tag:blogger.com,1999:blog-34755968545330631272024-03-19T04:02:23.616+01:00Philip Gerlee's ResearchCancer Modelling, Evolution and MetastasesPhiliphttp://www.blogger.com/profile/01689349973775910384noreply@blogger.comBlogger80125tag:blogger.com,1999:blog-3475596854533063127.post-42149938934442244162019-04-30T09:46:00.003+02:002019-04-30T09:46:49.281+02:00Plus-plus as a model of the creative processMy 4 year old son is currently playing around with Plus-plus, which is a construction toy not unlike Lego. The main difference is however that Plus-plus only has one type of brick (in many different colours), shaped as two joined plus signs (see figure below). The shape of the bricks has implications for how they can be joined up and consequently what type of patterns one can construct. For example it is impossible to construct a square since it will be jagged along the edges. Any shape you can imagine can thus only be approximately constructed with Plus-plus, and this is where my frustration sets in. I have clear idea of what I want to build, say a dog, but the substrate won't let me. I'm trying to be creative, but Plus-plus is putting constraints on what I can express. Of course the same happens when I build with Lego, but in that case I have already internalised the constraints and they therefore don't bother me to the same extent. I think the same holds true for any other creative process, such as doing research. The methods that we use for joining together known facts into as of yet unknown facts constrain our creative process. But most of the time we are not aware of our own limitations and happily build our jagged truths that only make up a tiny fraction of what could possibly be expressed.<br />
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Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-22963293378785196512017-03-24T13:29:00.001+01:002017-03-24T13:29:13.587+01:00"Bad luck" and cancerYesterday I was contacted by a journalist from SVT (Swedish public service) who asked for comments on <a href="http://science.sciencemag.org/content/355/6331/1330" target="_blank">a new paper by Tomasetti, Li & Vogelstein</a>. Time was short so I didn't have time to understand the paper in full detail, but the article contains some brief comments from yours truly.<br />
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http://www.svt.se/nyheter/vetenskap/ny-forskning-slumpen-vanligaste-orsaken-till-cancer Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-63760670300926977812017-03-21T14:24:00.000+01:002017-03-21T19:43:19.073+01:00The slope of solutions to the Fisher equationThis blog post describes what I believe to be a common misconception about solutions to the Fisher equation, namely that the slope is inversely proportional to the wave speed. I realised this during supervision of a Bachelor thesis when the students couldn't find agreement between the analytical result and their numerical solutions.<br />
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The Fisher equation is partial differential equation of the form:<br />
$$\frac{\partial u(x,t)}{\partial t}=D \nabla^2 u + r u(1-u)$$<br />
where <i>u(x,t)</i> represents the density of cancer cells at time t and location x, and the parameters of the model are D, the diffusivity of cancer cells (i.e. how fast they migrate) and <i>r</i>, the rate of cell division.<br />
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The Fisher equations exhibits travelling wave solution, i.e. a fixed front profile that is being translated in space as time progresses. These solutions are typically characterised by their velocity <i>c</i> and slope <i>s</i>. It has been shown that the wave speed is given by<br />
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$$c=2\sqrt{Dr}.$$<br />
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A partial proof of this can be found in Mathematical Biology by James Murray. In the same book it is claimed that the slope<br />
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$$s=1/4c,$$<br />
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which implies that faster waves are less steep. This statement is accompanied by the below figure.<br />
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Substituting the expression for <i>c</i> one is lead to believe that<br />
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$$s=\frac{1}{8\sqrt{D r}}.$$<br />
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This expression is never mentioned in Murray's book, but I would claim that the presentation is quite misleading, because if one looks closer at the analysis that leads up to the statement <i>s=1/4c</i>, then one finds that the analysis is done on a non-dimensional version of the Fisher equation, which has wavespeed <i>c = 2</i>. This implies that the statement <i>s=1/4c</i> simply means <i>s = 1/8</i>.<br />
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If one instead carries out the exact same analysis on the dimensional Fisher equation one finds that<br />
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$$s=1/8\sqrt{r/D}.$$<br />
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I think this fact has been missed by many mathematical biologist and I hope this blog post can shed some light on this misunderstanding.<br />
