though they still seem beautiful. Nevertheless, our approach continues to be to follow ideas from their conception to the latest developments. To this end, in this edition we have retained descriptions of classical experiments as well as the newest findings. In this way we hope to present key lines of research of interest for practicing research workers and teachers of neurobiology, as well as for readers who are not familiar with the field.

I’ve always believed the From Neuron to Brain did a great job describing the Hodgkin and Huxley model, a topic that Russ Hobbie and I cover in Chapter 6 of the 4th edition of Intermediate Physics for Medicine and Biology. Many of the key figures from the Hodgkin and Huxley papers are redrawn in a uniform, crisp, elegant style. Some pictures I remember from the first edition, such as the photos of Hodgkin and Huxley, but others—like the illustrations of the detailed structures of potassium and sodium ion channels—are obviously new. Someone put a tremendous amount of time and effort into creating an outstanding collection of illustrations and figures, all with an appropriate and effective use of color, clearly labeled axes, with an uncluttered and simple style. Bravo!

From Neuron to Brain uses little math, and the few equations that do appear are most often just presented, not derived. Those wanting to understand the mathematical basis of the Hodgkin-Huxley model would be well advised to keep a copy of IPMB nearby as you read From Neuron to Brain. Conversely, readers of IPMB who have a weak background in biology might want to keep a copy of From Neuron to Brain close at hand as the work their way through IPMB (especially Chapters 6-9). The two books are complimentary. You won’t find the cable equation written down, much less analyzed, in From Neuron to Brain. But with those gorgeous figures to look at, you may not notice the lack of math.

I really like two other features of From Neuron to Brain. They have an extensive glossary at the back of the book, defining important terms. When I was first learning nerve electrophysiology to prepare for graduate school, one of my biggest obstacles was the vocabulary. Biologists use strange words. I suppose it was more difficult back in those days because we didn’t have Google and Wikipedia (how did we get anything done?), but even today I still appreciate having the glossary handy. Also present in the first edition, and still there now, is an extensive bibliography. Perhaps the beginning student doesn’t refer to the bibliography much, but when you really start digging deep into a subject you want to consult the original papers. As Russ and I work on updating IPMB for the 5th edition, there is always a tension between citing older classic papers and adding new modern ones. From Neuron to Brain has an interesting mix of the new and the old. They provide over 60 pages of citations in small font; I estimate about 40 references per page, for something like 2400 articles. Now that’s a bibliography!

Readers of IPMB looking for more details about nerve electrophysiology will find the 5th edition of From Neuron to Brain to be a valuable text. I’m not familiar with the competing neuroscience textbooks, but I would be surprised if they’re all of this high quality.

Osmosis and the Kidneys

Physics of the Body,
by Cameron, Skofronick, and Grant.

One textbook that covers much of the same material as the 4th edition of Intermediate Physics for Medicine and Biology—but at a somewhat lower level—is Physics of the Body, by John Cameron, James Skofronick and Roderick Grant. They have chapter titles such as “Physics of the Skeleton,” “Physics of the Ear and Hearing,” and “Physics of the Lungs and Breathing.” They apparently didn’t have the expertise among the three coauthors to write a chapter on the “Physics of the Kidneys,” so they recruited an outside author familiar with both physics and the renal system to write it for them. That author is none other than Russ Hobbie. In their preface they write

Emeritus Professor Russell Hobbie of the University of Minnesota, the author of the more advanced text Intermediate Physics for Medicine and Biology, kindly contributed Chapter 6 [“Osmosis and the Kidneys”] on the physics of osmosis as it relates to fluid transport across membranes in the body. He also contributed to the revision of Chapter 9 [“Electrical Signals from the Body”]. His cooperation is greatly appreciated.

Russ’s chapter covers some of the same topics as in Chapters 4 and 5 of IPMB, such as diffusion and osmotic pressure. However, his Section 6.4 goes into more detail about the anatomy and physiology of the kidney that we do in IPMB. Here’s an excerpt.

The kidneys excrete much of the body’s metabolic waste products—except carbon dioxide and some water which leave through the lungs. They also regulate the concentration of most chemicals in the blood plasma. Each kidney contains over 1 million nephrons. Each nephron is a complete urine-forming unit. Figure 6.5 shows the kidneys and the ureters through which urine flows to the urinary bladder. Figure 6.6 shows a magnified view of a nephron.

