 Okay, so believe it or not, the first half of this class is basically going to be a traditional lecture class. This material is fair game for the final exam. The good news is it primarily builds on things we've already done in this class. It might exercise them in new ways, but the concepts are effectively being recycled. So I'm going to squeeze a little bit of nuclear physics into the lecture today. This will be thematically tied to some medicine as well, although I'm not a medical doctor, as many of you have constantly pointed out to me. That's okay. There's still a lot that physics, chemistry, biology, and medicine can all learn from each other to help advance the human species. All right, so what I'm going to do first is I'm going to start with the definition of nuclear medicine. It is actually fairly specific. As I was putting this lecture together, I came to realize that it's important to make some distinctions here. So nuclear medicine is specifically the employment of radioactive materials, that is materials that are inherently unstable and will spontaneously radiate energy and in the process may change underlying nuclear form. It's the use of such materials in the diagnosis and treatment of disease. And you can think of it as the application of nuclear and particle physics from the inside of the patient to the outside of the patient. Accelerator medicine, on the other hand, is an example of the case where you use a beam of particles, for instance, to go into a patient to do treatment from the outside to the inside without actually having to cut them open. Nuclear medicine is a little bit more invasive. It does involve getting things into the body first that may need to come out later or may come out on their own. And we'll talk about that a little bit at the end of the lecture. So some examples of this that you might have heard before are brachytherapy. So this is the introduction of small, what are called seeds. They contain radioisotopes, so again, unstable atomic elements. You implant them, so there's surgery involved. It may not be too invasive, but it is nonetheless surgery. It carries a risk. You implant them in a region of undesirable tissue. So a classic example of this would be cancerous growths. If a person has tumors and they're malignant and they need to be shrunk or destroyed, implanting a radioactive seed in or near the tumor material to attempt to kill it over the other healthy tissue is a strategy. So you use that emitted radiation to damage the tissue in the immediate region of the seed and then later on you may have to remove the seed, assuming that it isn't destroyed by the body or flushed by the body safely in some other way. Now what I'm going to focus on today, because thematically there's a lot that's the same between implanting a radioisotope and what you do in the case of a PET scan, I'm going to use the PET scan as kind of my all-encompassing walk-through example today of nuclear medicine. This involves first, injecting, so slightly less invasive than a surgery, injecting a radioisotope into the bloodstream of the patient. That then is taken up by specific tissues and again, one obvious place where this might be interesting would be cancerous tissues, though it's not necessarily limited only to those things as you'll see later. Wherever that radioisotope collects in the body, so the body will distribute it, tissue will take it up, the radioisotope is deployed chemically in a way so that it's readily taken up by the target tissues in the body, and then you wait and that isotope will decay over time and radiation will be emitted and if you're lucky it will penetrate out of the body and it can be captured by some device around the body. From that capture process, working out the geometry and everything, you can then try to form an image of the patient's sort of spatial location of the radioisotope from the emitted radiation. The specific process I'm going to focus on today is what is known as positron emission tomography. In this lecture I'm going to review first the history and nature of radioactivity, I'm going to dig into the nucleus and go into some of the details of the PET scan, again positron emission tomography will break that phrase down. Now the physics that's involved here really does neatly apply also to things like brachytherapy because again the idea is the same, you're going to try to get an isotope into a patient for some purpose. For a PET scan the purpose is to image the patient, for brachytherapy it's to intentionally destroy tissue ideally in the vicinity of the implant, the seed. But the core idea is the same, unstable nuclear isotope inside a human body, we'll look at radioactive decay and the interaction of emitted radiation with the body because that has some implications both good and bad for the patient. So let me begin with a brief history of radioactivity and I am really cherry picking my way through history across just a few key moments. So you can probably credit the discovery of what we would now think of as radiation, that is spontaneous emission of high energy particles from a system to this fellow right here. And you've seen him before in an earlier lecture in the class, this is Wilhelm Röntgen lived from 1845 to 1923, so you see his life neatly encapsulates that really radical period of transformation from the completion of the laws of thermodynamics and electromagnetism to special relativity and the resolving of the paradoxes between electromagnetism and classical mechanics into the quantum mechanical era. And he was a part of that force of people that ushered in the quantum era. Now he serendipitously discovered x-rays in 1895, so quite late in his life and career while experimenting with cathode rays. So cathode rays just to remind you are the emanations that come off of a metal when you either heat it or put it under a high voltage. And in that case we now know you strip electrons off the metal and those electrons will travel accelerated through the electric field that the metal is exposed to and they can do all kinds of things. They can use gas in the electric field, they can cause the gas to give off light, a cathode ray tube classically will give you a sort of greenish blue colored beam, that's the electrons exciting the molecules in the gas, but that beam has to end somewhere and it will crash often into material at the other end of the cathode