Friday, February 28, 2020

Magnetoencephalography: Theory, Instrumentation, and Applications to Noninvasive Studies of the Working Human Brain

Screenshot of the title and abstract of Hämäläinen, Hari, Ilmoniemi, Knuutila, and Lounasmaa, "Magnetoencephalography: Theory, Instrumentation, and Applications to Noninvasive Studies of the Working Human Brain. Rev. Mod. Phys. 65:413-497, 1993.
Hämäläinen et al. (1993).
In Chapter 8 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I cite one of my favorite review papers: “Magnetoencephalography: Theory, Instrumentation, and Applications to Noninvasive Studies of the Working Human Brain,” by Matti Hämäläinen, Rita Hari, Risto Ilmoniemi, Jukka Knuutila and Olli Lounasmaa (Reviews of Modern Physics, Volume 65, Pages 413-497, 1993). The authors worked in the Low Temperature Laboratory at Helsinki University of Technology in Espoo, Finland. Even though this review is over 25 years old, it remains an excellent introduction to recording biomagnetic fields of the brain. According to Google Scholar, this classic 84-page reference has been cited over 4500 times. Below is the abstract.
Magnetoencephalography (MEG) is a noninvasive technique for investigating neuronal activity in the living human brain. The time resolution of the method is better than 1 ms and the spatial discrimination is, under favorable circumstances, 2—3 mm for sources in the cerebral cortex. In MEG studies, the weak 10 fT—1 pT magnetic fields produced by electric currents flowing in neurons are measured with multichannel SQUID (superconducting quantum interference device) gradiometers. The sites in the cerebral cortex that are activated by a stimulus can be found from the detected magnetic-field distribution, provided that appropriate assumptions about the source render the solution of the inverse problem unique. Many interesting properties of the working human brain can be studied, including spontaneous activity and signal processing following external stimuli. For clinical purposes, determination of the locations of epileptic foci is of interest. The authors begin with a general introduction and a short discussion of the neural basis of MEG. The mathematical theory of the method is then explained in detail, followed by a thorough description of MEG instrumentation, data analysis, and practical construction of multi-SQUID devices. Finally, several MEG experiments performed in the authors laboratory are described, covering studies of evoked responses and of spontaneous activity in both healthy and diseased brains. Many MEG studies by other groups are discussed briefly as well.
Russ and I mention this review several times in IPMB. When we want to show typical MEG data, we reproduce their Figure 47, showing the auditory magnetic response evoked by listening to words (our Fig. 8.20). Below is a version of the figure with some color added.

Reproduction of Fig 47 from Hämäläinen et al. (1993), showing an auditory evoked magnetic field from the brain.
Effect of attention on responses evoked by auditorily presented words.
The subject was either ignoring the stimuli by reading (solid trace)
or listening to the sounds during a word categorization task (dotted trace);
the mean duration of the words is given by the bar on the time axis.
The field maps are shown during the N100m deflection and the sustained
field for both conditions. The contours are separated by 20 fT and the dots
illustrate the measurement locations. The origin of the coordinate system,
shown on the schematic head, is 7 cm backwards from the eye corner,
and the x axis forms a 45 angle with the line connecting the ear to the eye.
Adapted from Hämäläinen et al. (1993).
We also refer to the article when discussing SQUID gradiometers, which they discuss in detail. Russ and I have a figure in IPMB showing two types of gradiometers; here I show a color version of this figure adapted from Hämäläinen et al.
Red: a magnetometer. Green: a planer gradiometer.  Blue: an axial gradiometer. Purple: a second-order gradiometer.  Adapted from Hämäläinen et al. (1993).
Red: a magnetometer. Green: a planer gradiometer.
Blue: an axial gradiometer. Purple: a second-order gradiometer.
Adapted from Hämäläinen et al. (1993).
In Chapter 11 of IPMB, Russ and I reproduce my favorite figure from Hämäläinen et al.: their Fig. 8, showing the spectrum of several magnetic noise sources. Earlier in our book, Russ and I warn readers to beware of log-log plots in which the distance spanned by a decade is not the same on the vertical and horizontal axes. Below I redraw Hämäläinen et al.’s figure with the same scaling for each axis. The advantage of this version is that you can easily estimate the power law relating noise to frequency from the slope of the curve. The disadvantage is that you get a tall, skinny illustration.

