 Well, I'm going to talk this morning about radiobiology. Actually, I'm giving another talk at 12 o'clock because somebody couldn't come. And that will be a follow-up to this one on practical radiobiology. This will be the theory of radiobiology. But let me start by explaining why we as physicists need to know something about radiobiology. Obviously, it's interesting to us to know why the radiation is working the way it is. But also, we're usually the only scientists in the department with the doctors and the technicians. We're the only scientists in the department. And I've always found that the doctors and the technicians come to me to ask me about radiobiology because this is science. And anything to do with radiobiology, like modifying fractionation schemes, which we're going to talk a lot about, and the science behind that, things like the linear quadratic model, most of the radiation oncologists I've worked with hate mathematics. So they come to me and I do it. In fact, that's how I first got into radiobiology. Physician came into my department and asked me to explain about fractionation and the science behind it. And I found myself teaching radiobiology for the rest of my life. I was the radiobiology scientist in the department. Even though I'm actually a medical physicist and my salary's always been medical physics, but a lot of my interests and research have been in radiobiology, but I still consider myself a radiation physicist. I think that's probably what many of you will find, that you're the scientist or you're expected to know about radiobiology. So for this first lecture, I'm really going to go over the basic bookwork that you'll see in textbooks. And so I'm going to do it the way textbooks often do it. And I'm going to discuss the four hours of radiotherapy, sometimes called the four hours of radiobiology. This is what you find in textbooks. It's not the way I normally teach it, but since I've only got one hour and 50 minutes, I'll get through it a lot quicker if I do it that way. So we're going to talk about repair, repopulation, reoxygenation, and then redistribution. Then I'll finish off if I have time talking about let, the effective let of the radiation. So what is the most important R of radiobiology? Well, that's easy. It's repair. Most of what we do involves repair and taking advantage of repair. What do I mean by taking advantage of repair? That's what we're going to see in a minute. OK, so what does repair mean? Well, let's look at the DNA molecule and the double helix of the DNA molecule. How does it get damaged? OK, well, single strand breaks, as in the upper figure there, are usually repairable. They're repairable because all of the genetic information is on the other strand of the DNA, and it's still there. So it's not lost its genetic information, and so the cell has a way of copying the good information that hasn't yet been damaged and pasting it into the area that's been damaged, and that's called repair. So single strand breaks like that are easily repaired. On the other hand, double strand breaks, like in the lower figure, especially when the double strand breaks are close together, you've now lost that genetic information on the other arm of the DNA, and maybe the whole molecule will break apart. You'll get chromosome damage, obvious, and that can't be repaired, or it can't be repaired because you've lost the genetic information. So that's generally considered non-repairable damage. So you've got repairable damage, single strand breaks, double strand breaks, especially if they're close together are usually considered not repairable. If they're a long way apart, maybe they can get repaired. So what's the effect of dose on repair? Well, at low doses, DNA strands are unlikely to be hit at all. So it's very unlikely that you'll get double strand breaks because you're unlikely to get a single break anyway. It's unlikely, very unlikely you'll get a double strand breaks, so for low doses of radiation, you get mainly single strand breaks that can be repaired. So low doses can be repaired. And we'll see later on, that's why we give low doses of profraction every day instead of giving one big dose. At high doses, double strand breaks will start to become important because both strands of the DNA might be damaged at the same time. Before the first strand gets repaired, the second strand gets damaged, then you can't get any repair. So consequently, as you go to higher doses, survival curves get steeper because you're getting more double strand breaks. And survival means that the cell hasn't been repaired. So cell death increases more rapidly as you get to higher and higher doses. So this is what a cell survival curve will look like. Log survival is a function of dose. And it gets steeper as you get to higher doses. For cells that have a high capacity for repair, the curves are less steep at low doses, almost horizontal at low doses, as you can see. And then they get very steep and very curvy, curvyly steep as you get higher doses. Well, that's just cells. But in radiotherapy, we're not only involved with cells, we're involved with normal cells and with cancer cells. Is there any difference? And the answer is yes. Cancer cells, for some reason or other, are not usually as capable of repairing damage as our normal cells. And that's why radiotherapy works. Radiotherapy would never work if you always cause more damage to the normal cells than you do to the cancer cells. And it's all due to repair. It's the tumor