Friday, August 5, 2016

Zapping Their Brains at Home

A screenshot of Zapping Their Brains at Home, by Anna Wexler.
“Zapping Their Brains at Home,”
by Anna Wexler.
A couple weeks ago, Anna Wexler published an article in the New York Times titled “Zapping Their Brains at Home.”
Earlier this month, in the journal Annals of Neurology, four neuroscientists published an open letter to practitioners of do-it-yourself brain stimulation. These are people who stimulate their own brains with low levels of electricity, largely for purposes like improved memory or learning ability. The letter, which was signed by 39 other researchers, outlined what is known and unknown about the safety of such noninvasive brain stimulation, and asked users to give careful consideration to the risks.
I worked on brain stimulation when at the National Institutes of Health, and Russ Hobbie and I analyze neural stimulation in Intermediate Physics for Medicine and Biology. So what is my reaction to these do-it-yourselfers? My first thought was “Yikes…this sounds like trouble!” But the more I think about it, the less worried I am.

We are talking about transcranial direct current stimulation, which uses weak currents applied to the scalp. I have always been surprised that such tiny currents have any effect at all; see my editorial “What Does the Ratio of Injected Current to Electrode Area Not Tell Us About tDCS?” (Clinical Neurophysiology, Volume 120, Pages 1037–1038, 2009). My advice to the do-it-yourselfers is not so much “be careful” but rather “don’t get your hopes up.”

Of the four coauthors on the letter in Annals of Neurology, the only one I know is Alvaro Pascual-Leone, who I worked with while at NIH and who we cite several times in IPMB. Below I list the main points raised in the letter:
  • Stimulation affects more of the brain than a user may think 
  • Stimulation interacts with ongoing brain activity, so what a user does during tDCS changes its effects 
  • Enhancement of some cognitive abilities may come at the cost of others 
  • Changes in brain activity (intended or not) may last longer than a user may think 
  • Small differences in tDCS parameters can have a big effect 
  • tDCS effects are highly variable across different people 
  • The risk/benefit ratio is different for treating diseases versus enhancing function
What do I think of do-it-yourselfers in general? I have mixed feelings. Heaven help us if they start fooling around with heart defibrillators, which could be suicidal. For transcranial magnetic stimulation, I think the biggest risk would be the construction of a device that sends kiloamps of current through a coil. I have always thought that TMS is more dangerous for the physician (who often holds the coil) than for the patient. Moreover, the induced current in the brain is larger for TMS than for tDCS. I would be wary of do-it-yourself magnetic stimulation. But for D.I.Y.ers using relatively low-level electrical current applied to the scalp, if someone educates themself on the technique and follows reasonable safety recommendations, then I don’t see it as a problem.

Wexler ends her letter
The open letter this month is about safety. But it also a recognition that these D.I.Y. practitioners are here to stay, at least for the time being. While the letter does not condone, neither does it condemn. It sticks to the facts and eschews paternalistic tones in favor of measured ones. The letter is the first instance I’m aware of in which scientists have directly addressed these D.I.Y. users. Though not quite an olive branch, it is a commendable step forward, one that demonstrates an awareness of a community of scientifically involved citizens.
If you want to read more by Wexler, look here and here.

My final, and admittedly self-serving, advice to the D.I.Y.ers: go buy a copy of Intermediate Physics for Medicine and Biology, so you can learn the scientific principles behind this and other techniques.

Friday, July 29, 2016

Niels Bohr and the Stopping Power of Alpha Particles

In Chapter 15 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the interaction of charged particles with electrons.
15.11.1 Interaction with Target Electrons

We first consider the interaction of the projectile with a target electron, which leads to the electronic stopping power, Se. Many authors call it the collision stopping power, Scol. There can be interactions in which a single electron is ejected from a target atom or interactions with the electron cloud as a whole (a plasmon excitation). The stopping power at higher energies, where it is nearly proportional to β−2 [β = v/c, where v is the speed of the projectile and c is the speed of light], has been modeled by Bohr, by Bethe, and by Bloch (see the review by Ahlen 1980).
Niels Bohr's Times: In Physics, Philosophy, and Polity, by Abraham Pais, superimposed on Intermediate Physics for Medicine and Biology.
Niels Bohr's Times:
In Physics, Philosophy, and Polity,
by Abraham Pais.
Bohr is, of course, the famous Niels Bohr, one of the greatest physicists of all time. I am familiar with Bohr’s model of the hydrogen atom (see Sec. 14.3), but not as much with his work on the stopping power of charged particles. It turns out that Bohr’s groundbreaking work on hydrogen grew out of his study of the stopping power of alpha particles. Moreover, the stopping power analysis was motivated by Ernest Rutherford’s experiments on the scattering of alpha particles, which established the nuclear structure of the atom. This chain of events began with the young Niels Bohr arriving in Manchester to work with Rutherford in March 1912. Abraham Pais discusses this part of Bohr’s life in his biography Niels Bohr’s Times: In Physics, Philosophy, and Polity.
Bohr finished his paper on this subject [the energy loss of alpha particles when traversing matter] only after he had left Manchester; it appeared in 1913. The problem of the stopping of electrically charged particles remained one of his lifelong interests. In 1915 he completed another paper on that subject, which includes the influence of effects due to relativity and to straggling (that is, the fluctuations in energy and in range of individual particles)…

Bohr’s 1913 paper on α-particles, which he had begun in Manchester, and which had led him to the question of atomic structure, marks the transition to his great work, also of 1913, on that same problem. While still in Manchester, he had already begun an early sketch of these entirely new ideas. The first intimation of this comes from a letter, from Manchester, to Harald [Niels’ brother]: “Perhaps I have found out a little about the structure of atoms. Don’t talk about it to anybody…It has grown out of a little information I got from the absorption of α-rays.” I leave the discussion of these beginnings to the next chapter.
On 24 July 1912 Bohr left Manchester for his beloved Denmark. His postdoctoral period had come to an end.
So the alpha particle stopping power calculation Russ and I discuss in Chapter 15 led directly to Bohr’s model of the hydrogen atom, for which he got the Nobel Prize in 1922.