ray tube and that collision, that interaction with other material in the tube will actually cause x-rays to be produced and that's how they were discovered. They were discovered somewhat serendipitously and accidentally by Rentgen when he inadvertently exposed a sensitive photographic system to x-rays, not knowing x-rays were coming off the system and being curious why it caused his photographic emulsions basically to become exposed as if they had been exposed to daylight. Now this is following on that discovery that there's a new emanation coming off of cathode ray tubes caused by the collision of the cathode rays with material in the tube and the fact that it will cause a film to expose, he hit on the idea that if these rays are penetrating, which he found out that they were, you could take a human hand and you could put the hand between the beam of x-rays and the emulsion and so this is actually Anna Ludwig, Rentgen's wife, it's her hand, that is not a tumor that you see there, this thing here, right here I'll come back to that in a second, that's not a tumor or a bone growth, but you can see this is the world's first medical x-ray. He imaged the internal structure of his wife's hand non-invasively using the newly discovered x-rays which he serendipitously discovered. So this is the world's first medical x-ray and that blob of material on her hand, it's her ring. So the ring, just like the bone in the body, is the dense material and it will preferentially prevent x-rays from getting through, whereas the soft tissues allow the x-rays through fairly readily, we'll talk more about that later. So the x-rays were sourced from the cathode ray tube, I've already explained that process, that's an artificial way of making x-rays, so Rentgen discovered x-rays by artificially making them, but Henri Becquerel would go on to find out that that same radiation, x-rays, can be emitted naturally by uranium salts. It was naturally occurring, high energy photon radiation very similar to what Rentgen discovered, but unlike the cathode ray tube, it required no external input of energy, it happened spontaneously on its own. And you can see here, these experiments with uranium salts would have also marked the first moment that human beings realized that there is a power within the atom that's just there for the taking, if you can harness it. Now at this point it's random, the uranium salts spontaneously emit the radiation, there seemed to be no way to induce it to do that more, no changes in temperature, humidity, changing the electric field that the material was exposed to, lots of experiments were conducted on these to try to induce more of this spontaneous decay, and it was impervious to those kinds of environmental changes, and we'll see later exactly why that is, although I'm sure many of you are already familiar with the fact that what's going on here is a process inside the nucleus that isn't influenced by these factors. Now another major step here was the work first by Marie Curie, and then by her husband Pierre Curie, to really dig into what's going on in these naturally occurring radioactive materials. So she observed that materials like pitch blend and tober night were much more radioactive than uranium on its own, and based on this she was able to infer that these materials contained something in addition to what was just in uranium that itself was even more radioactive than uranium, more likely to spontaneously emit radiation. Pierre was so fascinated by the work that Marie was doing that he actually dropped his work on the research into crystals and crystal structure to become her collaborator. This would have been in the late 1800s, they would then go on to discover new elements which were called radium, given its highly radioactive nature, and polonium in honor of Marie Curie's home nation of Poland, and based on all of this work she would go on to develop the very first theory of radiation. Now, fascinating enough, she would also then be the first female scientist ever to win a Nobel Prize, the first to win a second Nobel Prize, and to date she's the only person who's ever won two Nobel Prizes in two completely different categories. She won for physics in 1903 and chemistry in 1911. Pierre died in 1906, he was struck in an accident on a roadway and killed in 1906. She continued to work in a lab in Paris, it became known as the Radium Institute, and later the Pierre and Marie Curie Institute. I had the pleasure of visiting it, it's very close to a place where I like to occasionally vacation in Paris if I can get there, and it's really neat. You can go in, you can visit the Radium Institute, you can see her office preserved effectively as it was at the time that she was the director of the institute. It's really, really quite fascinating. So let's talk about different kinds of radiation. So there are some scenes from moments in history of the discovery of radiation, radioactivity, and the understanding of its underlying causes. There are many more people that were involved in this than the ones I just mentioned, but I'm kind of fascinated by the people I cherry picked for today. There are three known kinds of radiation that's emitted from atoms. One is called alpha, another is called beta, and the third is called gamma in honor of alpha, beta, and gamma, the first three letters of the Greek alphabet. Now alpha radiation was later understood to be helium nuclei that are wholly ejected from an unstable atomic nucleus. They have a plus two elementary charge, so they're highly ionizing when they pass through material, but their strength is also their weakness, because while they can do a lot of ionization as they go through material, which for biological tissue means they can do a lot of damage, they're also very short-ranged, they tend to interact too much and they stop very quickly, and they can actually be stopped by soft tissue, your skin, even the outer, just the outer layers of your skin can stop alpha radiation, thin paper, things like that can stop alpha radiation. Beta radiation, on the other hand, later was understood to be high speed electrons that are ejected from the nucleus, and beta radiation is what we're going to spend a lot of time looking at today. It turns out they result, as we learned much later, from nuclear interactions induced by a new force in nature, not electromagnetism, not gravity, but a third