Vietnam: A Television History; Interview with Peter Paul Mahoney

I thank you. Thank you Glenn and thanks everybody for coming tonight. What I want to do is tell you a little bit about us and our mission and the mission of our sponsors here. So I'm going to take a few minutes before tonight's lecture to just go over some basic things because it's our first lecture telling you a little bit about our center. So this is the bill our research building. We are primarily on the first floor of this building and it's a center of Kansas systems biology and it's also the NASA center of specialized research because we're funded both by NCI and by NASA to do this work. So it's kind of interesting that those NASA center of research in Brighton but there is. So what I'm going to do is tell you a little bit about as I say who we are and what we do. And then I turned over to the speaker. But what goes on at the center is we have a team studying cancer from a systems approach. And besides being the center of kinds of systems biology for character St. Elizabeth's

and for Tuffs we're also associated with Tufts Medical School. We have funding from three very separate very diverse federal agencies NASA and CIA and. The reason these agencies are giving us funding is they think that systems biology which I'll tell you a little bit more about in a minute is is an important way that we're going to address and learn about cancer and cancer treatment in the future. So all these agencies have given us significant funding for these studies. So in our systems approach we do experimental work we do mathematical work and you'll hear some mathematics today. And also because NASA and the NCI think education outreach is so important. They've given us funding to do outreach for the public like what we're having lecture today right. But they've also

encouraged us to train sort of the next generation because they feel that both these agencies feel that really for people to do biology people do cancer biology in the future you will have to have a background both a quantitative background and a biological background. So that's what we're trying to train people to do and that's what you'll hear a little bit about how our lab embarks on these these issues. So who are we. Well we're at St. Elizabeth's where a group of individuals who are trained in various disciplines to do is to take a real systems approach. You need to look at cancer from a lot of different perspectives. So within our group after us we have cancer biologists we have people trained in physics trained in mathematics computational simulation molecular biology oncology bioinformatics developmental biology chemistry and pathology.

These are all people that are working tightly in in and sort of integrated team. And as you can see no one could cover all these different disciplines. So it's important to have these different members and working under one roof together interacting on a daily basis. We also get additional expertise and this isn't very clear here. From the University of California at Berkeley in theoretical physics we have some outstanding general relativists actually who are who are working with us. We work with noted cell biologists at New York University and we do bioinformatics work with the University of Heidelberg. So although we're based in Brighton our reach is large. So that's sort of who we are and what do we do. And this this slide just shows you sort of picture form a number of the things that we attempt to do in our lab. When we're looking at cancer when you're looking at cancer. Traditionally cancer has been looked at from a molecular point of view or a cellular point of view.

OK well we do the molecular work we do this. This is what work we do the cellular work. But then we also think of multi cell populations and we think of you know tissues and then the tumors themselves. This is the pathology of an actual human tumor. So. We tend to look at these multi-skilled approaches for what lab kinds of things experiments. But then you also have to sort of iterate this with the modeling efforts and we're going to hear a lot more about modeling tonight. But in our lab we do analytic modeling and we do computational modeling and this looks a lot like it. It looks quite a bit like this aggregate of cells. But here this is a computer simulation of a tumor growing so again these are all sort of little bits of pieces of modeling that was done because people are kind of surprised like there's always surprised when they hear. NASA's interested in cancer research. They're also still surprised when they hear mathematicians are doing cancer research because you want to know why would a mathematician be doing cancer research. I mean how does how does that

really work. And one thing that you can appreciate is mathematicians are trained in sort of built in dynamics and figuring out how things move forward and making models that predict action in the future. So this is one area that we're particularly interested in strong and I'll tell you a little bit more about it here for example our curves are simulations of tumor growth of from actual breast tumor patients and we're looking for sort of over arching principles that explain how tumors grow in the body. And this is something that because you would look at hundreds and hundreds of tumor sample tumors in patients and then look at multiple images from these patients then you would need mathematics to deal with a large set of information. So the actual programs that we have and what is the mission of the of the individuals that are funding us again this is supposed to be just a brief overview

just to sort of tell you where we're coming from with regard to NASA. NASA is interested in cancer risk in space. OK NASA wants to know if we send astronauts up astronauts go to Mars astronauts go on prolonged space missions. What is the risk of getting cancer. A lot of radiation space. That's really what we get funded for. But the hope of NASA and of course the work that we do and our investment is because what they learn there is going to be relevant for individuals here on Earth. So it's one of those kind of winwin things where NASA learns about carcinogenesis risk in space but we learn about cancer cancer dynamics and even ways that you could for cancer here on Earth. So this is an interesting this is really very interesting piece of work that we're doing and this is a five year program it's actually just up for renewal but. So hopefully we'll be doing another five years of this work. You actually do these studies at Brookhaven National Laboratory at Long Island. So what NASA does is it

sets up a lab for us in Long Island and people get in the car. They take the experimental flasks the cells everything else that they need for the experiments drive down to Long Island. And what you have to go to Long Island is we're looking at what is space radiation. So you're looking at the accelerators. Here's a fellow that used to work in our lab he's actually putting some samples in the beam. And so you have accelerators that you're putting these samples in front of to mimic space radiation because it's something that you know you don't get here on Earth. So this is this is NASA's interest. And again it's about cancer risk but it's also about how cancers grow and how do they develop. The NCI is is interested in the very same kind of thing. How do cancers grow but they're not interested in space radiation. So the NCI integrative cancer biology program which we are awarded and which is also partially funding this lecture tonight for their what we're looking at is the dynamics of cancer growth. So just this is

very briefly let me just say and this is sort of the only bit of real science that you'll see on this in the next slide is that when you start to get a cancer and cancer grows a lot of people think OK you've got a cancer or it just takes off and it gets bigger and bigger and maybe you get a metastases and that's it. But it's turning out that the dynamics of cancer that is sort of how they course through time of play is very different for different cancers. And you what you find out is there's actually a lot of cancers that grow and then they stay sort of dormant in your body and I'm going to come back to that in a moment. And we have individuals in our lab who are studying this and whose expertise is this. There's also work now that showing that tumors can regress that you can have tumors you could have breast tumors and then you go back people that have just decided not to be treated that go back and get another scan maybe some years later. And there is no tumor there. So the whole big issue about when you treat when you don't treat I'm sure you've you've heard a lot about this before but it tells you that there's there's a lot to be

