One of the homework problems in Intermediate Physics for Medicine and Biology (Problem 31 in Chapter 16) introduces a toy model for the Bragg peak. I won’t review that entire problem, but students derive an equation for the stopping power, S, (the energy per unit distance deposited in tissue by a high energy ion) as a function of the depth below the tissue surface, x
where S0 is the ion’sstopping power at the surface (x = 0) and R is the ion’s range. At a glance you can see how the Bragg peak arises—the denominator goes to zero at x = R so the stopping power goes to infinity. That, in fact, is why proton therapy for cancer is becoming so popular: Energy is deposited primarily at one spot well below the tissue surface where a tumor is located, with only a small dose to upstream healthy tissue.
One topic that comes up when discussing the Bragg peak is straggling. The idea is that the range is not a single parameter. Instead, protons have a distribution of ranges. When preparing the 6th edition of Intermediate Physics for Medicine and Biology, I thought I would try to develop a toy model in a new homework problem to illustrate straggling.
Section 16.10
Problem 31 ½. Consider a beam of protons incident on a tissue. Assume the stopping power S for a single proton as a function of depth x below the tissue surface is
Furthermore assume that instead of all the protons having the same range R, the protons have a uniform distribution of ranges between R – δ/2 and R + δ/2, and no protons have a range outside this interval. Calculate the average stopping power by integrating S(x) over this distribution of ranges.
This calculation is a little more challenging than I had expected. We have to consider three possibilities for x.
x < R — δ/2
In this case, all of the protons contribute so the average stopping power is
We need to solve the integral
First, let
With a little analysis, you can show that
So the integral becomes
This new integral I can look up in my integral table
Finally, after a bit of algebra, I get
Well, that was a lot of work and the result is not very pretty. And we are not even done yet! We still have the other two cases.
R — δ/2 < x < R + δ/2
In this case, if the range is less than x there is no contribution to the stopping power, but if the range is greater than x there is. So, we must solve the integral
I’m not going to go through all those calculations again (I’ll leave it to you, dear reader, to check). The result is
x > R + δ/2
This is the easy case. None of the protons make it to x, so the stopping power is zero.
Well, I can’t look at these functions and tell what the plot will look like. All I can do is ask Mr. Mathematica to make the plot (he’s much smarter than I am). Here’s what he said:
The peak of the “pure” (single value for the range) curve (the red one) goes to infinity at x = R, and is zero for any x greater than R. As you begin averaging, you start getting some stopping power past the original range, out to R + δ/2. To me the most interesting thing is that for x = R– δ/2, the stopping power is larger than for the pure case. The curves all overlap for x > R + δ/2 (of course, they are all zero), and for fairly small values x (in these cases, about x < 0.5) the curves are all nearly equal (indistinguishable in the plot). Even a small value of δ (in this case, for a spread of ranges equal to one tenth the pure range), the peak of the stopping power curve is suppressed.
The curves for straggling that you see in most textbooks are much smoother, but that’s because I suspect they assume a smoother distribution of range values, such as a normal distribution. In this example, I wanted something simple enough to get an analytical solution, so I took a uniform distribution over a width δ .
Will this new homework problem make it into the 6th edition? I’m not sure. It’s definitely a candidate. However, the value of toy models is that they illustrate the physical phenomenon and describe it in simple equations. I found the equations in this example to be complicated and not illuminating. There is still some value, but if you are not gaining a lot of insight from your toy model, it may not be worth doing. I’ll leave the decision of including it in the 6th edition to my new coauthor, Gene Surdutovich. After all, he’s the expert in the interaction of ions with tissue.
My Treeing Walker Coonhound Harvest is getting older and having some trouble with arthritis. The vet says she’s showing signs of hip dysplasia, but it’s not too severe yet. I want to nip this problem in the bud, so we have started a treatment regime that includes oral supplements, pain medication, moderate exercise, weight control, and massage. We’re also trying photobiomodulation, sometimes called low-level laser therapy or cold laser therapy.
We bought a device called Lumasoothe 2 Light Therapy for Pets (lumasoothe.com). I use it in it’s IR Deep Treatment Mode, which shines three wavelengths of light—infrared (940 nm), red (650 nm) and green (520 nm)—from an array of light emitting diodes. I doubt the green light can penetrate to the hip, but red and especially infrared are not attenuated as much. In IPMB, Russ and I talk about how red light is highly scattered, and you can see that by noticing how the red spreads out to the sides of the applicator (kind of like when you hold a flashlight up to your mouth and your checks glow red). The light is delivered in pulses that come at a frequency of about 2.5 Hz (I used the metronome that sits atop my piano to estimate the frequency). I can’t imagine any advantage to pulsing the light, and suspect it’s done simply for the visual effect. I apply the light to Harvest’s hips, about 15 minutes each side.