<br />Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-11521589012992896302016-12-06T16:59:00.004+01:002016-12-06T16:59:55.346+01:008th Swedish Meeting for Mathematical BiologyNext week on the 15th-16th Dec the Mathematical Sciences at Chalmers/GU is hosting the 8th Swedish Meeting for Mathematical Biology. The first meeting was held in 2009 organised by David Sumpter at Uppsala University, and this is the second time the meeting is held in Gothenburg (last time was 2010).<br />
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The purpose of the conference is to gather Swedish researchers who use mathematics in order to understand biological systems, e.g. in evolutionary biology, epidemiology, ecology and cancer research. The meeting spans two days and consists of two invited talks by <a href="http://people.exeter.ac.uk/ig232/Home.html" target="_blank">Ivana Gudelj</a> and <a href="http://calvino.polito.it/~preziosi/" target="_blank">Luigi Preziosi</a>. The remaining time is allocated for contributed talks with a typical duration of 20 minutes. Among these we prioritise PhD-students and young researchers. In addition to the talks there is also a poster session.<br />
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For more information please have a look at our <a href="https://www.chalmers.se/sv/institutioner/math/forskning/konferenser-pa-MV/8th-meeting-on-mathematical-biology-in-sweden/Sidor/default.aspx" target="_blank">webpage</a>. It still possible to register for the meeting. You can do so by sending me an email.<br />
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<br />Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-40847598575021105362016-11-14T08:45:00.000+01:002016-11-14T08:45:26.786+01:00The impact of anticipation in dynamical systemsWe have just submitted a manuscript that investigates the role of prediction in models of collective behaviour. The idea is quite simple: take a model where animals attract/repel each other based on a pairwise potential, and adjust it so that the animals act not on current, but on <i>future positions </i>(including their own). These anticipated or predicted position are assumed to be simple linear extrapolations some time T into the future. In other words, instead of using current positions <i>x </i>to calculate forces, we use <i>x+T*v</i>, where v is the velocity.<br />
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This seemingly simple modification changes the dynamics dramatically. For a typical interaction potential (e.g. Morse potential) the case of no prediction yields no pattern formation, simply particles attracting and colliding. But for an intermediate range of T we observe rapid formation of a milling structure. This means that prediction induces pattern formation and stabilises the dynamics.<br />
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<b>Abstract:</b> <br />
<i>The flocking of animals is often modelled as a dynamical system, in which individuals are represented as particles whose interactions are determined by the current state of the system. Many animals, however, including humans, have predictive capabilities, and presumably base their behavioural decisions - at least partially - upon an anticipated state of their environment. We explore a minimal version of this idea in the context of particles that interact according to a pairwise potential. Anticipation enters the picture by calculating the interparticle forces from linear extrapolation of the positions some time $\tau$ into the future. Our analysis shows that for intermediate values of $\tau$ the particles rapidly form milling structures, induced by velocity alignment that emerges from the prediction. We also show that for $\tau > 0$, any dynamical system governed by an even potential becomes dissipative. These results suggest that anticipation could play an important role in collective behaviour, since it induces pattern formation and stabilises the dynamics of the system. </i><br />
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arXiv: <a href="http://arxiv.org/abs/1611.03637">http://arxiv.org/abs/1611.03637</a><i> </i><br />
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<br />Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-57526602511291051972016-10-13T20:53:00.000+02:002016-10-13T20:53:22.963+02:00Copernicus was not rightDuring my parental leave I took the opportunity to learn more about areas that I normally don't have time to explore. One of these topics was history of science and in particular the changing world views that man has held throughout history.<br />
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Perhaps the largest shift in our view of the world happened when the geocentric world view was replaced by the heliocentric. Although some ancient philosophers argued for a heliocentric worldview (most notably Aristarchos of Samos), the general belief was that the earth was located at the centre of the universe and that the planets were carried round the earth on spheres, the outmost one holding the fixed stars. This framework was described in mathematical terms by <a href="https://en.wikipedia.org/wiki/Geocentric_model#Ptolemaic_model" target="_blank">Claudius Ptolemaeus</a> in the 2nd century AD, in his astronomical work <i>Almagest</i>. Ptolemaeus constructed a mathematical model in which all planets orbited the earth on circles, and in addition each planet travelled on a smaller circle, an epicycle, along its trajectory around the earth. The Ptolemaic system could predict the future positions of the planets with good accuracy, and in addition harmonised well with the world view of Christianity. These two reasons contributed to the fact that the Ptolemaic system remained dominant for over a thousand years.<br />
