 Okay, I'm going to carry on from what I talked about in radiobiology this morning and now going to the next step. Can we apply some of those things we learned about radiobiology this morning into treatment planning and treatment evaluation? And a lot of what I'm going to say is based on this document which is AAPM Task Group 166. Does everybody know how to get AAPM Task Group reports on the internet free? No? Yes? Yes. Good. Just go AAPM.org, go into publications, Task Group reports, they're all free. So you can go and look at this one, it's a long report and it's got a lot of the kind of things that I'm going to be talking about today. So what is in this report? Well they start by looking at the quadratic model, I already did it so we won't have to do that again, to account for a fractionation in dose rate effects. And then they start defining newer terms that we didn't talk about yet this morning, things like the effective volume, the effective dose, the uniform dose, I mentioned equivalent uniform dose this morning, they talk about that in this report and how this can be used in treatment planning to account for volume effects, I'm going to talk about each of those, and then things like tumor control probability and normal tissue complication probability, and can we apply these in our treatment planning? I'll go into that, and then are any of these being used on treatment planning computers today? Yes they are, and I'll go over that. So let's start by looking about how do we compare two different treatment plans to decide which is the best plan? And the way we always used to do it in the old days was simply show the physician treatment plans and say pick the best one, and that was very highly subjective. What we really would like to do is give him some numbers. I mean ideally what he wants us to know to tell him is what's the probability I'm going to cure my tumor, and what's the probability I'm going to damage normal tissues, that would be ideal, and we'll talk about that. But this is very highly subjective just to look at two treatment plans. What we've been talking a lot about in this course is comparing those volume histograms, and looking at those volume histograms that decide which is the best. Well that's still pretty subjective, because you're still just looking at figures, and they're different, and trying to decide, and I'll look at that in a minute and show you how subjective it is. What we really want is a quantitative measure of the quality of a plan. And this can be done by using the dose volume histogram itself, and looking at all these different parameters, the maximum dose, the minimum dose, D90, D98 we've talked a bit about, and so on. Or we can go a little bit further and look at things like the effective volume, or particularly the effective dose, and the equivalent uniform dose. And ultimately, as I said, what the physician really wants is TCPs and NTCPs, which is the best plan. So let's start by looking at visual inspection of isodose curves. And here's some isodose curves, four different plans. There's a top left is a photon and electron plan. And then there's a five-field photon plan to the bottom left. And then top right, five-field IMRT and nine-field IMRT. And if you look at those dose distributions, yeah, they're a bit different. And probably the really complex plans like the nine-field IMRT is probably better. But I couldn't tell that just looking at the treatment plans. It's too difficult just looking at treatment plans. Very subjective, and physicians like to do it. But they would like us to give them some numbers. They would prefer us to give them those volume histograms, for instance. So let's look at those volume histograms. There's a comparison of a simple dose volume histogram here, which is a simple APPA plan, two-field plan. That's the red curve. And this is the dose volume histogram for this particular tumor. And this is all hypothetical. This is an imagined tumor. And then you've got the IMRT plan. And they're different. They cross each other. The median dose is the same, 63.7 grade. But there are hotspots and cold spots around there in this tumor. Okay, let's get some numbers. That's probably what we need to do. So from those curves, I've derived these numbers. And you can see the numbers are quite different. For instance, for the IMRT, it's the most uniform dose. It's the lowest standard deviation, only 2.5 grade. But it's got a higher V90, but a lower D100. And that can be a problem. You've actually got a cold spot in there, considerable cold spot in there. The range, if you look, goes from 30 gray up to 65 gray. So even though the standard deviation is smaller, the actual range is bigger. And you've got a cold spot there. That's bad news. But what about the simple APPA field? Oh, it's got a bigger standard deviation, but the range is smaller. And you've only got the lowest dose is 55 gray. And that's much better. But the highest dose is 73 gray, which is worse. It's got a shorter range, but it's got a much higher high dose. And you get all these other numbers. Okay, we can present these numbers to the physician and they can