Tony Barker receives the International Brain Stimulation Award

In Chapter 8 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss transcranial magnetic stimulation. 

Since a changing magnetic field generates an induced electric field, it is possible to stimulate nerve or muscle cells without using electrodes. The advantage is that for a given induced current deep within the brain, the currents in the scalp that are induced by the magnetic field are far less than the currents that would be required for electrical stimulation. Therefore transcranial magnetic stimulation (TMS) is relatively painless….

One of the earliest investigations was reported by Barker, Jalinous and Freeston (1985). They used a solenoid in which the magnetic field changed by 2 T in 110 μs to apply a stimulus to different points on a subject’s arm and skull. The stimulus made a subject’s finger twitch after the delay required for the nerve impulse to travel to the muscle. For a region of radius a = 10 mm in material of conductivity 1 S m⁻¹, the induced current density for the field change in Barker’s solenoid was 90 A m⁻². (This is for conducting material inside the solenoid; the field falls off outside the solenoid, so the induced current is less.) This current density is large compared to current densities in nerves (Chap. 6).

Tony Barker was the lead engineer who developed the first useful magnetic stimulator. For this ground-breaking work, he recently received the International Brain Stimulation Award. An Institute of Physics and Engineering in Medicine news article states

The pioneer of Transcranial Magnetic Stimulation of the brain has become the first recipient of a new international award.

Professor Tony Barker, a Fellow of the Institute of Physics and Engineering in Medicine, has been awarded the International Brain Stimulation Award by publisher Elsevier.

The award acknowledges outstanding contributions to the field of brain stimulation. These contributions may be in basic, translational, or clinical aspects of neuromodulation, and must have had a profound influence in shaping this field of neuroscience and medicine.

Professor Barker, who recently retired after 38 years at Sheffield Teaching Hospitals’ Department of Medical Physics and Clinical Engineering, led the small team which developed the Transcranial Magnetic Stimulation (TMS) technique in the early 1980s.

He first started his research on using time-varying magnetic fields to induce current flow in tissue in order to depolarize neurons. Prior to this effort, direct electrical stimulation, with electrodes placed on the scalp (or other body part), was the principle method used to induce neuronal depolarization. This method, however, had several flaws and the high intensity of electrical stimulation is often painful. Magnetic fields, in contract, pass through the scalp and skull unimpeded and gives much more precise results.

In 1985, Professor Barker, together with his colleagues Dr Reza Jalinous and Professor Ian Freeston, reported the first demonstration of TMS. They produced twitching in a specific area of the hand in human volunteers by applying TMS to the motor cortex in the opposite hemisphere that controls movement of that muscle. This demonstrated that TMS was capable of stimulating a precise area of the brain and without the pain of electrical stimulation. Moreover, they did this with awake-alert human volunteers.

Today, TMS has become a vital tool in neuroscience, since, depending on stimulation parameters, specific brain areas can either be excited or inhibited. The TMS technique has evolved into a critical tool in basic neuroscience investigation, in the study of brain abnormalities in disease states, and in the treatment of a host of neurological and psychiatric conditions….

Professor Barker will receive his award at the 2nd International Brain Stimulation Conference in March, which is being held in Barcelona. He will also give a plenary lecture at the conference entitled Transcranial Magnetic Stimulation—past, present and future.

According to Google Scholar, Barker’s paper “Non-invasive magnetic stimulation of human motor cortex” in The Lancet has over 3400 citations, reflecting its impact (Oops…the citation to this article in IPMB left out the word “motor” in the title; yet another item for the errata). The figure below is from Barker’s Scholarpedia article about TMS.

The Sheffield group with the stimulator that first achieved
transcranial magnetic stimulation, February 1985.
From left to right: Reza Jalinous, Ian Freeston and Tony Barker.

Neuroskeptic

Over the Christmas break I discovered a blog written under the pen name Neuroskeptic.

Neuroskeptic is a British neuroscientist who takes a skeptical look at his own field, and beyond. His blog offers a look at the latest developments in neuroscience, psychiatry and psychology through a critical lens.

Neuroskeptic’s interests overlap topics covered in Intermediate Physics for Medicine and Biology. For instance, often Neuroskeptic writes about functional magnetic resonance imaging, a technique Russ Hobbie and I describe in Chapter 18 of IPMB.

“The term functional magnetic resonance imaging (fMRI) usually refers to a technique developed in the 1990s that allows one to study structure and function simultaneously. The basis for fMRI is inhomogeneities in the magnetic field caused by the differences in the magnetic properties of oxygenated and deoxygenated hemoglobin. No external contrast agent is required. Oxygenated hemoglobin is less paramagnetic than deoxyhemoglobin. If we make images before and after a change in the blood flow to a small region of tissue (perhaps caused by a change in its metabolic activity), the difference between the two images is due mainly to changes in the blood oxygenation. One usually sees an increase in blood flow to a region of the brain when that region is active. This BOLD contrast in the two images provides information about the metabolic state of the tissue, and therefore about the tissue function (Ogawa et al. 1990; Kwong et al. 1992).”