Figure 6.7 shows the essential functioning parts of the nephron. Blood from the renal artery passes first by a membrane in the glomerulus, where a large amount of fluid—about 250 ml per minute (~1 cup)—passes through the basement membrane of the glomerulus. This process is called filtration. Careful measurements of dog kidneys using radioactively tagged solute molecules of different radii suggest that the filtration is by pores of 5 nm radius in the basement membrane. The filtration rate is controlled by valves which control the rate of blood flow through the glomerulus and the pressure drop across the glomerular basement membrane. Substances with a molecular weight of 5000 or less pass easily through the membrane with the water. Most proteins, which have a molecular weight of 69,000 or more, do not pass through the pores and remain in the blood. The filtrate then passes through the tubules, where 99% of it is reabsorbed (if it were not reabsorbed, we would void 360 liters of urine per day [!]). The other 1% passes into the collecting system as urine. Unwanted substances are not reabsorbed, so their concentration in the urine increases. Creatinine, a metabolic waste product, and sucrose are not reabsorbed at all. About half of the urea, a nitrogenous product of protein metabolism, is reabsorbed.

One interesting appendix I found when thumbing through Physics of the Body is the “Standard Man.”

In medical physics, where we are concerned with the anatomy and physiology of humans, it is convenient to define the physical characteristics of a “standard man.” While the standard man is nonexistent, the following somewhat arbitrary values are useful for simulation and for computational purposes:

Age: 30 yr

Height: 1.72 m (5 ft 8 in)

Mass: 70 kg

Weight: 690 N (154 lb)

Surface area: 1.85 m²

Body core temperature: 37.0 C

Body skin temperature: 34.0 C

Heat capacity: 3.6 kJ/kg C (0.86 kcal/kg C)

Basal metabolism: 44 W/m² (38 kcal/m² hr, 70 kcal/hr, 1680 kcal/day)

Heart rate: 70 beats/min

Blood volume: 5.2 liters

Cardiac output: 5 liters/min

Blood pressure—systolic: 16 kPa (120 mm Hg)

Blood pressure—diastolic: 10.5 kPa (80 mm Hg)

Breathing rate: 15/min

O₂ consumption: 0.26 liter/min

CO₂ production: 0.21 liter/min

Total lung capacity: 6 liters

Tidal volume: 4.8 liters

Lung dead space: 0.15 liters

John Cameron, who passed away in 2005, was a giant in the field of medical physics. He was one of the founders of the well-known medical physics program at the University of Wisconsin. James Skofronick is emeritus professor in the department of physics at Florida State University. Roderick Grant is an emeritus professor in the department of physics and astronomy at Denison University.

How Well Does a Three-Sphere Model Predict Positions of Dipoles in a Realistically Shaped Head?

When I worked at the National Institutes of Health, I collaborated with Susumu Sato, a neurophysiologist interested in electroencephalography and magnetoencephalography. One of Sato’s goals was to develop methods to localize the source of epileptic seizures in the brain. In a small percentage of patients, these seizures cannot be controlled by drugs and are severe enough to be debilitating. In such cases, the best alternative is surgery: remove the region of the brain where the seizure originates, and you stop the seizures. Obviously, in these patients the surgeon must know what part of the brain to remove, and the more accurately that is known the better. Ideally, you want to localize the source using a noninvasive procedure such as electroencephalography. One way to model the sources of electrical activity in the brain is as a single dipole source. Russ Hobbie and I discuss dipoles and the EEG in Chapter 7 of the 4th edition of Intermediate Physics for Medicine and Biology.

Much can be learned about the brain by measuring the electric potential on the scalp surface. Such data are called the electroencephalogram (EEG). Nunez and Srinivasan have written an excellent book about the physics of the EEG. We briefly examine the topic here. The EEG is used to diagnose brain disorders, to localize the source of electrical activity in the brain in patients who have epilepsy, and as a research tool to learn more about how the brain responds to stimuli (“evoked responses”) and how it changes with time (“plasticity”). Typically, the EEG is measured from 21 electrodes attached to the scalp according to the “10–20 system” (Fig. 7.34). A typical signal from an electroencephalographic electrode is shown in the top panel of Fig. 11.38. One difficulty in interpreting the EEG is the lack of a suitable reference electrode. None of the 21 electrodes in Fig. 7.34 qualifies as a distant ground against which all other potential recordings can be measured. One way around this difficulty is to subtract from each measured potential the average of all the measured potentials. In the problems, you are asked to prove that this “average reference recording” does not depend on the choice of reference electrode; it is a reference independent method.

The reference is to Paul Nunez’s book Electric Fields of the Brain (Oxford University Press, 2005), which is a great starting point to learn about the physics of the EEG.

Sato wanted to localize the dipole as accurately as possible, even if that meant moving beyond the three-sphere model. Therefore, I was recruited to write a computer program to solve the EEG problem for a realistically-shaped head. This was not easy, because no software existed at that time for numerically solving the electric potential produced by a dipole in the brain when it is not spherical (at least, Sato and I didn’t have access to such software). I used a boundary element method to perform the calculation. I needed information about the shape of the skull, scalp, and brain surfaces, and I remember painstakingly digitizing those surfaces by hand from magnetic resonance images, and then tessellating the surfaces with triangles. Our resulting image of the brain graced the cover of the journal Electroencephalography and clinical Neurophysiology for several years.