learned about looking at the dynamics of cancer. As I say dynamics is something that modeling and mathematics handles very well. So this is just the one piece of information that I'm going to share with you because I think this is something that's important and interesting to a lay audience. And what this says is that. Beyond tumor's as we spoke before just growing in your body and keep growing tourist can be in your body and they can be dormant in your body and you might not even notice you have them. So people can live with tumor burden. And it gives them with minimal tumor burden and it gives them no ill effects during their lifetime. The way this was determined was that they looked at autopsies and of individuals who had died from accidents and they found in these autopsies of people from age 50 to 70 that virtually all had small thyroid tumors. So essentially everybody has a thyroid tumor. OK. And in this older population

everybody has a virus but only 1 percent of people at this age are actually diagnosed with this. So what this says is you can have tumors you can have tumor burden and you don't have to treat. And you know you can you can live fine with these small donor tumors. And what we're interested in is how tumors stay dormant or how they escaped dormancy. But the other thing that I would like to say is this really changes the emphasis from what causes a tumor and what causes a person to have a tumor to sort of what causes a tumor to stay dormant or expand in your body. So it's not all. It's not just about what causes the tumor or what you're exposed to carcinogens you're supposed to. It's also just about how does your hand your body handle this tumor burden. And that's something that the NCI is funding us to study. So finally the third program we have just to give you this introduction is a program from the Department of Energy. And what the Department of Energy is interested in is something

similar to what NASA is interested in. But the Department of Energy wants to know not what is your chance of getting cancer from going to space. But what is your chance of getting cancer if you had you know a C.T. scan or if you have if you fly on an airplane you know if you get radiation or it gets into this whole issue about background radiation and radiation that you would be exposed to on Earth. So there again the same kinds of questions. What risk do we have for these tumors when we're exposed to these radiations and these three programs the NCI program the NASA program and the program are all based at this center in Brighton and all with the interest of what is the dynamics of tumors and how does radiation perturb this dynamics. So in this one it's very short overview of course I can't tell you all the projects that are ongoing in our

center and but there are there are two more projects that I just want to mention that might be of interest to you that are sort of outside the realm of these of these big programs that I talked about. One is the study of prostate cancer and you might have seen Dr. cherch at the Museum of Science recently. He's the chief urologist and he operates on more prostate patients in New England than sort of any other surgeon and he does this using a robot or actually does it using several robots. Now we have a collaboration with him where when they remove the prostate tissue then we get both the normal and pieces of the normal and pieces of the tumor tissue from individuals who have signed and who have decided they wanted to give consent for us to do this to then bring these back to the lab and have this human tissue augment our ongoing prostate study. A cancer research study that's ongoing. The other thing that I wanted to

mention is the angiogenesis a large number of individuals that are here working in our bright and center worked with Judah Folkman at Children's for for a number of years. So we have a large number of people I think we have nine individuals in the lab who really were very significant in our collaborators or Team members of your focused team. So we have an extremely strong and eugenicist group. We also have individuals at the center that are working with us that are in the cardiovascular part of the center that worked with Jeff Wizner when he was around during Andrew just so so Andrew Johnson is extraordinarily strong at our center. And this is both these projects will be things you hopefully hear about in some of our next. Lectures. So the final thing is again this is the first in our public evening lecture series sponsored by NASA and the NCI because they're interested in the systems approach and they want to

as I say educate them the lay public and that sort of next generation of scientists and our fall public lecture will be given by Dr. Clement who's and her title is How to starve a hungry tumor angiogenesis an anti introject treatment. So hopefully you'll mark the calendars for October 4th and we'll see you again. Thanks. This. So good evening everybody. It is my honor and a great pleasure to introduce tonight's speaker. I met Mark Chaplin for the first time as an undergrad student some 11 years ago. Now when I had the opportunity to do an internship in a slap in Scotland I was so intrigued by how one can use mathematics to describe such complex and puzzling phenomena as cancer that I decided to obtain my doctorate degree by studying Bismarck in Scotland and studying solid tumor growth and radiotherapy modeling over the last 10 years. Mark has been a great mentor and we have become colleagues committed to furthering the use of mathematics in

medicine. Professor Chamblain is the head of the division of mathematics at the University of Dundee. He's the chair of Mathematica biology and he leads a research group of 25 students postdocs and grad students. He's a dedicated teacher graduate student supervisor and research advisor. Every summer he organizes and teaches a summer school for fifth graders. To introduce an early interest in mathematics and how mathematics can be used to study everyday problems he has received a number of prestigious awards including the London mathematical society Whitehead prize and became an elected fellow of the Royal Society of Edinburgh in 2003. Furthermore Mark is part of symbiotes the Scottish informatics mathematics biology and statistics program and has served as the president of the International Society for mathematics biology. My chaplain has been part of a very successful European framework which was called using mathematical modeling and

computer simulations to improve cancer treatment and recently received a multimillion dollar European Research Council advanced investigate a grant which is called from mutations to metastasis. Multi-skilled mathematical modeling of cancer old and spread. Professor Chaplin added a number of books wrote numerous book chapters and has authored and co-author of more than 130 peer reviewed publications. It's a great pleasure to introduce mark as to speak of the scent of cancer systems biology first public evening lecture and without any further ado I would like to welcome to the podium My longtime mentor and collaborator Professor Chaplin. So thanks very much for that very kind of action and some of which was true. It's a pleasure to be here. It's my first time in Boston and I really appreciate you taking the time to attend a lecture with

mathematics in the evening when you might be watching the Red Sox or something more interesting. We'll get to that in a minute. So just to put things in context like yourselves I'm a fellow east coast person it's just a little different these Coast AM. Most of you didn't know Dungy is on the east coast of Scotland just slightly north of a morphemic city Edinburgh which is the capital of Scotland. And we benefit from East Coast weather and not as nice to see a Pops with plenty rain and sunshine looks through their lives. And I'm originally from Dundee as well were studying and I spent a little time away in England but I managed to get back home. Some years ago when I've been there ever since we were when I met Haikal and also like Boston I support Celtic and the real Celtic. Unfortunately Celtic back home didn't do it justice but they did it just as badly as the Boston Celtics.

