James Mattiello, Medical Physicist (1958-2017)

James Mattiello passed away on March 19, 2017, at the age of 59, in Utica, Michigan. Jim was a friend of mine from when we both worked at the National Institutes of Health, where he contributed to the development of a magnetic resonance imaging technique called Diffusion Tensor Imaging. He was the first graduate of the Oakland University Medical Physics PhD Program, which I now direct. When I was at NIH, I had never heard of Oakland University until Jim mentioned it as his alma mater. Little did I know that I would have a 20-year career at OU, teaching and doing research.

Jim performed his PhD research with Prof. Fred Hetzel, and graduated with his PhD in 1987. His dissertation described an in vivo experimental investigation on the interaction between photodynamic therapy and hyperthermia. A copy of his dissertation sits in our Physics Department office, and I often show it to prospective students because it is the thickest dissertation on the shelf, over 480 pages. Hetzel, Norm Tepley, Michael Chopp, and Abe Liboff formed the dissertation committee (I didn’t arrive at OU until ten years later). Three journal articles resulting from this work are:

Mattiello J, Hetzel FW (1986) Hematoporphyrin-derivative optical-fluorescence-detection instrument for localization of bladder and bronchous carcinoma in situ. Review of Scientific Instruments 57:2339–2342.

Mattiello J, Hetzel F, Vandenheede L (1987) Intratumor temperature measurements during photodynamic theorapy. Photochemistry and Photobiology 46:873–879.

Mattiello J, Evelhoch JL, Brown E, Schaap AP, Hetzel FW (1990) Effect of photodynamic therapy on RIF-1 tumor metabolism and blood flow examined by 31P and 2H NMR spectroscopy. NMR in Biomedicine 3:64–70.

A news article about Jim’s research appeared in the Spring 1984 issue of The Oakland University Magazine (above right).

After graduation, Jim obtained a fellowship to work at the intramural program of the National Institutes of Health in Bethesda, Maryland, where I first met him. Below I quote from an NIH oral history interview with Peter Basser, which describes how Basser, Denis LeBihan, and Jim developed Diffusion Tensor Imaging in the early 1990s.

Well actually this was an amazing story too, because there’s so many people involved and activities that had to be done in order to bring this from bench to bedside. So the first thing is Denis and I started corresponding, and Jim Mattiello then, who was working with Denis and who was also working in our program [Biomedical Engineering and Instrumentation Program], was a little frustrated with some of the projects he was working on and decided that he wanted to start working with us. So I was excited about that because Jim had a technical background in MRI, he had been working in the area for a few–maybe a year and a half at that point, and he would provide a lot of experimental help which I really couldn’t provide because my knowledge at that point of the NMRI [Nuclear Magnetic Resonance Imaging] hardware and sequences and things was almost nonexistent. And so we started doing diffusion experiments with water. The first thing that we – in pork loin – the first thing that we started doing was – Denis got us some magnetic time down at the NMRI center and we started to – since we had this mathematical framework that related the signal that we measured to the diffusion tensor the first thing that you want to do is show that the diffusion tensor in water is an isotropic tensor, which means that if you look at the diffusion process along any direction that it appears the same and that has a characteristic – a special form when you write it as a tensor and it’s something that if you can’t do that you can’t look at other materials that are more complex.

I can remember the morning when Peter came in to NIH carrying a pork loin from a local grocery store. I asked him why he brought a chunk of raw meat to work, and he told me that he and Jim were going to use it that day in their first DTI experiment on muscle. Later in the oral history interview, Basser describes this experiment.

We wrote our first abstract describing it [Anisotropic Diffusion Tensor Imaging] at the ISMRM [International Society for Magnetic Resonance in Medicine Conference] I think which we presented in Berlin in 1992, we looked at a sample of pork loin and we showed that we first measured the diffusion tensor for a large region of that pork loin specimen, and then we actually physically rotated that – Jim Mattiello actually physically rotated the pork loin specimen in the magnet. We repeated the experiments, calculated the tensor and we were able to show that the directions that we calculated for the pork loin muscles followed the direction of the rotation that he had applied physically on that sample, so that we were measuring something intrinsic to the tissue. These principle directions that we were able to extract from the diffusion tensor were fundamental to the tissue architecture and were independent of the coordinate system that we made the measurement in, which was really, I think, a very important demonstration then.

Jim is a coauthor on two classic papers about DTI that are widely cited in the medical literature.