Mechanisms and Applications of the Anti-Inflammatory Effects of Photobiomodulation.
Photobiomodulation (PBM) was discovered almost 50 years ago by Endre Mester in Hungary. For most of this time PBM was known as “low-level laser therapy” as ruby laser (694 nm) and HeNe lasers (633 nm) were the first devices used. Recently a consensus decision was taken to use the terminology “PBM” since the term “low-level” was very subjective, and it is now known that actual lasers are not required, as non-coherent light-emitting diodes (LEDs) work equally well. For much of this time the mechanism of action of PBM was unclear, but in recent years much progress has been made in elucidating chromophores and signaling pathways.
Any time you are talking about a therapy, the dose is crucial. According to a study by medcovet, the output of Lumasoothe is 0.225 J/cm² per minute (it’s advertised at 6.4). I don’t know which of these values to use, so I’ll just pick something in the middle: 1 J/cm². If we divide by 60 seconds, this converts to about 0.017 W/cm². The intensity of sunlight that reaches the earth’s surface is about 0.1 W/cm², so the device puts out less than the intensity of sunlight (at noon, at the equator, with no clouds). The advertised intensity would be similar to the intensity of sunlight. Of course, sunlight includes a wide band of frequencies, while the Lumasoothe emits just three.
There seems to be an optimum dose, as is often found in toxicology. Hamblin explains
The “biphasic dose response” describes a situation in which there is an optimum value of the “dose” of PBM most often defined by the energy density (J/cm²). It has been consistently found that when the dose of PBM is increased a maximum response is reached at some value, and if the dose in increased beyond that maximal value, the response diminishes, disappears and it is even possible that negative or inhibitory effects are produced at very high fluences.
Joules per square centimeter per minute may not be the best unit to assess heating effects of the Lumasoothe. Let’s assume that 0.017 W/cm² of light penetrates into the tissue about one centimeter (a guess). This means that the device dumps 0.017 watts into a cubic centimeter of tissue. That volume of tissue has a density of about that of water: 1 g/cm3. So the specific absorption rate should be about 0.017 W/g or 17 W/kg. That’s not negligible. A person’s metabolism generates only about 1.5 W/kg. Diathermy to heat tissues uses about 20 W/kg. I don’t think we can rule out some heating using this device. (However, I shined it on my forearm for about two minutes and didn’t feel any obvious warming.)
Hamblin believes there are non-thermal mechanisms involved.
Cytochrome c oxidase (CCO) is unit IV in the mitochondrialelectron transport chain. It transfers one electron (from each of four cytochrome c molecules), to a single oxygen molecule, producing two molecules of water. At the same time the four protons required, are translocated across the mitochondrial membrane, producing a proton gradient that the ATP synthase enzyme needs to synthesize ATP. CCO has two heme centers (a and a3) and two copper centers (CuA and CuB). Each of these metal centers can exist in an oxidized or a reduced state, and these have different absorption spectra, meaning CCO can absorb light well into the NIR [near infrared] region (up to 950 nm). Tiina Karu from Russia was the first to suggest that the action spectrum of PBM effects matched the absorption spectrum of CCO, and this observation was confirmed by Wong-Riley et al in Wisconsin. The assumption that CCO is a main target of PBM also explains the wide use of red/NIR wavelengths as these longer wavelengths have much better tissue penetration than say blue or green light which are better absorbed by hemoglobin. The most popular theory to explain exactly why photon absorption by CCO could led [sic] to increase of the enzyme activity, increased oxygen consumption, and increased ATP production is based on photodissociation of inhibitory nitric oxide (NO). Since NO is non-covalently bound to the heme and Cu centers and competitively blocks oxygen at a ratio of 1:10, a relatively low energy photon can kick out the NO and allow a lot of respiration to take place.
That’s a considerable amount of biochemistry, which I’m not an expert in. I’ll assume Hamblin knows a lot more about it than I do. I worry, however, when he writes “the assumption that…” and “the most popular theory…” It makes me wonder how well this mechanism is established. He goes on to suggest other mechanisms, such as the production of reactive oxygen species and a reduction in inflammation.