They were defeated by the archrivals and the world series but the Scottish Football League. But I'm here from visiting relatives in the stove in Long Island and unfortunately I must have picked up some bad habits on the way and my own feel I'm a Yankees supporter. Boo who exactly. Audience participation that's good. So that's a little bit of my background so any more ado let's get into the part of the half of the talk the night was on mathematics and house on console. So am the mathematical part actually in my experience as being a mathematician. I don't know only two reactions to people. It's not pretty it's not very socially good thing to be a mathematician apart. Is it only just people up there are generally two reactions. First one is this they move to the opposite side of the room to get another drink or if they do manage to say something is usually there but that most was the worst subject we ever did at school. And they are going to tell you how they hit the subject and that's of no use. And so

you go under without politely. I hope I can convince you that maths is useful and it has applications for cancer but I've actually got a very nice job because I actually actually do modeling for my job. My wife doesn't know this but she thinks I'm just a sideman that sits in an office but I really really have a good good time modeling. I like to think that we also reduce supermodel's not just any more. So I really have a very privileged job. So anyway what are mathematical models and are they any use. So before I get into the concert I just like to put mathematics in context and everyday situation because I think I know math is used in everyday situations that you may not be aware of and it is actually a very useful subject that underpins a lot of things in society. But I'm going to tell you this evening it is really going to be wrong. And this was said it very elegantly. Fifty years ago violent shooting is what some of you may have had. Famous in the war for tracking the Enigma code and Alan Turing has a nice quote saying

that all models are an approximation because what you're trying to model is very complicated so you have to simplify things in an approximation and ultimately a falsification of reality. It's just that some models are less worse than others if you like but a good model will retain the important aspects of the system that is trying to look at. And in doing so and provide useful information about a complicated system so that that's a key part of our modeling you have to make certain assumptions you have to make simplifications but you have to and Lynde's put it very nicely in the U.S. here. The system's biology where you've got a huge range of people with different backgrounds from biology from surgery from cancer from computation from mathematics and they're all using their own different backgrounds to put together to form something that's bigger than just the sum of the parts. So in terms of maudling I didn't know what Lynne was putting on place but a few things of really are connected because the nice picture of the rocket

the way the not so rocket Saturn 5 or whatever it was going up into space. The mathematics for that was done a long time ago by Isaac Newton. So it's sending a rocket into space. It's really very straightforward. It's just between 60 and 87 and you know 1969 the 50s and 60s when rocket started going up. It was just a technological matter. It wasn't a scientific problem because Newton's laws of motion can tell you how to get something into space. The technology in 1967 wasn't there. You know a few hundred years to catch up. But you're intellectually The problem with so many hundred years. And it's all done. His new his second law of motion which says if you apply a force to an object it moves and it accelerates and and some bodies that you apply forces to are more complicated. A rock it's just a static thing that you can stand up and it comes back with a feeling at a sale. A sail was a far more complicated thing to deal with. So that's the first problem if you're wanting to

model biological objects they don't behave like lumps of iron which just behave and go up and down and even the laws of motion the fun will come back you know those of you are old enough may remember this man. This is an example of how mass is used. And so Mr. McEnroe 30 years ago used to shout and scream You cannot be serious. The ball was out of arguments with the umpire of course and the tennis ball is just an object that are being Newton's second law of motion and you can write down the mathematical reasons. Don't worry I'm not going to show you too many equations this evening but these are Newton's Second Law of Motion describing motion of a tennis ball. That's really and this is a simple model because we're only assuming that gravity acts on the tennis ball. Let's just ignore the resistance. You can solve these equations mathematically and you can predict where the tennis ball is at a given height for a given distance. And if you're wondering how this helps nobody with tennis this is really what's behind Hawk-Eye system. OK and this eliminates John

McEnroe's complains to the umpire. It might make tennis a bit more boring when you don't have the pantomime of John McEnroe arguing with the umpire. But you can find out if the ball was in the right. And this is all done with mathematics solving equations of motion for the tennis ball. But as I say a tennis ball is a simple thing. It just is hit and it moves and it is incorrect and I'll come back to this later with sales sales are unfortunately not like tennis balls and more complicated so that's what makes modeling sales and cancer more challenging. Another good example of applications of mathematics to everyday life is in weather forecasting and basically the weather forecast is just the prediction of how the atmospheric pressure and clouds will move over a given country. But underlying that there are mathematical equations. Again if you apply Newton's Second Law of Motion to a fluid and you can treat the atmosphere as just a special type of fluid and you apply forces to the fluid the fluid will move. So if

you knew the weather at one point in time and applying it in second law of motion and these are more complicated equations because the atmospheric The weather system isn't like a tennis ball moving it's far more complicated directions. So these are three dimensional equations predicting how the fluids are above. UK is moving in space and time. So he is x y z space and he has time. And if you have a knowledge of the weather at this point in time and you take data measurements from satellites and pressure and moisture content and temperature then you can put all this information into these equations and you can you solve these equations with some hyper computer and you can predict the weather changes over time. Now again you're all aware that not all weather forecasts are accurate over long on time. And some of them even argued over a short time and that's because these equations are not completely accurate to describe the complicated

weather systems on earth. So there are some times that you've got to it or there are errors in the way you solve these equations computationally which over a period of time will build up into bigger errors and eventually your estimated solution computationally will diverge so much from the real solution that the weather forecasts won't make a good prediction. But underlying all these every time you see somebody on your TV telling you about tomorrow whether somebody behind the scenes or a lot of people behind the scenes of solve complicated mathematical reasons in order to do so you can yes. So this is just so you know sometimes they get it wrong. Some things are predicting sunshine and suddenly they'll make a bit of a mistake and it's not so good if you're caught. And so these systems differ if you think of the original tennis ball in mathematics that's called a linear system. That means that you can make small changes to your system and you don't get big

changes in the grid. So if John McEnroe who serves at 85 miles an hour to you already seven miles an hour it's not making a big difference it's still difficult to return it. But if you have a small difference in a weather system that can lead to wildly different conditions later and I'm sure you've all heard of the butterfly effect the way the flapping of a butterfly wings in the Pacific makes a storm and somewhere else in the world because a small change at one point in your system can then lead to big differences later on in in time. And modern mathematics is actually good at trying to work out these small changes what effects it will make in a complicated system. So these systems mathematically are called complex nonlinear dynamical systems and as Lynn was saying modern mathematics are good at making predictions if you know information about the system at this point in time mathematics can predict how that system will evolve and develop into the future.