cells can't repair as well as the normal cells. Which means that the survival curves for the cancer cells will be straighter as we'll see in a moment. And what I call a window of opportunity exists at low doses and low doses per fraction, and by the way, also at low dose rates. And that's why we work at low doses per fraction instead of normally very high doses per fraction. And we'll come back to that later on. So there is this window of opportunity we like to work in. And this shows what I mean. There are two curves there. I hope you can see the green curve and the red curve. The red curve is the cancer cells. It's not so curvy because you haven't got so much opportunity for repair. And then the green curve is very curvy and shallower at lower doses because of repair, because they are more capable of repairing. And you can see there's that window of opportunity, in this case with the parameters I've used for plotting these curves, around about two grade per fraction where you're getting less cell kill in the normal cells and more cell kill in the cancer cells. You go to higher doses and it's just the opposite. So again, that's why, here we go, at low doses and at high doses and you get that window of opportunity in between. So what does this mean about fractionation, as I've explained? This is why we fractionate at low doses per fraction and typically this is around about two grade per fraction. That's why we, now, did we develop this from doing experiments in radiobiology? No, we developed it by clinicians treating cancer patients finding that about two grade per fraction was about the best that you got. You got less cell kill to the normal tissues and normal tissues didn't get injured. They found that by trial and error. Now we explain it because you're in that window of opportunity at about two grade per fraction. So here we go. This is what happens if you fractionate at two grade per fraction. You get the upper curve there, which is the fractionated cell survival curve for late reacting normal tissue cells that are gonna cause damage and the blue curve underneath it is the same thing for tumor cells and those two curves gradually get further and further apart. As you go to higher and higher doses you get a bigger differential between the killing of cancer cells and the killing of normal cells. And that's just what we need in radiotherapy. So the window of opportunity, what have we assumed here? Well, that curve I just showed assumed that you had exactly the same dose to the normal tissues as you do to the tumor cells. But is this a reasonable assumption this day and age when we have conformal radiotherapy? 30 years ago we didn't have conformal radiotherapy and the normal tissues did get the same dose as the tumor tissues. But now with conformal radiotherapy, is this a reasonable assumption? And of course the answer is no, it's not because the major advantage of conformal therapy is that normal tissues have less dose or at least effectively less dose. It's in homogeneous dose distribution but effectively less dose than does the tumor. So the effective dose to normal tissues usually less than the effective dose to the normal tissues is less than the effective dose to the tumor. But what do we mean by effective dose? There are lots of ways of defining it. One way I'm gonna use later on, in fact this afternoon at noon I'll be talking about this, the equivalent uniform dose is one way that we can define the effective dose. So it's the dose that if we give it in an inhomogeneous manner, what is the effective single number dose that we get that will give the same probability of control or probability of complication? So that's the EUD, that's one way of defining effective dose. I'll look at some other ways later on. So there is a geometrical sparing factor and we can define that as the effective dose to normal tissues divided by the effective dose to tumor. For example, this might be the EUD, the normal tissue divided by the EUD for tumor and that's gonna be less than one for conformal radiotherapy and the more conformal, the more less than one it gets. Well, does this make any difference to the window of opportunity? Yes, it makes a big difference and this shows you with just a modest sparing of normal tissue, a geometrical sparing factor of 0.8. So 20% sparing of normal tissues. Look how far those two curves now have gone apart. Now, they're well apart until well after 10 grade per fraction and with the curves I've drawn there, about seven grade per fraction is where the maximum of part. So what does this means? It means even with a modest sparing of normal tissue, the window of opportunity extends over 10 grade. So what does that mean in terms of practical radiotherapy? Well, what it means with highly conformal therapy, we can use much higher doses per fraction. So today with our modern technology, we can use much higher doses per fraction. What does that mean? It means for teletherapy, we can use hypofractionation and I'll be talking about that later and I think hypofractionation is probably the biggest change we're gonna see in our everyday practice because we're beginning to find by doing clinical trials that hypofractionation, higher doses per fraction can get just as good cure rates with no more complications and it's a lot less expensive and both time and effort and money. So hypofractionation is coming and it will be here quite soon. And for brachytherapy, it means high dose rate brachytherapy. We've been doing that for a long