force that works really only on ranges of the size of the nucleus of the atom, so about a femtometer, and it causes, for instance, a neutron to spontaneously convert into a proton emitting an electron and a little cousin of the electron called the neutrino in the process. I'll come back to neutrinos in a little bit. Now, beta rays, as they were known early on, now we know that they're just very fast electrons, they are harder to stop, but they can be stopped by thin metal, they tend to punch through less dense materials, and then finally there's gamma radiation. These are high-energy photons, we understand that well now and have understood that well since the early part of the 20th century, and we know now from understanding more about the structure of the nucleus that just like an atom can have excited states, a nucleus is just like a binding of nucleons and the nucleons can have excited states. So these photons get emitted whenever a neutron or a proton inside the nucleus of the atom will drop from an excited state to a lower allowed nuclear bound state, or if you capture a nucleon, a photon can be emitted in the process, just like if an atom captures an electron, it can emit a photon in the process. So nuclear physics and atomic physics have a lot in common from the quantum bound state perspective, but the force that does the capturing in the nucleus is far stronger, albeit short-ranged, compared to the electromagnetic or Coulomb force that's responsible for the structure of the atom. Now gamma rays typically have energies in the millions of electron volts scale. They can penetrate many centimeters even into dense material, and I'll come back to that point later. In human flesh, half of all gamma rays emitted from inside your body will tend to get absorbed every few centimeters. So if you start with 100 gamma rays, about four to seven centimeters later you'll have 50, four to seven centimeters later and you'll be down to 25. So if you have a lot of tissue in the way of a gamma ray, you might have to take that into account if you're using gamma rays to do imaging of the interior of the human body, they can be absorbed even by soft tissue, and if you don't take that fact into account, it can deteriorate your ability to build reliable images of the interior structures of the human body. I'll come back to that point later. But alpha, beta, and gamma, we're going to focus on beta and gamma today. Now the advent of the nuclear age really also ushered in the advent of the age of nuclear medicine. This is no accident. Once you build industrial infrastructure for weapons making and you no longer need to build weapons for war, that infrastructure looks for other ways to be used. This is a common theme in human experience. It was certainly true of the steam age and the industrial revolution, and it was no less true of the nuclear age of industrialization, medicine, science, and government. So what drove the nuclear age, as we understand it now, of course, was the race among several powers. The Nazi Germany in Europe, the United Kingdom, Britain, the United States, and Japan all had programs to attempt to rapidly construct the first atomic weapons once it was realized after the study of quantum mechanics that it was perhaps relatively straightforward to create an artificial atomic blast. All you had to do was engineer the thing. If that was possible, then you could build a weapon relatively easily. The race to build these atomic weapons, which was done essentially in a bid by all powers to bring World War II to a rapid close for whoever's side got one first, led to a massive industrial nuclear capability. So many of the national laboratories the United States has today, the Lawrence Livermore National Laboratory on the West Coast, the Los Alamos National Laboratory in the Southwest, the Oak Ridge National Laboratory in Tennessee closer to the East Coast and the South. Those were created to facilitate the production or design of weapons of war during and after World War II. Argonne National Lab near Chicago is another example of a weapons lab that was constructed for this purpose. The goal here was to be able to create artificial isotopes, that is to create uranium and also the much more potent plutonium and to generate these artificially in high quantities and to deliver those for the production of nuclear weapons. So the original way that this was done was to enrich existing isotopes that you could dig out of the ground. So you mine uranium, mining uranium was the first capability, getting your hands on uranium stores. Then to refine that, you can chemically separate the uranium from other elements in the rock. And now what you can do is you can enrich using various methods to get the uranium up to high purity. That's how you enrich uranium. There are gas methods and there are accelerator based methods for doing that enrichment. Plutonium on the other hand is so unstable that you don't find it really naturally occurring in the earth. You have to make it and the way you make it is by bringing a lot of uranium together in the same place. The splitting of the uranium nucleus spontaneously will release three neutrons. The three neutrons will then hit other nuclei nearby and fission them in the process which releases three neutrons per fission. And as I said in an earlier lecture on relativity, energy, momentum and mass, this leads within 20 to 30 generations of the fission process to an uncontrolled explosion capable of leveling a city or a city center. You slowing the process down by moderating the neutrons getting out of each fission reaction will allow you to breed isotopes without having a runaway chain reaction. So what you do is you build a reactor like the one depicted here on the right. You take slugs of uranium and you plug those slugs into regularly arranged holes in the side of the reactor complex. And every regular period of time you push new slugs into the holes that then takes the old slugs and moves them further down the tube. And you regularly industrially move the slugs down the tube by putting new ones in one end. And then at the other end of the reactor after a fixed amount of time, the first slug will pop out the end of the production line. And you time this so that you enrich in the useful isotope of plutonium without getting another isotope of plutonium that actually poisons the nuclear reaction and prevents