Friday, July 22, 2016

Error Rates During DNA Copying

Chapter 3 of Intermediate Physics for Medicine and Biology discusses the Boltzmann factor. In the homework exercises at the end of the chapter, we include a problem in which you apply the Boltzmann factor to estimate the error rate during the copying of DNA.
Problem 30. The DNA molecule consists of two intertwined linear chains. Sticking out from each monomer (link in the chain) is one of four bases: adenine (A), guanine (G), thymine (T), or cytosine (C). In the double helix, each base from one strand bonds to a base in the other strand. The correct matches, A-T and G-C, are more tightly bound than are the improper matches. The chain looks something like this, where the last bond shown is an “error.”
Drawing of a DNA molecule containing an error in the matching of bases.
A DNA molecule containing an error.
The probability of an error at 300 K is about 10−9 per base pair. Assume that this probability is determined by a Boltzmann factor e−U/kBT, where U is the additional energy required for a mismatch.
(a) Estimate this excess energy.
(b) If such mismatches are the sole cause of mutations in an organism, what would the mutation rate be if the temperature were raised 20° C?
This is a nice simple homework problem that provides practice with the Boltzmann factor and insight into the thermodynamics of base pair copying. Unfortunately, reality is more complicated.

Biophysics: Searching for Principles, by William Bialek, superimposed on Intermediate Physics for Medicine and Biology.
Biophysics:
Searching for Principles,
by William Bialek.
William Bialek addresses the problem of DNA copying in his book Biophysics: Searching for Principles (Princeton University Press, 2012). He notes that the A typically binds to T. If A were to bind with G, the resulting base pair would be the wrong size and grossly disrupt the DNA double helix (A and G are both large double-ring molecules). However, if A were to bind incorrectly with C, the result would fit okay (C and T are about the same size) at the cost of eliminating one or two hydrogen bonds, which have a total energy of about 10 kBT. Bialek writes
An energy difference of ΔF ~ 10 kBT means that the probability of an incorrect base pairing should be, according to the Boltzmann distribution, e-ΔF/kBT ~ 10−4. A typical protein is 300 amino acids long, which means that it is encoded by about 1000 bases; if the error probability is 10-4, then replication of DNA would introduce roughly one mutation in every tenth protein. For humans, with a billion base pairs in the genome, every child would be born with hundreds of thousands of bases different from his or her parents. If these predicted error rates seem large, they are—real error rates in DNA replication vary across organisms [see the vignette “what is the error rate in transcription and translation” in Cell Biology by the Numbers], but are in the range of 10−8–10−12, so the entire genome can be copied without almost any mistakes.
So, how is the does the error rate become so small? There are enzymes called DNA polymerases that proofread the copied DNA and correct most errors. Because of these enzymes, the overall error rate is far smaller than the 10−4 rate you would estimate from the Boltzmann factor alone.

Our homework problem is therefore a little misleading, but it has redeeming virtues. First, the error we show in the figure is G-A, which would more severely disrupt the DNA's double helix structure. That specific error may well have a higher energy and therefore a lower error rate from the Boltzmann factor alone. Second, the problem illustrates how sensitive the Boltzmann factor is to small changes in energy. If ΔE = 10 kBT, the Boltzmann factor is e−10 = 0.5 × 10−4. If ΔE = 20 kBT, the Boltzmann factor is e−20 = 2 × 10−9. A factor of two increase in energy translates into more than a factor of 10,000 reduction in error rate. Wow!

Friday, July 15, 2016

Word Clouds

I have always wondered about those funny-looking collections of different-sized, different-colored words: the word cloud. This week I learned how to create a word cloud from any text I choose using the free online software at www.wordclouds.com. Of course, I chose Intermediate Physics for Medicine and Biology. Here is what I got.

A word cloud based on Intermediate Physics for Medicine and Biology.
A word cloud based on Intermediate Physics for Medicine and Biology.
The word cloud speaks for itself, but let me add a few comments. First, I deleted the preface, the table of contents, and the index from a pdf copy of IPMB before submitting it. The software was having trouble with such a large input file, and reducing the size seemed to help. After the list of words and their frequencies was created, I edited it. The software is smart enough to not include common words like “the” and “is,” but I deleted others that seemed generic to me, like “consider” and “therefore.” I kept words that appeared at least 250 times, which was about 65 words. The most common word was “Fig,” as in “...spherical air sacs called alveoli (Fig. 1.1b).” The third most common was “Problem” as in “Problem 1. Estimate the number of....” I considered removing these, but illustrations and end-of-chapter exercises are an important part of the book, so they stayed. I was surprised by the second most common word: “energy.” Russ Hobbie and I did not set out to make this a unifying theme in the book, but apparently it is.

I’ll let you decide if this word cloud is profound or silly. It was fun, and I like to share fun things with the readers of IPMB. Enjoy!