time and the reason we can do it is brachytherapy is highly conformal. You put the radiation right into the cancer so it's highly conformal so we can do high dose rate brachytherapy. What about the dose rate and the time between fractions? So now we're talking about time. We've only talked about dose so far. What about time? Well, we're still talking about repair now. Repair takes time. It takes time to copy and paste that information. And anywhere, probably from about half an hour to one and a half hours, it takes to, on average, for that, it depends what part of the cell cycle the cell is in when it gets damaged, when one arm of the DNA gets damaged as to how quickly it gets repaired. So on average, anywhere between half an hour and one and a half hours. So the time between fractions decreases and the dose rate increases, we get this dose rate effect and the fractionation effect due to time. So what's the importance of the time between fractions? Radiobiologically, we don't know the answer to that, but if the half time for repair is half an hour to one and a half hours, most of the repair will be done in about six or eight hours. It turns out that clinical experience again, this isn't radiobiology in the lab, this is clinical experience, has shown that you need about six hours or more between fractions. How do we know that? Because we did hyperfractionation with less than six hours between fractions in the number of clinical trials about 30 years ago, 25 years ago. And we discovered that those patients who didn't get six hours between fractions got many more late reactions, more severe late reactions. And so we've learned by clinical practice about six hours between fractions. That's the number you'll see in the literature. So if you're doing two fractions a day, if you can, about six hours between fractions. What's the importance of dose rate now? Normal tissues repair better than cancer cells. So low dose rate enhances repair. Low doses gives you more repair. So low dose rate gives you more repair. This is the basis of low dose rate brachytherapy, which we did for 80 years before high dose rate brachytherapy started. We did low dose rate brachytherapy. People were frightened of doing high dose rate brachytherapy. They didn't know whether it worked or not until people started doing it clinically and finding it did work. Especially permanent implants, which is very low dose rate brachytherapy. Things like I-125 or Palladium 103. So that takes maximum advantage of the dose rate effect, which is why, for instance, with I-125, we can go up to doses like 140 gray, 140 gray. That's a very high dose. You can do it because it's exquisitely good at repairing at that dose rate, that very low dose rate. And that's probably why permanent brachytherapy for things like prostate cancer works, because you can go to enormously high doses. Well, how can we determine the best fractionation or best dose rate to use? And this is where we physicists come in because we now need a mathematical model and we're the ones that understand mathematics in the department. And what we need is a mathematical model that describes the effect of radiotherapy on both cancer cells and normal tissue cells. And this is this famous linear quadratic model that we're always talking about. So let me talk in detail about that. On Friday, I'm gonna give you some practical examples of the use of the LQ model in radiotherapy. So let's do the theory right now. According to linear quadratic model, there are two components. There's the linear component. And this is a double strand break. Remember, we're talking about cell killing now. So it's a double strand break caused by a single charged particle traversing through both arms of the DNA immediately after each other. So within the fraction of a second, you get both arms of the DNA broken. And what can cause that? Well, highly T radiations will do that because of the density of the ionization. But also, it's very slow electrons. The slower the electron, the higher the LET. So when we irradiate our patients with high energy linac photons, there are high energy electrons produced. They won't do this, because they're too high in energy. But when they slow down, then they start interacting as if they're high LET particles and you'll get double strand breaks. So you will get some double strand breaks with conventional photon radiotherapy due to the electrons. And then there's a quadratic component. The quadratic component is two separate single strand breaks that are close together by two separate particles. So let's have a look at that diagrammatically. Well, what about the mathematics of this? There has to be a way of mathematically describing this and developing the equation. What we do is we use a statistic called Poisson statistics that you all know about. It's the statistics of rare events. Why do we use the statistics of rare events here? Well, the probability that any specific DNA molecule is gonna be damaged is very low. Got lots of DNA molecules in our body. The probability that one of those is gonna be damaged is very low. So we can use Poisson statistics. According to Poisson statistics, the probability, P zero, that no event will occur. The probability that no event will occur is given by P zero is equal to e to the minus p where p is the mean number of hits per target molecule. And this is probability theory. We'll come back to this in other applications later on. Poisson statistics can be used here and it's a very simple