a bomb from being made. This is a whole fascinating subject in of itself. But you can see how this kind of industrial bomb making effort would have to then be converted in a post war age. And one of the ways that places like Oak Ridge national laboratories kept itself going afterward was peacetime nuclear applications. So post war, this production was bent toward things like making isotopes for nuclear medicine or doing peacetime nuclear reactor for power generation. So there are many ways that these labs were bent to other purposes after World War Two. Some of them remain building hydrogen bombs or atomic bombs. Others remain building nuclear bombs or atomic bombs. And that's what we're going to talk about in a little bit later on. We're going to talk a little bit about how we're going to return to our peacetime applications. Okay. So let's talk about some nuclear physics now before we get into the pet scam. First of all, I've talked about one way to artificially produce and enrich in certain target isotopes. You could take a naturally occurring isotope chemically enrich it, put it into a unit and then use it as a control means is to use a particle accelerator to do it. And I'm going to focus on this because this is actually how medical isotopes used for the pet scan are produced. And the most common medical isotope used for the pet scan is fluorine 18. And that's denoted here by this nice symbol, the superscript 18 next to the capital F up there on the upper left. Okay. Now it's produced not in a reactor, but actually using an office sized particle accelerator. And you see that depicted over here on the right, this photograph over here on the right, which is taken from a textbook about this kind of nuclear medicine and technology shows you one of these cyclotrons, a circular accelerator, you inject a beam of protons into the center of a region with strong electric and magnetic fields, they then circulate wider and wider orbits as they get to higher and higher kinetic energies. And then you shunt them off using a deflector or a target at one end of the of the circular racetrack. And then at the other end where you extract the beam, you have a target in this case, it would be water. And that target is where you're trying to make your isotope in this case, fluorine 18. So the goal here is to bring protons up to a design energy, and the energy is tuned so that the nucleus you're attempting to strike can be breached, not enough to break it, but enough to fuse the proton into the nucleus and create an isotope of your design. And the target here is Oxygen 18 enriched water. Now Oxygen 18 is a stable isotope of Oxygen 16, which is the most abundant isotope of oxygen. It has a 0.2% natural abundance and you can make 018 enriched water and use that as the target. So the 018 has 18 nucleons, that's what the 18 means. Eight of those are protons and the protons of course determine the chemistry, the binding properties of the atom. Fluorine 18 also has 18 nucleons, but nine of them are protons. You've got to get an extra proton into the 018 nucleus and you got to get a neutron out if you want it to be useful. So the protons from the beam, which have an energy of 6 million electron volts, that's the sweet spot for these accelerators for fluorine 18 production, they strike the 018 nuclei, they come close enough to be captured by the nucleus but not destroy the nucleus in the process and in that reaction in the nucleus, a neutron and gamma radiation are emitted. So you lose a neutron, the change of the nucleus settling down to its new ground state causes a gamma ray to be emitted and you've got your fluorine 18. And you can make usable medical amounts of this in just a couple of hours using one of these accelerators, which is remarkable. These have currents of about 150 microamps, so you can estimate how many protons per second that is on target knowing the fundamental charge of the proton is one elementary charge. So you can calculate how many protons per second that is on target and then using some nuclear physics you can estimate how long it will take to make a medically useful sample of fluorine 18 and it's not long and it has to be quick for me to tell you in a second. Now one thing I need to do before we go into the PET scan is I need to tell you a little bit more about the building blocks of matter and I need to tell you a little bit more about the forces of nature because what happens next with the fluorine 18 nucleus can seem a little weird but it's completely allowed by the known laws of physics and especially because we know a lot about the basic fundamental building blocks of matter and the very few forces that are needed to bind them together to make absolutely everything that we experience every day here in the universe. Now we focused a lot on the atom this semester that's been our playground for the most part we've teased the nucleus a little bit as we've done particle in a box and things like that but we really need to dive into the nucleus and we really need to see what fundamentally is rattling around in that thing because it ain't neutrons and protons. Atoms are made from electrons in orbit around that tightly packed nucleus alright and that structure the atom is maintained by the electromagnetic force okay so really the atom if you just look at it writ large is an electron a nucleus and the electromagnetic force to bind it together but nature doesn't only possess of those building blocks and that one force we of course we know of gravity gravity is so weak on the scale of things the size of the atom it plays really no role that we're aware of in the atom or anything smaller than that that we've been able to study to date. Now matter is not fundamentally neutrons protons and electrons as far as we know the electron is indivisible we've been trying to break it for 50 years to see if it's made of anything else and we haven't succeeded in doing so yet so we know that it's whatever it's made from those things are no bigger than about 10 to the negative 18 meters in size that's as far as we've been able to probe down basically but the neutrons and protons are actually made of other things called quarks and they're bound together by other forces the most prominent of which is the strong nuclear force the weak nuclear force is the impish destabilizer of the nucleus the strong nuclear force is the guardian of stability