And in many situations that's very useful to know what's going to happen in a few days time. So if we move more into biology it may be a novel thing that mathematics and be applied biology but a little bit of historical contact to Dundee about a century ago rather elegant Victorian gentleman called Professor Darcy Wentworth Thompson to get a name like that these days wrote a book called on growth and form. And this was a very early attempt to apply mathematical principles in his case it was geometry he was interested in the shape of shells different shells trying to work out similarities between different shapes shapes of cells and horns on animals and feed on animals and skulls of animals. He was applying mathematics and geometry to try and make predictions about how biological things changed and he said it in a quote from his book sale

and tissue et cetera et cetera. There are problems in the first instance or mathematical problems essentially because biological things are a little more complicated still will be the same laws of motion that a tennis ball will be so that people have been applying mathematics to biological and medical problems for perhaps a little longer than you may be aware. And that's also an ice contact sort of contact to University of Dundee if you're ever in the mathematics department and we've got a very very nice portrait of this mind in our coordinates. It's a very striking portrait it was very interesting. And he used to teach it it used to teach with a parrot on his shoulder and I don't know how the students are and that certainly if you talk with the parrot on your shoulder the day you will be put in jail by health and safety people. So he was a real real real character. So kind so a try to predict how a cancer grows and sprays

is really very similar to trying to work with a systems change except that and unfortunately a cancer and pretty much all biological systems are even more complex than a weather system and weather system is a very complicated system. So but even with systems complicated I don't think that should stop trying to your base to start modeling things and trying to make predictions. So that's what. I'm going to focus on. And so the next part of the talk will be on concert in order to try and motivate maudling So I've given a general overview of how maths is useful in daily events that you may not know where to look tell a little anecdote about. And the essence of good modeling. OK and this is a little joke. Once you've had the joke you can modify it to tell any two different parties that you may want to you'll see.

OK so goes because assume that three mathematicians and three biologists. They're going to a conference and the boat is just being well organized people who turned up at the train station on the time they went to the ticket office and they bought three single tickets to the conference destination and stood on the platform to wait for the train. The mathematicians not being well organized people ran into the last minute and went to the ticket office and only bought one ticket. So the well was just Although there's talk about collaboration and people getting together is always a bit of competition. In any system. And so the bosses were quite smug that the mathematicians were only giving one ticket and were anticipating some problems. And when they got on the train. So they both go on the train and they sit in the same carriage and of course the ticket collector eventually comes and goes. It's a really smug at this time because they think something bad is going to happen. But as soon as the ticket collector enters the college the mathematicians leave at the other end of the carriage and go in the toilet. So the ticket collector goes through the college getting a movie ticket and he comes to the toilet and knocks on the door.

And the mathematicians just put one ticket at the ticket collector stamps it puts it back on the door and carries on. So the mathematicians come back in the carriage and know they're looking smok. So they go to the conference and they have a good time as you do at conferences sometimes and then on the way back. And the same thing happens they're both just still well organized turn up at the station on time. Go to the ticket office and buy one ticket and go to the platform. Mathematicians or even late of his time run on the platform get on the train just as it's leaving and don't buy any ticket at all. So the bowsers really think there aren't a good thing here they just can't lose this time and sit down. Very smart The mathematicians are really going to be in trouble with the ticket collector who in due course appears in the cottage at which point the ball's just run to the toilet and lock themselves in. Then the mathematicians go to the toilet knock on the door take the ball stick it and hide in the other toilet.

And at the end of the day they think a collector takes the mathematicians stick it gives it back but throws the ball just off the train because they don't have a ticket. So the whole point of that story is that you don't want to model a system unless you understand the system. So in order to model cancer at it you really should start. If I'm a mathematician it would be easy for me to just ignore all the pathology textbooks and speak and semantics and just blunder in and start writing things and equations I think should more cancer but that wouldn't get me very far. So in order to model cancer I had to learn a little bit about cancer learn about the system. I was wanting to model in the first place. So here is a quote from a textbook. This is what a cancer is. As you may be aware it's essentially a disease of cells so any cells that are about 10 to the power of 14 cells in the body which is a lot of cells one with 14 zeroes after that and in some sense it's surprising that you know more people don't get cancer because that's a lot of cells and being a disease of the cell it only takes one cell to go wrong you can get cancer.

But and so the body has mechanisms to keep check on its healthy cells to make sure they're doing the right jobs. They differentiate it through the dye and they are replaced by other cells but a tumor in my morning focus on solid tumors that's tumors that are rising in tissue rather than for example leukemia which is a cancer of the blood. So tumors and cells that have gone wrong and essentially gone wrong and the key point of the proliferation the proliferate excessively and keep proliferating and growing. And so that's why you get a lump of tissue that forms that's not normal tissue. And if you look at the technical definition it's a mass of tissue that's formed as a result of abnormal excess of an inappropriate proliferation. The growth continues indefinitely and it escapes all the growth control mechanisms that the board has normally to keep things in check.

So it's a disease of the cell. And a little graph showing what happens if you don't treat a cancer it just keeps on growing and growing and growing fast becomes visible when there are ten or five or eight cells it becomes you can feel it you've got a tumor of the kind of apparent brain cells. And then if it grows to $10 per 12 cells you die. So I'm not good on American and UK billions and so anyway it's a lot of cells in a cancer and eventually unfortunately as you know people people die. But it all starts at the cellular level with various things interacting with genetic components in the cell nucleus and we These create genetic mutations. So there's something wrong with genes. And so those mutations are passed on to the daughter cells and that results in normal cells doing things that they shouldn't. And you get what's called transformed cells which then lead to cancer cells. And one of the key early change is an excess of proliferation which

leads to this lump of tissue. And in terms of solid tumors there are two main phases of the growth of a soul a tumor in the body. And you can grow these in the laboratory because that's a good place to look and examine and work out what they're doing. And then the Laborde either grown as multi-cellular or steroids and these grow to around about a million cells and as Lynn mentioned some tumors of the bill are dormant and these and multi-celled steroids or vascular tumors are something called and stop growing at around about a million cells. So there are about two millimeters in diameter. Here's a picture of one of these as you can see there really are like little balls of cells and they stop growing basically because of a lack of nutrient supply. And they are and they gain the nutrients from the surrounding tissue by diffusion of oxygen. But that can only sustain the growth up to a certain size and

after two millimeters in size if you kind of take a slice through these models as far as you see a very well-defined internal structure. On the other side there are cells that are alive they're proliferating. They can actually have access to the oxygen that's inside. But cells towards the center because they're far away from the oxygen supply and all the proliferating cells are using up the oxygen they die and become what's called necrotic. So that's just dead useless cells surrounded by life cells. They're also in between these two regions. There's also what's called acquiescent region. The cells are either dead or alive and they can become related proliferating sales of the oxygen supply becomes improved or if the oxygen supplies worsens they become a chronic. So there are three distinct regions inside these solar tumors and they stop growing at a small size and if that's all that every cancer did then.