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The first serious attack on it was delivered by Nicolaus Copernicus, who in the book <i>De revolutionibus orbium coelestium</i> (1543) suggested a heliocentric system. The motivation for this was two-fold. Firstly, Copernicus did not like the fact that the ordering of the planets in the Ptolemaic systems was arbitrary and simply a convention (since both the distance to earth and the speed of the planet could be adjusted to fit the data there was in modern terms one free parameter in the solution), secondly he disapproved of Ptolemaeus use of an <a href="https://en.wikipedia.org/wiki/Equant" target="_blank">equant point</a> in his system. The equant is the point from which the centre of the epicycle of each planet is perceived to move with a uniform angular speed. In other words, to a hypothetical observer placed at the equant
point, the center of the epicycle would appear to move at a steady
angular speed. However, in order to account for the retrograde motion of planets Ptolemaeus had to place the equant point next to earth (not at the centre of the universe). This meant that although the Ptolemaic system was constructed from circular motion there was something asymmetric about it. In conclusion Copernicus critique was aesthetic in nature. It was not about having a good fit to the data, but an elegant model.<br />
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The point I want to make is that Copernicus was not driven by an urge to create a system that was more accurate at predicting planetary motion. In fact the initial heliocentric model made predictions that were on par with the Ptolemaic system. In addition Copernicus insisted that planetary orbits were circular (and he avoided the equant) and therefore he needed even more epicycles than the Ptolemaic system. Since the system was modified several times an exact number is difficult to come up with, but it is estimated that Copernicus initially used <a href="https://en.wikipedia.org/wiki/Deferent_and_epicycle#cite_note-12" target="_blank">48 epicycles</a>. <br />
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This is in complete contrast with the folk science story that claims that the Ptolemaic system had to be amended with more and more epicycles in order to explain data on planetary motion. And along came Copernicus and fixed the problem and got rid all epicycles by proposing a heliocentric model.<br />
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No, Copernicus took a step in the right direction, but it was not until Johannes Kepler in 1609 discovered that planetary orbits are elliptical that epicycles could be discarded from the heliocentric model.<br />
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I'm not quite sure about the take home message of this post. But one thing that I've learnt is that the scientists that we most often associate with the scientific revolution (which by extension reduced the powers of the Church) were deeply devout and held metaphysical beliefs similar to those of Aristotle and Plato. For example Kepler was convinced that the radii of the planetary orbits could be explained by <a href="https://en.wikipedia.org/wiki/Mysterium_Cosmographicum" target="_blank">circumscribing Platonic solids within one another</a>. And as we have seen above Copernicus thought that the equant point disturbed the circular symmetry and therefore suggested a model containing only circles.<br />
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So I guess my conclusion is this: Copernicus was not right, he was just less wrong. And I guess this applies to all scientists. We can never expect to be right, just less wrong than our predecessors.<br />
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Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-54943098082421203182016-09-01T14:10:00.000+02:002016-09-01T14:10:14.206+02:00Parameter variation or a take on interdisciplinary scienceThis text is written from a personal perspective and I'm not sure how well it applies to other scientists. If you agree or disagree please let me know. <br />
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A standard tenet of experimental science is that the number of parameters that one varies in an experimental set-up should be kept to a minimum. This makes is possible to disentangle the effects of different variables on the outcome of the experiment. It has been claimed that the pace at which physics has moved forward in the last century (and molecular biology in the last half century) is due to possibility of physicists to isolate phenomena in strict experimental set-ups. In such a setting each variable can be varied individually, while all others are kept constant. This is in stark contrast to e.g. sociology, where controlled experiments are much harder to perform.<br />