exponential equation. And all we need to do now is find out what P is. P is the mean probability of the event. So let's look at single particle events now. Again, single particle events, P is a linear function of dose. If we double the dose, we'll get twice as many of these particles that go and cut straight across both DNA arms at the same time. Get a double strand break, all in one go. You double the dose, you get twice as many of those. So it's a linear function of dose. So the mean number of lethal events is a linear function of dose and the proportionality constant we call alpha. So it's alpha times the dose. And then the equation becomes e to the minus alpha d. So that's the linear part of the linear quadratic model. And it's due to double-strand break breaks caused by a single charged particle. Okay, let's now go and look at the single particle events. For a single particle to damage both arms of the DNA at the same time. So single particle events are caused primarily by the high LET part of the radiation, as I explained. And that's the low energy electrons when you're treating with high energy photons, okay? What about two particle events? With two particle events, the probability that one arm of the DNA is gonna be damaged is gonna be a linear function of dose. Because if I double the dose, I'll double the probability that that one arm is gonna be damaged. The probability that the other arm is gonna be damaged is also a linear function of dose. So the probability that both will be damaged more or less the same time, I say more or less, you've still got half an hour or one and a half hours. You've still got that repair half time to think about. But before the first one is repaired, a second one comes along and damages it, that's gonna be a linear function of dose. So the probability that both arms will be damaged is a function of dose squared. So the surviving fraction of cells is S equals E to the minus beta. We use that as the proportionality constant for this type of damage, beta D squared. So the, and this shows it diagrammatically. What we're talking about here, you've got the effect shown in the top curve there. That's the single particle event, damaging both arms at the same time. And then you've got two separate single particle events that cause the damage in both arms of the DNA, but not at exactly the same time. Certainly within the period that the first one is being repaired before it gets repaired. So the LQ equation then is quite simple. It's the probability of single particle events times the probability of two particle events. So it's E to the minus alpha D plus beta D squared. And I'm going to reduce that by taking the natural log of both sides. So the log minus the log, I'm going to take minus, is equal to alpha D plus beta D squared. And we'll see why I did that later on. So the log surviving fraction minus log S is a linear function of dose and a quadratic function of dose. Alpha represents the probability of single particle events. We call them alpha type events. And beta represents the probability of independent two-party events. We call those beta type events. Well, what's the problem with this model? The problem with this model in practical radiotherapy, if we want to apply this to radiotherapy, is it's got too many unknowns. It's got alpha and beta. And in clinical work, it's not like working in a lab with cells. In clinical work, how do we determine two unknown biological parameters? Very difficult to do. What we'd like to do is try to reduce this if we can. We can. We can reduce this to one parameter by dividing, now you see why I said minus log S, dividing minus log S by alpha. So let's do that and see what that does to the equation. Here's the minus log S equation. Let's divide, and for n fractions, this is just one fraction. For n fractions, you just want to apply by n. So each fraction reduces the cell survival the same. So what we call the biologically affected dose, take minus log S divided by alpha, and you get Nd into one plus D over alpha of beta, the famous LQ equation that we all use. And yeah, there's now only one unknown radiobiological parameter, alpha divided by beta. It's just reduced it all to one parameter. This was the big breakthrough. The linear quadratic model, I remember reading a publication on that, I hate to tell you, 1973, 1963. I read an article by Jack Fowler in the British Journal of Radiology where he defined a linear quadratic equation for practical use in radiotherapy. What he didn't do was reduce it to a single parameter. He had two parameters and he could never find out what these parameters were, so he never got used. When maybe 20 years before it actually started getting used as what we now call the BED equation. What are the assumptions we make for typical values for alpha over beta? Well, it turns out for tumors and acute reactions, typically alpha over beta is about 10 grade and for late reacting normal tissues that are going to cause late complications somewhere between two and three grade. So these are the numbers I'll use most of the time. There are exceptions that have been discovered by analyzing clinical data, which is what you have to do to determine the proper parameters to use. And the two examples that are usually quoted are for prostate cancer, maybe alpha over beta is as low as 1.5 grade instead of 10 grade. Lots of analysis of clinical data, lots of prostate cancer patients are treated with radiation with all different dose rates and fractionation