Neuroskeptic’s author is obviously an expert in this method, but is suspicious about some of its claims. Often he—I will use the masculine pronoun for convenience, but I have no idea about his gender—analyzes new papers in the field. For instance, in his recent New Year’s Eve blog post he writes

Earlier this year, neuroscience was shaken by the publication in PNAS of “Cluster Failure: Why fMRI Inferences for Spatial Extent have Inflated False-Positive Rates.” In this paper, Anders Eklund, Thomas E. Nichols and Hans Knutsson reported that commonly used software for analysing fMRI data produces many false-positives. But now, Boston College neuroscientist Scott D. Slotnick has criticized Eklund et al.’s alarming conclusions in a new piece in Cognitive Neuroscience. In my view, while Slotnick makes some valid points, he falls short of debunking Eklund et al.’s worrying findings.

Another area Neuroskeptic analyzes is functional electrical stimulation. In Chapter 7 of IPMB, Russ and I write

stimulating electrodes…may be used for electromyographic studies; for stimulating muscles to contract called functional electrical stimulation (Peckham and Knutson 2005); for a cochlear implant to partially restore hearing (Zeng et al.2008); deep brain stimulation for Parkinson’s disease (Perlmutterand Mink 2006); for cardiac pacing (Moses andMullin 2007); and even for defibrillation (Dosdall et al.2009). The electrodes may be inserted in cells, placed in or on a muscle, or placed on the skin.

Two recent Neuroskeptic posts (here and here) analyze a controversial method of electrical stimulation called transcranial direct current stimulation (tDCS). I share his doubts about this technique, in which week currents (about 1 mA) are applied to the scalp. In a post last August, I hinted at some of my concerns, but my suspicions continue to grow. The electric fields induced in the brain by a 1 mA current to the scalp are minuscule.

Neuroskeptic also wonders if nonionizing radiation can cause cancer, a topic covered extensively in Chapter 9 of IPMB. He writes

Does non-ionizing radiation pose a health risk? Everyone knows that ionizing radiation, like gamma rays, can cause cancer by damaging DNA. But the scientific consensus is that there is no such risk from non-ionizing radiation such as radiowaves or Wi-Fi. Yet according to a remarkable new paper from Magda Havas, the risk is real: it’s called “When Theory and Observation Collide: Can Non-Ionizing Radiation Cause Cancer?”... Non-ionizing radiation such as radiowaves and microwaves consists of photons, just like visible light, but at a lower frequency. Because the energy of a photon is proportional to its frequency, very high frequency photons (like gamma rays) have enough energy to disrupt atoms…But visible light can’t do this, and still less can microwaves or radiowaves. There’s no known mechanism by which such low-energy photons could harm living tissue – except that they can heat tissue up in high doses, but the amount of heating produced by radio and wireless devices is tiny.

Neuroskeptic is not merely a debunker. Sometimes he examines promising new methods, but always with a questioning eye. For instance, his review of a paper developing new contrast agents for MRI is fascinating.

In a new paper called “Molecular fMRI,” MIT researchers Benjamin B. Bartelle, Ali Barandov, and Alan Jasanoff discuss technological advances that could provide neuroscientists with new tools for mapping the brain.

Currently, one of the leading methods of measuring brain activity is functional MRI (fMRI)…. Recent work, however, holds out the hope that a future “molecular fMRI” could be developed to extend the power of fMRI…. Molecular fMRI would involve the use of a molecular probe, a form of “contrast agent,” which would modulate the MRI signal in response to specific conditions.

I would be interested in knowing what Neuroskeptic (I always want to type “the Neuroskeptic” but he never uses the definite article before his name, so I won’t either) thinks about claims of using the biomagnetic field as the gradient field in MRI, as I discussed in my June 2016 blog post.

Everyone has their own gimmick, and Neuroskeptic’s is that he keeps his real identity secret. Some of you are thinking: “Oh, I wish Roth would be anonymous! We hear far too much about him and his little dog Suki and his own research in this blog.” Well, sorry. It’s too late to change now, so you are stuck hearing about Suki and me in addition to learning about physics in medicine and biology. But if you want a well-written, anonymous, and sometimes dissenting view of neuroscience, read the Neuroskeptic.

The Story of the World in 100 Species

The Story of the World
in 100 Species,
by Christopher Lloyd.

I recently finished reading The Story of the World in 100 Species. The author Christopher Lloyd writes in the introduction

This book is a jargon-free attempt to explain the phenomenon we call life on Earth. It traces the history of life from the dawn of evolution to the present day through the lens of one hundred living things that have changed the world. Unlike Charles Darwin’s theory published more than 150 years ago, it is not chiefly concerned with the “origin of species,” but with the influence and impacts that living things have had on the path of evolution, on each other and on our mutual environment, planet Earth.

Of course, I began to wonder how many of the top hundred species Russ Hobbie and I mention in Intermediate Physics for Medicine and Biology. Lloyd lists the species in order of impact. The number 1 species is the earthworm. As Darwin understood, you would have little agriculture without worms churning the soil. The highest ranking species that was mentioned in IPMB is number 2, algae, which produces much of the oxygen in our atmosphere. According to Lloyd, algae might provide the food (ick!) and fuel we need in the future.

Number 6 is ourselves: humans. Although the species name Homo sapiens never appears in IPMB, several chapters—those dealing with medicine—discuss us. Number 8 yeast (specifically, S. cerevisiae) is not in IPMB, although it is mentioned previously in this blog. Number 15 is the fruit fly Drosophila melanogaster, which made the list primarily because it is an important model species for research. IPMB mentions D. melanogaster when discussing ion channels.

