Cerenkov Luminescence Imaging: Physics Principles and Potential Applications in Biomedical Sciences

When a particle travels faster than the speed of light, it emits Cerenkov radiation. This phenomenon has resulted in new medical imaging applications, as described in a 2017 review paper by Esther Ciarrocchi and Nicola Belcari (Cerenkov Luminescence Imaging: Physics Principles and Potential Applications in Biomedical Sciences, EJNMMI Physics, Volume 4, Article 14). This is an open access article, so you can read it for free.

Russ Hobbie and I don’t discuss Cerenkov Luminescence Imaging in Intermediate Physics for Medicine and Biology, but you can learn a lot about it using the physics we do discuss. For example, can particles  travel faster than the speed of light? They can’t travel faster than the speed of light in a vacuum, but they can travel faster than the speed of light in a material such as water or tissue where light is slowed and the medium has an index of refraction. Below is a new homework problem, in which we consider electrons emitted in tissue by beta decay of the isotope iodine-131, used in many medical applications.

Problem 9 ¼. The end point kinetic energy (see Fig. 17.8) for beta decay of ¹³¹I is 606 keV, and tissue has an index of refraction of 1.4. Do any of the emitted electrons have a speed faster than the speed of light in the tissue? To determine this speed, use Eq. 14.1. Because the electrons move near the speed of light, to determine their speed as a function of their kinetic energy use a result from special relativity, Eq. 17.1.

For those who don’t have IPMB at your side (shame on you!), Eq. 14.1 is c_n = c/n, where c_n is the speed of light in the medium, c is the speed of light in a vacuum (3 × 10⁸ m/s), and n is the index of refraction, and Eq. 17.1 is T + mc² = mc²/√(1 − v²/c²), where v is the speed of the particle, T is its kinetic energy, and mc² is the rest mass of an electron expressed as energy (511 keV).

If you solved this problem correctly, you found that some of the more energetic electrons emitted during beta decay of ¹³¹I do travel faster than the speed of light in tissue.

Cerenkov radiation is emitted at an angle θ with respect to the direction that the particle is moving. This distribution of light is characteristic of a shock wave, and is similar to the distribution of sound in a sonic boom made by a plane when it flies faster than the speed of sound. The new problem below requires the reader to calculate θ.

Problem 9 ½. The drawing below shows a particle moving to the right faster than the speed of light in the medium. The position of the particle at several instants is indicated by the purple dots. The location of light emitted by the particle at each position is shown by the black circles. The light adds to form a conical wave front, shown by the green lines. 

(a) Use the red right triangle to calculate the angle θ as a function of the particle speed, v, and the index of refraction, n. 

(b) Compute the value of θ for the fastest electrons emitted by beta decay of ¹³¹I in tissue.

The number of photons emitted tends to be greatest at short wavelengths, so Cerenkov radiation often has a blue tinge. However, readers of IPMB learned in Chapter 14 that the spectrum of radiation can look different when viewed as a function of frequency (or energy) rather than as a function of wavelength. Below is a new problem to explore this effect.

Problem 9 ¾. The number of photons dN emitted with a wavelength between λ and λ + dλ is approximately dN = Cdλ/λ², where C is a constant.

(a) Sketch a plot of dN/dλ versus λ. Don’t worry about the scale of the axes (in other words, don't worry about the value of C); just make the plot qualitatively correct. 

(b) Use methods similar to those introduced in Section 14.8 to determine the number of photons emitted with an energy between E and E + dE. Don’t worry about constant factors, just determine how dN/dE varies with E. 

(c) Sketch a plot of dN/dE versus E. Again, just make the plot qualitatively correct.

If you solved part (c) correctly, you should have drawn a plot with a flat line, because dN/dE is independent of E. Of course, there must be some limits to this result, otherwise the particle would emit an infinite amount of energy when integrated over all photon energies. See Ciarrocchi and Belcari’s review for an explanation.

Perhaps the most interesting part of Ciarrocchi and Belcari’s article is their discussion of biomedical applications. You can use Cerenkov radiation to image beta emitters like ¹³¹I, positron emitters like ¹⁸F used in positron emission tomography, and high-energy protons required for proton therapy.