Ali anybody would die because something is two millimeters is hardly detectable let alone cause you any damage. But unfortunately that's not what the cancers just don't stop there. They've evolved mechanisms which allow them to spread further. And one of these mechanisms involves secretion of chemicals which eats away at your healthy tissue and slows the cancer cells to spread into the tissue. In this rather irregular shape and the technical term for one of these solid tumors arising from empathy tissue is called a carcinoma. And that comes from a Greek word for Crab. And so the ancient Greeks were aware of cancer and they could see these these types of tumors in ancient Greeks who died from cancer and they could see the shape and that's why it's been incarcerated. And and unfortunately this does not remain localized it penetrates into the tissue.

And if the rany as we see in the next life any blood vessels nearby or in the lymphatic vessels these kinds of cells can get into the limb system in the blood system and then be spread throughout the body and you get second which humans are metastasis. And a key escape route and for cells to spread through the body is the process of angiogenesis which I'll touch on in the maudling and Lynn has already indicated that you know this is a lot of this work was initiated by Judah Folkman here in Boston and I'm Chuma angiogenesis involves the creation salesroom a few slides ago in an multi-celled spheroid screeding and eugenic factors. These are chemicals which stimulate the growth of new blood vessels Normally blood vessels are very inert structures. Their sole job is to slow the passage of blood through the body and not to lower the blood to leak out. But these chemicals that are secreted by the cancer cells

affect the endothelial cells of blood vessels and stimulate these endothelial cells to grew into new sprouts and new vessels. These vessels form loops and then you get blood flow through these loops and eventually these new blood vessels connect up with the tumor and blood gives oxygen to the tumor. And of course the cancer then expands and far bigger than two major sites in the book the candidates can also get into the blood vessels and are transported through the body and then can land in the brain of a breast or whatever. And secondly sites. And if you have a static spread then almost surely Unfortunately you die. So just to summarize all that with a little movie. So we have a sale which goes wrong and it's genetic mutation material leads to excessive proliferation. So we then have the formation of the very early

stage of a tumor. These these green cells are the lump of human tissue. Which then grows the size of a few millimeters and stops. But then co-op's the blood vessels to grow towards it or uses blood vessels that are very close to it. These blood vessels then supply the cells with oxygen which allows it to expand more rapidly and then crucially as we see just in a second. We can get invasion of the blood vessels by a little conses are we going to see a little green say lookee here. So this is a cancer cell. There's no go inside the blood vessels and because of the flu in the blood vessels it's transported throughout the body and then is it starts the whole process again process again in a secondary location in the body. So it starts to grow you know sort of once human to change. And of course the start of tumors can themselves spread. And that's very complicated and almost

impossible thing to treat. So trying to understand cancer and in all its complexity is is a big problem. And I'm not going to try and focus on some modeling which hopefully will show that mathematics has something to see as provide some insight into how cancer this is grows and develops and how we can feed back information to all the experimentalists and clinicians who are working hard to to cure the disease. So first of all let's go back to this and nothing else Fairlight and examine the structure there just to remind you that it grows to a size of two millimeters through limitations of oxygen. So as a mortal we've looked that tries to look at how quickly it grows and when it stops and the size of the necrotic core and the size of the region and this is important to understand the structure because as we've seen these quiescent cells that are the ones that secrete the angelic factor that in just the blood vessel growth.

So here's a little mathematical model. We've got some mathematical equations which describe how the cancer cells grow in response to oxygen and we've got an equation for the oxygen which tells how it's distributed in the tissue and that feeds back into the cancer cells and allows them to proliferate and grow. And we're going to look at the normal cells and the necrotic cells. And I also have another question for the cells. So we've got three equations for the cancer cells and a mathematical equation for the oxygen the cancer cells eat up the oxygen which then changes how the cancer cells react. And that's the general framework. It's a little bit more complicated than making out here. But just to give you a flavor that we now have to solve these equations using computational techniques rather like you predict the weather. And here's a little mathematical simulation. So we put a little bunch of cancer cells at the start the red cells the rate we're going to be proliferating and then and blue are going to be essence and brain are going to

be necrotic. And this is using experimental data. It's easy to write down a bad model and right then find the simulation that looks as though it's giving you results. But the more that we produce as the Good morning gets done and the consensus in both the center uses experimental data to fit into the model to make quantitative predictions as long as we're ready to. So this is simulated on a four millimeter sized domain with a very small bunch of cells in the middle and that's going to be using up some oxygen that's been Sarette been distributed in the tissue. So just play the movie and what you can see happening is that because of the oxygen distribution the cancer cells are now beginning to grow and proliferate and expand. We've now got some blue cells here. That's because the oxygen in the middle. You can see here there's a dark color so that's a low concentration. If you have a low concentration in the middle that's not enough to keep the cells proliferating so the

cells in the middle because of the low oxygen of on blue which means that yes. But they can still expand and no you can see a slightly later time in the simulation. This is 18 days. We now have some brain cells in the middle and that's because the oxygen concentration has dropped even lower which isn't enough to sustain the cells. And so they die. So that continues until 45 days. And because we worked hard and got the equations sort of correct our little mathematical models Freud had stopped growing at a size of a few millimeters in diameter with a nice rim of proliferating cells on the outside and quiescent cells in the middle and then necrotic cells in the center. So this is no really maudling the figures we just saw with a slice through the markets elsewhere that we saw experimentally. And so we know we can change some

parameters in the model we can say what happens if the cancer cells use up the oxygen more quickly or if the oxygen is limited by you know shutting off some blood vessels and we can make little predictions about how that affects the growth of this vascular tumor. So the next mortal's that we've worked on in a department and focus on angiogenesis and see all the androgenous all the human induced angiogenesis work is done to Dr. Judah Folkman who worked here at the Children's Hospital in Boston and and in the early 70s he posed the hypothesis that these evil sickle of tumors were limited through their oxygen supply. And so the regenerated blood vessel networks through coopting the vessels with some some some some chemical factors goals and objectives and he is a classic experiment that was and that arose from

from the model of Dr. Folkman. This is the eye of a rabbit. And at this point here is either a little pellet that's been soaked in one of these factors to get the blood vessels to generate or he can actually put a little solid and mucus elsewhere or there but the net effect is the same. As the blood vessels that are here in the thigh. Normally you don't get all these new vessels but because of the implant of the tumor even just these new blood vessels to grow through and eugenic factors. And this is a little schematic as to what happens you implant the tumor of a pallet soaked in factors a few millimeters away from this and mean vein these main vessels. And after a few weeks you get the growth of a completely new network of blood vessels which connect supply the tumor with oxygen and allow it to expand to a far bigger size and also allow the cancer cells to escape.

