Physics question: are TPSs right or wrong? Why or why not?

scarbrtj

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Been thinking. The issue is the principle of least time. You can read about it in The Story of Your Life. It was the basis for Arrival. In a nutshell: light will not travel the least distance, it will travel the path of least time. When light goes from one medium to another (ie air to water), if there's a difference in the light propagation speed between the two media the light will refract.

How to think about it: let's say you're standing some distance from a shoreline (you're "A"). You throw something into the water ("B"), but not perpendicular to the shoreline--you throw it out let's say at a ~45 degree angle to the shoreline. Now you need to go fetch the item as quickly as possible. You can run faster than swim. Do you take the straight AB path (dotted line)? Calculus will show that the solid path line is fastest (if you can swim ~3/4 as fast as you run): it's a minimization problem. Light always takes the quickest, not shortest, path to a point. This also explains why mirages happen: light travels different speeds through different pockets of air at different temps, so the light refracts to give that optical illusion.

All of this means when you're in air, and you look at something in the water, it's not "where it actually is." This is due to refraction, which is a result of the principle of least time, and the speed of light being different in air than water.

Here's something I have never read in Khan or Hall. But I am ~100% certain it's true. (And why there's Cherenkov radiation with EBRT.) Inside the body, x-rays slow from 3E8 m/s to about 2.25E8 m/s. That is to say, the speed of light is not c in the body but about 0.75c. If this is true, then x-rays should refract when they hit at an oblique angle. However Eclipse...

...seems very happy to show that an x-ray beam just travels straight through the air, then through the back, then hits oblique angle lung (mostly air), then leaves lung and back into tissue... all going straight. If this were a light beam (like a laser)...

... through an optically clear water/air phantom shaped in the same way, that light beam would refract.

So here is the question: is Eclipse right? Or wrong? I asked a couple physicists. They have not given me satisfactory answers

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elementaryschooleconomics

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Been thinking. The issue is the principle of least time. You can read about it in The Story of Your Life. It was the basis for Arrival. In a nutshell: light will not travel the least distance, it will travel the path of least time. When light goes from one medium to another (ie air to water), if there's a difference in the light propagation speed between the two media the light will refract.

How to think about it: let's say you're standing some distance from a shoreline (you're "A"). You throw something into the water ("B"), but not perpendicular to the shoreline--you throw it out let's say at a ~45 degree angle to the shoreline. Now you need to go fetch the item as quickly as possible. You can run faster than swim. Do you take the straight AB path (dotted line)? Calculus will show that the solid path line is fastest (if you can swim ~3/4 as fast as you run): it's a minimization problem. Light always takes the quickest, not shortest, path to a point. This also explains why mirages happen: light travels different speeds through different pockets of air at different temps, so the light refracts to give that optical illusion.

All of this means when you're in air, and you look at something in the water, it's not "where it actually is." This is due to refraction, which is a result of the principle of least time, and the speed of light being different in air than water.

Here's something I have never read in Khan or Hall. But I am ~100% certain it's true. (And why there's Cherenkov radiation with EBRT.) Inside the body, x-rays slow from 3E8 m/s to about 2.25E8 m/s. That is to say, the speed of light is not c in the body but about 0.75c. If this is true, then x-rays should refract when they hit at an oblique angle. However Eclipse...

...seems very happy to show that an x-ray beam just travels straight through the air, then through the back, then hits oblique angle lung (mostly air), then leaves lung and back into tissue... all going straight. If this were a light beam (like a laser)...

... through an optically clear water/air phantom shaped in the same way, that light beam would refract.

So here is the question: is Eclipse right? Or wrong? I asked a couple physicists. They have not given me satisfactory answers

Considering I'm part of the cohort that has been granted Bonus Physics Pain:

X-ray beams, while on the electromagnetic spectrum, have a much higher energy than visible light (duh). Therefore, while there is some refraction, it's generally not enough to matter (especially when what Eclipse is modeling there is dose from secondary electrons, not the path of x-rays themselves necessarily). This seems to matter more for astronomy than for RadOnc.

If you really want to go down this rabbit hole:

https://people.eecs.berkeley.edu/~attwood/sxr2009/lecnotes/04_Reflection_And_Refraction_2009.pdf

Regardless, I do get frustrated when people take Eclipse modeling as gospel, because it's basically a computer using a watered down Monte Carlo to make estimations. Very good estimations, sure, but a "best guess" nonetheless.

scarbrtj

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Considering I'm part of the cohort that has been granted Bonus Physics Pain:

X-ray beams, while on the electromagnetic spectrum, have a much higher energy than visible light (duh). Therefore, while there is some refraction, it's generally not enough to matter (especially when what Eclipse is modeling there is dose from secondary electrons, not the path of x-rays themselves necessarily). This seems to matter more for astronomy than for RadOnc.