look at them. Well, that's only half the story. Which is the better plan? Well, you've got to now take into account the normal tissue deviations and the normal tissue deviation numbers. So it's getting more complicated now, rapidly. What we really want is good coverage of the target, low D max to normal tissues and low volume of normal tissues receiving doses close to tolerance. That's what we want. Well, can we come up with a single number or maybe two numbers to represent what's going on in the dose volume histogram so that we can compare them with single numbers? That would be ideal. And that's what we would like the treatment planning computer to be able to do and give us the best plan. This is what we want to do in optimization. Well, yes, can we do this? What we need is a volume effect model of dose response in normal tissues and tumors. And the volume effect model that is most commonly used in all of these computers that we use to do this is the power law model. Is it new? No, it's not new at all. We had a power law model first published in 1939 for skin doses and a power law model for volumes published in 1946. And we still use these today. This is the power law model we use today. So this is nothing new. It's just that now we have the computers capable of doing this. Up until 20 years ago, we really didn't have computers that were capable of applying the power law model, plotting deviations and analyzing deviations to get to use this model. So the model's been around a long time using it's been a problem, but now we can use it. And this is the power law model. Dv is the dose which if delivered to fractional volume v. So v is a fraction of the total volume. Let's say we're radiating the liver and we're radiating 10% of the liver to this dose. Then dv is the dose which if delivered it to 10% of the liver would reduce the same biological fact as the dose d1 to give them to the whole organ. So this is the volume effect model. And this is the basis of all the models are used in treatment planning computers today to calculate things like EUDs and TCPs and NTCPs. So it's a volume effect model and it's simple equation. So what does the exponent mean in the volume effect model? And I won't go over details of it, but if you sit and think about it, you'll realize that N is negative for tumors and N is positive for normal tissues. You'll realize that when you look at it and spend some time with that model. You realize that very quickly. N equals zero means that cold spots in tumors or hot spots in normal tissues are not tolerated. So when I show you some N values in a minute, you'll realize that a very low value of N, whether it's negative or positive, very low value of N means small hot spots and small cold spots are not tolerated. N equals one means that ISO effect doses change linearly with volume and N large means that cold spots in tumors and hot spots in normal tissues are very well tolerated. So let's look at a clinical example. This is the dose that will produce 50% damage in the spinal cord as a function of the partial volume. And notice that even though you go to very small volumes, as you decrease the volume, the dose that it will tolerate, the dose that will give you 50% damage is not changing much. There's not a big volume effect. And that's because N is small for spinal cord. At the other extreme, you've got something like the liver where N is large for the liver and there's an enormous volume effect. And you can go to extremely high doses to small volumes of the liver and liver function will not change significantly and the patient can go on without too much problem in the liver. So that gives you an idea of how important this value of N is for different tissues. Okay, what we would like to do now is use this volume effect power law model to convert dose volume histograms into single numbers. And this was published a long while ago. Here's the solid line represents a dose, a two step dose volume histogram for simplicity just to see this. It's a two step dose volume histogram. You can reduce it to a single number two different ways. You can reduce it to an effective volume and this is called the Kutcher and Berman model. And all you can reduce it to an effective dose which is called the Lyman and Wauberst model. And again, these were published probably 20 or 30 years ago. Couldn't use them because we didn't have to treat many computers capable of doing it. So this was published before we could use it. In fact, one of my graduate students published this in his thesis in the 1970s. We never could use it because we just didn't have the treatment of computers available in those days. They just weren't powerful enough to do all these calculations. Well, here's the equation for the effective dose. Unfortunately, when those papers were first published this equation wasn't in there. So somebody had to go in and look for the equation and came out with the equation and this is your power law equation. This is the volume effect power law equation. So that was in the original paper that calculated the effective dose but they didn't give the equation. So VI is the sub