schemes. So we've been able to determine that and breast cancer probably around about four grade. So there are two exceptions, but most of the time I'll use 10 grade and maybe two to three grade for the normal tissues. What about the effect of dose rate? Because we do use different dose rates. For instance, in brachytherapy, we use different dose rates. Well, for low dose rate brachytherapy, where the time for each fraction is long enough for repair to take place between fractions. So if you are fractionating low dose rate brachytherapy, which we do sometimes, not a lot anymore because we, most of us, beginning to use high dose rate brachytherapy. But there is an equation and again, this was actually published, this equation was published long before the LQ model. This equation used to be known as the Liversage equation. I remember it in the 1970s. We never used it, but it was published. It was there and it just sat there until somebody came along. Roger Dale, I think, came along and published this in the British Journal of Radiology. What you see is now, we've got alpha over beta, but we've got another term in there, mu, where mu is the repair rate constant. So it's the equivalent to the decay constant of radioisotope. In this case, it's a repair rate constant. 0.693 over that will be the half time for repair. So you've got now a rate of repair that has to come into the picture, not just the dose rate. The dose rate is R there. So two things have to be taken into account. There is fortunately a way to approximate this equation. If you put numbers into that equation, you'll soon see. But the treatment time is long, typically greater than about 100 hours. The BED equation comes down to something very much simpler. It's simply a linear quadratic equation. It's linear in dose rate and it's quadratic in dose rate. So it's a linear quadratic equation, which almost looks the same as the conventional BED equation for fractionated radiotherapy, very similar to that. So as long as the treatment time is longer than 100 hours, and that's often true with low dose rate rachytherapy, it's longer than 100 hours. What if the dose rate now decreases while you're treating? For instance, I do a permanent implant on a patient, but while the patient's being irradiated, the source is also decaying at the same time. So now you've got another parameter to come in, the decay rate of the radioactive source. Then things start getting quite complicated mathematically, and this is the equation. I'm just showing it to you. You don't want to have to use this. I've used it on my calculator lots of times and it's not easy. You make a lot of mistakes when you put it in. Obviously nowadays I've got it on the computer, but so if you're studying the effect of dose rate and decay rate on the BED, this is the equation you'll finish up using. Quite complicated. And the initial dose rate there was r0. So the BED equation for permanent implants, let the time go to infinity in those equations. That simplifies it again. Very simply, if the time goes to infinity, you put the isotope in the patient, it stays there, rest of the patient's life, it decays fully. Then the equation is much more simple. Again, it's a linear quadratic equation. It's linear in initial dose rate and it's quadratic in initial dose rate. And now you've got this new, and you've got the lambda, the decay constant of the radioisotope. Pretty simple equation. That I can use easily on my pocket calculator. Okay, let's look at the next r of radiotherapy. Let's look at repopulation. Cancer cells and cells have acutely responded normal tissue proliferate while you're treating them. It's called repopulation. Cells of late reacting normal tissues don't repopulate much at all. In fact, we usually assume they don't repopulate at all. So the shorter the overall time, the better. We don't want those cancer cells proliferating while we're trying to treat them. And it's not gonna help us with the normal tissues anyway. So that's why we try, if we can, to accelerate the treatment, particularly for rapidly growing cancers. We would like to do that. But you can't make it too short because the acutely responding normal tissues are also repopulating. You've got to give them enough time during the course of radiotherapy to repopulate. And that's been a problem with accelerated fractionation schemes that people have tried in clinical practice, in trials. Usually the acute reactions get you, or get the patient. And the patient just can't stand the treatment and you have to give them a rest. Once you give them a rest, you've wasted the time of accelerating the treatment because you're giving the cancer cells a rest too. It's the same. So a lot of these accelerated fractionation schemes haven't worked. What about the OQ equation? Can we bring repopulation in? Yes, we can. We can bring it in, take the overall treatment time T into account. And what we do is to assume that repopulation of the cells, particularly cancer cells, is exponential. And so the equation simply adds a term, 0.693T over alpha T part. T part is the potential doubling time. T is the overall treatment time. There's a problem with doing this. A lot of people use this equation. I see it as a big problem. You've got too many unknowns. So difficult to determine unknowns from clinical data. You've not only got alpha over beta now, you've got alpha and you've got T part. You've now got three unknowns instead of just one in this equation. Well, I always like to reduce those