To learn more about Cerenkov radiation, watch this video by Don Lincoln. Enjoy!

How does Cerenkov radiation work?

https://www.youtube.com/watch?v=Yjx0BSXa0Ks

Science-Based Medicine

Why is my field—bioelectromagnetics—so prone to pseudoscience? I don’t know. But I do know that we need to be more skeptical about alternative medical treatments. That’s why I’m a fan of the website sciencebasedmedicine.org.

Science-Based Medicine is dedicated to evaluating medical treatments and products of interest to the public in a scientific light, and promoting the highest standards and traditions of science in health care. Online information about alternative medicine is overwhelmingly credulous and uncritical, and even mainstream media and some medical schools have bought into the hype and failed to ask the hard questions.

We provide a much needed “alternative” perspective—the scientific perspective.

Good science is the best and only way to determine which treatments and products are truly safe and effective. That idea is already formalized in a movement known as evidence-based medicine (EBM). EBM is a vital and positive influence on the practice of medicine, but it has limitations and problems in practice: it often overemphasizes the value of evidence from clinical trials alone, with some unintended consequences, such as taxpayer dollars spent on “more research” of questionable value. The idea of SBM is not to compete with EBM, but a call to enhance it with a broader view: to answer the question “what works?” we must give more importance to our cumulative scientific knowledge from all relevant disciplines.

To me, this means that medical claims must not violate the laws of physics. Some do. For instance, magnetic therapy suggests that permanent magnets can prevent many diseases. Powerline (60 Hz) magnetic fields are said to cause cancer. A few people claim to be hypersensitive to weak electromagnetic fields. Many people believe that electromagnetic radiation associated with cell phones is dangerous. This belief has increased recently with the development of 5G technology. Somehow (and this is really weird), doubts about covid-19 vaccines became mixed up with these 5G concerns.

Yet, bioelectromagnetics has enormous potential for medical applications: cardiac pacing and defibrillation, transcranial magnetic stimulation, functional electrical stimulation, deep brain stimulation, and prostheses such as cochlear implants.

How do we separate the wheat from the chaff? It’s not easy. Reading Intermediate Physics for Medicine and Biology is a good place to start. Many of these readers would benefit from a short course about science-based medicine. Does such a course exist? Yes! Harriet Hall (the SkepDoc, who I discussed previously in this blog) has recorded a series of ten videos about science-based medicine. She debunks much of the nonsense out there. Below, I link to the videos. Your homework assignment is to watch them.

If the coronavirus pandemic has taught us anything, it’s that we must base medicine on science.

 

Lecture 1: Science-based medicine versus evidence-based medicine

 

Lecture 2: Complimentary and alternative medicine

 

 

Lecture 3: Chiropractic

 

Lecture 4: Acupuncture

 

 

Lecture 5: Homeopathy

 

 

Lecture 6: Naturopathy

 

 

Lecture 7: Energy medicine

 

 

Lecture 8: Miscellaneous

 

 

Lecture 9: Pitfalls in research

 

 

Lecture 10: The media and politics

Inspire

I suspect you’ve seen some of the recent ads for Inspire, a new treatment for obstructive sleep apnea.

An Inspire TV ad. 

https://www.youtube.com/watch?v=bn5-ydF4_QQ 

How does Inspire work? It uses electrical stimulation, like Russ Hobbie and I discuss in Chapter 7 of Intermediate Physics for Medicine and Biology.

7.10 Electrical Stimulation

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 (Perlmutterand Mink 2006); for cardiac pacing (Moses andMullin 2007); and even for defibrillation (Dosdall et al.2009).

Like the cardiac pacemaker, the Inspire device is implanted in the upper chest. Instead of monitoring the electrocardiogram, the device monitors breathing; instead of stimulating the heart, it stimulates the hypoglossal nerve controlling muscles in the tongue.

A patient with obstructive sleep apnea has their airway blocked while sleeping, causing the body to crave oxygen. This results in a brief reawakening as the person opens their airway for better airflow. Once oxygen is restored, the patient goes back to sleep. Then, the entire process starts again, so sleep is frequently and repeatedly interrupted.