A reproduction of Fig. 1 from Hämäläinen et al. (1993), showing peak amplitudes and spectral densities of fields due to typical biomagnetic and noise sources.
Peak amplitudes (arrows) and spectral densities of
fields due to typical biomagnetic and noise sources.
Adapted from Hämäläinen et al. (1993).
I like many things about Hämäläinen et al.’s the review. They present some lovely pictures of neurons drawn by Ramon Cajal. There’s a detailed discussion of the magnetic inverse problem, and a long analysis of evoked magnetic fields. In IPMB, Russ and I mention using a magnetically shielded room to reduce the noise in MEG data, but don’t give details. Hämäläinen et al. describe their shielded room:
The room is a cube of 2.4-m inner dimensions with three layers of μ-metal, which are effective for shielding at low frequencies of the external magnetic noise spectrum (particularly important for biomagnetic measurements), and three layers of aluminum, which attenuate very well the high-frequency band. The shielding factor is 103—104 for low-frequency magnetic fields and about 105 for fields of 10 Hz and above.
They show a nice photo of a subject having her MEG measured in this room; I hope she’s not claustrophobic.

The authors were members of a leading biomagnetism group in the 1990s. Matti Hämäläinen is now with the Athinoula A. Martinos Center for Biomedical Imaging at Massachusetts General Hospital and is a professor at Harvard. Rita Hari is an emeritus professor at Aalto University (formerly the Helsinki University of Technology). Risto Ilmoniemi is now head of the Department of Neuroscience and Biomedical Engineering at Aalto. Olli Lounasmaa (1930—2002), the leader of this impressive group, was known for his research in low temperature physics. In 2012 the Low Temperature Laboratory at Aalto was renamed the O. V. Lounasmaa Laboratory in his honor.

What do I like best about the Finn’s landmark review? They cite me! In particular, the experiment I performed as a graduate student working with John Wikswo to measure the magnetic field of a single axon.
Wikswo et al. (1980) reported the first measurements of the magnetic field of a peripheral nerve. They used the sciatic nerve in the hip of a frog; the fiber was threaded through a toroid in a saline bath. When action potentials were triggered in the nerve, a biphasic magnetic signal of about 1 ms duration was detected. Later, the magnetic field of an action potential propagating in a single giant crayfish axon was recorded as well (Roth and Wikswo, 1985). The measured transmembrane potential closely resembled that calculated from the observed magnetic field. From these two sets of data, it was possible to determine the intracellular conductivity.
The videos below, presented by several of the authors, augment the discussion of biomagnetism in Intermediate Physics for Medicine and Biology, and provide a short course in magnetoencephalography. Enjoy!

Matti Hämäläinen: MEG and EEG Signals and Their Sources, 2014.

Rita Hari: How Does a Neuroscientist View Signals and Noise in MEG Recordings, 2015.

Interview with Risto Ilmoniemi, Helsinki, 2015.

Friday, February 21, 2020

Replacement of the Axoplasm of Giant Nerve Fibres with Artificial Solutions

When discussing the electrophysiology of nerve and muscle fibers in Section 6.1 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I write
The axoplasm has been squeezed out of squid giant axons and replaced by an electrolyte solution without altering appreciably the propagation of the impulses—for a while, until the ion concentrations change significantly.
Really? The axoplasm can be squeezed out of an axon like toothpaste? Who does that?

Screenshot of the start of Baker et al. "Replacement of the Axoplasm of Giant Nerve Fibres with Artificial Solutions," J. Physiol., 164:330-354, 1962.
Baker et al. (1962).
The technique is described in an article by Baker, Hodgkin and Shaw (“Replacement of the Axoplasm of Giant Nerve Fibres with Artificial Solutions,” Journal of Physiology, Volume 164, Pages 330-354, 1962). The second author is Alan Hodgkin, Nobel Prize winner with Andrew Huxley “for their discoveries concerning the ionic mechanisms involved in excitation… of the nerve cell membrane.”