by assuming that by creating a radiobiological parameter K, which is 0.693 over alpha T part. And you determine K by looking at clinical data. So the equation then becomes much simpler. And this is the equation I personally always use. The unknown biological parameters are two, just alpha over beta and K. What kind of values can I use here? Typically I use about 0.2 to 0.3 BED units per day for acutely responding normal tissues. For late responding normal tissues, probably zero. Some people use 0.1 BED units per day. For tumor, it varies and we'll see that later on. But note something, these are not gray per day. You look in the literature and more than 50% of the articles and literally call them gray per day, not gray per day because BED is a linear quadratic in dose. So you can't say gray, which is dose. So it's BED units per day. But as I say, most publications call it gray per day. These are the values I use personally for tumors. I ask the radiation oncologist when he comes to me and asks me, solve this problem for me. What do I have to do? I'll ask him, is it a slow growing tumor, a fast growing tumor or something in between? And these are the values I use for K for those three situations. Oh, I think I can go backwards, yeah. Notice I say, assuming no accelerated repopulation up in the title there. What do I mean by no accelerated repopulation? Well, there's a theory that there is a thing called accelerated repopulation and what that means is when you first start irradiating a tumor, it doesn't repopulate much at all until a certain time later on called the kicking time and suddenly it starts accelerating in its repopulation. I don't really believe it, but a lot of people do. It also complicates things. I don't like complications. So there's no repopulation before a kicking time and then there is, and then there's a considerable repopulation called accelerated repopulation afterwards. So that's what happens to the BED equation. You get now T minus TK, either kicking time, where K is zero when, before you've reached the kicking time, okay? This is all based on what we all call in the field the withers hockey stick. What Rob Withers did is he analyzed lots and lots of clinical trials of head and neck cancer and he plotted the dose that you need to cure the head and neck cancer patients against the overall treatment time and he found it looked like the shape of a hockey stick. This is called the Withers hockey stick and if you look at that data, up to about 28 days, four weeks, you don't seem to get much repopulation. Look at the error bars, so you gotta take that into account and he didn't do that. I mean, he's got error bars there but he was already determined to show that there was a kicking time because that's been going on for many years before and he says he showed it with this. This, so this has this kicking time of maybe four weeks, four weeks from the start of treatment. This has been re-analyzed by other statisticians and radiobiologists who found that they could draw a straight line through this that never had any kicking time at all with equal probability of being correct, took into account all these error bars of all the points and there was no kicking time at all, so kicking time was zero. So that's what I believe because it's easier to believe that but I know some of my colleagues would insist there's a kicking time. I don't even see any rationale behind it personally. Why would the cancer cells not be dividing and divide? They're dividing before we treat it, why can't they keep dividing as the way they were dividing before? That's my theory. Okay, so I'm not gonna use kicking time too much. What about repopulation with permanent implants? We didn't say that, did we? When we talked about permanent implants and we showed the equation for, the BED equation for permanent implants to infinity, nice simple equation but we didn't take into account that the cancer cells might be repopulating while we're treating them. Now things start to get complicated. The maximum BED has been reached at a time when the rate at which the cells are repopulating equals the rate at which the radioisotope is decaying. You'll get a certain point and that's the maximum BED you're ever gonna get because from then on, the dose rate is lower because now you've crossed over and I'll show you that graphically in a minute. And it can be shown that the effective treatment time is given by this equation. It's not difficult to derive that. It's in the literature in a lot of papers. So we do have an equation for the effective treatment time. And this is what it looks like graphically. This was published many years ago. I don't have a date on that. Oh yeah, 1992. This was published a long time ago just showing what the linear quadratic model would do if you put that into the equation. And you can see that for palladium with, if the K value, the repopulation parameter is 0.46 BED units per day, then palladium reaches its maximum after, I can't see about 30 days and ID 125 maybe 100 days. And that's what the complicated equation will give you. Where there is an equation for it and so there's the equation we saw before for the BED for permanent implants. And now what you have to do for T in that equation, whenever you see T in that equation, you put T effective. Making sure everything's in the right units. You can easily get messed up here because the decay rates usually in hours, the decay constant maybe in days and the T effective is often in days and you