Cows are number 17; a homework problem in IPMB contains the phrase “consider a spherical cow.” The flea is number 18, and is influential primarily for spreading diseases such as the Black Death. In IPMB, we analyze how fleas survive high accelerations. Wheat reaches number 19 and is one of several grains on the list. In Chapter 11, Russ and I write: “Examples of pairs of variables that may be correlated are wheat price and rainfall, ….” I guess that wheat is in IPMB, although the appearance is fairly trivial. Like yeast, number 20 C. elegans, a type of roundworm, is never mentioned in IPMB but does appear previously in this blog because it is such a useful model. I am not sure if number 21, the oak tree, is in IPMB. My electronic pdf of the book has my email address, roth@oakland.edu, as a watermark at the bottom of every page. Oak is not in the appendix, and I am pretty sure Russ and I never mention it, but I haven’t the stamina to search the entire pdf, clicking on each page. I will assume oak does not appear.

Number 24, grass, gets a passing mention: in a homework problem about predator-prey models, we write that “rabbits eat grass…foxes eat only rabbits.” When I searched the book for number 25 ant, I found constant, quantum, implant, elephant, radiant, etc. I gave up after examining just a few pages. Let’s say no for ant. Number 28 rabbit is in that predator-prey problem. Number 32 rat is in my favorite J. B. S. Haldane quote “You can drop a mouse down a thousand-yard mine shaft; and arriving at the bottom, it gets a slight shock and walks away. A rat is killed, and man is broken, a horse splashes.” Number 33 bee is in the sentence “Bees, pigeons, and fish contain magnetic particles,” and number 38 shark is in the sentence “It is possible that the Lorentz force law allows marine sharks, skates, and rays to orient in a magnetic field.” My favorite species, number 42 dog, appears many times. I found number 44 elephant when searching for ant. I am not sure about number 46 cat (complicated, scattering, indicate, cathode, … you search the dadgum pdf!). It doesn’t matter; I am a dog person and don’t care for cats.

Number 53 apple; IPMB suggests watching Russ Hobbie in a video about the program MacDose at the website https://itunes.apple.com/us/itunes-u/photon-interactions-simulation/id448438300?mt=10. No way am I counting that; you gotta draw the line somewhere. Number 58 horse; “…horse splashes…”. Number 59 sperm whale; we mention whales several times, but don’t specify the species—I’m counting it. Number 61 chicken appears in one of my favorite homework problems: “compare the mass and metabolic requirements…of 180 people…with 12,600 chickens…” Number 65 red fox; see predator-prey problem. Number 67 tobacco; IPMB mentions it several times. Number 71 tea; I doubt it but am not sure (instead, steady, steam, ….). Number 77 HIV; see Fig. 1.2. Number 85 coffee; see footnote 7, page 258.

Altogether, IPMB includes twenty of the hundred species (algea, human, fruit fly, cow, flea, wheat, grass, rabbit, rat, bee, shark, dog, elephant, horse, whale, chicken, fox, tobacco, HIV, coffee), which is not as many as I expected. We will have to put more into the 6th edition (top candidates: number 9 influenza, number 10 penicillium, number 14 mosquito, number 26 sheep, number 35 maize aka corn).

Were any important species missing from Lloyd’s list? He includes some well-known model organisms (S. cerevisiae, D. melanogaster, C. elegans) but inexplicably leaves out the bacterium E. coli (Fig. 1.1 in IPMB). Also, I am a bioelectricity guy, so I would include Hodgkin and Huxley’s squid with its giant axon. Otherwise, I think Lloyd’s list is pretty complete.

If you want to get a unique perspective on human history, learn some biology, and better appreciate evolution, I recommend The Story of the World in 100 Species.

Implantable microcoils for intracortical magnetic stimulation

When I worked at the National Institutes of Health in the 1990s, I studied transcranial magnetic stimulation. Russ Hobbie and I discuss magnetic stimulation in Chapter 8 of Intermediate Physics for Medicine and Biology. Pass a pulse of current through a coil held near the head; the changing magnetic field of the coil induces an electric field in the brain that stimulates neurons. Typical magnetic stimulation coils are constructed from several turns of wire, each turn carrying kiloamps of current in pulses that last for a tenth of a millisecond. Most are a few centimeters in size. Researchers have tried to make smaller coils, but these typically require even larger currents, resulting in magnetic forces that tear the coil apart as well as prohibitive Joule heating.

Imagine my surprise when Russ told me about a recently published paper describing magnetic stimulation using microcoils, written by Seung Woo Lee and his colleagues (“Implantable microcoils for intracortical magnetic stimulation,” Science Advances, 2:e1600889, 2016). Frankly, I am not sure what to make of this paper. On the one hand, the authors describe a careful study in which they perform all the control experiments I would have insisted on had I reviewed the paper for the journal (I did not). On the other hand, it just doesn’t make sense. 

Lee et al. built a coil by bending a 50 micron insulated copper wire into a single tight turn having a diameter of about 100 microns (see figure). Their current pulse lasted a few tenths of a millisecond, and had a peak current of….drum roll, please….about fifty milliamps. Yes, that would be nearly a million times smaller than the kiloamp currents used in traditional transcranial magnetic stimulation. Can this be? If true, it is a breakthrough, opening up the use of magnetic stimulation with implanted coils at the single neuron level.

