Welcome to the first module of the physics section on cardiovascular PET. Here are our disclosures. And in this module, we're going to look at positrons, where they come from, the mechanics of their annihilation, how we try to make images of them, and then we'll distinguish PET imaging from SPECT imaging. So by the time you're done with the module, hopefully you'll be in position to describe what positrons are, what is meant by positronium annihilation, explain a little bit about the mechanics of physics imaging in order to make a PET image, and to be able to talk to your colleagues and explain the difference between SPECT images and PET images. So first, let's look at positrons. There's a bunch of different kinds of particles that can emerge from a nuclear decay, and people naturally break these into massive particles versus massless particles. And the massive particles include electrons and positrons, and crucially, this is what we're interested in, of course, is the positrons. But in addition, other things can emerge from nuclear decays, including protons and neutrons, and alpha particles, which are basically helium nuclei. So here's a little summary of the massive particles that can be emitted, and the kind of radiation we worry about is ionizing radiation. So principally, you and I today are interested in the positrons that can emerge, and those are just basically the antimatter versions of electrons, and so they have exactly the same mass, and this is a good number to remember, of 511 KeV or 0.511 MeV. When we talk about ionizing radiation, what we worry about are any kinds of radiation above 33 electron volts. So in addition to the massive particles that can emerge from nuclear decay, we also have electromagnetic radiation that can emerge from nuclear decays, and these are called gamma rays. They are anything above 33 electron volts is something that we worry about because that can break nuclear DNA molecules. The electromagnetic radiation includes light, ultraviolet light, X-rays, and gamma rays, and what distinguishes one kind of electromagnetic radiation from another is really what produced it. So anything that is a gamma ray is a little quantum of electromagnetic radiation that has emerged from a nuclear decay. X-rays come from smashing electrons into metal foils, and then you and I live down here in this realm of one electron volt light photons, and these all are really just forms of electromagnetic radiation, the whole way down to radio waves, microwaves, and so forth. In terms of the nuclear decays, what happens is some nuclei are very close to stable, but not quite. They have maybe one extra neutron, and if they have one extra neutron, what can happen is they can go to a lower overall energy state by emitting a proton, an electron, and an anti-neutrino. Now, this does happen in free space. This other reaction doesn't. So here we have a nucleus with one too many protons to be stable, and it will decay into another nucleus as along with a neutron, a positron, and a neutrino. Of course, that's what we're mostly interested in. And if you have a nucleus is very, very heavy and on the verge of decaying, it can get rid of a lot of energy all at once with alpha decays, which are the most damaging forms of ionizing radiation. So a free neutron left to itself in a vacuum will decay in five minutes. Protons never decay. And as we said, the nuclear decays that produce the positron are those with nuclei that have just a little too much proton in them to be stable. Because they decay into three products, namely the positron, the neutrino, and the neutron, they will, in fact, equally share the kinetic energy, the extra energy between the mass of the parent nucleus and the mass and all the decay products of the final daughter nucleus. And because this is a completely random quantum mechanical product, what happens is the different three decay products can have all the energy or none of the energy. It's completely random. So if you think of a nuclear transition that has an overall energy difference of 1.2 MeV, the positrons that you and I are in position to measure can have that total energy and nothing for the neutrino and nothing for the other nucleus, or it can have the whole way down to zero. And on average, it has about a third. So an example of that is fluorine 18, which decays to oxygen 18, a positron, and a neutrino. The neutrino, like I said, might carry all the energy, none of the energy, but what you and I can measure is the positron. We can't really measure the neutrinos. So in this case, the positron can have as much as 635 KeV or as little as zero. And on average, it has 215 KeV. So now let's look a little bit more about positron annihilation. Once we've generated the positron, it's been expelled from the fluorine nucleus, it's going to bounce around a bit in tissue. So it's going to interact with various different isotopes inside the various different cells of the nuclei and potentially break their bonds and eventually slow down enough to find an electron that's going at about the same speed. And when it does, it will bind and form temporarily a positronium atom. So these atoms are really similar to hydrogen atoms. The difference is it's not a proton and electron, it's a positron and electron. And in only 10 to the minus 10 seconds, that will spontaneously vanish. The mass of the electron and the positron disappear, and instead you have two gamma rays coming out. Since this whole thing was not moving, the two gamma rays have the same energy and the same energies of the masses of the electron and the positron. So if we have surrounded the realm in which these positrons are being generated with detectors, then what we're going to see is if we have two detectors fire within a narrow time window, we can say that there's highly probable situation in which the positronium atom decayed in the middle. When we draw a line between two detectors, we're generating what's called a line of response. And we'll talk more about that in a minute. So forming a image from a positronium decay means we must detect both gamma rays at about the same time. And doing that, it sounds very straightforward. The