in the nucleus and so I like to think of them as kind of the siblings that don't get along the strong force is always trying to maintain order and the weak forces break is causing chaos to spontaneously break out in the nucleus and any of you who are science fiction fans of things like Babylon 5 these are the vorlanz versus the shadows okay vying for control of the nucleus all playing strong together on the scale of the nucleus so so far as we know there are 12 fundamental building blocks of nature six of them in a category called quarks and six of them in a category called leptons electrons are leptons the muon is a lepton and it's a heavy unstable cousin of the electron we met the muon earlier in the semester they have an even heavier and even more unstable cousin called the tau and then each of them has this little almost no mass cousin called the neutrino there's an electron neutrino a muon neutrino and a tau neutrino and I like to think of them as the annoying little baby sibling that wants to follow you around everywhere and you just want to be left alone and hang out with your friends that's kind of what the neutrino is whenever you basically make an electron a muon or a tau you're kind of forced to bring your neutrino to you to conserve some fundamental things in nature protons and neutrons are not fundamental they're made from quarks and in principle they're made from just two kinds of quarks up and down the lightest of the quark species so protons are an up up down in triplet combination with each other and neutrons are up down down in triplet combination you see they differ by only one kind of quark change an up to a down inside of a proton and you can make a neutron it's no accident protons and neutrons have almost the same mass it's guaranteed by the physics of the quarks and the strong nuclear force now the forces to the best of our knowledge come in four kinds of gravity electromagnetism and the weak and strong nuclear forces the impish destabilizer and the and the purveyor of order okay the latter two these nuclear forces are transmitted by short-ranged particles they're short ranged for different reasons the weak forces transmitted by what are called weak bosons they're like heavy heavy heavy cousins of the photon they're very massive so they can't live very long and they're known as the W and the Z and then the strong forces transmitted by the gluons and there are eight gluons in nature eight kinds of gluon they're massless too but they like to interact not only with themselves but with quarks much that they can only go about a femtometer before they get trapped in a strong bound state of nature like a neutron or a proton and those get packed into a nucleus so it's no accident that the nucleus is about a femtometer in size that's the typical range of the strong nuclear force and it's no accident that nuclei sometimes can fall apart that's the impish hand of the weak nuclear force and the weak bosons that transmit that force and I'll come back to that in a bit ok so this is our periodic table of nature on the right to the best of our knowledge these are the things we have definitely established make up matter and forces in nature there is much we don't know about the universe we don't know what makes up that other parts of the universe we don't understand and maybe one of you will add those missing pieces to this new periodic table of the universe now I should note that gravitation is not on this chart because gravitation is described by the general theory of relativity whereas the strong weak forces and electromagnetism are described by relativity married with quantum mechanics quantum field theory we've never been able to make gravity play nice with quantum field theory we don't know if it's required but we've never been able to achieve it so we can't really put gravity on this table because it's not described by the same mathematics that describe all this stuff that's a one which maybe one of you will solve someday too ok so let's wrap up and talk about the pet scan we're going to synthesize all of this together and talk about the pet scan and then I'm going to turn things over to you for the rest of the class so first of all we got to get into a little bit of biology and chemistry and some radiology here so let's go back to fluorine 18 so fluorine 18 is an unstable radio isotope of fluorine it's half life that is the time it would take for half your sample to go away is just 110 minutes you see the urgency of the particle accelerator problem you have to solve to make it you can't take three days to make your fluorine 18 it'll be gone by then anything you made two days ago is basically gone so you have to make this stuff within a couple of hours and transport it to the hospital that needs it so you need everything to be close by and these machines are expensive not every hospital can have one so facilities may have to be centralized in states to do radio isotope production with rapid delivery to hospitals and you can see how for instance in a pandemic how supply lines like this could break down relatively fast okay so something to keep in mind if you're thinking about the sort of infrastructure required to maintain a medical establishment that relies on things like this to do diagnosis or treatment now it's used in the production you don't just take fluorine 18 and stick it in the human body that's a really stupid thing to do instead what you do is you make a molecule that the body can process and take up without risk and the choice here is to manufacture that fluorine 18 from the water target where it's produced right into fluorodeoxy glucose which is a kind of glucose FDG is the short name for it that can be taken up just like glucose by cells that need it okay and lots of cells need glucose to function okay they need to metabolize that to produce energy to drive the cellular processes in the body now a typical medical dose of the FDG will represent a radiation dosage that's known in units called cverts I'll get to a cvert in a second the dose represented by a typical medical injection of this isotope into your bloodstream is 7.6 millis cverts of radiation exposure now I've given you a context free exposure number so I'm going to put this in context for you okay this by the way is a structural representation of the FDG molecule where one of the fluorines has been replaced with the F18 isotope