 Figure from Lee et al. Science Advances, 2:e1600889, 2016.

Why am I skeptical? You can calculate the induced electric field E from the product of μ_o/4π times the rate of change of the current times an integral over the coil,

where R is the distance from a point on the coil to the point where you calculate E. The constant μ_o/4π is 10^-7 V s/A m. The rate of change of the current is about 0.05 A/0.0001 s = 500 A/s. The product of these two factors is roughly 5 × 10^-5 V/m. The difficult part of the calculation is the integral. However, it is dimensionless and if the coil size and distance to the field point are similar it should be on the order of unity. Maybe a strange geometry could provide a factor of two, or π, or even ten, but you don’t expect a dimensionless integral like this one to be orders of magnitude larger than one (Lee et al. derived an expression for this integral containing a logarithm, and we all know how slowly that function changes). So, the electric field induced by such a microcoil should on the order of 10^-4 V/m. Hause has estimated an electric field threshold for a neuron of about 10 V/m. How do you account for the missing factor of 100,000?

Lee et al. focus on the gradient of the electric field, rather than on the electric field itself. The gradient of the electric field plays an important role when performing traditional magnetic stimulation of a long straight axon, as you might find in the median nerve of the arm. However, when the spatial extent over which the electric field varies is smaller than the length constant, the relationship between the transmembrane potential and the electric field gradient becomes complicated. Also, in the brain neurons bend, branch, and bulge, so that the electric field may be the more appropriate quantity to use when estimating threshold. Yet, the electric field induced by a microcoil is really small.

So what is going on? I don’t know. As I said, the authors do several control experiments, and their data is convincing. My hunch is that they stimulated by capacitive coupling, but they examined that possibility and claim it is not the mechanism. I don’t have an answer, but their results are too strange to believe and too important to ignore. One thing I know for sure: the experiments need to be consistent with the fundamental physical laws outlined in Intermediate Physics for Medicine and Biology.

Optical Magnetic Detection of Single-Neuron Action Potentials using Quantum Defects in Diamond

A figure from Barry et al., PNAS, 113:14133-14138, 2016.

Last week in this blog, I discussed using a wire-wound toroid to measure the magnetic field of a nerve axon. In the comments to my November 25 post, my friend Raghu Parthasarathy (of the Eighteenth Elephant) pointed me to a recent article by Barry et al.: “Optical magnetic detection of single-neuron action potentials using quantum defects in diamond” (Proceedings of the National Academy of Sciences, 113:14133–14138, 2016). I liked the article, and not just because it cited five of my papers. It presents a new method for measuring biomagnetic fields that does not require toroids or SQUID magnetometers, the only two methods discussed in Chapter 8 of Intermediate Physics for Medicine and Biology.  You can read it online; it’s open access.

Barry et al.’s abstract states:

Magnetic fields from neuronal action potentials (APs) pass largely unperturbed through biological tissue, allowing magnetic measurements of AP dynamics to be performed extracellularly or even outside intact organisms. To date, however, magnetic techniques for sensing neuronal activity have either operated at the macroscale with coarse spatial and/or temporal resolution—e.g., magnetic resonance imaging methods and magnetoencephalography—or been restricted to biophysics studies of excised neurons probed with cryogenic or bulky detectors that do not provide single-neuron spatial resolution and are not scalable to functional networks or intact organisms. Here, we show that AP magnetic sensing can be realized with both single-neuron sensitivity and intact organism applicability using optically probed nitrogen-vacancy (NV) quantum defects in diamond, operated under ambient conditions and with the NV diamond sensor in close proximity (∼10 μm) to the biological sample. We demonstrate this method for excised single neurons from marine worm and squid, and then exterior to intact, optically opaque marine worms for extended periods and with no observed adverse effect on the animal. NV diamond magnetometry is noninvasive and label-free and does not cause photodamage. The method provides precise measurement of AP waveforms from individual neurons, as well as magnetic field correlates of the AP conduction velocity, and directly determines the AP propagation direction through the inherent sensitivity of NVs to the associated AP magnetic field vector.

Here is my poor attempt to explain how their technique works; I must confess I don’t understand it completely. Nitrogen-vacancy defects in a diamond create a spin system that you can use for optically detected electron spin resonance. You shine light onto the system and detect the fluorescence with a photodiode. The shift in the magnetic resonance spectrum contained in the fluoresced light provides a measurement of the magnetic field. For our purposes we can think of the system as a black box that measures the magnetic field; new type of magnetometer.

Barry et al.’s paper started me thinking about the relative advantages and disadvantages of toroids versus optical methods for measuring magnetic fields of nerves.