Below is my color version of Baker et al.’s Figure 1.
Internal perfusion of an axon.  Adapted from Figure 1D of Baker, Hodgkin and Shaw  J. Physiol., 164:330-354, 1962.
Internal perfusion of an axon.
Adapted from Figure 1D of Baker, Hodgkin and Shaw,
J. Physiol., 164:330-354, 1962.
Their methods section (with my color coding in brackets) states
A cannula [red] filled with perfusion fluid [baby blue] was tied [green] into the distal end of a giant axon [black] of length 6-8 cm. The axon was placed on a rubber pad [dark blue] and axoplasm [yellow] was extruded by passing a rubber-covered roller [purple] over it in a series of sweeps…
I like how a little mound of axoplasm piles up at the end of the fiber (yellow, right). They continue
After an axon had been extruded and perfused it was tied at the lower end, filled with perfusion fluid and impaled with an internal electrode by almost exactly the same method as that used with an intact axon…

One might suppose that this would be disastrous and axons were occasionally damaged by the internal electrode. However, in many instances we recorded action potentials of 100-110 mV for several hours.
This experiment is a tour de force. I can think of no better way to demonstrate that the action potential is a property of the nerve membrane, not the axoplasm.

You may already know Hodgkin, but who is Baker?

Hodgkin was coauthor of an obituary of Peter Frederick Baker (1939-1987), published in the Biographical Memoirs of Fellows of the Royal Society. After describing Baker’s childhood, Hodgkin wrote that he met the undergraduate Baker
when he had just obtained a first class in biochemistry part II. Partly at the suggestion of Professor F. G. Young, Peter decided that he would like to join Hodgkin’s group in the Physiological Laboratory in Cambridge. He also welcomed the suggestion that he should divide his time between Cambridge and the Laboratory of the Marine Biological Association at Plymouth, where there were many experiments to be done on the giant nerve fibres of the squid.
Hodgkin then describes Baker's experiments on internal perfusion of nerve axons.
Peter started work at Plymouth with Trevor Shaw in September 1960 and almost immediately the pair struck gold by showing that after the protoplasm had been squeezed out of a giant nerve fibre, conduction of impulses could be restored by perfusing the remaining membrane and sheath with an appropriate solution... Later, Baker, Hodgkin and Shaw… spent some time working out the best method of changing internal solutions while recording electrical phenomena with an internal electrode. It turned out that it did not matter much what solution was inside the nerve fibre as long as it contained potassium and little sodium. Provided that this condition is satisfied, a perfused nerve fibre is able to conduct nearly a million impulses without the intervention of any biochemical process. ATP is needed to pump out sodium and reabsorb potassium but not for the actual conduction of impulse.

There were also several unexpected findings of which perhaps the most interesting was that reducing the internal ionic strength caused a dramatic shift in the operating voltage characteristic of the membrane... This effect, which finds a straightforward explanation in terms of the potential gradients generated by charged groups on the inside of the membrane, helped to explain several unexpected results that were sometimes thought to be inconsistent with the ionic theory of nerve conduction.
Baker went on to perform an impressive list of research projects (his obituary cites nearly 200 publications). Unfortunately, he died young. Hodgkin concludes
Peter Baker’s sudden death from a heart attack at the early age of 47 has deprived British science of one of its most gifted and versatile biologists. He was at the height of his scientific powers and had many ideas for new lines of research, particularly in the borderland between molecular biology and physiology.
Both Baker and Hodgkin appear in this video. They are demonstrating voltage clamping, not internal perfusion.

Watch Alan Hodgkin and Peter Baker demonstrate voltage clamping.

Friday, February 14, 2020

Titan: The Life of John D. Rockefeller

Titan: The Life of John D. Rockefeller, Sr., by Ron Chernow, superimposed on Intermediate Physics for Medicine and Biology.
Titan: The Life of John D. Rockefeller, Sr.,
by Ron Chernow.
Recently I listened to an audio recording of Titan: The Life of John D. Rockefeller, Sr. by Ron Chernow. Rockefeller reminds me of Bill Gates: corporate corruption, fantastic fortune, and phenomenal philanthropy. Chernow says that Rockefeller’s “good side was every bit as good as his bad side was bad. Seldom has history produced such a contradictory figure.”