okay so what is a cvert a cvert is the modern unit of radiation exposure and what's nice about a cvert as opposed to a becquerel which is another unit of radiation exposure is that cverts take into account the biological impact of the radiation a becquerel just tells you how many radiated particles are emitted per second but it doesn't tell you the biological impact of each of those particles on flesh bone and other tissue a cvert is a jewel of radiation into a kilogram of human tissue calibrated to the level of biological damage that that dose can do so here's some handy numbers so for instance if you're hanging out next to your family in close proximity while you're social distancing from everybody else being around a person for about 8 hours will give you 50 nano cverts of radiation exposure we are littered with unstable radioisotopes that's the normal background radiation of everyday life and it's not that much so if you're next to a person for 8 hours you can expect to get 90 nano cverts of radiation damage living within 50 miles of a nuclear power plant and breathing in the air that comes from that will expose you to 90 nano cverts of additional dosage per year now one fun unit that I'll come back to later in the class is the banana equivalent dose so many of you may consume bananas bananas are a rich source of potassium and unfortunately some of that potassium in nature is an unstable radioisotope of potassium and it's just chemically the same as it's stable cousin so it winds up in bananas and other things that have potassium in them you get 98 nano cverts from consuming one banana and this is known as a BED or a banana equivalent dose of radiation okay one banana day is 98 nano cverts of additional radiation exposure or roughly about you know sitting next to two people for 8 hours living within 50 miles of a coal fired power plant for one year will give you 300 nano cverts of radiation exposure and if you're curious about why it's more dangerous to live within 50 miles of a coal fired power plant than it is to live within 50 miles of a nuclear power plant cycle back and ask me a question later we'll talk about it one set of dental x-rays which may be a common experience for many of you annually or maybe every other year is 5 to 10 micro cverts of radiation okay so now we've upped to the next you know three orders of magnitude here we're up to 5 to 10 micro cverts of exposure one and a half to 1.7 mila cverts is the annual dose that flight attendants on airlines get they actually get quite a bit of radiation for a typical worker in the united states or anywhere in the world the people who are most exposed to potential forms of radiation of course power plant workers and nuclear power plants but actually flight attendants are way up there and this is why pilots and flight attendants have to have their doses closely monitored it's why they are not allowed to fly for more than so many hours per week it's part of the reason why they're not allowed to fly for so many hours more than a certain number of hours per week a single full body CT scan which is a whole body dose of x-ray radiation is 10 to 30 mila cverts okay so we're still in the realm of medical procedures here a six month stay at the international space station will give you 80 mila cverts roughly three times the equivalent of a single full body CT scan a six month trip to Mars which is what people are talking about doing is try to get a you know a trip to Mars within a year or two for human passengers that's going to expose you to 250 mila cverts mostly due to cosmic ray radiation you're not protected by the Earth's magnetic field when you're between Earth and Mars and Mars doesn't have a magnetic field to protect colonists so this is a serious problem that anyone talking about colonizing Mars needs to solve maximum annual shallow depth skin dose allowed by occupational work and health standards in the US is 500 mila cverts if you exceed that dose in an occupational environment in a year you are supposed to be relieved of your duties that are exposing you to radiation for that year now it's not a lethal dose but it's beginning to approach uncomfortable because it's halfway to one sever and one sever is the maximum lifetime lifetime dose allowed for NASA astronauts at that dose level you now have accumulated a 5.5 percent chance of developing a malignant cancer sometime in your lifetime okay one sever four to five severts has a 50 percent chance of killing you in 30 days okay so the decay of fluorine 18 is interesting because when fluorine 18 decays it returns back to that stable rare isotope of oxygen oxygen 18 and it primarily emits beta radiation when it does this most of the time when it decays it's emitting beta radiation that's the last electron things now let's think about what it means for fluorine 18 to be able to spontaneously decay to oxygen 18 while emitting beta radiation so fluorine 18 as I said has 18 nucleons nine of which are protons it's going to convert into oxygen 18 which has a slightly lower mass it still has 18 nucleons but it's got slightly less mass and now it only has eight protons why is it have slightly less mass this is one of the interesting details of nuclear physics a nucleus is more than the sum of its parts if you just blindly take the number of nucleons 18 and multiply blindly by one atomic mass unit so one am you times 18 you will get wrong answers for the masses of nuclei because the binding energy of those nuclei becomes mass energy and makes the nucleus a little heavier or if there's less binding energy makes the nucleus a little lighter remember E equals mc squared any more energy that goes into binding a nucleus together will increase its mass if it relaxes the binding energy if it takes less binding energy to hold the nucleus together then its mass will be slightly lower and nature takes advantage of these little differences so in order to convert from fluorine 18 to oxygen 18 fluorine 18 has got to lose a proton while at the same time gaining a neutron to maintain that mass number of 18 so you can imagine what the reaction equation for this has got to look like it's got to look something like this a proton in fluorine 18 spontaneously converts into a neutron ok but in the process to conserve charge it's got to emit something else well the only radiation that it could emit that will conserve charge appropriately