1. A disadvantage of toroids is that you have to thread the nerve through the toroid center, which usually requires cutting the nerve. My PhD advisor John Wikswo created a “clip-on” toroid that avoids any cutting, but that technique never really caught on. In the optical method, you just drape the nerve over the detector like you would lie down on a bed. Winner: optical method.
2. The toroid appears to provide a better signal-to-noise ratio than the optical method. Figure 3a in Roth and Wikswo (1985) shows that a signal of about 300 pT peak-to-peak can be detected with a signal-to-noise ratio of roughly 20 with no averaging (I don’t need to look at our 1985 paper to know this, I have a framed copy of this data on display in my office). Figure 2c of Barry et al. (2016) shows a 4000 pT peak-to-peak signal measured optically with a signal-to-noise ratio of about 10 after 600 averages. Perhaps this comparison is unfair because in 1985 we had spent several years optimizing our toroids, whereas this is a first measurement using the optical technique. Nevertheless, I think the toroids have a better signal-to-noise ratio. Winner: toroids.
3. The optical technique appears to have better spatial resolution, although not dramatically so. Our toroids were typically one or two millimeters in size. In the optical method, the sensing layer is only 13 microns thick, but the length over which the detection occurs is two millimeters, so their method corresponds to a wide but small-diameter toroid. The spatial resolution of both methods could probably be improved, but once the size of the recording device is less than the length over which the action potential upstroke extends (about a millimeter) there is little to be gained by making the detector smaller. Both methods integrate the magnetic signal over the area of the device. Interestingly, the solution to last weeks new homework problem--integrating the biomagnetic field over the cross section of the toroid--is derived in the page 8 of the Barry et al.'s supplementary information. Winner: optical method.
4. The optical method has better temporal resolution. Both, however, have  temporal resolution adequate to record action potentials with an upstroke of a tenth of a millisecond or longer. The toroid does not record the time course of the magnetic field directly, but rather a mixture of the magnetic field and its derivative, and the technique requires a calibration pulse to get the “frequency compensation” correct. As best I can tell, the optical method measures the magnetic field directly. However, I believe any errors arising from frequency compensation of the toroids are small, and that the temporal resolution of both methods is fine. Winner: optical method.
5. The toroids are encapsulated in epoxy, so they are biocompatible. I don’t know how biocompatible the optical method is, but I suspect it could be made biocompatible if a thin insulating layer covered the detecting layer, with a very small and probably negligible reduction in spatial resolution. Winner: tie.
6. The question of convenience is tricky. I am accustomed to using the toroids, so that to me they are not difficult to use, whereas I have never tried the optical method. Nevertheless, I think toroids are more convenient. The optical method requires a static bias magnetic field, and toroids do not. Toroid measurements are insensitive to the exact position of the nerve within the toroid, whereas the optical method appears to be sensitive to the exact placement of the nerve on or near the detector. The optical method requires a spectroscopic analysis of the light signal; the toroid only needs an amplifier to record the current induced in the toroid winding. Finally, the optical method is based on magnetic splitting of spin states and magnetic resonance, whereas toroids rely on good old Faraday induction—my kind of physics. Although I consider toroids more convenient, I would not want to defend that opinion against a skeptical scientist holding a different view, because it is more a matter of taste than science. Winner: toroids.

The result is 3 for the optical method, 2 for toroids, and 1 tie. However, the optical method victories for spatial and temporal resolution were close calls, whereas the toroid victory for signal-to-noise ratio was a landslide. This is not the electoral college: I declare toroids to be the overall winner. (It’s my blog!)

Perhaps a more interesting comparison is for situations where you want to make two-dimensional measurements of current distributions. Barry et al. discuss how the optical method might be extended to do 2D imaging. The traditional method that would be the main competition would be Wikswo’s microSQUID or nanoSQUID: an array of small superconducting coils placed over a sample. But in that case you need cryogenics to keep the coils cold, and I could easily see how a room-temperature array of quantum defect detectors in diamond, recorded optically with a camera, might be simpler.

Both the optical method and toroids require placing a detector near the nerve, so both are invasive. However, if (IF!) the biomagnetic field can be used as the gradient field for magnetic resonance imaging (see my June 3 post) then that technique becomes totally noninvasive. Winner: MRI.

Capabilities of a Toroid-Amplifier System for Magnetic Measurement of Current in Biological Tissue

In Section 8.9 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the detection of weak magnetic fields.

If the [magnetic] signal is strong enough, it can be detected with conventional coils and signal-averaging techniques that are described in Chap. 11. Barach et al. (1985) used a small detector through which a single axon was threaded. The detector consisted of a toroidal magnetic core wound with many turns of fine wire... Current passing through the hole in the toroid generated a magnetic field that was concentrated in the ferromagnetic material of the toroid. When the field changed, a measurable voltage was induced in the surrounding coil. This neuromagnetic current probe has been used to study many nerve and muscle fibers (Wijesinghe 2010).

I have discussed the neuromagnetic current probe before in this blog. One of the best places to learn more about it is a paper by Frans Gielen, John Wikswo, and me in the IEEE Transactions on Biomedical Engineering (Volume 33, Pages 910–921, 1986). The paper begins

In one-dimensional tissue preparations, bioelectric action currents can be measured by threading the tissue through a wire-wound, ferrite-core toroid that detects the associated biomagnetic field. This technique has several experimental advantages over standard methods used to measure bioelectric potentials. The magnetic measurement does not damage the cell membrane, unlike microelectrode recordings of the internal action potential. Recordings can be made without any electrical contact with the tissue, which eliminates problems associated with the electrochemistry at the electrode-tissue interface. While measurements of the external electric potential depend strongly on the distance between the tissue and the electrode, measurements of the action current are quite insensitive to the position of the tissue in the toroid. Measurements of the action current are also less sensitive to the electrical conductivity of the tissue around the current source than are recordings of the external potential.