One way to treat obstructive sleep apnea is using continuous positive airway pressure (CPAP), which requires wearing a mask attached by a hose to a pump. Some people can’t or won’t tolerate CPAP, and it’s hard to imagine that anyone likes it.

When Inspire detects that you’re taking a breath it stimulates the tongue to contract, opening the airway. You only need it when sleeping, so it has a button you can push to turn it on before bed and turn it off when you wake up.

Inspire is yet one more example of how physics can be applied to medicine, and in particular how electrical stimulation can be used to treat patients. I’m into it. 

Dr. Ryan Soose explains the Stimulation Therapy for Apnea Reduction (STAR) clinical trial.

https://www.youtube.com/watch?v=AvQoxv7iDP4

The Bidomain Model of Cardiac Tissue: Predictions and Experimental Verification

“The Bidomain Model of Cardiac Tissue:
Predictions and Experimental Verification”

In the early 1990s, I was asked to write a chapter for a book titled Neural Engineering. My chapter had nothing to do with nerves, but instead was about cardiac tissue analyzed with the bidomain model. (You can learn more about the bidomain model in Chapter 7 of Intermediate Physics for Medicine and Biology.) 

“The Bidomain Model of Cardiac Tissue: Predictions and Experimental Verification” was submitted to the editors in January, 1993. Alas, the book was never published. However, I still have a copy of the chapter, and you can download it here. Now—after nearly thirty years—it’s obsolete, but provides a glimpse into the pressing issues of that time.

I was a impudent young buck back in those days. Three times in the chapter I recast the arguments of other scientists (my competitors) as syllogisms. Then, I asserted that their premise was false, so their conclusion was invalid (I'm sure this endeared me to them). All three syllogisms dealt with whether or not cardiac tissue could be treated as a continuous tissue, as opposed to a discrete collection of cells.

The Spach Experiment

The first example had to do with the claim by Madison Spach that the rate of rise of the cardiac action potential, and time constant of the action potential foot, varied with direction.

Continuous cable theory predicts that the time course of the action potential does not depend on differences in axial resistance with direction.

The rate of rise of the cardiac wave front is observed experimentally to depend on the direction of propagation.

Therefore, cardiac tissue does not behave like a continuous tissue.

I then argued that their first premise is incorrect. In one-dimensional cable theory, the time course of the action potential doesn’t depend on axial resistance, as Spach claimed. But in a three-dimensional slab of tissue superfused by a bath, the time course of the action potential depends on the direction of propagation. Therefore, I contended, their conclusion didn’t hold; their experiment did not prove that cardiac tissue isn’t continuous. To this day the issue is unresolved.

Defibrillation

A second example considered the question of defibrillation. When a large shock is applied to the heart, can its response be predicted using a continuous model, or are discrete effects essential for describing the behavior?

An applied current depolarizes or hyperpolarizes the membrane only in a small region near the ends of a continuous fiber.

For successful defibrillation, a large fraction of the heart must be influenced by the stimulus.

Therefore, defibrillation cannot be explained by a continuous model.

I argued that the problem is again with the first premise, which is true for tissue having “equal anisotropy ratios” (the same ratio of conductivity parallel and perpendicular to the fibers, in both the intracellular and extracellular spaces), but is not true for “unequal anisotropy ratios.” (Homework Problem 50 in Chapter 7 of IPMB examines unequal anisotropy ratios in more detail). If the premise is false, the conclusion is not proven. This issue is not definitively resolved even today, although the sophisticated simulations of realistically shaped hearts with their curving fiber geometry, performed by Natalia Trayanova and others, suggest that I was right.

Reentry Induction

The final example deals with the induction of reentry by successive stimulation through a point electrode. As usual, I condensed the existing dogma to a syllogism.

In a continuous tissue, the anisotropy can be removed by a coordinate transformation, so reentry caused by successive stimulation through a single point electrode cannot occur, since there is no mechanism to break the directional symmetry.

Reentry has been produced experimentally by successive stimulation through a single point electrode.

Therefore, cardiac tissue is not continuous.