Hamblin concludes
The clinical applications of PBM have been increasing apace in recent years. The recent adoption of inexpensive large area LED arrays, that have replaced costly, small area laser beams with a risk of eye damage, has accelerated this increase in popularity. Advances in understanding of PBM mechanisms of action at a molecular and cellular level, have provided a scientific rationale for its use for multiple diseases. Many patients have become disillusioned with traditional pharmaceutical approaches to a range of chronic conditions, with their accompanying distressing side-effects and have turned to complementary and alternative medicine for more natural remedies. PBM has an almost complete lack of reported adverse effects, provided the parameters are understood at least at a basic level. The remarkable range of medical benefits provided by PBM, has led some to suggest that it may be “too good to be true”. However one of the most general benefits of PBM that has recently emerged, is its pronounced anti-inflammatory effects. While the exact cellular signaling pathways responsible for this anti-inflammatory action are not yet completely understood, it is becoming clear that both local and systemic mechanisms are operating. The local reduction of edema, and reductions in markers of oxidative stress and pro-inflammatory cytokines are well established. However there also appears to be a systemic effect whereby light delivered to the body, can positively benefit distant tissues and organs.
I have to admit that Hamblin makes a strong case. But there is another side to the question. Hamblin himself uses that worrisome phrase “complementary and alternative medicine.” I have to wonder about thermal effects. We know that temperature can influence healing (that’s why people often use a heating pad). If photobiomodulation causes even a little heating, this might explain some of its effect.
I’ve talked a lot in this blog about websites or groups that debunk alternative medicine. Stephen Barrett of quackwatch looked at Low Level Laser Therapy in 2018, and concluded that “At this writing, the bottom line appears to be that LLLT devices may bring about temporary relief of some types of pain, but there’s no reason to believe that they will influence the course of any ailment or are more effective than standard forms of heat delivery.”
Mark Crislip writing for Science Based Medicine in 2012 concluded “I suspect that time and careful studies on the efficacy of low level laser will have the same results as the last decade of acupuncture studies: there is no there there.” Jonathan Jarry wrote about “The Hype Around Photobiomodulation,” saying
“That is not to say that all of PBM’s applications are hogwash or that future research will never produce more effective applications of it. But given biomedical research’s modest success rate these days and the ease of coming up with a molecular pathway that fits our wishes, we’re going to need more than mice studies and a plausible mechanism of action to see photobiomodulation in a more favourable light. A healthy skepticism is needed here, especially when it comes to claims of red light improving dementia.”
So, what’s the bottom line? In my book Are Electromagnetic Fields Making Me Ill?, I divided different medical devices, procedures, and hypotheses into three categories: Firmly Established, Questionable, and Improbable (basically: yes, maybe, and no). I would put photobiomodulation therapy in the maybe category, along with transcutaneous electrical nerve stimulation, bone healing using electromagnetic fields, and transcranial direct current stimulation. As a scientist, I’m skeptical about photobiomodulation therapy. But as dog lover, I’m using it every day to try and help Harvest’s hip dysplasia. This probably says more about how much I love Harvest than about my confidence in the technique. My advice is to not get your hopes up, and to follow your vet’s advice about traditional and better-established treatments. The good news: I don’t see much potential for side effects. Is it worth the money to purchase the device? My wife and I were willing to take a moderately expensive bet on a low probability outcome for Harvest’s sake. because she’s the goodest gurl.
Mechanisms & History of Photobiomodulation with Dr. Michael Hamblin
I’ve written about FLASH radiotherapy previously in this blog (here and here). FLASH is when you apply radiation in a single brief pulse rather than slowly or in several fractions. It’s one of the most important developments in radiation therapy in the last decade, but no one is sure why FLASH works better than conventional methods. (Skeptics might say no one is sure if FLASH works better than conventional methods, but I’ll assume in this post that it’s better.)
FLASH is too new for Russ Hobbie and I to mention it in the 5th edition of Intermediate Physics for Medicine and Biology, but Gene Surdutovich and I will add a discussion of it to the 6th edition.
“Mechanisms of the FLASH Effect: Current Insights and Advances,” by Giulia Rosini, Esther Ciarrocchi, and Beatrice D’Orse
I recently read a fascinating mini review in Frontiers in Cell and Developmental Biology by Giulia Rosini, Esther Ciarrocchi, and Beatrice D’Orse of the Institute of Neuroscience in Pisa, Italy. They’re trying to address that why question. Their article, titled “Mechanisms of the FLASH Effect: Current Insights and Advances,” is well worth reading. (Some scientific leaders in the United States claim that modern medicine focuses on treating symptoms rather than addressing underlying causes. This article shows that scientists do just the opposite: They search for basic mechanisms. Bravo! At least in Italy science is still alive.)