Figure 1 of this paper shows the toroid geometry

When I was measuring biomagnetic fields back in graduate school, I wanted to relate the magnetic field in the toroid to the current passing through it. For simplicity, assume the current is in a wire passing through the toroid center. The magnetic field B a distance r from a wire carrying current i is (Eq. 8.7 in IPMB)

where μ is the magnetic permeability. The question is, what value should I use for r? Should I use the inner radius, the outer radius, the width, or some combination of these? The answer can be found by solving this new homework problem.

Section 8.2

Problem 11 1/2. Suppose a toroid having inner radius c, outer radius d, and width e is used to detect current i in a wire threading the toroid’s center. The voltage induced in the toroid is proportional to the magnetic flux through its cross section.

(a) Integrate the magnetic field produced by the current in the wire across the cross section of the ferrite core to obtain the magnetic flux.

(b) Calculate the average magnetic field in the toroid, which is equal to the flux divided by the toroid cross-sectional area.

(c) Define the “effective radius” of the toroid, r_eff, as the radius needed in Eq. 8.7 to relate the current in the wire to the average magnetic field. Derive an expression for r_eff in terms of the parameters of the toroid.

(d) If c = 1 mm, d = 2 mm, e = 1 mm, and μ=10⁴μ_o, calculate r_eff.

The solution to this homework problem, the effective radius, appears on page 915 of our paper.

Finally, and just for fun, below I reproduce the short bios published with the paper, which appeared 30 years ago.

The Millikan Oil Drop Experiment

Selected Papers of
Great American Physicists.

When I was in college, I was given a book published by the American Institute of Physics titled Selected Papers of Great American Physicists. Of the seven articles reprinted in this book, my favorite was “On the Elementary Electrical Charge and the Avogadro Constant” by Robert Millikan. Maybe I enjoyed it so much because I had performed the Millikan oil drop experiment as an undergraduate physics major at the University of Kansas. (I have discussed Millikan and his experiment previously in this blog.)

The charge of an electron is encountered often in Intermediate Physics for Medicine and Biology. It’s one of those constants that’s so fundamental to both physics and biology that it’s worth knowing how it was first measured. Below is a new homework problem requiring the student to analyze data like that obtained by Millikan. I have designated it for Chapter 6, right after the analysis of the force on a charge in an electric field and the relationship between the electric field and the voltage. I like this problem because it reinforces several concepts already discussed in IPMB (Stoke's law, density, viscosity, electrostatics), it forces the student to analyze data like that obtained experimentally, and it provides a mini history lesson.

Section 6.4

Problem 11 ½. Assume you can measure the time required for a small, charged oil drop to move through air (perhaps by watching it through a microscope with a stop watch in your hand). First, record the time for the drop to fall under the force of gravity. Then record the time for the drop to rise in an electric field. The drop will occasionally gain or lose a few electrons. Assume the drop’s charge is constant over a few minutes, but varies over the hour or two needed to perform the entire experiment, which consists of turning the electric field on and off so one drop goes up and down.

(a) When the drop falls with a constant velocity v₁ it is acted on by two forces: gravity and friction given by Stokes’ law. When the drop rises at a constant velocity v₂ it is acted on by three forces: gravity, friction, and an electrical force. Derive an expression for the charge q on your drop in terms of v₁ and v₂. Assume you know the density of the oil ρ, the viscosity of air η, the acceleration of gravity g, and the voltage V you apply across two plates separated by distance L to produce the electric field. These drops, however, are so tiny that you cannot measure their radius a. Therefore, your expression for q should depend on v₁, v₂, ρ, η, g, V, and L, but not a.

(b) You perform this experiment, and find that whenever the voltage is off the time required for the drop to fall 10 mm is always 12.32 s. Each time you turn the voltage on the drop rises, but the time to rise 10 mm varies because the number of electrons on the drop changes. Successive experiments give rise times of 162.07, 42.31, 83.33, 33.95, 18.96, and 24.33 s. Calculate the charge on the drop in each case. Assume η = 0.000018 Pa s, ρ = 920 kg m^-3, V = 5000 V, L = 15 mm, and g = 9.8 m s^-2.

(c) Analyze your data to find the greatest common divisor for the charge on the drop, which you can take as the charge of a single electron. Hint: it may be easiest to look at changes in the drop’s charge over time.

What impressed me most about Millikan’s paper was his careful analysis of sources of systematic error. He went to great pains to determine accurately the viscosity of air, and he accounted for small effects like the mean free path of the air molecules and the drop's buoyancy (effects you can neglect in the problem above). He worried about tiny sources of error such as distortions of the shape of the drop caused by the electric field. When I was a young graduate student, Millikan’s article provided my model for how you should conduct an experiment.

Intermediate Physicist for Medicine and Biology

In my more contemplative moments, I sometimes ponder: who am I? Or perhaps better: what am I? In my personal life I am many things: son, husband, father, brother, dog-lover, die-hard Cubs fan, Asimov aficionado, Dickens devotee, and mid-twentieth-century-Broadway-musical-theatre admirer.

