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

Therefore the growth rate is slowed to

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).

“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).

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.

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, 4	Chpt 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 1	Chpt 17	Nuclear Medicine
April 4, 6, 8	Chpt 18	Magnetic Resonance Imaging
April 11, 13, 15	Chpt 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, 31	due Wed, Feb 17
Chapter 11:	9, 11, 15, 20, 21, 36, 37, 41	due 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, 22	due Wed, Mar 30
Chapter 17:	29, 30, 40, 54, 57, 58, 59, 60	due Wed, Apr 6
Chapter 18:	9, 10, 13, 14, 15, 18, 35, 49	due 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.

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.

“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 (ΔB_z) along the main field (B_o) 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 = γΔB_zTE

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, ΔB_z(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.