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In a sense the process of doing science is similar to an experiment with a number of parameters. The 'experiment' corresponds to a specific scientific question and the 'parameters' correspond to different approaches to solving the problem. However, we do not know which approach will be successful. If not, it would not classify as research.<br />
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Most approaches or methods are in fact aggregates of many submethods. To give an example, say that I would like to describe some biological system using ordinary differential equations. Then the equations I write down might be novel, but I rely on established methods for solving these equations. I try to describe the system by trying (varying) the equations that describe the dynamics until I find the ones I'm happy with. In this sense we use both existing and new methods when trying to solve some scientific question. However, in order to actually make progress we often minimise the number of novel methods in our approach. If possible we only vary one method and keep all others fixed.<br />
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The problem with interdisciplinary research is that it often calls for novelty on the part of all the involved disciplines. In the case of mathematical biology for example we are asked to invent new mathematics at the same time as we discover new biology. Maybe this is not always the case, but to a certain extent these expectations are always present. A mathematician is expected to develop new mathematical tools, while a biologist is expected to discover new things about biology.<br />
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If both parts enter a project with the ambition of advancing their own discipline this might introduce too much uncertainty in the scientific work (we are now varying two "parameters" in the experiment), which could lead to little or no progress. If the mathematician stands back then new biology can be discovered using existing mathematical tools, while existing biological knowledge and data could serve as a testing ground for novel mathematics.<br />
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So what is the solution to this problem? I'm not sure. But being clear about your intentions in an interdisciplinary project is a good starting point. And maybe taking turns when it comes to novelty with an established collaborator.<br />
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<br />Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-82245552370021366822016-09-01T13:43:00.002+02:002016-09-01T13:43:48.727+02:00Back from parental leaveAs of the 15th Aug I'm back to science and teaching. It's been some great 9 months, but now it's time to get serious about work again. This autumn I'm looking forward to lecturing on mathematical modelling and learning more about cell migration and the extra-cellular matrix.Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-55267984996001469972016-09-01T13:40:00.000+02:002016-09-01T13:40:10.653+02:00Scientific ModelsIn 2009 when I was a postdoc at <a href="http://cmol.nbi.dk/" target="_blank">Center for Models of Life at the Niels Bohr Institute</a> my former MSc-supervisor Torbjörn Lundh came to visit me. As usual we had a great time together, but what I remember most from that visit was that we started talking about scientific models, and in particular how little is actually written (outside philosophy of science) about modelling. Then and there we wrote down an outline of a book that now 7 years on is published. A Swedish edition was in fact published in 2012, but now there's an English edition out on Springer.<br />
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Read more <a href="http://www.springer.com/gp/book/9783319270791" target="_blank">here and get your copy</a>!<br />
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<br />Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-76286370023713311022016-03-10T10:49:00.001+01:002016-03-10T10:49:58.814+01:00Travelling wave analysis of a mathematical model of glioblastoma growthThis paper has been on arxiv for a while (and the work dates back to 2011), but it was at last accepted for publication in Mathematical Biosciences after 1.5 years of review. The paper contains an analysis of a PDE-model of brain tumour growth that takes into account phenotypic switching between migratory and proliferative cell types. We derive an approximate analytic expression of the rate of spread of the tumour, and also show (and this is in my view the most intruiging result) that <b>the inverse relationship
between wave front steepness and its speed observed for the Fisher equation no
longer holds when phenotypic switching is considered. By tuning the switching rates we can obtain steep fronts that move fast and vice versa.</b><br />
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Accepted version: http://arxiv.org/abs/1305.5036<b> </b>
Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-10802706686502645192015-09-30T21:52:00.000+02:002015-10-01T14:21:48.593+02:00Creative force fieldsYesterday (29th september) I made an appearance as an opponent at a seminar on the topic of mathematical modelling for predicting the spread of culture (Swedish title: "Kan algoritmer ge oss bättre förståelse för kultur och regional utveckling?").<br />