What I am professionally is not as clear. By training I’m a physicist. Each month I read Physics Today and my favorite publication is the American Journal of Physics. But in many ways I don’t fit well in physics. I don’t understand much of what’s said at our weekly physics colloquium, and I have little or no interest in topics such as high energy physics. Quantum mechanics frightens me.

The term biophysicist doesn’t apply to me, because I don’t work at the microscopic level. I don’t care about protein structures or DNA replication mechanisms. I’m a macroscopic guy.

My work overlaps that of biomedical engineers, and indeed I publish frequently in biomedical engineering journals. But my work is not applied enough for engineering. In the 1990s, when searching desperately for a job, I considered positions in biomedical engineering departments, but I was never sure what I would teach. I have no idea what’s taught in engineering schools. Ultimately I decided that I fit better in a physics department.

Mathematical biologist is a better definition of me. I build mathematical models of biological systems for a living. But I’m at heart neither a mathematician nor a biologist. I find math papers—full of  theorem-proof-theorem-proof—to be tedious. Biologists celebrate life’s diversity, which is exactly the part of biology I like to sweep under the rug.

I’m not a medical physicist. Nothing I have worked on has healed anyone. Besides, medical physicists work in nuclear medicine and radiation therapy departments at hospitals, and they get paid a lot more that I do. No, I’m definitely not a medical physicist. Perhaps one of the most appropriate labels is biological physicist—whatever that means.

Another question is: at what level do I work? I’m not a popularizer of science or a science writer (except when writing this blog, which is more of a hobby; my “Hobbie hobby”). I write research papers and publish them in professional journals. Yet, in these papers I build toy models that are as simple as possible (but no simpler!). Reviewers of my manuscripts write things like “the topic is interesting and the paper is well-written, but the model is too simple; it fails to capture the underlying complexity of the system.” When my simple models grow too complicated, I change direction and work on something else. So my research is neither at an introductory level nor an advanced level.

I guess the best label for me is: Intermediate Physicist for Medicine and Biology.

Molybdenum-99 for Medical Imaging

Molybdenum-99 for Medical Imaging,
published by the National Academies Press.

Between 2007 and 2011, I wrote several blog posts about a shortage of the radioisotope technetium-99m (here, here, here, and here). Chapter 17 of Intermediate Physics for Medicine and Biology discusses the many uses of ^99mTc in nuclear medicine. It is produced from the decay of molybdenum-99, and shortages arise because of dwindling sources of ⁹⁹Mo.

Recently, the Committee on State of Molybdenum-99 Production and Utilization and Progress Toward Eliminating Use of Highly Enriched Uranium addressed this issue in their report Molybdenum-99 for Medical Imaging, published by the National Academies Press. Below I reproduce excerpts from the executive summary.

This Academies study was mandated by the American Medical Isotopes Production Act of 2012. Key results for each of the five study charges are summarized below…

Study charge 1: Provide a list of facilities that produce molybdenum-99 (Mo-99) for medical use including an indication of whether these facilities utilize highly enriched uranium (HEU)… About 95 percent of the global supply of Mo-99 for medical use is produced in seven research reactors and supplied from five target processing facilities located in Australia, Canada, Europe, and South Africa. About 5 percent of the global supply is produced in other locations for regional use. About 75 percent of the global supply of Mo-99 for medical use is produced using HEU targets; the remaining 25 percent is produced with low enriched uranium targets….

Study charge 2: Review international production of Mo-99 over the previous 5 years … New Mo-99 suppliers have entered the global supply market since 2009 and further expansions are planned. An organization in Australia (Australian Nuclear Science and Technology Organisation) has become a global supplier and is currently expanding its available supply capacity; existing global suppliers in Europe (Mallinckrodt) and South Africa (NTP Radioisotopes) are also expanding ... A reactor in France (OSIRIS) that produced Mo-99 shut down permanently in December 2015. The reactor in Canada (NRU) will stop the routine production of Mo-99 after October 2016 and permanently shut down at the end of March 2018.

Study charge 3: Assess progress made in the previous 5 years toward establishing domestic production of Mo-99 and associated medical isotopes iodine-131 (I-131) and xenon-133 (Xe-133) … The American Medical Isotopes Production Act of 2012 and financial support from the Department of Energy’s National Nuclear Security Administration … have stimulated private-sector efforts to establish domestic production of Mo-99 and associated medical isotopes. Four NNSA-supported projects and several other private-sector efforts are under way to establish domestic capabilities to produce Mo-99; each project is intended to supply half or more of U.S. needs…. it is unlikely that substantial domestic supplies of Mo-99 will be available before 2018. Neither I-131 nor Xe-133 is currently produced in the United States, but one U.S. organization (University of Missouri Research Reactor Center) is developing the capability to supply I-131; some potential domestic Mo-99 suppliers also have plans to supply I-131 and/or Xe-133 in the future.

Study charge 4: Assess the adequacy of Mo-99 supplies to meet future domestic medical needs, particularly in 2016 and beyond …The United States currently consumes about half of the global supply of Mo-99/technetium-99m (Tc-99m) for medical use; global supplies of Mo-99 are adequate at present to meet domestic needs. Domestic demand for Mo-99/Tc-99m has been declining for at least a decade and has declined by about 25 percent between 2009-2010 and 2014-2015; domestic medical use of Mo-99/Tc-99m is unlikely to increase significantly over the next 5 years. The committee judges that there is a substantial ... likelihood of severe Mo-99/Tc-99m supply shortages after October 2016, when Canada stops supplying Mo-99, lasting at least until current global Mo-99 suppliers complete their planned capacity expansions (planned for 2017) and substantial new domestic Mo-99 supplies enter the market (not likely until 2018 and beyond)….