volume irradiated to dose DI and then you sum it over all of the volume within the dose volume histogram. VT total is the total volume of the organ or tissue and N is the tissue equivalent volume effect parameter that we've been talking about. Mohan called this the effective uniform dose 1992, the effective uniform dose. He did not call it the EUD even though effective uniform dose could have been called EUD. It wasn't until 1999 that Namirco published his paper on EUD. He renamed the effective, the equivalent uniform dose, he hadn't really published anything different from what had been published before several years earlier but he got all the accolades for developing the EUD model even though the equation was published many years earlier. So here's his equation and you'll realize it's exactly the same equation as we just saw from Mohan and colleagues. The only difference here is that instead of N, we now have A as the exponent where A is simply one over N. So we just changed the equation and put the reciprocal of N and called it A. Exactly the same equation. So EUD was first published in its current format in 1999 but it actually had been published many years before. And this is just some values from Namirco on tumors, values of N for tumors and value of N for normal tissues. Note liver for normal tissues, the value of A is a small number. So one over A is a big number so that would tolerate hot spots and look down the bottom, spinal cord, right down the bottom, the value of A is a large number. So one over A, the old N, one over A is a very small number. Remember small number means for A means, for N means that the hot spots are not tolerated. We already knew that from observation in patients of course. So how can we apply, how can we calculate the EUD? How can computers do it? Or we could even do it manually. Well let's take a tumor and let's divide it into three parts. 90% of it gets the dose that will produce 50% cure, 50% local control. 5% of it gets half of that dose and 5% gets one and a half times that dose. What's the EUD? Okay, what we need to do is a cold spot and there's a hot spot. The cold spot we know in the tumor is bad news. Hot spot probably doesn't make a lot of difference. So what we need to do is add these up. The EUD is then the sum of the three parts with the power law, exponent A. And if you do that for breast, with an A of minus 7.2, remember A of negative is tumors. N of negative is tumors as well. And what you find is, look at the bottom line there, 8% tumor control probability. So instead of 50% tumor control probability, we've got 8% tumor control probability. So a cold spot made a big difference in breast. The A number is pretty big. That means a small value of N, cold spots aren't well tolerated. It's the same model. Okay, and how did we get tumor control probability out of this? Here's a typical sigmoid type curve for tumor control probability against EUD. And this is an equation that will fit it. There are multiple equations that will fit these sigmoid shaped curves. This one's called a logistic function. And it's simply a mathematical model. And that's what he used. This is from Nomeco's data I just showed. That's what he used to do those calculations of TCP and NTCP2. In fact, I've done the same thing for, oh, this is for a number of different types of cancers with his values of A shown. And you can see the higher the value of A, like Cordoma minus 13, the lower the tumor control probability, you get less tolerance for cold spots. And I've done the whole same thing for normal structures. I've taken a normal structure divided into three parts, just the way we did before, with a cold spot and the bad news for normal structures, a hot spot. And then I've looked at the probability of normal tissue complications and sure enough, liver can tolerate this very well. So instead of 5% damage exceeding tolerance, I'm down to actually 4.6% is ridiculous. I'm actually, with a non-uniform dose distribution with a hot spot and a cold spot in liver, I'm actually doing better. This is all mathematical. And it may be true, it may be true that I can do better because this cold spot might help even more with something like the liver. Whereas to go all the way to the bottom, spinal cord, instead of a 5% complication probability, I've got 55% probability of complication because the hot spot is really bad news in the spinal cord. So how do we do optimization? The objective is to develop the treatment plan which would deliver a dose distribution to ensure the highest TCP that meets the NTCP constraints. So tolerance constraints. This will usually be close to the peak of the probability of uncomplicated local control curve. So let's look at one of those. This is the probability of uncomplicated control curve for a 2D treatment plan and a 3D treatment plan. And you can see the way this is calculated. You take the TCP and multiply it by one minus the NTCP and you get the probability of uncomplicated control. And what you can see there is the 3D plan is better. You can get a higher probability of uncomplicated control. And by the way, at a higher prescribed dose