Basser PJ, Mattiello J, LeBihan D (1994) MR Diffusion Tensor Spectroscopy and Imaging. Biophysical Journal 66:259–267. (4495 citations in Google Scholar as of 9-23-2017)

Basser PJ, Mattiello J, LeBihan D (1994) Estimation of the Effective Self-Diffusion Tensor From the NMR Spin Echo. Journal of Magnetic Resonance B 103:247–254. (3261 citations)

I know many scientists who have had long and successful careers, but few of them can claim they contributed to a paper with over 4000 citations, a significant achievement (that averages to one citation every other day for over two decades). My most cited article, published about the same time, has only 500 citations, and I consider myself to be a successful scientist. Jim was also the lead author on two related papers.

Mattiello J, Basser PJ, LeBihan D (1994) Analytical Expressions for the B Matrix in NMR Diffusion Imaging and Spectroscopy. Journal of Magnetic Resonance A, 108:131–141. (224 citations)

Mattiello J, Basser PJ, LeBihan D (1997) The B Matrix in Diffusion Tensor Echo-Planar Imaging. Magnetic Resonance in Medicine 37:292–300. (227 citations)

In addition, Jim is listed as an inventor on a key patent for DTI.

Basser PJ, Mattiello JH, LeBihan D. Method and System for Measuring the Diffusion Tensor and for Diffusion Tensor Imaging. US Patent 5,539,310.

Russ Hobbie and I cite the 1994 Biophysical Journal paper and the 1994 Journal of Magnetic Resonance A paper in Intermediate Physics for Medicine and Biology. Our Figure 18.40 is based in part on the pulse sequence he helped developed for DTI. Nowadays Diffusion Tensor Imaging is used to make beautiful maps of fiber tracts in the brain.

Jim spent the later part of his career teaching physics at St. Clair County Community College in Port Huron, Michigan. I last saw him when he returned to Oakland University in 2002 to give a physics colloquium about DTI.

James Mattiello’s contributions to magnetic resonance imaging, and specifically to diffusion tensor imaging, have had a lasting impact on the field of medical physics. He will be missed.

The Beautiful Brain: The Drawings of Santiago Ramon y Cajal

The Beautiful Brain: The Drawings
of Santiago Ramón y Cajal.

An art exhibit titled “The Beautiful Brain: The Drawings of Santiago Ramón y Cajal,” which is traveling through museums in the United States and Canada, relates to topics covered in Intermediate Physics for Medicine and Biology. Unfortunately it won’t pass through Detroit, but I was able to enjoy the wonderful book that accompanies the exhibit (thank you Oakland University Interlibrary Loan Department). The introduction begins

Santiago Ramón y Cajal has rightly been credited as the father of modern neuroscience, the study of the structure and function of the brain. Cajal, who lived from 1852 to 1934, was a neuroanatomist who, over the course of five decades, produced more than twenty-nine hundred drawings that reveal the nervous system as we know it today. He studied many aspects of the brain, from the structure of individual neurons…and the connections between them, to the changes that occur in the brain during early life and following injury. He did this by examining thin slices of the brain under a microscope. He treated these slices with chemical stains to highlight different types of brain cells and structures within these cells. Most notably, he used a stain developed by the Italian biologist Camillo Golgi, which colors brain cells a deep, rich black. Cajal improved upon the original formulation of the Golgi stain to obtain exquisite images of neurons.

The introduction then summarizes the contents of the book.

This book presents eighty of Cajal’s original drawings of the brain... Some of these drawings are well known, while others have not been published previously except in Cajal’s original scientific papers. Captions accompanying the drawings describe their subject matter and their scientific importance. Two essays focus respectively on Cajal’s life and scientific achievements, and his mastery of the art of drawings. A third essay brings us up-to-date, describing modern neuroscience imaging methods that Cajal, undoubtedly, would have appreciated. We hope you enjoy Cajal’s vision of the beautiful brain.

As a teaser, below I present some of Cajal’s drawings.

The structure of the retina.

Cells of the cerebellum.

Purkinje neurons from the cerebellum.

A pyramidal neuron in the cerebral cortex.

I especially like the last drawing, because it is the one Sheldon was supposed to give to Amy Farrah Fowler for Valentine’s Day, but he decided to keep it for himself instead!