The cover of Electroencephalography
and Clinical Neurophysiology.

This research culminated in a paper published almost exactly 20 years ago: Roth, B. J., M. Balish, A. Gorbach and S. Sato, 1993, “How well does the three-spheres model predict dipoles in a realistically-shaped head?” Electroenceph. clin. Neurophysiol., Volume 87, Pages 175–184. The introduction of the paper is presented below, with references removed.

Electroencephalographic data, such as interictal spikes and evoked responses, are increasingly analyzed using the moving dipole method. The source of the EEG activity is represented as one or more dipoles within the brain; their location, orientation and strength are determined using an iterative least-squares algorithm to fit the calculated potential to the measured EEG data. Although the dipole approximation is an oversimplification, it is a convenient representation of the complex cortical sources. Most often, the potential produced by a dipole is calculated using the 3-sphere model. In this model the brain, skull and scalp are represented as concentric, spherical shells that differ in conductivity. More computationally demanding models use a realistically shaped head; the electrical potential produced by a dipole source is computed either by solving a system of integral equations governing the potential on the brain, skull, and scalp surfaces or by using a finite element model of the head.

In this paper, we compare the 3-sphere model to a realistically shaped head model, in which the brain, skull and scalp surfaces are obtained from magnetic resonance images. We consider a dipole in the temporal or frontal lobe of the brain, and perform a forward calculation using the realistically shaped head model to determine the potential at the 10-20 electrode positions. We then use these data to predict the dipole position by performing an inverse calculation with the 3-sphere model. The average difference between the original and predicted dipole positions is about 2 cm, though differences as large as 4 cm are seen under certain circumstances. Our results are particularly significant for localization of EEG sources of epileptic spikes, which commonly lie in the temporal and frontal lobes.

Medical Physics Qualifying Exams

We have a Medical Physics PhD program here at Oakland University, and this was the week we administered the oral qualifying exam to our current crop of graduate students. Happily, they all passed. In August they also took a battery of written exams about theoretical physics, mathematical methods, and biophysical sciences (Physics, Math, and Biology for short). I have mentioned these exams before in this blog. We consider them to be a common core that our graduate students are expected to master.

These exams do not require knowing extremely advance material, but they do cover a broad range of topics. I take them to be a minimum that our students must know, rather than a target they should aim for. A student who has a strong undergraduate background in physics, math and biology should be able to survive. Some of the more advanced homework problems and examples from the 4th edition of Intermediate Physics for Medicine and Biology sometimes make their way onto these exams.

Let me add a few words about our PhD program. It is aimed at producing research students who can apply physics to medical and biological problems, rather than preparing students for traditional medical physics positions in a hospital. We are not CAMPEP accredited, because that accreditation is mainly for programs aimed narrowly at producing clinical medical physicists. Our students get broad training in both mathematics and medicine, and in both physics and physiology. Their depth comes from doing their research dissertation. After graduating, they go on to a variety of positions in academia, industry, and research laboratories.

Readers of IPMB who want to see how well they would do on our qualifying exam can find over ten years of the written exams at https://files.oakland.edu/users/roth/web/qualifierexams.htm. I have four reasons for posting these exams on the web. First, I assume the exams, or at least some of the questions from them, would make the rounds among our graduate students, or at least among some subset of the graduate students, and I would rather they all have equal access. Second, I am often asked to provide guidance and suggestions as to what specific topics might be on these exams (I admit, all of physics, math, and biology is a lot to master), and my answer is have them look at the previous exams. Third, it can be a useful recruiting tool; if a potential applicant wants to know what they are expected to master to succeed in our program, I can send them to the old exams and be confident that they realize what they are getting into. Fourth, failing our qualifying exam is a serious issue. The students only get two tries, and then they must leave the program. I prefer to give a student some direction and help rather wondering if the exam was unfair as I tell them that they failed. The downside to posting these exams is that I need to keep coming up with new problems each year. While some identical problems from old exams appear on later exams, I try to minimize this. So, writing the exams (which I do largely myself, although with input from the other faculty in the program) is a little harder than it otherwise would be. One useful side effect of posting the exams is that they are all “out there” available to anyone, including our dear readers of IPMB. So, feel free to use them as you wish. Sorry, but I don’t have solutions I can send you.

In addition to these written exams, each student must stand in front of a group of (intimidating?) faculty and answer questions about “everything”: all the topics from the written exams, plus questions related to their research, and to any other part of physics, mathematics, or biology that might strike the questioner’s fancy. This grilling is what our students went through on Wednesday, successfully. I think the students fear this part of the exam most of all, but I believe they grow from the experience.

Congratulations to this year’s students. I hope readers of IPMB find these exams useful.