Study charge 5: Assess progress made by the DOE and others to eliminate worldwide use of HEU in reactor targets and medical isotope production facilities and identify key remaining obstacles for eliminating HEU use… The American Medical Isotopes Production Act of 2012 is accelerating the elimination of worldwide use of HEU for medical isotope production [to reduce the amount of HEU available for production of weapons of mass destruction by terrorist groups]. Current global Mo-99 suppliers have committed to eliminating HEU use in reactor targets and medical isotope production facilities and are making uneven progress toward this goal. Progress is … being impeded by the continued availability of Mo-99 produced with HEU targets … Even after HEU is eliminated from Mo-99 production, large quantities of HEU-bearing wastes from past production will continue to exist at multiple locations throughout the world…

News articles associated with the release of the report can be found here, here, here, and here. The message I get from this report is that the long-term prognosis for ⁹⁹Mo supplies is promising, but the short-term outlook is worrisome. Let us hope I’m too pessimistic.

Mathematical Physiology

Mathematical Physiology,
by James Keener and James Sneyd.

In a comment to the blog last week, Frankie mentioned the two-volume textbook Mathematical Physiology (MP), by James Keener and James Sneyd. Russ Hobbie and I cite Keener and Sneyd in Chapter 10 (Feedback and Control) of Intermediate Physics for Medicine and Biology. The Preface to the first edition of MP begins:

It can be argued that of all the biological sciences, physiology is the one in which mathematics has played the greatest role. From the work of Helmholtz and Frank in the last century through to that of Hodgkin, Huxley, and many others in this century [the first edition of MP was published in 1998], physiologists have repeatedly used mathematical methods and models to help their understanding of physiological processes. It might thus be expected that a close connection between applied mathematics and physiology would have developed naturally, but unfortunately, until recently, such has not been the case.

There are always barriers to communication between disciplines. Despite the quantitative nature of their subject, many physiologists seek only verbal descriptions, naming and learning the functions of an incredibly complicated array of components; often the complexity of the problem appears to preclude a mathematical description. Others want to become physicians, and so have little time for mathematics other than to learn about drug dosages, office accounting practices, and malpractice liability. Still others choose to study physiology precisely because thereby they hope not to study more mathematics, and that in itself is a significant benefit. On the other hand, many applied mathematicians are concerned with theoretical results, proving theorems and such, and prefer not to pay attention to real data or the applications of their results. Others hesitate to jump into a new discipline, with all its required background reading and its own history of modeling that must be learned.

But times are changing, and it is rapidly becoming apparent that applied mathematics and physiology have a great deal to offer one another. It is our view that teaching physiology without a mathematical description of the underlying dynamical processes is like teaching planetary motion to physicists without mentioning or using Kepler’s laws; you can observe that there is a full moon every 28 days, but without Kepler’s laws you cannot determine when the next total lunar or solar eclipse will be nor when Halley’s comet will return. Your head will be full of interesting and important facts, but it is difficult to organize those facts unless they are given a quantitative description. Similarly, if applied mathematicians were to ignore physiology, they would be losing the opportunity to study an extremely rich and interesting field of science.

To explain the goals of this book, it is most convenient to begin by emphasizing what this book is not; it is not a physiology book, and neither is it a mathematics book. Any reader who is seriously interested in learning physiology would be well advised to consult an introductory physiology book such as Guyton and Hall (1996) or Berne and Levy (1993), as, indeed, we ourselves have done many times. We give only a brief background for each physiological problem we discuss, certainly not enough to satisfy a real physiologist. Neither is this a book for learning mathematics. Of course, a great deal of mathematics is used throughout, but any reader who is not already familiar with the basic techniques would again be well advised to learn the material elsewhere.

Instead, this book describes work that lies on the border between mathematics and physiology; it describes ways in which mathematics may be used to give insight into physiological questions, and how physiological questions can, in turn, lead to new mathematical problems. In this sense, it is truly an interdisciplinary text, which, we hope, will be appreciated by physiologists interested in theoretical approaches to their subject as well as by mathematicians interested in learning new areas of application.

If you substitute the words “physics” for “mathematics,” “physical” for “mathematical,” and “physicist” for “mathematician,” you would almost think that this preface had been written by Russ Hobbie for an early edition of IPMB.

Many of the topics in MP overlap those in IPMB: diffusion, bioelectricity, osmosis, ion channels, blood flow, and the heart. MP covers additional topics not in IPMB, such as biochemical reactions, calcium dynamics, bursting pancreatic beta cells, and the regulation of gene expression. What IPMB has that MP doesn’t is clinical medical physics: ultrasound, x-rays, tomography, nuclear medicine, and MRI. Both books assume a knowledge of calculus, both average many equations per page, and both have generous collections of homework problems.

Which book should you use? Mathematical Physiology won an award, but Intermediate Physics for Medicine and Biology has an award-winning blog. I’ll take the book with the blog. I bet I know what Frankie will say: “I’ll take both!”