Friday, July 8, 2016

Cell Biology by the Numbers

Cell Biology by the Numbers, by Ron Milo and Rob Phillips, superimposed on Intermediate Physics for Medicine and Biology.
Cell Biology by the Numbers,
by Ron Milo and Rob Phillips.
Six years ago I wrote an entry in this blog about the bionumbers website. Now Ron Milo and Rob Phillips have turned that website into a book: Cell Biology by the Numbers. Milo and Phillips write
One of the central missions of our book is to serve as an entry point that invites the reader to explore some of the key numbers of cell biology. We hope to attract readers of all kinds—from seasoned researchers, who simply want to find the best values for some number of interest, to beginning biology students, who want to supplement their introductory course materials. In the pages that follow, we provide a broad collection of vignettes, each of which focuses on quantities that help us think about sizes, concentrations, energies, rates, information content, and other key quantities that describe the living world.
One part of the book that readers of Intermediate Physics for Medicine and Biology might find useful is their “rules of thumb.” I reproduce a few of them here
• 1 dalton (Da) = 1 g/mol ~ 1.6 × 10−24 g.
• 1 nM is about 1 molecule per bacterial volume [E. coli has a volume of about 1 μm3].
• 1 M is about one per 1 nm3.
• Under standard conditions, particles at a concentration of 1 M are ~ 1 nm apart.
• Water molecule volume ~ 0.03 nm3, (~0.3 nm)3.
• A small metabolite diffuses 1 nm in ~1 ns.
The book consists of a series of vignettes, each phrased as a question. Here is an excerpt form one.
Which is bigger, mRNA or the protein it codes for?

The role of messenger RNA molecules (mRNAs), as epitomized in the central dogma, is one of fleeting messages for the creation of the main movers and shakers of the cell—namely, the proteins that drive cellular life. Words like these can conjure a mental picture in which an mRNA is thought of as a small blueprint for the creation of a much larger protein machine. In reality, the scales are exactly the opposite of what most people would guess. Nucleotides, the monomers making up an RNA molecule, have a mass of about 330 Da. This is about three times heavier that the average amino acid mass, which weighs in at ~110 Da. Moreover, since it takes three nucleotides to code for a single amino acid, this implies an extra factor of three in favor of mRNA such that the mRNA coding a given protein will be almost an order of magnitude heavier.
It’s obvious once someone explains it to you. Here is another that I liked.
What is the pH of a cell?

…Even though hydrogen ions appear to be ubiquitous in the exercise sections of textbooks, their actual abundance inside cells is extremely small. To see this, consider how many ions are in a bacterium or mitochondrion of volume 1 μm3 at pH 7. Using the rule of thumb that 1 nM corresponds to ~ 1 molecule per bacterial cell volume, and recognizing that pH 7 corresponds to a concentration of 10−7 M (or 100 nM), this means that there are about 100 hydrogen ions per bacterial cell…This should be contrasted with the fact that there are in excess of a million proteins in that same cellular volume.
This one surprised me.
What are the concentrations of free matabolites in cells?

…The molecular census of metabolites in E. coli reveals some overwhelmingly dominant molecular players. The amino acid glutamate wins out…at about 100 mM, which is higher than all other amino acids combined…Glutamate is negatively charged, as are most of the other abundant metabolites in the cell. This stockpile of negative charges is balanced mostly by a corresponding positively changed stockpile of free potassium ions, which have a typical concentration of roughly 200 mM.
Somehow, I never realized how much glutamate is in cells. I also learned all sorts of interesting facts. For instance, a 5% by weight mixture of alcohol in water (roughly equivalent to beer) corresponds to a 1 M concentration. I guess the reason this does not wreak havoc on your osmotic balance is that alcohol easily crosses the cell membrane. Apparently yeast use the alcohol they produce to inhibit the growth of bacteria. This must be why John Snow found that during the 1854 London cholera epidemic, the guys working (and, apparently, drinking) in the brewery were immune.

I’ll give you one more example. Milo and Phillips analyze how long it will take a substrate to collide with a protein.
…Say we drop a test substrate molecule into a cytoplasm with a volume equal to that of a bacterial cell. If everything is well mixed and there is no binding, how long will it take for the substrate molecule to collide with one specific protein in the cell? The rate of enzyme substrate collisions is dictated by the diffusion limit, which as shown above, is equal to ~ 109 s−1M−1 times the concentration. We make use of one of our tricks of the trade, which states that in E. coli, a single molecule (say, our substrate) has an effective concentration of about 1 nM (that is, 10−9 M). The rate of collisions is thus 109 s−1M−1 × 10−9 M. That is, they will meet within a second on average. This allows us to estimate that every substrate molecule collides with each and every protein in the cell on average about once per second.
Each and every one, once per second! The beauty of this book, and the value of making these order-of-magnitude estimates, is to provide such insight. I cannot think of any book that has provided me with more insight than Cell Biology by the Numbers.

Readers of IPMB will enjoy CBbtN. It is well written and the illustrations by Nigel Orme are lovely. It may have more cell biology than readers of IPMB are used to (Russ Hobbie and I are macroscopic guys), but that is fine. For those who prefer video over text, listen to Rob Phillips and Ron Milo give their views of life in the videos below.

I’ll give Milo and Phillips the last word, which could also sum up our goals for IPMB.
We leave our readers with the hope that they will find these and other questions inspiring and will set off on their own path to biological numeracy.



Friday, July 1, 2016

The Wien Exponential Law

In Section 14.8 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss blackbody radiation. Our analysis is similar to that in many modern physics textbooks. We introduce Planck’s law for Wλ(λ,T) dλ, the spectrum of power per unit area emitted by a completely black surface at temperature T and wavelength λ
An equation for Planck's law of blackbody radiation.
where c is the speed of light, h is Planck’s constant, and kB is Boltzmann’s constant. We then 1) express this function in terms of frequency ν instead of wavelength λ, 2) integrate over all wavelengths to derive the Stefan-Boltzmann law, and 3) show that the wavelength of peak emission decreases with temperature, often known as the Wien displacement law.