problem is there are various other things that might complicate our ability to distinguish events that we do want from events we don't want, called scattered and random events. And we're going to talk about those now a bit more when we talk about PET image quality. So there are several factors that affect image quality in general. First, let's just concentrate on spatial resolution. In the case of positron imaging, there's several things that make our ability to localize where the positronium atom decayed a little more complicated than we'd like. The first is the fact that the positron, once it's emitted from the nucleus, will move around a bit. So it has a spatial range. Also, the positronium atom may not be move, may not be completely stable in our system. And that's going to have an effect on the angles at which the gamma rays emerge. And then finally, there's just the physical limitations of the detectors. So first of all, in terms of the range, what happens is once the positron has been emitted, it's going to need to find an electron before it can form a positronium atom. And the electrons, of course, are in motion too. So the positronium atom, once it's formed, may not be completely at rest. So that's one thing to be aware of. The positron is going to knock around a bit before it binds with an electron. And so one of the consequences of that is while you and I might want to know the location of the nucleus that emitted the positron, we're really not going to be quite able to do that. The best we're going to be able to do is to say where the positronium atom emitted its two gamma rays. So that's one thing that complicates things. Now, as you'll see a couple of times in this talk, fluorine-18 and rubidium-82 are the two main isotopes that we deal with on a clinical basis for nuclear cardiology. Something to be aware of right from the outset is that the positrons that are emitted from fluorine-18 decay have the least maximum kinetic energy of all the different isotopes you might try to image. And consequently, fluorine has the best spatial resolution because even though positron migrates away from the fluorine atom, it migrates away the least of all the different positrons are emitted. On the other hand, the rubidium positrons have the most kinetic energy. In fact, they're about five times more energetic than the fluorine-18 positrons and they travel further. And this little table summarizes that. So with the fluorine positrons, the average range in water is something less than a millimeter, but in the case of rubidium, it's over four millimeters. Notice also a very big difference in the half-lives of almost two hours for fluorine and only a little bit more than a minute for rubidium and we'll return to that in a little bit. So that's one thing that complicates our ability to say where the positron was emitted. Another is because the electrons with which the positron binds can be in motion because things at normal room temperature are in motion. That means that when the two gamma rays are emitted, they might not actually come out at exactly 180 degrees. So that's going to complicate things a little bit for us. We would like to be able to draw a line of response through where there are detectors, but here we're going to be stuck with making a little bit of a mistake because the angles really aren't quite 180 degrees. And then finally, the biggest contributor to the difficulty in localizing, really where the positronium atom decayed is the fact that we have to use a scintillator and it has to have a physical dimension in order to do this. So imagine here are two scintillation detectors, typically LYSO crystals these days, and imagine that they are the dimension you're seeing here. Now, if we wanted to make this gray bar in the middle, so that we make a better discrimination in drawing the line of response and a more accurate determination of where along the line the nucleus was that emitted the positronium atom, what we would do is we would shrink the footprint of both these detectors. And in fact, that has been the evolution continuously in detector design. Now, there are many, many, many thousands of very tiny equivalent detectors in order to do this. And the trend has been more detectors and smaller of them in order to make this discrimination to help out with the component of the imprecision that is due to the detector. So the way this all comes together is the sum of the squares of the different components of the imprecision of figuring out where things are coming from from the range, the angles and the detector properties all combine into the overall system resolution. Now, as we said before, the two main isotopes that are used clinically are fluorine and rubidium. Because fluorine has a nice long half-life, it's feasible to have a central location, a cyclotron that generates these, and then those unit doses can be distributed in a large geographic area. But in the case of rubidium, the half-life is so rapid that really the only feasible way to make use of this is with generators, a strontium rubidium generator. So here are two examples of some commercially available generators, and notice both of these have saline bags. And the way these work is the columns of strontium are continually decaying away into rubidium, and by flushing the saline down through them, it leaches out through rubidium and is fed directly and injected into the arm of the patient who is already in the PET scanner beside the generator. Because the strontium has a nice long half-life of 25 days, while the rubidium is a very short half-life, what this means is people who use this kind of system will typically get a generator every month, and as they're using it, they inject the patient, and because the half-life of the rubidium is so rapid, it means that in only a few minutes, you're going to be ready to inject the same person again, if you want, or ready to generate, to inject a completely different patient. So this is a very efficient delivery method for a month, but then you do have to swap out the generator. Now let's talk a little bit about the process of forming a PET image. It would be nice if