Rockefeller intersects with Intermediate Physics for Medicine and Biology through the Rockefeller Foundation and The Rockefeller Institute for Medical Research, now known as the Rockefeller University. Russ Hobbie and I mention the name “Rockefeller” once in IPMB, a Chapter 6 reference to a report written by neuroscientist Rafael Lorente de Nó, who worked at Rockefeller University for decades.
Davis L Jr, Lorente de Nó R (1947) Contribution to the mathematical theory of the electrotonus. Stud Rockefeller Inst Med Res Repr 131(Part 1):442–496.
Lady Luck, by Warren Weaver, superimposed on Intermediate Physics for Medicine and Biology.
Lady Luck, by Warren Weaver.
In Chapter 3 we cite Lady Luck by Warren Weaver, the director of the Division of Natural Sciences at the Rockefeller Foundation. Their website states that in 1932
Warren Weaver comes to the Foundation and during his 27-year association becomes the principal architect of programs in the natural sciences. He sees his task as being “to encourage the application of the whole range of scientific tools and techniques, and specially those which had been so superbly developed in the physical sciences, to the problems of living matter.”
He sounds like an IPMB kind of guy.

Ion Channels of Excitable Membranes,  by Bertil Hille, superimposed on Intermediate Physics for Medicine and Biology.
Ion Channels of Excitable Membranes,
by Bertil Hille.
In Chapter 9, Russ and I discuss Roderick MacKinnon, who first determined the structure of the potassium channel. MacKinnon leads a laboratory at Rockefeller University, located in Manhattan along the East River about a mile north of the United Nations headquarters. Nowadays students earn graduate degrees from Rockefeller University. Bertil Hille, author of Ion Channels of Excitable Membranes, is an alum.

Rockefeller University hosts the Center for Studies in Physics and Biology, whose website states
The Center for Studies in Physics and Biology was conceived by physicists and biologists to increase communication between their disciplines, with the goal of developing innovative solutions to biological questions. Much of the work at the center aims to understand how physical laws govern the operation of biochemical machinery and the processing of information inside cells. To this end, researchers study both the basic physical properties of biological systems (such as elasticity of DNA and DNA-protein interactions) and the application of physical techniques to the modeling of neural, genetic, and metabolic networks.
Although the research is more microscopic that you would typically find in our book, the Center epitomizes the goal of Intermediate Physics for Medicine and Biology: apply physics and mathematics to research in medicine and biology. I sometimes see the Center advertising for fellows, and suspect it would be an interesting place to work.

A photo of John D. Rockefeller.
John D. Rockefeller,
from Wikipedia.

John D. Rockefeller was one of the greatest philanthropists of all time. Besides Rockefeller University and the Rockefeller Foundation, he helped found both the University of Chicago and Spelman College. His family has carried on his philanthropic tradition. Three years ago, Rockefeller’s grandson David Rockefeller passed away. The university website said
The entire Rockefeller University community deeply mourns the loss of David Rockefeller, our beloved friend and benefactor, Honorary Chairman, and Life Trustee. During its long and storied history, no single individual had a more profound influence on the University than David. His inspired leadership, extraordinary vision, and immense generosity have been essential factors in the University’s success. His integrity, strength, wisdom, and judgment—and especially his unequivocal commitment to excellence—shaped the University and made it the powerhouse of biomedical discovery it is today.
One of the greatest philanthropists of our time, as well as one of the world’s foremost leaders in the spheres of finance, international relations, and public service, David Rockefeller dedicated his life to improving the world and the lives of all who share our planet. David was born in New York City in 1915, the youngest of Abby Aldrich Rockefeller and John D. Rockefeller, Jr.’s six children and a grandson of John D. Rockefeller.
One of my favorite parts of Titan is the story about Rockefeller’s dad, William Rockefeller, a bigamist, con artist, and snake oil salesman. Chernow isn’t fond of Ida Tarbell, the muckraking journalist who wrote influential articles in McClure’s Magazine condemning Standard Oil, the company founded by Rockefeller. Tarbell’s articles led the trust buster Teddy Roosevelt to brake up the monopoly.