gotta get everything in the right units. Everything in the right units is a workout. If it doesn't, you get horrendous results. Nothing like what you should be getting. You gotta be careful. Let's look at the next R of radiobiology, reoxygenation relates to the oxygen effect. Oxygen's the most powerful radio sensitizer of cells that we know. Hypoxic tumors, a lot of tumors are hypoxic. We don't know really how many because we haven't really studied it but quite a lot are hypoxic. And we believe that these can reoxygenate during a course of treatment and that's why we can treat hypoxic tumors because they reoxygenate the resistant cells become sensitive while we're treating through a course of radiotherapy. And we define an oxygen enhancement ratio as the ratio of the dose under hypoxic conditions divided by the dose under well oxygenated conditions aerobic conditions to produce the same biological effect. And what's going on here? Well, we call this the oxygen fixation process whereby oxygen reacts with the damaged DNA strand that would normally repair. There's a single strand there that would normally repair. The oxygen interacts with it and fixes the damage. That's why we call it fix. It fixes the damage. That's called the oxygen fixation process. So that means it can't repair. So it's preventing repair. So this is called the oxygen fixation process. Oxygen is a function of dose and dose rate as you can see from those two curves. High dose rate at the top and low dose rate at the bottom. Sorry, low dose and high dose. OER at low doses and low dose rates tends to be lower than the OER for high doses. So OER is the difference between hypoxic cells and normal cells. If it's three, that means you need to give three times as much dose to the hypoxic cells to kill them as you do the well oxygenated cells. So what you really want is a low value of that difference. And the difference becomes lower as you go to lower doses of profraction than lower dose rates. So this is why sometimes we believe giving lower than two grade profraction might work, hyperfractionation or giving very low dose rates like with permanent implants, you can get better results. Nobody's ever really proven that, but that's the theory of it. So why does OER decrease as the dose decreases? Well, the sensitization relates to fixing of the single strand breaks. So it enhances beta type damage at low doses, alpha type damage dominates. So the effect of oxygen sterilization is reduced. So that's why you get that difference. So reduced effect of oxygen means lower oxygen enhancement ratio. Why might this be important in radiotherapy? I already mentioned it. Reduce dose profraction and reduce dose rate. But tele-therapy hyperfractionation might be better for hypoxic cancers and for brachytherapy, very low dose rate brachytherapy like permanent implants. Then you've got acute and chronic hypoxia that will reoxygenate. Chronic hypoxia is due to the diffusion of oxygen through tissue. It has to go too far from the supply of oxygen and cells can remain hypoxic for extended periods of time. With acute hypoxia, what you're doing, you're choking out the blood vessels and then when the tumor shrinks, they open back up again. So it's temporary closing of blood vessels that's transient and they'll reoxygenate faster. And that's shown pictorially here. You've got chronic hypoxia, which is these areas. They're a long way from the blood vessels shown in the middle there. And for acute hypoxia, you've got narrowing of the blood vessels, but they'll open up as the tumor shrinks. What about timing? Well, the rapid component causes the acutely responding cells to become reoxygenated. And then there's the slow component, the chronically hypoxic cells become radio. And you also get a thing called revascularization of tumors that's been observed. Tumors get a lot of blood vessels produced. So in clinical practice, spreading the irradiation over long periods of time or very low dose rate ought to help. Modifications of the LQ model to account for this have been published. We don't use them. I don't know, anybody who uses them, they're quite complicated and you've got more unknown biological parameters to determine, but it has been published. I'm not gonna do it. As I said, I don't know anyone using it. Redistribution, the final hour of radiotherapy relates to the cell cycle effect. Cells are most sensitive, add or close to mitosis. And survival curves for cells in the M phase are linear. There's absence of repair. So apparently when you're near mitosis, there isn't much repair. Cells, cell survival curves become pretty linear. Cells in late G2 are usually equally sensitive as cells in mitosis. So when they get close to mitosis, they're very sensitive. At the other end, resistant cells mostly in the latter part of the S phase, they're resistant. So what is redistribution? Well, because when you give a fraction of radiation to a tumor, the majority of cells that are gonna be killed are those that are near mitosis, late G2, or in the M phase of the cell cycle. And now you've got a bolus of cells that were resistant that started in the late S phase. Then they're gonna work their way around the cell cycle. So they're redistributing themselves. The cells are redistributing as a bolus going through the cell cycle. So after exposure, cells are thus partially synchronized. That's what we call redistribution, or sometimes reassortment, the fourth R. Well, is that important in fractionary radiotherapy? The