we only had what are called true events. So here we have a patient surrounded by many little detectors, and we want to draw a line of response through the coincidences that we've seen two detectors have fired, and that would be nice if that's all that happens, but it isn't, so not uncommonly, what'll happen is one of the gamma rays that have been emitted from the positronium decay will undergo a Compton scatter, and if it's low angle Compton scatter, the secondary gamma ray that comes out and hits the detector has an energy that's not really a lot lower than 511 KeV, and the different manufacturers all use a very wide energy window, so there's a lot of these scattered events, and so now you get fooled. You think the line of response you're gonna draw is through here, but that's erroneous, and even worse is random events. So here you have two of the gamma rays that are completely lost due to attenuation, and you have these just accidental firings of two nuclei generating two positronium atoms, two positronium atoms, and they have nothing to do with each other, and you don't know any better, and neither does the computer, so it just draws a line through there, and you have a false event. So to keep account of all that, there's this notion of noise equivalent counts. So you might think that in order to make things better, what you would do is just add more and more activity. You get lots of additional true counts, everything which should be fine, but what happens is as you try to do that, the number of random events and the number of scattered events goes up too, and so the concept of noise equivalent counts basically tells you this is the useful kind of number of counts that you've gotten equivalent to generating an image of a similar noise level. So here's what I meant about adding more and more activity. Here we have a little graph showing the trues, randoms, and scatters, and as you increase the amount of activity you're injecting into a patient, the true events do go up, but so do the scatters and the randoms, and so imagine you have a couple different systems that you're considering buying. They all have their different noise equivalent counts properties. So for instance, suppose you have a system with this kind of green noise equivalent counts response. It would make sense to have a protocol in which you routinely inject 10 millicuries because you're actually right at the peak of the noise equivalence counts. It wouldn't make too much sense to try to use this same device and use twice the activity because, as you'll see, you're not really using this efficiently. As opposed to this other system that has a rather different curve with higher overall noise equivalent counts, there you might look for the kinds of protocols in which it is feasible to use 20 millicuries, bearing in mind, of course, that you need to be a bit careful with the radiation dosing issues. So these are the kinds of worries that people have who have their own in-house cyclotrons who can generate a lot of isotopes in addition to fluorine and rubidium because they have all of their own properties in terms of the amount of energies that are delivered into the patient in terms of radiation dose. Now let's look a little bit more about PET imaging systems. So as we said before what we would like to do is surround the person with a whole lot of detectors and I'll come back to that in a minute. So here we have a 2D image in which we have what is called a single ring of detectors and as you can see we've drawn lines through some opposing pairs of detectors and if you have the money to do it you have all sorts of circuits to look at every reasonable pair of different detectors and link those together but there's no need to have only this one ring of detector. If you can afford it you have more than one ring and typically now you'll buy a three or four or even five ring system with the rings nested above and below. So as long as you have the money for the electronics to do it you link all the possible detectors together for all different possible combinations of coincidences and you really build up a complete three-dimensional volume of lines of response in order to make a very efficient process. I mean if we had the money to do it we would construct rooms completely floor to ceiling and walls of nothing to detect but detectors and look at all different possible combinations of coincidences but no one has the money to do that. This is very different scheme as spec cameras. So most spec cameras are anger cameras. These are and we'll come back to this in a second. These are basically devices generated invented a very long time ago in the 1950s. Nice big pizza size and pizza shaped sodium iodide crystal and it has a collimator in front of it and the reason you need the collimator in front of it is because you're going to have the gamma rays scintillating inside the crystal but you have to be able to draw back your own line of response through the patient to say where this single gamma ray was emitted. You cannot make an image with this kind of technology without the collimator. The problem is the collimator is very inefficient. It's going to let in only maybe two to three gamma rays out of every 10,000 that are emitted from the patient but you must have it because if you don't have the collimators in place what's going to happen is you're just going to have a blur of activity and you're not going to be able to make any sense out of where it comes from. So even the most advanced current solid state detectors that are and systems that are being replacing now anger technology they also have collimators a bit different but they must have collimators. Now in the case of anger cameras which are primarily what are used for most spec systems in use in the world they also have a bank of photomultiplier tubes in back because you have to be able to figure out from where the scintillation happened inside the crystal of where that was. So you look at the different amounts of current flowing in the tubes you have a little program running a little circuit to compute the location inside the crystal and all that takes time. So this is one reason