Once again, that pesky first premise is the problem. In tissue with equal anisotropy ratios you can remove anisotropy by a coordinate transformation, so reentry is impossible. However, if the tissue has unequal anisotropy ratios the symmetry is broken, and reentry is possible. Therefore, you can’t conclude that the observed induction of reentry by successive stimulation through a point electrode implies the tissue is discrete.

I always liked this book chapter, in part because of the syllogisms, in part because of its emphasis on predictions and experiments, but mainly because it provides a devastating counterargument to claims that cardiac tissue acts discretely. Although it was never published, I did send preprints around to some of my friends, and the chapter took on a life of its own. This unpublished manuscript has been cited 13 times!

Trayanova N, Pilkington T (1992) “The use of spectral methods in bidomain studies,” Critical Reviews in Biomedical Engineering, Volume 20, Pages 255–277.

Winfree AT (1993) “How does ventricular tachycardia turn into fibrillation?” In: Borgreffe M, Breithardt G, Shenasa M (eds), Cardiac Mapping, Mt. Kisco NY, Futura, Chapter 41, Pages 655–680.

Henriquez CS (1993) “Simulating the electrical behavior of cardiac tissue using thebidomain model,” Critical Reviews of Biomedical Engineering, Volume 21, Pages 1–77.

Wikswo JP (1994) “The complexities of cardiac cables: Virtual electrode effects,” Biophysical Journal, Volume 66, Pages 551–553.

Winfree AT (1994) “Puzzles about excitable media and sudden death,” Lecture Notes in Biomathematics, Volume 100, Pages 139–150.

Roth BJ (1994) “Mechanisms for electrical stimulation of excitable tissue,” Critical Reviews in Biomedical Engineering, Volume 22, Pages 253–305.

Roth BJ (1995) “A mathematical model of make and break electrical stimulation ofcardiac tissue by a unipolar anode or cathode,” IEEE Transactions on Biomedical Engineering, Volume 42, Pages 1174–1184.

Wikswo JP Jr, Lin S-F, Abbas RA (1995) “Virtual electrodes in cardiac tissue: A common mechanism for anodal and cathodal stimulation,” Biophysical Journal, Volume 69, Pages 2195–2210.

Roth BJ, Wikswo JP Jr (1996) “The effect of externally applied electrical fields on myocardial tissue,” Proceedings of the IEEE, Volume 84, Pages 379–391.

Goode PV, Nagle HT (1996) “On-line control of propagating cardiac wavefronts,” The 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Amsterdam.

Winfree AT (1997) “Rotors, fibrillation, and dimensionality,” In: Holden AV, Panfilov AV (eds): Computational Biology of the Heart, Chichester, Wiley, Pages 101–135.

Winfree AT (1997) “Heart muscle as a reaction-diffusion medium: The roles of electric potential diffusion, activation front curvature, and anisotropy,” International Journal of Bifurcation and Chaos, Volume 7, Pages 487–526.

Winfree AT (1998) “A spatial scale factor for electrophysiological models of myocardium,” Progress in Biophysics and Molecular Biology, Volume 69, Pages 185–203.

I’ll end with the closing paragraph of the chapter.

The bidomain model ignores the discrete nature of cardiac cells, representing the tissue as a continuum instead. Experimental evidence is often cited to support the hypothesis that the discrete nature of the cells plays a key role in cardiac electrophysiology. In each case, the bidomain model offers an alternative explanation for the phenomena. It seems wise at this point to reconsider the evidence that indicates the significance of discrete effects in healthy cardiac tissue. The continuous bidomain model explains the data, recorded by Spach and his colleagues, showing different rates of rise during propagation parallel and perpendicular to the fibers, anodal stimulation, arrhythmia development by successive stimulation from a point source, and possibly defibrillation. Of course, these alternative explanations do not imply that discrete effects are not responsible for these phenomena, but only that two possible mechanisms exist rather than one. Experiments must be found that differentiate unambiguously between alternative models. In addition, discrete junctional resistance must be incorporated into the bidomain model. Only when such experiments are performed and the models are further developed will we be able to say with any certainty that cardiac tissue can be described as a continuum.