here is beta radiation it has the right number of elementary charges to make this work out plus any other things x that might be emitted like a neutrino to conserve energy in the process among other things so I have some questions for the class now and first to raise your hand I'll take your answer first of all free protons don't spontaneously just take a proton and you trap it it will live forever and in fact we have done that experiment for decades now and so far as we know the lifetime of a stable of a free proton exceeds the lifetime of the universe so it's far in excess of 14 billion years so free protons don't decay is that a problem here so any hands on this one is do you think this is a problem in this case that free protons do not spontaneously decay so it's stable beyond the lifetime of the universe raise your hand if you have a thought as to why this is or isn't a problem I mean for instance we know this isotope gets used for medical applications it must work why might it work why might it decay this way yeah yeah yeah so it ain't free and remember it's made of other things right it's made of quarks bound together with gluons and this things packed pretty closely to all the other nucleons so the probability that they're acting like independent little billiard balls or spheres is pretty low they're leaking into each other's territory having little quark gluon reactions all the time in this messy suburb that they're packed into okay yeah so yeah they're not free so you know the all bets are off for the stability of the proton so here's another question what electric charge must the beta radiation have sounds like it could be a problem yep and the good news is this thing wouldn't happen if this fact weren't true about nature that nature has both matter and its opposite antimatter and that was predicted by uh paul derrack in the 1920s and within a couple of years after his prediction which was effectively the basis of his phd thesis it was discovered uh antimatter in fact the positron the antimatter electron was discovered within two years of its prediction and so suddenly it's like there's a whole other half of the universe you didn't even know existed and derrack was the first person to ever figure this out and he was rewarded by being correct not all physicists are rewarded with being correct but derrack was lucky so if this is an antimatter electron with the opposite charge of the electron we're good and in fact it's that antimatter electron that comes out in the form of a fast moving data ray that is the positron in positron emission tomography so this answers the first question about PET scans what is the P and the P is positron antimatter electron so this reaction produces antimatter which is kind of cool so you can naturally get antimatter to be spontaneously produced through nuclear reactions like this okay and I'm going to go more into that in a second alright well let's dig down into the decay of fluorine 18 and take a quark level view of what's going on so as I said protons are not really free in the nucleus they're smashing into and invading each other's space all the time in the nucleus so really it's quarks and gluons near the boundaries of the protons and neutrons that are kind of stickily overlapping with each other and interacting through gluons and things like that so it's going to happen that you know quarks have interactions with each other and not only that we know from this picture protons are really neither fundamental nor point like they're spread out in space over about one femtometer or so of radius they're built from quarks and gluons so they're really messy and as I mentioned earlier the weak nuclear interaction is the guardian of instability and it's impishly capable of taking for instance an up quark and spontaneously converting it to a down quark so if you look over here at the right this is a cartoonish and not very accurate depiction of a proton on the top alright so this is a proton up here and down here we have a neutron on the bottom and they differ by only one quark kind you take an up you turn it into a down and you go from being a proton to becoming a neutron that's that's it that's the thin wall that separates a proton from a neutron is one spontaneous transformation of one of those up quarks well sure enough the weak force can do this and it doesn't do it very often but it does it enough to cause radioactive decay to occur so viewed as a collection of quarks it's not really a surprise that UUD might spontaneously through some interaction become UDD in a very short order and in fact the reaction equation is this you have the one of the up quarks in the proton spontaneously converts into a down quark making that bound state into a neutron and in the process radiates off one of these weak bosons now this weak boson can't live very long it's very heavy it's very unstable and so its mass energy actually converts into a positron and a neutrino that's one of its allowed modes of decay and that's where your beta ray comes from your beta ray comes from the fact that the weak boson is like you know I've changed it up into a down jokes on it less than a femtometer later it spontaneously converts its mass energy into an electron a positron and a neutrino neutrinos have almost no mass and positrons have the same mass as the electron so far as we know all matter counterparts to antimatter have the same mass as one another so there's the positron and positron emission tomography okay so now positron being antimatter isn't going to get very far because anytime antimatter meets its matter counterpart anytime a positron meets an electron they can fully convert their mass energy into other forms of energy like kinetic energy for photons and things like that so you know the positron might go for half a millimeter or a millimeter but on average it doesn't get more than about a couple of millimeters from the nucleus where it was produced and it will smash into an atomic electron and that is where you get the radiation that you ultimately detect in the tomographic scan so the positron emission leads to the production of gamma radiation and it's the gamma radiation you detect outside the body so you get radiologically inert oxygen 18 from this process and now you want to build a map of where FDG has been distributed within the body where that glucose substitute is being metabolized and so