that anger camera technology is much slower and the counts that make up a spec image are much lower than they are for a PET image. In addition you have to have a pulse height analyzer to look at the amount of current flowing in all these tubes in order to figure out what the energy was of the gamma ray because without that you'd have lots of gamma rays getting up through the patient and through the collimator but they would be scattered events and you really would like to weed those out. So single photon emission computed tomography is based on exactly what it sounds like isotopes that emit just one single gamma ray at a time and as you know the most common isotope we use is technetian 9 to 9m with the 140 keV gamma ray. PET imaging of course is positron emission tomography and it relies on looking at two gamma rays simultaneously. Now while we're at it we're not just going to see that we coincidentally two detect so here is one detector and here's another detector and these are going to be timed because we need to make sure that the two have a high probability of being correlated with one another otherwise we're just going to have lots and lots of random coincidences. Now while we're at it though what we can do is we can also look a little bit more carefully at the time at which the two gamma rays hit the detectors because if the isotope has emitted its positron and therefore the positronium atom is closer to this detector than that one this gamma ray is going to get to the detector a little bit sooner than that one. So if we have the electronics fast enough and the crystals responding fast enough we'll be able to say where at least in a volume that gamma ray pair was emitted. So if you really want to get down to a nice tight volume of only 10 centimeters in diameter you would need a 600 picosecond electronics. Where does that computation come from? Well you really just look at the size of the object for which you would like to confine the volume and you just divide by the speed of light three times 10 to the 10th centimeters per second and that will tell you the timing that you need. So in the case of coning down the possible location from which the positronium atom decayed to 20 centimeters that would require 1300 picoseconds. In fact you can now go out and buy nice fast digital pet detectors that will get you down to about 200 picoseconds. So these as you'll see in later modules in this course the time of flight option is a very valuable and really helps tremendously in improving the signal to noise ratio of the reconstructions. So let's in fact talk a little bit more about reconstructions in a minute. One thing to be aware of is there are big differences between SPECT and PET scans that have to do with the detector geometry. So in the case of SPECT systems which use anchor cameras with collimators you're probably all aware already that the closer you are of the source to the collimator the better the spatial resolution for SPECT cameras. So here we have a little graphic of a couple different what are called point spread functions and what this means is this a probability curve that says if you have a source here at this central location there is a significant probability that you'll have the gamma rays show up in the ultimate system a little bit off center. As you go away from the center of the surface of the collimator you still have the same total probability but your ability to say where that event occurred really where the actual gamma ray hit becomes more and more difficult to see. So the spatial resolution degrades. Now modern SPECT iterative reconstructions take all this into account and this is part of what happens with PET reconstructions as well as we'll see. But first let me just demonstrate to you here is a typical SPECT phantom reconstruction and you'll notice that the rods here at the periphery seem much sharper than the same size rods deeper inside the phantom and that's because this part of the image is formed from the collimator being as close to the surface of the phantom as the technologist could manage. This is what happens if the technologist is kind of sleepy that day and forms a SPECT phantom image with the collimator far away. Now PET scanners are exactly the opposite so that's an important thing to realize. We'll come back to that slide in a second. So it's easiest to see if we look at this graphic if you have a point source that's emitting positron gamma rays and it's very close to one of the detectors then the called the point spread function is practically a box curve and it's more or less the width of the detector. If on the other hand you have the point source here in the middle which means dead center in the middle of a patient you will have a very different kind of point spread function that's much more peaked. So in fact the best spatial resolution that you're going to see is for objects that are right in the middle of the patient the furthest away from the detector crystals. And here again is a representation of that. So again with our SPECT phantom things get murkier and fuzzier as you go towards the center but here with a PET scan you have the sharpest image here in the center and things get a little bit murkier and fuzzier as you go away from the center. So an advantage of that for specifically for oncology imaging or cardiac imaging for really large patients is that the spatial resolution really is the best right in the middle of the person. Now something the the kind of information we get from nuclear studies is that some of the gamma rays and some of the events we'd like to image just vanish. They get gobbled up in attenuation. In the case of a SPECT camera what happens is if you have a patient who is 30 centimeters wide let's say which would be kind of a small patient but nonetheless and you look at the probability of a gamma ray getting out from the middle to the edge of the person and therefore being available to be seen by the anger camera. For a typical technetium 9 to 9 m gamma ray at 140 keV that's about a 10 percent probability that it's going to get out. Now the higher energy 511 keV gamma rays from positronium emission have a