Russ and I like to provide homework problems that reinforce the concepts in the text. Ideally, the problem requires the reader to repeat many of the same steps carried out in the book, but for a slightly different case or in a somewhat different context. Below I present such a homework problem for blackbody radiation. It is based on an approximation to Planck’s law at short wavelengths derived by Wilhelm Wien.
Problem 25 ½. Consider the limit of Planck’s law, Eq. 14.33, when hc/λ is much greater than kBT, an approximation known as the Wien exponential law.
(a) Derive the mathematical form of Wλ(λ,T) in this limit.
(b) Convert Wien’s law from a function of wavelength to a function of frequency, and determine the mathematical form of Wν(ν,T).
(c) Integrate Wν(ν,T) over all frequencies to obtain the total power emitted per unit area. Compare this result with the Stefan-Boltzmann law (Eq. 14.34). Derive an expression for the Stefan-Boltzmann constant in terms of other fundamental constants.
(d) Determine the frequency νmax corresponding to the peak in Wν(ν,T). Compare νmax/T with the value obtained from Planck’s law.
Subtle is the Lord: The Science and the Life of Albert Einstein,  by Abraham Pais. superimposed on Intermediate Physics for Medicine and Biology.
Subtle is the Lord,
by Abraham Pais.
The Wien exponential law predated Planck’s law by several years. In his landmark biography ‘Subtle is the Lord…’: The Science and the Life of Albert Einstein, Abraham Pais discusses 19th century attempts to describe blackbody radiation theoretically.
Meanwhile,proposals for the correct form of [Wλ(λ,T)] had begun to appear as early as the 1860s. All these guesses may be forgotten except one, Wien’s exponential law, proposed in 1896…

Experimental techniques had sufficiently advanced by then to put this formula to the test. This was done by Friedrich Paschen from Hannover, whose measurements (very good ones) were made in the near infrared, λ = 1-8 μm (and T = 400 -1600 K). He published his data in January 1897. His conclusion: “It would seem very difficult to find another function…that represents the data with as few constants.” For a brief period, it appeared that Wien’s law was the final answer. But then, in the year 1900, this conclusion turned out to be premature…
And the rest, as they say, is history.

Friday, June 24, 2016

Chemostat Homework Problems

In the 5th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I added a section on the chemostat.
2.6  The Chemostat
The chemostat is used by bacteriologists to study the growth of bacteria (Hagen 2010). It allows the rapid growth of bacteria to be observed over a longer time scale. Consider a container of bacterial nutrient of volume V. It is well stirred and contains y bacteria with concentration C = y/V. Some of the nutrient solution is removed at rate Q and replaced by fresh nutrient. The bacteria in the solution are reproducing at rate b. The rate of change of y is
An equation governing the number of bacteria in a chemostat.
Therefore the growth rate is slowed to
A mathematical expression for the bacteria growth rate in a chemostat.
and can be adjusted by varying Q.
However, Russ and I didn’t write any new homework problems for this section. If a topic is worth discussing in the text, then it’s worth creating homework problems to reinforce and extend that discussion. So, here are some new problems about the chemostat.
Problem 21.1.  Often a chemostat is operated in steady state.
(a) Determine the solution removal rate Q required for steady state, as a function of the bacteria reproduction rate b and the container volume V, using Eq. 2.22. Determine the units of b, Q, and V, and verify that your expression for Q has the correct dimensions.
(b) If the rate Q is larger than the steady-state value, what is happening physically?
(c) Sometimes b varies with some external parameter (for example, temperature or glucose concentration), and you want to determine b as a function of that parameter. Suppose you can control Q and you can measure the number of bacteria y. Qualitatively design a way to determine b as your external parameter changes, assuming that for each value of the parameter your chemostat reaches steady state. (If unsure how to begin, take a look at Sec. 6.13.1 about the voltage clamp used in electrophysiology.)
Problem 21.2.  Consider an experiment using a chemostat in which the bacteria's reproduction rate b slows as the number of bacteria y increases.
(a) Modify Eq. 2.22 so that “b” becomes “b (1 − y/y),” analogous to the logistic model (Sec. 2.10).
(b) Determine the value of y once the chemostat reaches steady state, as a function of Q, V, b, and y.
(c) Suppose your chemostat has a volume of 1.7 liters. You measure the steady state value of y (arbitrary units) for different values of Q (liters per hour), as shown in the table below. Plot y versus Q, and determine b and y.

 Q    y
 0.2 11.64
 0.4   9.47
 0.6   7.31
 0.8   5.14
 1.0   2.98

Problem 21.3.  Let the growth rate of the bacteria in your chemostat be limited by a small, constant amount of some essential metabolite, so the term “by” in Eq. 2.22 is replaced by a constant “a.”
(a) Find an expression for the solution removal rate Q in terms of a, the number of bacteria y, and the chemostat volume V, when the chemostat is in steady state.
(b) Determine the time constant governing how quickly the chemostat reaches steady state (Hint: see Sec. 2.8).
Screenshot of Exponential Growth of Bacteria: Constant Multiplication Through Division, by Stephen Hagen (American Journal of Physics, 78:1290–1296, 2010).
“Exponential Growth of Bacteria:
Constant Multiplication Through Division,”
by Stephen Hagen.
Russ and I cite an American Journal of Physics article about the exponential growth of bacteria, written by Stephen Hagen (Volume 78, Pages 1290-1296, 2010). Here’s what Hagen says about the chemostat.
Because the growth rate of the cell determines its size and chemical composition, a device that allows us to fine tune the growth rate will select the physiological properties of the cells. The bacterial chemostat is such a machine. In the chemostat a bacterial culture grows in a well-stirred vessel while a supply of fresh growth medium is fed into the vessel at a fixed flow rate Q (volume/time). At the same time, the medium (containing bacteria) is continuously withdrawn from the vessel at the same rate so as to maintain constant volume V. Thus, the bacterial population is continuously diluted at a rate D = Q/V. If this dilution rate exceeds the growth rate k [our b], the population is diluted, which allows its growth to accelerate until it matches the dilution rate, k = Q/V. (If D is too large, the culture will be diluted away entirely.) Therefore, the chemostat allows the experimenter to select the growth rate by selecting Q. Because it harnesses an exponential growth process to produce a tunable, steady output, we might think of the chemostat as the microbiological analog of a nuclear fission reactor. Interestingly, the chemostat reactor was first described by the physicist Leo Szilard (with Aaron Novick), who also (with Enrico Fermi) patented the nuclear reactor."
I like the analogy to the nuclear reactor. Adjusting the flow rate in a chemostat is like pulling the cadmium control rods in and out of an atomic pile (except it’s less dangerous).