So again we have some equations and these are equations describing how they end the fetal cells of the blood vessels respond to these factors in the Matrix I don't want to dwell too much on that but just to look you know behind all these computer simulations there are some quite technical mathematical details. But again here's the output of our simulations. So this is an experiment where we have one of these pellets and you get a nice object response from the blood vessel. And this is our computational simulation we've mathematically put a little pellet here and we've got a mathematical pin vessel here. And our model predicts the growth of a blood vessel network which is rather similar to the experimentalists. And then when you hit your next grant and you get a bigger computer you can do it in three dimensions. So this is a two millimeter cube of tissue. And we've got a parent vessel here and we get a nice and you can color and read and make it look like blood vessels. And in this case we've put a little multi-celled spheroid in the center of our

domain and we get blood vessel growth from the surrounding tissue which grooves in and connects up with the veins and for example what you can do with a mortal. Is that no with the model you can really zoom in and look at these complicated structures experimentally if you look at the microscope all these vessels are a real mess. But no we can begin to examine just how they are connected and where the connections are how many connections there there are from one vessel to another and really try to make predictions on the structure of the network because the main function of blood vessels is to carry and transport blood to the body. So knowing the structure of the vessels will determine how the blood flows. And this was the next stage of our Maudling. And rather than just generate nice hollow vessels we wanted to put some blood flow in. Because the blood not only oxygenates the tumor but the blood actually changes the

vessel sizes. And so the the structure of the network adapts to the flow of the blood that's in it. So here is a simulation of a model with blood flow through it. And what you're going to see is initially we've got all green vessels coming off a pier vessel that's at the top and green means that the vessels are rather small and narrow. And as the simulation runs you're going to see the colors change to more orange and orange or wider vessels. So the flow is going to make some vessels larger and some vessels as small as so here's a simulation running. And initially we have some blood flow through it goes through to the bottom and then as you see some orange start and this is a thickening blood vessel to red blood vessel. So at the end of the simulation what's happened is that. We get only a very few thick red blood vessels which carry

almost all of the blood. And the other blood vessels have been taken away because if they don't have blood flowing through them they naturally are wasted away. And so the blood doesn't flow through them. So the the flow itself is adapting to the network into some very efficient path which is taking all the blood through. No you might think this is a bad thing because if you have a cancer here so the tumor here is getting oxygenated by these blood vessels. That's a bad thing. However angiogenesis is a two edged sword because if you have a very good blood vessel network like this with good flu what you can do is put in a chemotherapy drug. And we can no mathematically predict how much chemotherapy drug is getting through our network and how much drug is reaching the cancer cells in a specific time. And the structure of the blood vessel network is clearly very important here because if you have some networks that are very badly connected and you give a chemotherapy drug

then the chemotherapy drug will not reach the concepts and I'm sure you're all aware of it. And although chemotherapy drugs can be very useful and a lot of them can can cure patients they have terrible side effects. So you don't want to be giving a chemotherapy drug if it's doing a lot of harm to the patient. At the same time it's trying to cure the cancer. And delivering the chemotherapy drug really is about getting it across this blood vessel network that is being induced by the concert itself. And so the flow and the connections in this blood vessel network are crucial to the rate of delivery of the drug to the cancer. Now the modeling that we do can indicate how connected the networks are. Is it an efficient network. Can you make changes to the parameters of the model the viscosity of the blood give warfarin or something like to thin the blood because that affects the structure of the neck. So can you adapt the network to get it into efficient flowing system. Well you can give chemotherapy drug very effectively and get the

chemotherapy drug all the cancer cells and do the job. Rather than hanging about in the system for a long period of time with nasty side effects. So moving on to the other bad aspect of cancer growth the invasive aspect where we again rather than having a localized spherical mass we have secretion of chemicals which degrade the body's tissue and although the cancer cells to spread in this rather heterogeneous way which make it again treatment different for in a way that I'll pick up in a few minutes. So again we looked at the system closely and read experimental literature and try to work out the key variables in the system where some cancer cells were ex-sailor Matrix and we have various chemicals which do various things to the Matrix and degrade them and we have an inhibitor which tries to counteract these chemicals that the cancer cells are secreted. So we can put all these into

mathematical equations and again try and solve these equations computationally and make predictions about how a cancer will in the tissue. And these are the computational results from our simulation of this. This again is meant to represent some tissue domain of a few millimeters in size. And we've got some cancer cells in the middle of the tissue which over a period of time then begin to spread into the tissue by degrading the the tissue and migrating and proliferating in. And you'll see that over time they don't just invade is a bigger circle of cells they have a rather heterogeneous distribution and if I make this a bit clearer what I've done here is put a white line around 99 percent of all the cancer cells. So inside this white line or 99 percent of the cells. But unfortunately although the resolution on this might not be so good unfortunately

outside this white line there are a few cancer cells. No. Another way of trying to treat cancer is to surgically remove the lump of cancerous tissue. And and this is what's called a visible margin and many saw that humans where the surgeon knows that inside this white line it's cancerous tissue death outside it. It looks as though it's healthy tissue. But the surgeon will know from experience that if all he or she did was to cut around this white line that would run a high risk of leaving a few cancer cells in what looked like healthy tissue. And unfortunately because cancer cells are so mutated it would only take leaving one or two cancer cells in the tissue and then the patient record would have recurrence of cancer a few years later. So you're not really cuing the patient is just delaying the onset of an of another kind. But with a mathematical model like this what we can do