too. So you can prescribe more dose because you've got a 3D plan that is more conformal. So how do we create a score function that could be used in optimizing treatment plans? How does the treatment planning computer do this? Well, it starts by DVH data. You've got all the data in a DVH. And then you can calculate the EUD for that particular tissue and then either the TCP or the NTCP depending on whether it's tumor or normal tissue. Do that for different plans. So you might run three plans. Do all that for three plans. And then get a score which is some function of the TCP throughout the tumor or tumors if there are multiple tumors. The TCP times one minus the NTCP for all the normal tissues that are in the beam. And you might want to use some kind of waiting factor for each of these depending on the type of tissue. So that's the way you can do some scores. So what does AAPM Task Group 166 tell us? What it tells us is, according to their report, that incorporating EUD based cost functions into inverse planning for the optimization of IRT plans may result in improved sparing of organs at risk without sacrificing target coverage. In other words, they believe from their studies that it's better than just using physics. You want to throw some biology in there in terms of the volume effect of the tissues. Now, do we have to go through EUDs to calculate things like TCPs or NTCPs? No, we don't. We could actually do it directly. The Pinnacle Treatment Planning System, for instance, uses the Kutcher and Burman DVH reduction method I mentioned before to calculate the effective volume. And these are the equations that it actually uses. And halfway down there, you'll see the volume effect snuck in there. There's a volume effect. And it's the power law volume effect. It's reducing the whole inhomogeneous dose distribution into a single number by using, and to convert that into NTCPs directly, using a probit type of dose response function for that particular tissue. So this is what is in the Pinnacle System for, and I'll go over some of the treatment planning systems later on that we have available to us. And all of them have these kinds of algorithms to calculate NTCPs and TCPs. It's all done by the volume effect model. Another way to calculate TCPs directly, and that's in some of the treatment planning systems, and you'll see a lot of this in the literature, is to use Poisson statistics, just like we did this morning to explain the shape of cell survival curves and the linear quadratic model. You can also use them in terms of designing treatments and calculating TCPs. If the number of patients with similar tumors are treated with a certain regimen, the probability of local control, i.e. the probability that no cancer cells will survive, that's local control, is given by exactly the same kind of equation as we saw this morning. In this case, NM is the mean number of cancer cells surviving in any one patient. So for instance, I've got 10 patients, and on average, I've got one cancer cell surviving in 10 patients. You put that in here, e to the minus one, and you finish with about 90%. You've got 90% of the patients cured, because on average, there's only one cancer cell in 10 patients. It's not quite 90% because some patients might have two cancer cells in them, and you might have 20 patients, and one patient has two cancer cells surviving. It's very close to 90% in that case, so this is another way that the treatment planning computer can do it. So if the average number of cancer cells in each patient's tumor, before treatment is N, it's zero, and the mean surviving fraction in all these patients is SM, then the number surviving is N zero times the fraction of surviving cells. So the equation for TCP becomes e to the minus N zero times the surviving fraction, okay? Which is better for optimization? EUD or TCP or NTCP or a combination of both? Well, AAPM Tasker report says, although both concepts can be used interchangeably for planned optimization, the EUD has the advantage of fewer model parameters, really just one A, as compared to TCP and NTCP models, which have to describe the shape of the dose response curve. So it allows more clinical flexibility. So that report prefers EUD for optimization over trying to calculate TCP and NTCP. A properly calibrated EUD model has the potential to provide a reliable ranking of rival treatment plans and it's most useful when a clinician needs to select the best plan from several alternates. So the physician says, well, try and get the best plan for me and you're showing three plans. And he'll say, give me the bottom line. You say, this one's better because it ranks better. He may or may not believe you. Can we take dose perfraction into account? I've mentioned dose perfraction. Well, of course we can. We can use the linear quadratic model in either calculating any of these terms that we've done before. I'm not gonna spend any time on doing that. The way it's being done most of the time is to convert every dose in every voxel within the particular organ or tissue weeks around the patient into the equivalent at two grade perfraction. Because the