Friday, June 17, 2016

Neural Lacing

One feature of blogging that I like are the comments. I don’t get many, but I appreciate those I do get. Each week I share my new blog entry on the Intermediate Physics for Medicine and Biology Facebook page, which provides another venue for comments, likes, and other interactions with readers. A couple weeks ago I received the following on Facebook:
Neeraj Kapoor
June 3 at 1:36pm
Yesterday, during a conference with Elon Musk at a coding conference, he mentioned something about Neural Lacing (this group at harvard seems to be one of the few major groups working on it...http://cml.harvard.edu/) . I'm wondering if you have any knowledge of this Brad Roth and if so, if you could do a blog post on it.
After a bit of googling, I found a Newsweek article about neural lacing, Elon Musk, and the coding conference.
Billionaire polymath Elon Musk has warned that humans risk being treated like house pets by artificial intelligence (AI) unless they implant technology into their brains.

Musk believes that a technology concept known as “neural lace” could act as a wireless brain-computer interface capable of augmenting natural intelligence.

Speaking at the Code Conference in California on Wednesday, Musk said a neural lace could work “well and symbiotically” with the rest of a human’s body.

“I don’t love the idea of being a house cat, but what’s the solution? I think one of the solutions that seems maybe the best is to add an AI layer,” Musk said.
So what does all this talk about neural lacing mean, and how does it relate to Intermediate Physics for Medicine and Biology? As best I can tell, neural lacing would be used to monitor and excite nerves. The technology to stimulate nerves already exists, and is described in Chapter 7 of IPMB.
The information that has been developed in this chapter can also be used to understand some of the features of stimulating electrodes. These 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 (Perlmutter and Mink 2006); for cardiac pacing (Moses and Mullin 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.
The best example of what I think Mr. Musk is talking about is the cochlear implant. A microphone records sound and analyzes it with a computer, which decides what location along the auditory nerve it should stimulate in order to fool the brain into thinking the ear heard that sound. For this technique to work, electrode arrays must be implanted in the cochlea so different spots can be stimulated, mimicking the sensitivity of different locations along the cochlea to different frequencies of sound.

What is different between a cochlear implant and a neural lace? Musk talks about the stimulating electrodes being wireless. Wireless neural stimulation is fairly common, and most cochlear implants are wireless (no wire passing through the skin). Most wireless systems work by transferring energy and information using electromagnetic induction. Chapter 8 of IPMB discusses induction, mainly in the context of magnetic stimulation. In fact, transcranial magnetic stimulation could be thought of as a low-spatial-resolution precursor to neural lacing. It allows neurons to be excited with no wires penetrating the body so the method is completely noninvasive. The problem is, transcranial magnetic stimulation provides a resolution of about 1 cm—some claim as low as 1 mm—which is a factor of a hundred to a thousand too coarse to stimulate individual neurons. If you could somehow build very small magnetic stimulators (there are enormous technical challenges in doing this), you still would not be able to excite deep neurons without simultaneously activating shallow neurons even more strongly. To make something like neural lacing work, you would need to use electromagnetic induction to transfer energy to a stimulator implanted in the body, and then distribute the excitation using small wires or some other technology that provides the necessary spatial resolution and the ability to excite deep neurons. Wireless deep brain stimulation is one example.

Spatial scale is a key factor in developing the technology of neural lacing. Cochlear implants only work because the electrodes are small enough that individual sites along the auditory nerve can be excited locally. I believe that neural lacing would require miniaturization to be increased dramatically. If you are going to stimulate the brain in a truly selective way, you need to be able to excite individual neurons. This means you need electrodes spaced by about ten microns or closer, and you need a lot of them. Neural lacing would therefore require advances in electrode array miniaturization. This is where the Lieber group at Harvard—which Kapoor mentioned in his Facebook comment—enters the picture. They are developing the arrays of microelectrodes that would be necessary to provide a fine-grained interaction between a computer and the human brain. For example, their paper “syringe-injectable electronics” (Nature Nanotechnology, Volume 10, Pages 629–636, 2015) discusses small scale arrays of electrodes that can be injected through a syringe.
Seamless and minimally invasive three-dimensional interpenetration of electronics within artificial or natural structures could allow for continuous monitoring and manipulation of their properties. Flexible electronics provide a means for conforming electronics to non-planar surfaces, yet targeted delivery of flexible electronics to internal regions remains difficult. Here, we overcome this challenge by demonstrating the syringe injection (and subsequent unfolding) of sub-micrometre-thick, centimetre-scale macroporous mesh electronics through needles with a diameter as small as 100 μm. Our results show that electronic components can be injected into man-made and biological cavities, as well as dense gels and tissue, with [greater than] 90% device yield. We demonstrate several applications of syringe-injectable electronics as a general approach for interpenetrating flexible electronics with three-dimensional structures, including (1) monitoring internal mechanical strains in polymer cavities, (2) tight integration and low chronic immunoreactivity with several distinct regions of the brain, and (3) in vivo multiplexed neural recording. Moreover, syringe injection enables the delivery of flexible electronics through a rigid shell, the delivery of large-volume flexible electronics that can fill internal cavities, and co-injection of electronics with other materials into host structures, opening up unique applications for flexible electronics.
Is neural lacing science or science fiction? Hard to say. I am skeptical that in the future we will all have electrode arrays hardwired into our brains. But 50 years ago I would have been skeptical that cochlear implants could restore hearing to the deaf. I will reserve judgment, except to say that if neural lacing is developed, I am certain it will be based on the basic concepts Russ Hobbie and I discuss in Intermediate Physics for Medicine and Biology. That is the beauty of the book: it teaches the fundamental principles upon which you can build the amazing biomedical technologies of the future.