Cajal shared the 1906 Nobel Prize in Physiology or Medicine with Golgi, “in recognition of their work on the structure of the nervous system.” Below is a photo of Cajal sitting at his microscope. He was a pioneer in photography as well as drawing.

Santiago Ramón y Cajal.

Here is the schedule for the exhibit, in case you are lucky enough to have it visit your town.

• Jan 28 – May 21, 2017 | Weisman Art Museum, Minneapolis MN
• Sept 5 – Dec 3, 2017 | Morris and Helen Belkin Art Gallery, Vancouver, Canada 
• Jan 9 – March 31, 2018 | Grey Art Gallery, New York, NY
• May 2, 2018 – Jan 1, 2019 | MIT Museum, Cambridge, MA 
• Jan 27 – April 7, 2019 | Ackland Art Museum, Chapel Hill, NC

You can listen to a National Public Radio broadcast about the exhibit here, and read a review of the exhibit here.

Enjoy!

The Gompertz Mortality Function

In Section 2.4 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss exponential decay with a variable rate. If the rate is constant, the fraction of a population remaining after a time t decays exponentially. This is not a good way to estimate the lifespan of humans, because as we age the likelihood of death increases. A simple model is to assume that the mortality rate increases exponentially, leading to the Gompertz mortality function. IPMB explores this behavior in a homework problem.

Problem 15. When we are dealing with death or component failure, we often write Eq. 2.17 in the form y(t) = y₀ exp[-∫₀^t m(t') dt'] and call m(t) the mortality function. Various forms for the mortality function can represent failure of computer components, batteries in pacemakers, or the death of organisms. (This is not the most general possible mortality model. For example, it ignores any interaction between organisms, so it cannot account for effects such as overcrowding or a limited supply of nutrients.)

(a) For human populations, the mortality function is often written as m(t) = m₁e ^−b₁t + m₂ + m₃e ^+b₃t . What sort of processes does each of these terms represent?

(b) Assume that m₁ and m₂ are zero. Then m(t) is called the Gompertz mortality function. Obtain an expression for y(t) with the Gompertz mortality function. Time t_max is sometimes defined to be the time when y(t) = 1. It depends on y₀. Obtain an expression for t_max.

I won’t solve this problem for you (after all, it’s your homework problem). Instead, I’ll examine this behavior in a different way. First, let’s recast the governing differential equation in terms of dimensionless variables. Let p(t) = y(t)/y₀ be the fraction surviving after time t, where y₀ is the initial number at t = 0. Also, define a dimensionless time scale as T = m₃t, and a dimensionless ratio of rates as X = b₃/m₃. The differential equation governing p(T) is then

dp/dT = - exp(XT) p

where p = 1 at T = 0. This form of the equation shows that, aside from scale factors, the behavior depends only on X.

The homework problem asks you to find an analytical expression for p(T). This is a valuable exercise, but you can also learn about the behavior by solving for p(T) numerically. The figure below shows p(T) for several values of X, calculated using Euler’s method. If the increase in mortality is slow compared to the decay of p (that is, X is much less than 1), the decay is approximately exponential (the red X=0 curve). However, if X is large the decay starts exponentially (for T less than about 0.1 the curves in the figure are all nearly equal) but then accelerates as the rate grows.

The surviving fraction p as a function of time T, for different values of X.

An exponential decay of mortality was first analyzed by Benjamin Gompertz (1779-1865), an English mathematician and actuary. His 1825 article “On the Nature of the Function Expressive of the Law of Human Mortality” helped establish two fields of study: actuarial science and the biology of aging. Thomas Kirkwood’s 2015 paper describes Gompertz’s life and work. The title and abstract are below.

Deciphering death: a commentary on Gompertz (1825) ‘On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies’

In 1825, the actuary Benjamin Gompertz read a paper, “On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies,” to the Royal Society in which he showed that over much of the adult human lifespan, age-specific mortality rates increased in an exponential manner. Gompertz’s work played an important role in shaping the emerging statistical science that underpins the pricing of life insurance and annuities. Latterly, as the subject of ageing itself became the focus of scientific study, the Gompertz model provided a powerful stimulus to examine the patterns of death across the life course not only in humans but also in a wide range of other organisms. The idea that the Gompertz model might constitute a fundamental ‘law of mortality’ has given way to the recognition that other patterns exist, not only across the species range but also in advanced old age. Nevertheless, Gompertz’s way of representing the function expressive of the pattern of much of adult mortality retains considerable relevance for studying the factors that influence the intrinsic biology of ageing.