is again this is a theoretical model but it indicates the potential of mathematics because and if we have patient specific data so we can put biopsies and parameter data in the tissue of the patient and we can work at the stage and greed of the cancer cells and parameterize the growth of the cancer with patient specific data. We can start to make predictions as to where at a certain point in time the concert is located. So at this point in time the model would predict that 99 percent of the cells are in the white region but 100 percent of the cells are enclosed in this rate cut. So by having a dialogue with surgeons and getting enough parameter values in theory we could make some quantitative predictions as to how much of the tissue a surgeon should cut out in order to make sure that all of the cancer cells were and were removed and none were left. And again that's all done using computational simulations of a

mathematical model and here's just an illustration with some colleagues at the local hospital in Dundee which is the teaching hospital of the university. And here's a mammogram of a patient with. A primary breast tumor. And there are some spread of the cancer in two regions away from the primary location. These small fragments sort of broken off from the main tumor mice are in this case big enough to be visible on a mammogram but you can imagine that there may be other small fragments which aren't visible at the resolution of this mammogram which are elsewhere. And again that's where a model could come in and make these predictions and help the surgeon make a good clinical decision on this particular patient. And here's some other recent work that we've been doing again with colleagues at the local hospital in Dundee that they've done some in-vitro experiments of invading cancer cells with different malignancies of cancer

cells and with different malignancies at the cancer penetrates a different depth into the tumor much is different depth. But you've got all these different patterns of invasive painted penetration. And our computational models again are beginning to match up and indicate the reasons why some cancers envied less of a depth than other cancers. We were changing parameters are a mathematical model and this simulation matches this part of the experiment where you have a very heterogeneous distribution of cancer cells which has penetrated deeply into the tissue. This simulation is matching here where you have a late penalty of death unless heterogeneity in the tissue. So our models are using parameters from the original experiment and then we are changing parameters in the model and feeding back extra information to the in this case the experiment. Now all these models so far of just treat the cells essentially like tennis balls the

behave. You give them a force and they move but of course cells aren't like tennis balls. Cells are pretty complicated. And just to give you an analogy and this isn't my car by the way unfortunately so this is and is a car and I'm sure you'll drive. And as we know driving is very useful it gets for me to be and we probably couldn't live without cars but I'm also certain that hardly any of you would really know how to fix a car if it broke or how to make a car move faster and make it more efficient. And it sounds a little like that if you open the arm it's not the bone under the hood. If you open the hood you get into the engine and the engine is out of the car and works. So a sale is a little like that if you just move this schematic. Here's a schematic diagram of what it's like under the hood of a cell. OK so it's just not like a tennis ball inside with empty space. It's got all sorts of things happening which these are called

signal transduction pathways which are essentially proteins inside the cell controlled by genes in the nucleus. And these proteins that make the cell bill these are the engine of a cell. So if you mess about with ease you can make this go faster or you get it wrong you can make the cell go bad. And of course in concert a lot of these policies are mutated and that's what's causing the cells to go wrong. So really to try and get a better and mathematical models we really tried to take into account how these pathways affect the sale at the same level and home sales interact with each other governed by these internal pathways. And as Lynn has indicated one of the key things that are in the Mormon community this is a multi-skilled maudling So you're not just modeling a sales or tennis ball with nothing else happening you're modeling yourself with things happening inside it then signaling to others that that makes the model more difficult. So rather if you remember a few slides ago I had three equations for

cancer cells and the oxygen. Now we've got 19 equations which are maudling various signal transduction pathways inside one cell. And no we are trying to put together many cells in a multi cell scale model so here's a simulation of home and a single cancer cell tumor may arise. So this is a starting off from one cancer cell and inside the cell we are modeling lots of signal transduction pathways. At some point the cell will see it'll change color and it will divide the change in color is representative of the adhesive properties of cells the cell and that's very important for cancer. And because one of the hallmarks of cancer is a loss of it lesion to the cells and that's another way that it starts to move through the tissue. So you can see that some of these cells are yellow which means a reduction in their adhesive properties. And if other parameters in the model change then you'll see that the cells don't stick together.

They can move a part of it to the cells. He will start to break away. So the cell he didn't know detached from the main body. In this simulation what happens is the other cells proliferate more quickly and then catch up the cells. But again this is simulating cancer that are very very early stage which is impossible to do in vivo because by the time it is detected these processes have happened along pain. So malting can really begin to shed light on what's happening at a very early stage. And as you can see the simulations indicating he's got a lot of changes in sales here in these different colors and the evolution of the cancer is not quite symmetrical it's quite heterogeneous. And again if we change some parameters we'll get a different scenario scenarios happening in cells beginning to break off and. Go into the tissue. And this is. Represented in this simulation where we've taken a tumor that stopped a few millimeters in diameter and now changed some of the adhesive properties.

And what you're going to see now is like the cancer cells have lost that region and they're beginning to invade the tissue. So this is a few three dimensional simulation in a tumor of human tissue. And this approach is allowing us to make predictions on the invasive properties of the cancer cells which are governed by these internal signal construction pathways which are what controls real cells. And again we can make predictions of this or that rate of invasion and the time of invasion. And again using this multi-skilled technique we've been able to start to morrow real crucial process in metastasis which is how a cancer cell gets into the blood vessel in the first place. If a cancerous cell doesn't get in the blood vessel it won't spread. And this is a bit dark. There's a little red cancer cell here and it's going to move along and interact with these and endothelial cells of the blood vessel. And

again you're going to see some changes in color. It's going to yellow and that's because our model has been able to predict the force that the cancer cell has to exert to break the bones between in the fetal cells in order to get inside the blood vessel and then get transported. So our model again can change the parameters. And we can get situations where the cancer cell count exerting the force or the end to see our bones are too tight that the cancer cell can get in or we can make other mutations in our model to make predictions again over for some time. Things that can really be measured nowadays with things like atomic force microscopes and really get to the heart of the key processes which facilitate or facility and interview Zeeshan into a blood vessel by cancer. So just to finish off with the last simulation and and one nice part of maudling is when

over a period of time you have different components of your model come to kind of maturity and you can start putting different models together to make a bigger model. And this is what we've done here. If you remember back a few slides I had the moral of the cancer cells on the oxygen and it stopped it for five days with proliferating cells and cells and necrotic cells. And no we use this moral in our own eugenicist moral and put the two together. And so what we're going to see you know is that we've a vessel here it creates an cells will secrete and eugenic factors. And then the blood vessels will grow the flu will grow through the blood vessels and when the blood vessels connect with the tumor then it will get various nice interactions that we wouldn't be able to predict with a mathematical model. So you see what we've done is we've grown the blood vessels and we've now got an blood flow that is essentially the blood. We've got an oxygen distribution and we can work out the size of the vessels. So know you can see what's happening is that the blood vessels of connected with the