View attachment 315141

If you really want to go down this rabbit hole:

https://people.eecs.berkeley.edu/~attwood/sxr2009/lecnotes/04_Reflection_And_Refraction_2009.pdf

Regardless, I do get frustrated when people take Eclipse modeling as gospel, because it's basically a computer using a watered down Monte Carlo to make estimations. Very good estimations, sure, but a "best guess" nonetheless.
Even that graph shows there's SOME refraction for X-rays, as much as a 0.5-0.7 factor. Eclipse shows NO refraction. I get that the beam goes straight in the body (but I don't like it's still going straight as it cross from tissue into lung). I think there's gotta be some refraction! When physicists commission machines and measure outputs they aim that beam straight down at the device in the water, perpendicular to the water surface. They don't do any measurements at highly oblique angles as far as I know where refraction could give wacky readings (or not, if it doesn't exist).

Also wonder if the "K,L,M" is pointing out photoelectric effects. We deal with that, but Compton a little more. And we don't necessarily need to know about internal refraction as much as that medium-to-medium refraction. You're doing radiosurgery... the scalp is obviously slope-y and round, and you're trying to hit sub-cm targets... if there's any refraction I'd like to know.

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elementaryschooleconomics

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Even that graph shows there's SOME refraction for X-rays, as much as a 0.5-0.7 factor. Eclipse shows NO refraction. I get that the beam goes straight in the body (but I don't like it's still going straight as it cross from tissue into lung). I think there's gotta be some refraction! When physicists commission machines and measure outputs they aim that beam straight down at the device in the water, perpendicular to the water surface. They don't do any measurements at highly oblique angles as far as I know where refraction could give wacky readings (or not, if it doesn't exist).

Well, with the phantom commissioning, they're really measuring secondary electrons as well, right? Highly oblique angles are going to push Dmax towards the surface anyway, because "secondary electrons take the path of least resistance" - so even if refraction happened, it would probably be lost in that noise.

I think you're right, and in a perfect model you would see refraction of x-rays in matter. But since what we really care about/measure is the behavior of electrons affected by x-rays, I don't know how much refraction of photons matters compared to say, scatter of electrons.

I'm sure someone who's really a physicist can say this with fancy math equations but...I cannot.

scarbrtj

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I think you're right, and in a perfect model you would see refraction of x-rays in matter. But since what we really care about/measure is the behavior of electrons affected by x-rays, I don't know how much refraction of photons matters compared to say, scatter of electrons.
1) We care about the electrons, yes. But some photons go a foot (some less, some more!) before they interact with any electron in the body.
2) Again, I want the refraction not in matter (but ultimately I'd like tissue/lung refraction modeled too) but at the medium interface where the X-ray goes from 1.0c to 0.75c. X-rays go a certain speed in air, then slow in tissue, then speed up in lung: that's all part of my disturbing hypothesis.

This is pretty easily testable. Set up patient with beam and angle etc just like in my Eclipse example above (needs to be oblique beam/skin angle, and air-to-tissue-through-lung-through-tissue-back-into-air). Take an MV film, maybe place it (film) on skin surface or something to make measuring easier. See if the "beam spot" is where Eclipse predicts it will be. If it's on, great (but explain why!). If off, how much?

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elementaryschooleconomics

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1) We care about the electrons, yes. But some photons go a foot (some less, some more!) before they interact with any electron in the body.
2) Again, I want the refraction not in matter (but ultimately I'd like tissue/lung refraction modeled too) but at the medium interface where the X-ray goes from 1.0c to 0.75c. X-rays go a certain speed in air, then slow in tissue, then speed up in lung: that's all part of my disturbing hypothesis.

I guess the other question I have here - are we sure about the 0.75c statement? I'm trying to find a primary source on that one.

scarbrtj

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I guess the other question I have here - are we sure about the 0.75c statement? I'm trying to find a primary source on that one.
I am sure. (in)Direct evidence that there's a potential for x-ray refraction in the radiotherapy clinic.

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elementaryschooleconomics

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I am sure. (in)Direct evidence that there's a potential for x-ray diffraction in the radiotherapy clinic.