Friday, June 10, 2016

PHY 325 and PHY 326

One reason I write this blog is to help instructors who adopt Intermediate Physics for Medicine and Biology as their textbook. I teach classes from IPMB myself; here at Oakland University we have a Biological Physics class (PHY 325) and a Medical Physics class (PHY 326). Instructors might benefit from seeing how I structure these classes, so below are my most recent syllabi.  

Syllabus, Biological Physics
Fall 2015

Class: Physics 325, MWF, 8:00–9:07, 378 MSC

Instructor: Brad Roth, Dept. Physics, 166 Hannah Hall, 370-4871, roth@oakland.edu, fax: 370-3408, office hours MWF, 9:15–10:00, https://files.oakland.edu/users/roth/web

Text: Intermediate Physics for Medicine and Biology, 5th Edition, by Hobbie and Roth (An electronic version of this book is available for free through the OU library)
Book Website: https://files.oakland.edu/users/roth/web/hobbie.htm (get the errata!).
Book Blog: http://hobbieroth.blogspot.com

Goal: To understand how physics influences and constrains biology

Grades

Point/Counterpoint
    5 %
Exam 1 Feb 5   20 %   Chapters 1–3
Exam 2 March 18  20 %   Chapters 4–6
Exam 3 April 20  20 %   Chapter 7, 8, 10
Final Exam April 20  10 %   Comprehensive
Homework
  25 %

Schedule

Sept 4
  Introduction
Sept 9, 11   Chapter 1   Mechanics, Fluid Dynamics
Sept 14–18   Chapter 2   Exponential, Scaling
Sept 21–25   Chapter 3   Thermodynamics
Sept 28–Oct 2     Exam 1
Oct 5–9   Chapter 4   Diffusion
Oct 12–16   Chapter 5   Osmotic Pressure
Oct 19–23   Chapter 6   Electricity and Nerves
Oct 26–30     Exam 2
Nov 2–6   Chapter 7   Extracellular Potentials
Nov 9–13   Chapter 8   Biomagnetism
Nov 16–20   Chapter 10   Heart Arrhythmias, Chaos
Nov 23, 25   Chapter 10   Feedback
Nov 30–Dec 4   Chapter 10   Feedback
Dec 7
  Review
Dec 9
  Final Exam


Homework

Chapter 1:6, 7, 8, 16, 17, 33, 40, 42  due Wed, Sept 16
Chapter 2:3, 5, 10, 29, 42, 46, 47, 48  due Wed, Sept 23
Chapter 3:29, 30, 32, 33, 34, 40, 47, 48  due Wed, Sept 30
Chapter 4:7, 8, 12, 20, 22, 23, 24, 41  due Wed, Oct 14
Chapter 5:1, 3, 5, 6, 7, 8, 10, 16  due Wed, Oct 21
Chapter 6:1, 2, 22, 28, 37, 41, 43, 61  due Wed, Oct 28
Chapter 7:1, 10, 15, 24, 25, 36, 42, 47  due Wed, Nov 11
Chapter 8:3, 10, 24, 25, 27, 28, 29, 32  due Wed, Nov 18
Chapter 10:12, 16, 17, 18, 40, 41, 42, 43  due Wed, Dec 2


Syllabus, Medical Physics
Winter 2016 

Class: Physics 326, MWF, 10:40–11:47, 204 DH

Instructor: Brad Roth, Department of Physics, 166 HHS, (248) 370-4871, roth@oakland.edu, fax: (248) 370-3408, office hours MWF 9:30–10:30, https://files.oakland.edu/users/roth/web.

Text: Intermediate Physics for Medicine and Biology, 5th Edition, by Hobbie and Roth. An electronic version of the textbook is available through the OU library.
Book Website: https://files.oakland.edu/users/roth/web/hobbie.htm (get the errata!).
Book Blog: http://hobbieroth.blogspot.com

Goal: To understand how physics contributes to medicine

Grades

Point/Counterpoint
    5 %
Exam 1   Feb 5   20 %   Chapters 13–15
Exam 2   March 18   20 %   Chapters 16, 11–12
Exam 3   April 20   20 %    Chapter 17, 18
Final Exam   April 20   10 %
Homework
  25 %

Schedule

Jan 6, 8                   Introduction
Jan 11, 13, 15 Chpt 13   Sound and Ultrasound
Jan 20, 22 Chpt 14   Atoms and Light
Jan 25, 27, 29 Chpt 15   Interaction of Photons and Matter
Feb 1, 3, 5
  Exam 1
Feb 8, 10, 12 Chpt 16   Medical Uses of X rays
Feb 15, 17, 19 Chpt 11   Least Squares and Signal Analysis
Feb 22, 24, 26
  Winter Recess
Feb 29, March 2, 4Chpt 12   Images
March 7, 9, 11 Chpt 12   Images
March 14, 16, 18
  Exam 2
March 21, 23, 25 Chpt 17   Nuclear Medicine
March 28, 30, Apr 1Chpt 17   Nuclear Medicine
April 4, 6, 8 Chpt 18   Magnetic Resonance Imaging
April 11, 13, 15Chpt 18   Magnetic Resonance Imaging
April 18
  Conclusion
April 20
  Final Exam