The Goiania Accident

Thirty years ago this week (September 13, 1987) a cesium-137 radiotherapy unit was taken from a abandoned hospital in Goiania Brazil, triggering a tragic radiological accident. Below I reproduce part of the executive summary of a report about this accident published in 1988 by the International Atomic Energy Agency.

It is now known that at about the end of 1985 a private radiotherapy institute, the Institute Goiano de Radioterapia in Goiania, Brazil, moved to new premises, taking with it a cobalt-60 teletherapy unit and leaving in place a caesium-137 teletherapy unit without notifying the licensing authority as required under the terms of the institute's licence. The former premises were subsequently partly demolished. As a result, the caesium-137 teletherapy unit became totally insecure. Two people entered the premises and, not knowing what the unit was but thinking it might have some scrap value, removed the source assembly from the radiation head of the machine. This they took home and tried to dismantle.

In the attempt the source capsule was ruptured. The radioactive source was in the form of caesium chloride salt, which is highly soluble and readily dispersible. Contamination of the environment ensued, with one result being the external irradiation and internal contamination of several persons. Thus began one of the most serious radiological accidents ever to have occurred.

After the source capsule was ruptured, the remnants of the source assembly were sold for scrap to a junkyard owner. He noticed that the source material glowed blue in the dark. Several persons were fascinated by this and over a period of days friends and relatives came and saw the phenomenon. Fragments of the source the size of rice grains were distributed to several families. This proceeded for five days, by which time a number of people were showing gastrointestinal symptoms arising from their exposure to radiation from the source.

The symptoms were not initially recognized as being due to irradiation. However, one of the persons irradiated connected the illnesses with the source capsule and took the remnants to the public health department in the city. This action began a chain of events which led to the discovery of the accident. A local physicist was the first to assess, by monitoring, the scale of the accident and took actions on his own initiative to evacuate two areas. At the same time the authorities were informed, upon which the speed and the scale of the response were impressive. Several other sites of significant contamination were quickly identified and residents evacuated.

The report then addresses the health consequences of the radiation exposure.

Shortly after it had been recognized that a serious radiological accident had occurred, specialists — including physicists and physicians — were dispatched from Rio de Janeiro and Sao Paulo to Goiania. On arrival they found that a stadium had been designated as a temporary holding area where contaminated and/or injured persons could be identified. Medical triage was carried out, from which 20 persons were identified as needing hospital treatment.

Fourteen of these people were subsequently admitted to the Marciho Dias Naval Hospital in Rio de Janeiro. The remaining six patients were cared for in the Goiania General Hospital. Here a whole body counter was set up to assist in the bioassay programme and to monitor the efficacy of the drug Prussian Blue, which was given to patients in both hospitals to promote the decorporation of caesium. Cytogenetic analysis was very helpful in distinguishing the severely irradiated persons from those less exposed who did not require intensive medical care…

Four of the casualties died within four weeks of their admission to hospital. The post-mortem examinations showed haemorrhagic and septic complications associated with the acute radiation syndrome. The best independent estimates of the total body radiation doses of these four people, by cytogenetic analysis, ranged from 4.5 Gy to over 6 Gy. Two patients with similar estimated doses survived…. 

Cesium-137 is a notorious radioactive isotope that has been released in many nuclear accidents. It undergoes beta decay to metastable barium-137m, with an average beta energy of 512 keV and a half-life of about 30 years. ^137mBa has a half-life of 153 seconds and decays to ¹³⁷Ba by emitting a 662 keV gamma ray.

In Chapter 16 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the risk of radiation exposure. Typical background exposures are a few mSv per year (the unit of a sievert, Sv, is related to a gray, Gy, by multiplying by a dimensionless factor called the relative biological effectiveness; for ¹³⁷Cs the decays are all beta and gamma, this factor is about one, and we can take the sievert and gray to be the same). Typically about 5 Sv is a fatal dose.

For those of you who would prefer to learn visually, below is a video about the Goiania accident.

Anode Break Excitation

Problem 57 in Chapter 6 of Intermediate Physics for Medicine and Biology analyzes anode break excitation.