problem is that you're treating the liver. Parts of the liver are getting one grade perfraction. Other parts are getting three grade perfraction. It's very heterogeneous. Convert every single voxel to what it should be using the LQ model at two grade perfraction. And then you'll get a two grade perfraction EUD. So that's how it's done. And simple was that. Very simple, you just use the basic LQ model. Now notice we haven't made any complications here like correction for repopulation, correction for overall treatment time. You can do that. I don't think any of the treatment planning systems have become that sophisticated but they could be that sophisticated if you wanted them to be. I think they just use this very simple plan. And most people would do that. Alternatively, you could use the LQ model directly in TCP calculations for instance. And it's very simple. Here's the equation we derived earlier. Using the LQ model, you now have an equation, the linear quadratic equation for cell survival and you just wrap that in to the TCP equation. You get this complicated equation that actually you see quite often if you read the literature. It's a double exponential. It's an exponential. And in the exponential is another exponential to calculate the effect of those perfraction using the linear quadratic model. You want more on the calculation of TCPs as a lot in the literature. Task group 166, for example. But there's a very good article, tumor control probability and radiation treatment, if you want to read that. And it's in medical physics by Zeta and Hanin published a couple of years, three years ago. So, this is a possibility if you want to read a bit more about it. Let me just look now then at biological models in treatment planning systems. The monocoe system, what does it have? I've looked on the internet to find out what's in there. I've actually contacted the manufacturers and asked them what's in their system. And it seems to me that to calculate tumor control probabilities, the way they do it, they use the Poisson statistic cell kid model that I just talked about, the last thing I talked about. For normal tissues, they use the UDs. The pinnacle system, they use the Poisson TCP model and the UDs for tumor, either one, both. And for normal tissues, they use the Lyman-Kutcher NTCP model and EUDs. Notice they're all using EUDs. Task Group 166 says that's the best way to do it. May or may not be. And then the EQUIP clip system uses the Poisson TCP model and EUDs. And for normal tissues, it uses the LQ-based Poisson NTC model. So they take into account the dose-perfraction as well. And probably the others can do that too, but it's not on the internet that they do it. I suspect all of them can convert everything to two-grade-perfraction equivalents throughout the tumor or normal tissue volume. So that's one of them. Now, do we know what parameters to use in all these models? And the answer isn't that easy. Kind of we do know, and we're getting to know better all the time, partly because of this Quantech initiative that the AAPM stimulated about six or seven years ago and they've started collecting lots and lots of data. You've heard this from other speakers. Lots of data is going in to this system, data on dose distributions, data on outcomes, did it work, fractionations and so on. And that's all being analyzed. I'm sure there are dozens of PhD students around the world that are going in to get that data and trying to analyze it, to find out the best parameters to use in different models. And maybe also designing new models. LQ model, as I said earlier, is really too simple. You need some more complicated models. Maybe somebody's gonna come up with a slightly more complicated model if it's better, we don't know. But they're all using this initiative, this Quantech initiative. Unfortunately, that's just normal tissues, but at the same time, tumor data's going in there and response data's going in there. So ultimately, we'll get a lot of analysis of the tumor control data as well as the normal tissue complication data. Very large databases are being created. They're accessible. You can get in there and look at them and you can evaluate models and analyze the data to get the best fitting parameters. So let me summarize, what have we learned? Biological models can be used for treatment planning, optimization, and evaluation. The power law volume effect models are used extensively. Let me, I didn't say anything about that. How can it be that simple? It can't be that simple. First of all, they were invented almost 100 years ago, about 80 years ago. How can we not have advanced? We really haven't. We're still using the power law volume effect model. Hopefully, studies like Quantech, they'll come up with better models than just a simple power law model. Biology doesn't work that simply. In homogeneous dose distribution, possibly corrected for the effective fractionation can be reduced to a single number but we've talked about EUDs, TCPs, NTCPs, or probability of uncomplicated local control. So let me stop, and you can look at that, your leisure, where we can stop and take any questions.