Ron Chernow is an excellent writer who’s written fine books about Grant and Washington. He’s best known for his wonderful biography of Alexander Hamilton, which inspired Lin Manuel-Miranda’s musical masterpiece Hamilton.

Listen to Ron Chernow talk about John D. Rockefeller.

My favorite song from Hamilton: “It’s Quiet Uptown.”

Friday, February 7, 2020

Influence of a Perfusing Bath on the Foot of the Cardiac Action Potential

Roth BJ, “Influence of a Perfusing Bath on the Foot of the Cardiac Action Potential,” Circ. Res., 86:e19-e22, 2000.
Roth BJ, “Influence of a Perfusing Bath on the
Foot of the Cardiac Action Potential,”
Circ. Res., 86:e19-e22, 2000.
Twenty years ago this week, I published a Research Commentary in Circulation Research about the “Influence of a Perfusing Bath on the Foot of the Cardiac Action Potential” (Volume 86, Pages e19-e22, 2000). I like this article for several reasons: it’s short and to the point; it’s a theoretical paper closely tied to data; it’s well written; and it challenges a widely-accepted interpretation of an experiment by a major figure in cardiac electrophysiology.

Back in my more pugnacious days, I wouldn’t hesitate to take on senior scientists when I disagreed with them. In this case, I critiqued the work of Madison Spach, a Professor at Duke University and a towering figure in the field. In 1981, Spach led an all-star team that measured cardiac action potentials propagating either parallel to or perpendicular to the myocardial fibers.
Spach MS, Miller WT III, Geselowitz DB, Barr RC, Kootsey JM, Johnson EA. “The Discontinuous Nature of Propagation in Normal Canine Cardiac Muscle: Evidence for Recurrent Discontinuities of Intracellular Resistance that Affect the Membrane Currents. Circulation Research, Volume 48, Pages 39–45, 1981.
Spach et al., “The Discontinuous Nature of Propagation in Normal Canine Cardiac Muscle: Evidence for Recurent Discontinuities of Intracellular Resistance that Affect the Membrane Currents,” Circ. Res., 48:39-45, 1981.
Spach et al., “The Discontinuous Nature of
Propagation in Normal Canine Cardiac Muscle:
Evidence for Recurrent Discontinuities of
Intracellular Resistance that Affect the
Membrane Currents,” Circ. Res., 48:39-45, 1981.
They found that the rate-of-rise of the action potential and the time constant of the action potential foot depend on the direction of propagation. Continuous cable theory predicts that the rate-of-rise and time constant should be the same, regardless of direction. Therefore, they concluded, cardiac tissue is not continuous. Instead, they claimed that their experiment revealed the tissue’s discrete structure.

To be sure, cardiac tissue is discrete in a sense. It’s made of individual cells, coupled by intercellular junctions to form a “syncytium.” Often, however, you can average over the cellular structure and treat the tissue as a continuum, just as you can often treat a material as a continuum even through it’s made from discrete atoms. For example, the bidomain model is a continuous description of the electrical properties of a microscopically heterogeneous tissue (See Section 7.9 of Intermediate Physics for Medicine and Biology for more about the bidomain model).

I’m skeptical of Spach’s interpretation of his data, and I’m not convinced that his observations imply the tissue’s discrete nature. I didn’t waste any time making this point in my article; I mention Spach by name in the first sentence of the Introduction. (In all quotes, I don’t include the references.)
In 1981, Spach et al observed a smaller maximum rate of rise of the action potential,max, and a larger time constant of the action potential foot, τfoot, during propagation parallel to the myocardiac [sic] fibers (longitudinal) than during propagation perpendicular to the fibers (transverse). They attributed these differences to the discrete cellular structure of the myocardium. Their research has been cited widely and is often taken as evidence for discontinuous propagation in cardiac tissue.

Several researchers have suggested that the observations of Spach et al may be caused by the bath perfusing the tissue rather than the discrete nature of the tissue itself... The purpose of this commentary is to model the experiment of Spach et al using a numerical simulation and to show that the perfusing bath plays an important role in determining the time course of the action potential foot.
I performed a computer simulation of wave fronts propagating through a slab of cardiac tissue that is perfused by a tissue bath. The tissue is represented as a bidomain, so its discrete nature was not incorporated into the model. I found that the rate-of-rise of the action potential is slower when propagation is parallel to the fibers compared to perpendicular to the fibers, just as Spach et al. observed. However, when I eliminated the purfusing bath this effect disappeared and the rate-of-rise was the same in both directions.