Below I reproduce their introduction (references removed and Wikipedia links added). If you want more detail, I suggest reading the review in its entirety (it’s open access, so you don’t need a subscription to the journal).
Radiotherapy is one of the most effective treatments for cancer, used in more than 60% of cancer patients during their oncological care to eliminate/reduce the size of the tumor. Currently, conventional radiotherapy (CONV-RT) remains the standard in clinical practice but has limitations, including the risk of damage to surrounding healthy tissues. A recent innovation, FLASH radiotherapy (FLASH-RT), employs ultra-high-dose rate (UHDR) irradiation to selectively spare healthy tissue while maintaining its therapeutic effect on tumors. However, the precise radiobiological mechanism behind this protective
“FLASH effect” remains unclear. To understand the FLASH effect, several hypotheses have been proposed, focusing on the differential responses of normal and tumor tissues to UHDR irradiation: (i) Oxygen depletion: FLASH-RT may rapidly deplete oxygen in normal tissues, creating transient hypoxia that reduces oxygen-dependent DNA damage; (ii) Radical-radical interaction: The rapid production of reactive oxygen species (ROS) during UHDR irradiation may lead to radical recombination, preventing oxidative damage to healthy tissues; (iii) Mitochondrial preservation: FLASH-RT appears to
preserve mitochondrial integrity and ATP production in normal tissues, minimizing oxidative stress. Conversely, FLASH-RT may promote oxidative damage and apoptosis in tumor cells, potentially improving therapeutic efficacy; (iv) DNA damage and repair: The differential response of normal and tumor tissues may result from variations in DNA damage formation and repair. Normal cells rely on highly conserved repair mechanisms, while tumor cells often exhibit dysregulated repair pathways; and (v) Immune response: FLASH-RT may better preserve circulating immune cells and reduce inflammation in normal tissues compared to CONV-RT. In this mini-review, we summarize the current insights into the cellular mechanisms underlying the FLASH effect. Preclinical
studies in animal models have demonstrated the FLASH effect, and early-phase clinical trials are now underway to evaluate its safety and efficacy in human patients. While FLASH-RT holds great promise for improving the balance between tumor control and
normal tissue sparing in cancer treatment, continued research is necessary to fully elucidate its mechanisms, optimize its clinical application, and minimize potential side effects. Understanding these mechanisms will pave the way for safer and more effective
radiotherapy strategies.
I’ll take advantage of this paper being open access to reproduce Rosini et al.’s Figure 1, which is a beautiful summary of their article.
Figure 1 from “Mechanisms of the FLASH Effect: Current Insights and Advances,” by Giulia Rosini, Esther Ciarrocchi and Beatrice D’Orsi
If I were a betting man, I’d put my money on the radical-radical interaction mechanism. But don’t trust me, because I’m not an expert in this field. Read this well-written review yourself and draw your own conclusion.
I’ll end by giving Rosini, Ciarrocchi, and D’Orse the final word. Their conclusion is quoted below.
FLASH-RT has emerged as a promising alternative to CONV-RT, offering potential advantages in reducing normal tissues toxicity while maintaining or even potentially enhancing tumor control. However, the underlying mechanisms remain incompletely understood. Oxygen depletion, radical recombination, mitochondrial preservation, DNA repair and immune response modulation, have all been proposed as contributing factors… but no single mechanism fully explains the FLASH effect. This further highlights the complex interplay between physical, biological, and immunological factors that might behind the FLASH effect. Importantly, combining FLASH-RT with adjuvant therapies, such as radioprotectors, immunotherapy or nanotechnology, could synergize with these mechanisms to further widen the therapeutic window. FLASH-RT’s ability to reduce inflammation, preserve immune function, and minimize damage to healthy tissues contrasts sharply with CONV-RT, which often
induces significant toxicity. However, despite promising preclinical findings, critical questions remain regarding the precise mechanisms driving the FLASH effect and its clinical applicability. Continued research is essential to fully elucidate these mechanisms, optimize FLASH-RT delivery, and translate its benefits into safe and effective clinical applications. By addressing these challenges, FLASH-RT has the potential to significantly improve therapeutic outcomes for cancer patients, offering a paradigm shift in radiation oncology.
I am an emeritus professor of physics at Oakland University, and coauthor of the textbook Intermediate Physics for Medicine and Biology. The purpose of this blog is specifically to support and promote my textbook, and in general to illustrate applications of physics to medicine and biology.