the positrons with the energies that are typical of this nuclear decay will only get maybe half a millimeter one millimeter max two millimeters away and even soft tissue from where they were produced so your spatial resolution on the body at best is going to be around a millimeter that's the best you'll be able to determine where FDG is located in the body so you still got to detect it so once the positron interacts with an atomic electron imagine they have a head on collision like this or the electrons that rest and the positron smashes into it the mass energy of that interaction completely converts into kinetic energy for other particles or to make mass energy for other kinds of particles and you in this case wind up with a reaction matter anti matter that gives you a pair of gamma rays and we actually looked at this process the problem solving exercises for the lecture on energy momentum and mass in special relativity okay so you can dig back through the notes there and take a look at that to see that kind of collision process that we looked at now annihilation of matter and anti-matter means total conversion of mass energy into other general forms of energy could be momentum could be mass for other particles in this case it's pure kinetic energy in the form of two gamma ray photons in my opinion matter anti-matter annihilation is nature's most perfect form of energy conversion it's the holy grail of energy conversion 100% conversion of mass energy into other forms of energy which is why a matter anti-matter reactor sounds like a cool idea until you realize that the ratio of matter to anti-matter in the universe is a billion matter particles for every one anti-matter particle now you have a problem because you're not going to have a ready-made source of anti-matter you're going to have to make it yourself if you want to use it okay so this is a schematic of what happens um let me go into the detection process you get these two photons imagine an fdg molecule has a fluorine nucleus that spontaneously decays in the brain that's one of the places that will take up glucose the gamma ray photons will roughly come out back to back from this reaction to conserve momentum and what you do is you put a ring of dense detector material around the body and you look for coincidental pairs of gamma rays striking the detector you make the detector out of dense scintillating crystals with optical mounting to tubes at the back that can detect light from the crystals so the gamma radiation isn't visible to the eye and most detector technologies are not capable of seeing a gamma ray directly you've got to get the gamma ray to dump its energy into other forms of energy that you can detect so the scintillator crystals are dense but they're doped with a material so that when the gamma ray stops and ionizes a bunch of electrons out of atoms the electrons will travel through the scintillator crystal and they'll cause the dopant to give off light and that light will often be in the visible range the photomultiplier tubes mounted to the back will take that visible light they'll convert it into an electric current and that's how you detect the gamma ray photons by looking for coincidences in electric current in two different photomultiplier tubes and then you track back along lines projecting through the body and where they cross is the most likely place the gamma ray photons came from that's the trick that's how you make the three-dimensional map and you scan along the body to get a longitudinal perspective of where all the stuff is in the body so you scan this ring of detectors down the body and you do this slowly over about an hour or so photomultiplier tubes are a common technology for doing this their modern version of these are what are known as silicon photomultipliers or SIPMs they're very tiny they feed the size of the cell phone camera sensor so you can make very small compact photomultiplier devices these days they're basically light bulbs in reverse when you get into a light bulb you get light a photomultiplier tube takes in light and it gives you back an electric current so it's a light bulb in reverse so that's the basic idea here you have an isotope you injected in the body it's taken up by wherever the body takes up glucose and metabolizes it you then wait a little bit so it spreads out in the body then you image along the long axis of the body over a period of time meanwhile this radioisotope is declining in the body as it decays away and if you do this all right you can build a 3D map of where this FDG has been distributed to the body and so here's an example showing you an animation on the right in three dimensions rotating a personal long around their long axis showing you where FDG has been detected this is a heat map so red means lots of FDG yellow would mean less and blue would mean almost none at all okay and what you can see here and let me pause this is we'll wait till they come around again here is there's a large mass in the body over here that is not supposed to be there and that's evidence of liver metastases of a colorectal tumor so this is actually to detect for instance cancerous material that's very sugar and blood hungry and basically this tells you FDG is in a place in the body where it's not supposed to be you'll also notice that it's accumulated in the bladder the body is capable of processing removing and excreting FDG so this will naturally process the radio isotope out of your body and you'll also notice it's accumulated up here in the brain as well which has a high uptake for glucose okay so this is to give you the end result of nuclear medicine okay and what I want you to do for the rest of the class is just do some problem solving in nuclear medicine alright so I'll give you a little while to play around with this the slide should be available on canvas and I'm gonna break you into your rooms and I just want you to you know work on pick one of these questions and work on it you don't have to work through them in any particular order you could work on you know four instead of three or you could well I guess two three and four go together but you can work on one and five without working on two three and four I would do two three and four in order unless you're gonna go look up numbers for three and four to help support your calculations otherwise you need to calculate the number from problem two okay