Problem 57. When a squid nerve axon is hyperpolarized by a stimulus (the transmembrane potential is more negative than resting potential) for a long time and then released, the transmembrane potential drifts back towards resting potential, overshoots v_r and becomes more positive than v_r, and eventually reaches threshold and fires an action potential. This process is called anode-break excitation: anode because the membrane is hyperpolarized, and break because the excitation does not occur until after the stimulus ends. Modify the program in Figure 6.38 [to solve the Hodgkin-Huxley equations], so that the stimulus lasts 3 ms, and the stimulus strength is −0.15 A m⁻². Show that the program predicts anode break stimulation. Determine the mechanism responsible for anode break stimulation. Hint: pay particular attention of the sodium inactivation gate (the h gate). You may want to plot h versus time to see how it behaves.

Anode break is interesting because it is an unexpected, peculiar behavior. I first learned about anode break in Hodgkin and Huxley’s Nobel Prize-winning paper “A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve” (Journal of Physiology, 117:500–544, 1952). They write:

Anode break excitation. Our [squid] axons with the long electrode in place often gave anode break responses at the end of a period during which current was made to flow inward through the membrane. The corresponding response of our theoretical model was calculated for the case in which a current sufficient to bring the membrane potential to 30 mV above [Hodgkin and Huxley used an unusual sign convention, in which a transmembrane potential “above” rest means hyperpolarization] the resting potential was suddenly stopped after passing for a time long compared with all the time constants of the membrane. To do this, eqn. (26)

was solved with I = 0 and the initial conditions that V = + 30 mV, and m, n and h [gates opening and closing the sodium and potassium channels] have their steady state values for V = + 30 mV, when t = 0. The calculation was made for a temperature of 6 3° C. A spike resulted, and the time course of membrane potential is plotted in Fig. 22A. A tracing of an experimental anode break response is shown in Fig. 22B; the temperature is 18-50 C, no record near 6° being available. It will be seen that there is good general agreement. (The oscillations after the positive phase in Fig. 22B are exceptionally large; the response of this axon to a small constant current was also unusually oscillatory as shown in Fig. 23.)

The basis of the anode break excitation is that anodal polarization decreases the potassium conductance and removes inactivation [of the sodium channel]. These effects persist for an appreciable time so that the membrane potential reaches its resting value with a reduced outward potassium current and an increased inward sodium current. The total ionic current is therefore inward at V = 0 and the membrane undergoes a depolarization which rapidly becomes regenerative.

Russ Hobbie and I have prepared a solution manual for IPMB that we distribute to instructors. Below is a sample from the solution manual for Problem 57 about anode break excitation. We introduce each homework question by a sentence or two explaining why the problem is important. If you are an instructor—Russ and I will ask you to verify this—and would like a copy of the solution manual, contact us by email.

6.57* Sometimes the true power of a mathematical model becomes evident when it correctly predicts unexpected, odd behavior. In this example, students use numerical computations to show that the Hodgkin-Huxley model predicts anode break excitation.

The plot shows the transmembrane potential as a function of time for anode break stimulation. A stimulus of −0.15 A m⁻² lasts from 0.5 to 3.5 ms. The action potential fires about 6 ms after the end of the stimulus.

Anode break excitation.

The mechanism for anode break stimulation can be understood from the plots of the gate variables. During the hyperpolarizing stimulus, the h-gate opens to a value of about 0.8, which is higher than its resting value of about 0.6. After the stimulus ends, the h-gate decreases, but very slowly. Once the transmembrane potential returns to rest (about t = 8 ms), the sodium current is larger than at rest because of the still large value of h. This causes the membrane to further depolarize, until it reaches threshold and fires an action potential. The closing of the n-gate during the hyperpolarizing stimulus also contributes to the anode break mechanism, but because the n-gate is slightly faster than the h-gate, the h-gate provides the main effect. Note that the stimulus must be long enough so the h-gate has time to open. Brief stimuli will not work well.

Hodgkin and Huxley observed anode break excitation in their 1952 paper.

I’m not surprised that the Hodgkin-Huxley model correctly describes voltage clamp data from the squid axon; it was designed to do that and the model parameters were fit to the voltage clamp data. Moreover, I’m not too surprised that the model correctly predicts the action potential; the purpose of Hodgkin and Huxley’s research was to understand nerve excitation and conduction. But I am surprised that the model is so good that it can reproduce oddball behavior such as anode break excitation. That’s impressive!

Finally, anode break excitation in nerves is very different from anode break excitation in cardiac tissue. That is another story.