My favorite part of the article is in the Discussion, where I summarize my conclusion using a syllogism.
The data of Spach et al are cited widely as evidence for discontinuous propagation in cardiac tissue. Their hypothesis of discontinuous propagation is supported by the following logic: (1) During 1-dimensional propagation in a tissue with continuous electrical properties, the time course of the action potential (including max and τfoot) does not depend on the intracellular and interstitial conductivities; (2) experiments indicate that in cardiac tissue max and τfoot differ with the direction of propagation and therefore with conductivity; and (3) therefore, the conductivity of cardiac tissue is not continuous. A flaw exists in this line of reasoning: when a conductive bath perfuses the tissue, the propagation is not 1-dimensional. The extracellular conductivity is higher for the tissue near the surface (adjacent to the bath) than it is for the tissue far from the surface (deep within the bulk). Therefore, gradients in Vm exist not only in the direction of propagation, but also in the direction perpendicular to the tissue surface. Reasoning based on the 1-dimensional cable model (such as used in the first premise of the syllogism above) is not applicable.
In biology and medicine, the main purpose of computer simulations is to suggest new experiments, so I proposed one.
One way to distinguish between the 2 mechanisms ([the discrete structure] versus perfusing bath) would be to repeat the experiments of Spach et al with and without a perfusing bath present. The tissue would have to be kept alive when the perfusing bath was absent, perhaps by arterial perfusion. The results … indicate that when the bath is eliminated, the action potential foot should become exponential, with no differences between longitudinal and transverse propagation. Furthermore, the maximum rate of rise of the action potential should increase and become independent of propagation direction. Although this experiment is easy to conceive, it would be susceptible to several sources of error. If Vm were measured optically, the data would represent an average over a depth of a few hundred microns. Because the model predicts that Vm changes dramatically over such distances, the data would be difficult to interpret. Microelectrode measurements, on the other hand, are sensitive to capacitative [sic] coupling to the perfusing bath, and the degree of such coupling depends on the bath depth. The rapid depolarization phase of the action potential is particularly sensitive to electrode capacitance. Although it is possible to correct the data for the influence of electrode capacitance, these corrections would be crucial when comparing data measured at different bath depths.
A later paper by Oleg Sharifov and Vladimir Fast (Heart Rhythm, Volume 3, Pages 1063-1073, 2006) suggests a better way to perform this experiment: use optical mapping but with the membrane dye introduced through the perfusing bath so it stains only the surface tissue. In this case, there is no capacitive coupling (no microelectrode) and little averaging over depth (the optical signal arises from only surface tissue). This would be an important experiment, but it hasn’t been performed yet. Until it is, we can’t resolve the debate over discrete versus continuous behavior. 

The last paragraph in the paper sums it all up. I particularly like the final sentence.
We cannot conclude from our study that [discrete structures] are not important during action potential propagation. Nor can we conclude that discontinuous propagation does not occur (particularly in diseased tissue). These factors may well play a role in propagation. We can conclude, however, that the influence of a perfusing bath must be taken into account when interpreting data showing differences in the shape of the action potential foot with propagation direction... Therefore, differences in action potential shape with direction cannot be taken as definitive evidence supporting discontinuous propagation... if a perfusing bath is present. Finally, without additional experiments, we cannot exclude the possibility that in healthy tissue the difference in the shape of the action potential upstroke with propagation direction is simply an artifact of the way the tissue was perfused.
Has my commentary had much impact? Nope. Compared to other papers I’ve written, this one is a citation dud. It has been cited only 27 times (22 if you remove self-citations); barely once a year. Spach’s 1981 paper has over 800 citations; over 20 per year. Even a response by Spach and Barr (Circ. Res., Volume 86, Pages e23-e28, 2000) to my commentary has almost twice as many citations as my original commentary. Does this difference in citation rate arise because I’m wrong and Spach’s right? Maybe. The only way to know is to do the experiment.