better chance of getting out. In fact they have about a 23 percent chance of getting out from the same size 15 centimeter person but you're not going to be able to get a PET scan from that. You have to get a PET scan from both gamma rays and so what that means is you have a 23 percent of a 23 percent so more like a five percent chance because you have to get the gamma rays out as a pair. It's like potato chips you can't have only just one you have to have at least two. For SPECT imaging you only have one gamma ray for PET you have two gamma rays necessarily and so the implication of that is as a broad statement attenuation problems are much worse for PET imaging than they are for SPECT imaging and that's one of the reasons that you always have a CT scan now with the PET scan. In fact this is so ubiquitous that you can't actually go out and buy a new PET scanner. You can go out and buy a couple different kinds of PET CT scanners but not a PET scanner by itself. You must have the attenuation correction. There are some additional things that happen that complicate the formation of the image ultimately in forming a PET scan and these include the fact that the gamma rays may not hit dead on when they come out of the person. This is a little illustration of that. Here you have two gamma rays that do hit head-on. They have this kind of nice narrow point spread function but of course the person may have isotope all throughout them and if the positronium gamma rays happen to be emitted here and the gamma rays hit at an oblique angle you have a rather different point spread function. So you'd like to have the algorithm that figures out the locations inside the person where the positronium atoms decayed include all that information and this is done through means of the attenuation correction and the scatter correction and all those other corrections including these detector corrections by means of the reconstruction algorithms. So the reconstruction algorithms are going to do a lot of different kinds of corrections as we just said and the mathematical models actually mimic the physical processes that are involved in generating the information basically of transporting the gamma rays from the inside of the person to the outside where you and I have our detectors set up. These algorithms as a class are called maximum likelihood expectation maximization algorithms and this is a nice little schematic to show you what's involved. You can start with just a guess of uniform activity spread throughout a person and say well if that's what I had all the detectors would see the same amount of counts per second but I have the CT scan. So as the gamma rays are coming out they're going to interact with the bones inside the person and some of the detector areas are not going to get as many counts as areas without bones in the way. In addition some of the radiation is going to scatter off the tissue in the person and especially off the bone. So you can you can model that and so you can predict what the different detector pairs should see once the gamma rays have got out from the middle of the person to the outside of the person. You can add your information that you know about your particular scanner about how many random events you expect to see and the other different phenomenon like what happens when gamma rays hit on the edges of detectors rather than in the center of detectors. You make all these predictions and then you compare it to what you actually saw. What did you really see in all the different pairs of detectors. You then update your guess and you start back at the beginning and say well with the second guess and with the attenuation scan and with my knowledge about how radiation scatters I'll make a next set of generation of guesses and you keep doing that until you converge on a solution. This works remarkably well. This works so well that while previously people routinely did just two-dimensional scans of patients in using their PET systems even if they had multiple rings now everyone just does full three-dimensional reconstructions of the information because the algorithms are so sophisticated at modeling these different systems and these different physical phenomena that the reconstructions are very rapid and very accurate. The end result of that is that now if you go out and buy a nice new PET scanner and you image a patient with fluorine you'll typically get spatial resolutions of something like four to five millimeters which is a huge advantage over SPECT imaging because with a typical SPECT rotating anger SPECT camera the kind of spatial resolution you get in the part of the heart that you and I are interested in is more like one centimeter. Now the newer solid state detectors that are used for SPECT systems do better. They have higher counts and better spatial resolution but it's not nearly as high counts and it's not nearly as good spatial resolution as a PET scan and in fact now with the most recent digital PET scans the spatial resolutions for fluorine are even below four millimeters. So in summary SPECT imaging is performed for isotopes that emit just one gamma ray at a time. That's why you have S for SPECT for single photon and PET meanwhile is relying on seeing two gamma rays at the same time. We're still using scintillation detectors and mostly using photomultiplier tubes although increasingly these are being replaced now by silicon photomultiplier tubes inside PET systems and CZT detectors and other kinds of solid state detectors are being used increasingly more frequently for more sophisticated SPECT systems. The SPECT spatial resolution and counts are not nearly as good as they are for PET in general but the trade-off is that the attenuation problems are considerably worse for PET than for SPECT and really require CT attenuation correction and that's why modern PET devices all have all are really PET CT devices not just PET devices. Well thank you for your attention. I hope you enjoyed this module and I hope you'll enjoy all the other modules in this physics course.

cardiovascular PET

positrons

PET imaging

SPECT imaging

ionizing radiation

positron annihilation

detector systems