Homework

Chapter 13:   7, 10, 12, 21, 22, 27, 30, 36                due Fri, Jan 22   
Chapter 14:4, 5, 16, 21, 22, 47, 48, 49 due Wed, Jan 27
Chapter 15:2, 4, 5, 10, 12, 14, 15, 16 due Wed, Feb 3
Chapter 16:4, 5, 7, 16, 19, 20, 22, 31due Wed, Feb 17
Chapter 11:9, 11, 15, 20, 21, 36, 37, 41due Wed, Mar 2
Chapter 12:7, 9, 10, 23 due Wed, Mar 9
Chapter 12:25, 32, 34, 35, and 27 (extra credit)due Wed, Mar 16
Chapter 17:1, 2, 7, 9, 14, 17, 20, 22due Wed, Mar 30
Chapter 17:29, 30, 40, 54, 57, 58, 59, 60due Wed, Apr 6
Chapter 18:9, 10, 13, 14, 15, 18, 35, 49due Wed, Apr 13

Point/Counterpoint articles

Jan 8: The 2014 initiative is not only unnecessary but it constitutes a threat to the future of medical physics. Med Phys, 38:5267–5269, 2011.

Jan 15: Ultrasonography is soon likely to become a viable alternative to x-ray mammography for breast cancer screening. Med Phys, 37:4526–4529, 2010.

Jan 22: High intensity focused ultrasound may be superior to radiation therapy for the treatment of early stage prostate cancer. Med Phys, 38:3909–3912, 2011.

Jan 29: The more important heavy charged particle radiotherapy of the future is more likely to be with heavy ions rather than protons. Med Phys, 40:090601, 2013.

Feb 12: The disadvantages of a multileaf collimator for proton radiotherapy outweigh its advantages. Med Phys, 41:020601, 2014.

Feb 19: Low-dose radiation is beneficial, not harmful. Med Phys, 41:070601, 2014.

March 4: Recent data show that mammographic screening of asymptomatic women is effective and essential. Med Phys, 39:4047–4050, 2012.

March 11: PDT is better than alternative therapies such as brachytherapy, electron beams, or low-energy x rays for the treatment of skin cancers. Med Phys, 38:1133–1135, 2011.

March 25: Submillimeter accuracy in radiosurgery is not possible. Med Phys, 40:050601, 2013.

April 1: Within the next ten years treatment planning will become fully automated without the need for human intervention. Med Phys, 41:120601, 2014.

April 8: Medical use of all high activity sources should be eliminated for security concerns. Med Phys, 42:6773, 2015.

April 15: MRI/CT is the future of radiotherapy treatment planning. Med Phys, 41:110601, 2014.

Notes:
  • The OU library has an electronic version of IPMB that students can download. If they are willing to read pdfs, they have no textbook expense in either class.
  • I skip Chapter 9. I have nothing against it. There just isn’t time for everything.
  • I cover Chapters 13-16 before the highly mathematical Chapters 11-12.  I don’t like to start the semester with a week or two of math.
  • In Medical Physics, we spend the last 15 minutes of class each Friday discussing a point/counterpoint article from the journal Medical Physics. The students seem to really enjoy this.
  • I let the students work together on the homework, but they cannot simply copy someone else’s work. They must turn in their own assignment.
  • Both PHY 325 and PHY 326 are aimed at upper-level undergraduates. The prerequisites are a year of introductory physics and a year of introductory calculus. The students tend to be physics majors, medical physics majors, bioengineering majors, plus a few biology, chemistry, math, and mechanical engineering majors. The typical enrollment is about ten.
  • I encourage premed students to take these classes. Occasionally one does, but not too often. I wish more would, because I believe it provides an excellent preparation for the MCAT. Unfortunately, they have little room in their busy schedule for two extra physics classes.
  • OU offers a medical physics major. It consists of many traditional physics classes, these two specialty classes (PHY 325 and PHY 326), plus some introductory and intermediate biology.
  • I am a morning person, so I often teach at 8 A.M. The students hate it, but I love it. Sometimes, however, I can’t control the time of day for the class and I teach at a later time.

Friday, June 3, 2016

Direct Neural Current Imaging in an Intact Cerebellum with Magnetic Resonance Imaging

I amIn the 5th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I added a paragraph to Chapter 18 (Magnetic Resonance Imaging) about using MRI to image neural activity.
Much recent research has focused on using MRI to image neural activity directly, rather than through changes in blood flow (Bandettini et al. 2005). Two methods have been proposed to do this. In one, the biomagnetic field produced by neural activity (Chap. 8) acts as the contrast agent, perturbing the magnetic resonance signal. Images with and without the biomagnetic field present provide information about the distribution of neural action currents. In an alternative method, the Lorentz force (Eq. 8.2) acting on the action currents in the presence of a magnetic field causes the nerve to move slightly. If a magnetic field gradient is also present, the nerve may move into a region having a different Larmor frequency. Again, images taken with and without the action currents present provide information about neural activity. Unfortunately, both the biomagnetic field and the displacement caused by the Lorentz force are tiny, and neither of these methods has yet proved useful for neural imaging. However, if these methods could be developed, they would provide information about brain activity similar to that from the magnetoencephalogram, but without requiring the solution of an ill-posed inverse problem that makes the MEG so difficult to interpret.
The first page of “Direct Neural Current Imaging in an Intact Cerebellum with Magnetic Resonance Imaging,” by Sundaram et al. (NeuroImage, 132:477-490, 2016), superimposed on Intermediate Physics for Medicine and Biology.
“Direct Neural Current Imaging in an
Intact Cerebellum with
Magnetic Resonance Imaging,”
by Sundaram et al.
I’m skeptical about most claims of measuring neural currents using MRI. However, a recent paper (Sundaram et al., NeuroImage, Volume 132, Pages 477–490, 2016) from the laboratory of Yoshio Okada has forced me to reconsider. Below I reproduce the introduction to this article (with references removed), which introduces the topic nicely.
Functional study of the human brain has become possible with advances in non-invasive neuroimaging methods. The most widely used technique is blood oxygenation level-dependent functional MRI (BOLD-fMRI). Although BOLD-fMRI is a powerful tool for human brain activity mapping, it does not measure neuronal signals directly. Rather, it images slow local hemodynamic changes correlated with neuronal activity through a complex neurovascular coupling. At present, only electroencephalography (EEG) and magnetoencephalography (MEG) detect signals directly related to neuronal currents with a millisecond resolution. However, they estimate neuronal current sources from electrical potentials on the scalp or from magnetic fields outside the head, respectively. Measurement of these signals outside the brain leads to relatively poor spatial resolution due to ambiguity in inverse source estimation.