solar Chuma and they've brought oxygen to the tumor but because things aren't perfect and symmetric the oxygenation is not symmetrical so that the solar tumor is no growing in an asymmetric way. What's also happening to the the blood vessels is that when the get inside the tumor there's some internal pressure feels and the internal pressure field compresses the blood vessels and if the blood vessels are compressed that shuts down oxygen which makes the internal hypoxic interior region hypoxic again. And if it's hypoxic it'll keep more factors growth factors to trying to recruit more blood vessels. So you've got all these complicated feedback loops connecting up with each other. And unless you are a mathematical model it's very it's impossible to imagine what will happen if he connects with Beacon X with See you when you've got all these big box that by simulating the model you can see here we get the prediction that the

tumor will continue to grow but will develop in a very heterogeneous way and break up and will have multiple necrotic and reaction force. Now this is just a nice simulation at the moment. But again if you want to consider how to treat this or to given an unchanging Genesis drug or chemotherapy drug the structures that we're modeling and predicting you know of a very good beginning to the reality that it's very difficult to model in vivo because something like this in vivo is very difficult to capture even with something like a window chamber on the back of a mouse. That's still not what's really happening inside. So these models can really give a genuine insight into the complicated dynamics that are happening in cancers. So with that that's one of the latest models that we've been developing and pushing modeling techniques around further. So with that leave the modeling and get back to the the

title of the talk and answer my own questions you can cancer so you can cultivars cure of cancer. And unfortunately I would say no. And so but that's because cancer itself I don't think can be cured any more because it's not a single disease. It's not like the flu vaccine. The concert is a really complicated disease. In individual patients the same cancer will present in different ways and develop in different ways. And there are cancers from all siblings of the body. So it's not a single single thing that you can treat with one thing. So and of course that's known experimentally and clinically you've got to treat in multiple ways with multiple drugs with radiotherapy with surgery. And so although you can't calculous can't cure cancer I hope that this talk has shown you first of all that. Mathematical models can offer insight into complex biological systems

and the good mathematical models can be quantitatively predictive. If we get enough data from experimentalists and clinicians we can create good models which generally predict some cancers are going to grow and develop or get treated and then that mortal's really then can be used to feed back information to clinicians and experimentalists that they want to find out and not use the mathematical. When I give some of these talks to medic's which I don't know who's a medic but some medics get a bit bristly because you know mathematics is going to take over and put them out of a job. That's not true at all and just emphasize that you know mathematical models can certainly be complementary tools that can be used with other things that give insight into how cancer groups. So just to finish off with so Darcy Thompson again and to see that to emphasize again that basically mathematics is highly important for lots and lots of things and given enough information enough good

data parameters then mathematic mathematicians and mathematical models can do great things. I'll just stop there and thank you very much for your attention. You've got a microphone set up in the middle of the room if anybody has any questions for Mark. I think if the spitted on first has a slide on top the network find a way into a similar neighborhood that is disorder. Can you predict by your model whether the functions that we do not know and to predict what they will do. Well our model doesn't include any genetics. I mean we can only predict from data that we are given we can't

predict compain decks. You know it's not there. So if we include in our moral equations modeling certain routines and any predictions we make will only be for that system we can't predict anything that's not been discovered or known and model at the moment doesn't include any genetics so we can't make any genetic predictions because that's not the scale of our model. Our models really focused at the same level with. Some interesting pathways incorporated in each cell. And then if you simulate a few thousand cells together you're kind of moving towards the tissue scale. So we're moving from interstellar scale to the cell scale towards the tissue scale but at the moment our models don't have any genetic information. The other question that I have is like most of the models that you are sowing are basically about a group of cells. Yeah but in reality there are only very few cells that are contributing to that. Most of the cells that actually knocked out and love. Then

getting on them. Now because your models are based on this whole group of cells. How do you really explain this aspect impact the ones that are mostly these cancer stem cells that are doing the job. Well we're a lot of our models assume that cancer has been initiated and it's at a certain size and it's already exists. If you want to model things from the very beginning and look at you know the stem cell hypothesis or you can certainly do that. In fact a lot of the excellent modeling here is focused on that very topic. But what we are what we are turning the model is a lump of cancerous tissue that already exists. And we know that it's doing damage to the local tissue. We know that it's interacting with blood vessels. We know that secluding makes getting enzymes etc. etc. So that's where we're starting more because that's a that's a that's a that's a that's a fact that so many of us and most cancers present when they're at that stage you're not really worried about if it came from a stem cell or a mutated cell you've

got to deal with the fact that you've got you know a billion cells in a lump that are spreading locally in the long run in the brain or something like that. But you can also model things at the beginning. That's a different approach and that will give you insight into whether you know stem cells are responsible for the growth or mutate. And as I say a lot of the excellent modeling here is working on these hypotheses. I'm sorry that you took another commitment I missed that part of your presentation but I had a question. Are there examples where the predictions that the model makes in the best of input from existing knowledge is so striking that innocence anticipates new knowledge and leads the war over to a different

pathway in that research. Well at the moment our predictions I would say have been you know small increments. Unfortunately we haven't made any as shattering predictions but compared with say 20 years ago I feel has been a big big advance. I think 20 years ago when I first started it based on modal very crudely reproduced what was already known experimentally but. But but no the model was especially multi-skilled more I think really shedding insight into key processes. Mainly at this stage in a qualitative way. And if for example the simulations I showed with the mowgli's scale an individual based model what we were looking at was could hand be the Catinat pathway. And we've shown that if you do certain things that pathway you get changes

in sales with healing properties which then affect the development of the tissue left and the limiting factor is always going to be the quality of the data that you get. And we're aware of that and although we may have although we've perhaps got the correct biochemical schematic and written down the correct equations some of the parameter values the rate constants etc. are really really very difficult to measure. So to make a real quantitative prediction and can be very difficult. But the model can still be useful by giving qualitative indications as to what's important and what's not in danger. Another site like I've been living in Dundee for five years and to predict the weather in Dundee you don't hear such conflicting claims. If you say will rain to morrow you're probably safe bet Sanomat would be.

Here we have a bit of food set up on the back of the room. Please stay around for some coffee. I'm tired of it Barkworth people from our centre and thank you all for coming. Thank you.