Hmm, I know two physicists who would probably love this question that I can think of, I'll try to corner them and see what they say.

mheat3

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1) We care about the electrons, yes. But some photons go a foot (some less, some more!) before they interact with any electron in the body.
2) Again, I want the refraction not in matter (but ultimately I'd like tissue/lung refraction modeled too) but at the medium interface where the X-ray goes from 1.0c to 0.75c. X-rays go a certain speed in air, then slow in tissue, then speed up in lung: that's all part of my disturbing hypothesis.

This is pretty easily testable. Set up patient with beam and angle etc just like in my Eclipse example above (needs to be oblique beam/skin angle, and air-to-tissue-through-lung-through-tissue-back-into-air). Take an MV film, maybe place it (film) on skin surface or something to make measuring easier. See if the "beam spot" is where Eclipse predicts it will be. If it's on, great (but explain why!). If off, how much?

"Nerds" - Paul Wallner

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scarbrtj

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Hmm, I know two physicists who would probably love this question that I can think of, I'll try to corner them and see what they say.
The key here is, again, the media interface. In that boundary, light (x-rays) instantaneously slow to adhere to Fermat's principle. This could have implications as to why multi-beam (IMRT) treatments have shown a tendency toward better LC, and some other observations in clinic perhaps. Also of note, the x-rays' wavelengths should compress in tissue. Ie, a 6MeV (or ~2MeV photon in a "6MV" beam) photon will become something like a 7+ MeV photon. Don't know about the implications of that yet!

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Here I am trying to eat my microwaved lean cuisine over the lunch hour, with 90% of my brain occupied to barely avoid food from falling into my lap, and this is the discussion I stumble into between Scarbrtj and Elementaryschooleconomics!

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elementaryschooleconomics

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Here I am trying to eat my microwaved lean cuisine over the lunch hour, with 90% of my brain occupied to barely avoid food from falling into my lap, and this is the discussion I stumble into between Scarbrtj and Elementaryschooleconomics!

This is why the internet was invented! I have another friend who doesn't use SDN who I will be texting about this later...

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scarbrtj

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This is why the internet was invented! I have another friend who doesn't use SDN who I will be texting about this later...
If they do refract, I guess what we see in Eclipse is wrong a lot of the time. Especially at not very perpendicular beam/skin angles? And with a lot of lung plans? Surely to God I'm not first person to suss this problem. This is right up there with me discovering that a gray equals/reduces to m*m/s*s; i.e., is mass/matter invariant even though phrased as joules per kilogram.

Lamount

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This is a fun question...
My understanding is that refractive index decreases as a function of wavelength. This makes sense conceptually as higher frequency/lower wavelength EMR has more momentum thus is less impacted by the medium it is traversing (similarly, the bigger the particle and the faster it is moving, the lower it's de broglie wavelength would be). Looking at this paper, it demonstrates that, for wavelengths of 10^-12 meters (around the MV range), the index of refraction of water approaches one. This means that MV X-rays should not be bent much by tissue

scarbrtj

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This is a fun question...
My understanding is that refractive index decreases as a function of wavelength. This makes sense conceptually as higher frequency/lower wavelength EMR has more momentum thus is less impacted by the medium it is traversing (similarly, the bigger the particle and the faster it is moving, the lower it's de broglie wavelength would be). Looking at this paper, it demonstrates that, for wavelengths of 10^-12 meters (around the MV range), the index of refraction of water approaches one. This means that MV X-rays should not be bent much by tissue

View attachment 315146
If this is true in the radiotherapy clinic, then those photons MUST be traveling at ~1.0c in tissue. However if that were true we wouldn't have much Cherenkov. But we have Cherenkov. Cherenkov means sub-c photons which means refraction. So I remain skeptical.

scarbrtj

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This is a fun question...
My understanding is that refractive index decreases as a function of wavelength. This makes sense conceptually as higher frequency/lower wavelength EMR has more momentum thus is less impacted by the medium it is traversing (similarly, the bigger the particle and the faster it is moving, the lower it's de broglie wavelength would be). Looking at this paper, it demonstrates that, for wavelengths of 10^-12 meters (around the MV range), the index of refraction of water approaches one. This means that MV X-rays should not be bent much by tissue

View attachment 315146
Lamount (and ESE) is right. "Mystery" solved. No physicist explained this to me, they all went off on Compton and photoelectric and what not. But the answer is the refractive index for high energy photons in all matter is ~1. However I suppose that there is a tiny spectrum of low energy photons, or just enough of sub-c photons in the body (it's close to one but not EXACTLY one), that patients are able to see light flashes when getting irradiated. Thanks Lamount.

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evilbooyaa

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Oh good you've given them more ammunition to fail people on the physics board exam. Thanks guys!

But in seriousness, interesting discussion.

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