timing of the subsequent fraction makes a difference. For example, the next fraction is delivered at a time when the bolus of cells that were in the S phase when you get the first fraction has now reached a sensitive phase of the cell cycle. They'll now be very sensitive. So can be very important. Well, what about in daily fractionation? In daily fractionation, you've got 24 hours roughly between fractions. And that's ample time for the cell to go way past the sensitive phase of the cell cycle. You get all mixed up and all the cells now are all mixed up. So probably no cell cycle effect, really, of significance. It hasn't any effect on daily fractionation. But what if we allow hyperfractionation? For instance, what if we do three times a day fractionation with six hours between fractions? It's conceivable that six hours is just enough time for those cells to reach a sensitive phase of the cell cycle. Now they're exquisitely sensitive. Wouldn't that be great if we could do that? But we haven't found a way of using it. We've tried hard, doing lots of experiments, not too many on humans, lots of experiments on animals, and it hasn't really worked. We haven't been able to find a way of taking advantage of that. Maybe it doesn't really exist, but we've tried and it doesn't seem to work. And also the LQ model has been modified for redistribution. Again, it's something that nobody ever uses. It was a nice theoretical paper that was published on it, but I've never known anybody to actually use it. So it's there. So finally, let me talk about, that's the four hours of radiotherapy. Now, let's talk about the LED of the radiation. Repair decreases as the LED increases. Of course it does, because the higher the LED, the more double-strand breaks you're gonna get in your DNA molecule and in a single charged particle phone through. The cell survival curves become straighter, not curvy, which represents curvy represents repair. They become straighter. The OER decreases. Sorry, the OER decreases as the LED increases. So you get left. So we're better up. We're better at treating hypoxic cancers with high LED radiations. And that's one of the big theories behind using high LED radiation therapy. And the cell fights, if we also find by experiments on animals and cells that the cell cycle effect also decreases as the LED increases. So might this be important in radiotherapy? Well, for the treatment of cancers that are very good at repairing, that ought to help. For treatment of hypoxic cancers, lower oxygen enhancement ratio, it ought to help. For the treatment of cancers that get trapped with the cancer cells that get trapped in a resistant phase of the cell cycle. We didn't talk about that in much detail, but there are phases of the cell cycle where cells can get trapped. And maybe the reason why some types of cancers, like glioblastomas, for instance, in the brain, maybe one of the main reasons why they're so resistant to treatment is the cancer cells, some of the cancer cells are trapped in a resistant phase of the cell cycle. Bad news, high LED radiotherapy might be able to get over that. So that's the rationale. The one of the rationals between doing high LED radiotherapy. The reason we don't do it all the time is it very, very expensive. You're talking about at least an order of magnitude more expensive than your best linear accelerators, probably two orders of magnitude, than your best radiotherapy machines now. So we don't all do that. Some centers are doing it in the world more as experimental than anything else. If we can start producing high LED machines inexpensively, then we'll all be doing it, but I don't see that happening for at least 10 years. So let me summarize. Radiotherapy is governed by the four R's. At least that's what the textbooks tell us. The four R's of radiotherapy. Since normal tissue cells are better able to repair than cancer cells, there's this magical window of opportunity at low doses, low doses per fraction, and low dose rates. That's why we use low doses per fraction in radiotherapy. Unless we have considerable geometrical sparing in the normal tissues with highly conformal radiotherapy, or by the way, brachytherapy, very highly conformal, then this window of opportunity widens. So for instance, high dose rate brachytherapy, we can do at seven grade per fraction, whereas we always thought we couldn't do that. The reason we can is there's this widening window of opportunity due to the conformal therapy that HDR gives us. The LQ model can be used to calculate the effects of dose per fraction and dose rate and overall treatment time. We'll do that on Friday. I'll give you lots of examples of how that can be used. And then finally, high LED radiotherapy has the potential advantage over conventional radiotherapy. And I haven't even mentioned the Bragg peak, because you can get that with protons as well as very high LED radiations. What you don't get with protons is the LED advantage, because by the time the protons reach the cancer, they're low LED, they've lost their high LED component. And the Bragg peak's too narrow to be able to treat a cancer, unless you've got a tiny little cancer, maybe an ocular melanoma or something, that you can use the high LED Bragg peak advantage. But most of the time you can't. So with proton therapy, there isn't really an LED advantage. You have to use these big, heavy particles like carbon ions that are, as I say, maybe a hundred times as expensive to produce than your conventional protons.