Our understanding of human brain function would significantly accelerate if it were possible to noninvasively detect neuronal currents inside the brain with superior spatiotemporal resolution. This possibility has led researchers to look for a method to detect neuronal currents with MRI. Many MRI approaches have been explored in the literature. Of these, the mechanism most commonly used is based on local changes in MR phase caused by neuronal magnetic fields. Electrical currents in active neurons produce magnetic fields (ΔB) locally within the tissue. The component of this field (ΔBz) along the main field (Bo) of the MR scanner alters the precession frequency of local water protons. This leads to a phase shift ΔΦ of the MR signal. For a gradient-echo (GE) sequence,

ΔΦ = γΔBzTE

where γ is the gyromagnetic ratio for hydrogen (2π × 42.58 MHz/T for protons) and TE is the echo time. According to Biot-Savart's law, ΔBz(t) is proportional to the current density J(t) produced by a population of neurons in the local region of the tissue. Thus, measurements of the phase shift ΔΦ can be used to directly estimate neuronal currents in the brain.

Many attempts have been made to detect neuronal currents in human subjects in vivo, but the results so far are inconclusive. The literature contains several reports of positive results which conflict with reports of negative results. This difficulty is presumably due to confounding factors such as blood flow, respiration and motion. Theoretical models, phantoms and cell culture studies indicate that it should be possible to detect neuronal currents with MRI in the absence of physiological noise sources.

Although these studies indicate that MRI technology should have enough sensitivity to detect neural currents, two types of key evidence are still lacking for demonstrating how MRI can be useful for neural current imaging: (1) there are no data showing that the phase shift is timelocked to some measure of population activity and that the phase shift time course matches that of a concurrently recorded local field potential (LFP), and (2) there is still no report showing how the phase shift data can be used to estimate the neuronal current distribution in the brain tissue, even though this should be the goal for neural current imaging.

Our work demonstrates that it is possible to measure an MR phase shift time course matching that of the simultaneously recorded evoked LFP in an isolated, intact whole cerebellum of turtle, free of physiological noise sources. We show how these MR phase maps can be used to estimate the neuronal current distribution in the active region in the tissue. We show that this estimated current distribution matches the distribution predicted based on spatial LFP maps. We discuss how these results can provide an empirical anchor for future development of techniques for in vivo neural current imaging.
After presenting their methods and results, Sundaram et al. write:
We demonstrated that the ΔΦ can be detected reliably in individual cerebelli and that this phase shift is time-locked to the concurrently recorded LFP. The temporal waveform of the ΔΦ matched that of the LFP. Both the MR signal and LFP were produced by neuronal currents mediated by mGluRs. The measured values of ΔΦ in the individual time traces corresponded to local magnetic fields of 0.67–0.93 nT for TE = 26 ms. According to our forward solutions, these values correspond to a current dipole moment density q of 1–2 nA m/mm2,which agrees with the reported current density of 1–2 nA m/mm2 determined on the basis of MEG signals measured 2 cm above the cerebellum.

We also show that the MR phase data can be used to estimate the active neuronal tissue. This second step is important if MRI were to be used for imaging neuronal current distributions in the brain. We were able to use the minimum norm estimation technique developed in the field of MEG to estimate the current distribution in the cerebellum responsible for the measured phase shift. The peak values of ΔΦ in the phase map averaged across 7 animals were 0.15° and −0.10°, corresponding to peak ΔB values of +0.37 nT and −0.25 nT, respectively. The empirically obtained group-average ΔΦ of 0.12° and ΔB of 0.30 nT are close to the predicted values of 0.2° and 0.49 nT assuming q = 1 nA m/mm2. The slightly smaller group-average ΔΦ and ΔB may be due to variability in the spatial phase map and responses across animals.
They conclude
Our results for metabotropic receptor mediated evoked neuronal activity in an isolated whole turtle cerebellum demonstrate that MRI can be used to detect neuronal currents with a time resolution of 100 ms, approximately ten times greater than for BOLD-fMRI, and with a sensitivity sufficiently high for near single-voxel detection. We have shown that it is possible to detect the MR phase shift with a time course matching that of the concurrently measured local field potential in the tissue. Furthermore, we showed how these MR phase data can be used to accurately estimate the spatial distribution of the current dipole moment density in the tissue.
I’ve been interested in this topic for a while, publishing on the subject with Ranjith Wijesinghe of Ball State University (2009, 2012) and Peter Basser of the National Institutes of Health (2009, 2014). My graduate student Dan Xu (2012) examined the use of MRI to measure electrical activity in the heart, where the biomagnetic fields are largest. I remain skeptical that magnetic resonance imaging can record neural activity of the human brain in a way as accurate as functional MRI using BOLD. Yet, this is the first claim to have measured the magnetic field of neurons using MRI that I believe. It’s a beautiful result and a landmark study. I hope that I’m wrong and the method does have the potential for clinical functional imaging.