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The work that I was reviewing was that of Massimo Buscema at the <a href="http://www.semeion.it/semeion/index.php/it/" target="_blank">Semeion Institute</a> in Rome, who has been collaborating with several counties in Sweden in order to make predictions of how culture in the region will grow in the future.<br />
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The central tool for this analysis is the 'topological weighted centroid' (TWC) which can be viewed as a generalisation of centre of mass of set of points representing cultural activities.<br />
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I am highly critical of the validity and utility of these tools, since it is unclear what the TWC actually represents.<br />
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If you want to know more please have a look at the video:<br />
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<a href="http://bambuser.com/v/5820575">http://bambuser.com/v/5820575</a><br />
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(I make my appearance around 2:20 into the video)Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-60459259821811479452015-08-18T21:22:00.000+02:002015-08-18T21:24:37.634+02:00Photos of natureThis summer I spent almost two months in a cottage in the Swedish countryside with my family. The cottage is fairly isolated with the closest neighbours a kilometer or so away. This meant living closer to nature than I have ever done, and resulted in me taking an interest in the flora and fauna of the surrounding meadow and forest. The below photos document some of my findings. I will in future post (with the tentative title 'The doubts of a mathematical biologist') write more about my impressions of living close to nature.<br />
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<tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-HHzD34AsRPA/VdODFeNsF8I/AAAAAAAAAwY/uaIVgYeOKuA/s1600/2015-06-30%2B12.58.48.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="265" src="http://2.bp.blogspot.com/-HHzD34AsRPA/VdODFeNsF8I/AAAAAAAAAwY/uaIVgYeOKuA/s400/2015-06-30%2B12.58.48.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Crab spider that has caught a hover fly.</td></tr>
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<tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-xWmxPBmho70/VdOCsG3R4HI/AAAAAAAAAuQ/SluJkJNoGsw/s1600/2015-07-23%2B10.54.20.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="266" src="http://3.bp.blogspot.com/-xWmxPBmho70/VdOCsG3R4HI/AAAAAAAAAuQ/SluJkJNoGsw/s400/2015-07-23%2B10.54.20.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Mini forest</td></tr>
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<tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-egd8nFh-4hY/VdOCt5UOZuI/AAAAAAAAAug/dANRESXXd8o/s1600/2015-07-21%2B15.37.31.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="http://4.bp.blogspot.com/-egd8nFh-4hY/VdOCt5UOZuI/AAAAAAAAAug/dANRESXXd8o/s400/2015-07-21%2B15.37.31.jpg" width="266" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Dragon fly trying to hide</td></tr>
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<tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-TwiBeHM9Wao/VdOC5bgxZtI/AAAAAAAAAvg/Wuv_CAem2Vo/s1600/2015-07-10%2B15.45.46.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="266" src="http://2.bp.blogspot.com/-TwiBeHM9Wao/VdOC5bgxZtI/AAAAAAAAAvg/Wuv_CAem2Vo/s400/2015-07-10%2B15.45.46.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Lady bug</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-hGwXJUkjAoU/VdOCmtn70kI/AAAAAAAAAto/cp1wniOe5xU/s1600/2015-07-25%2B10.58.12.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="http://4.bp.blogspot.com/-hGwXJUkjAoU/VdOCmtn70kI/AAAAAAAAAto/cp1wniOe5xU/s400/2015-07-25%2B10.58.12.jpg" width="266" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Cloud berry that is slowly ripening</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-1DedEWTa7D0/VdOCn3JDoRI/AAAAAAAAAtw/GKqrEzrwzyQ/s1600/2015-07-24%2B09.48.58.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="http://3.bp.blogspot.com/-1DedEWTa7D0/VdOCn3JDoRI/AAAAAAAAAtw/GKqrEzrwzyQ/s400/2015-07-24%2B09.48.58.jpg" width="266" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Pine sap (<i>Monotropa hypopitys</i>) is plant without clorophyll that parasitises on fungi</td></tr>
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<tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-Euc8iuqbcoE/VdOClosGoII/AAAAAAAAAtg/OV3d3LyasUw/s1600/2015-08-05%2B14.27.36.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="http://1.bp.blogspot.com/-Euc8iuqbcoE/VdOClosGoII/AAAAAAAAAtg/OV3d3LyasUw/s400/2015-08-05%2B14.27.36.jpg" width="266" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Common self-heal (<i>Prunella vulgaris</i>)</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-Gf8xa63_GUw/VdOCi3KqCtI/AAAAAAAAAtQ/MYThKvCXVqQ/s1600/2015-08-05%2B20.20.37.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="http://2.bp.blogspot.com/-Gf8xa63_GUw/VdOCi3KqCtI/AAAAAAAAAtQ/MYThKvCXVqQ/s400/2015-08-05%2B20.20.37.jpg" width="266" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Cross spider (<i>Araneus diadematus</i>)</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-y2jxvj6hzAc/VdOCxdiGgrI/AAAAAAAAAu8/1OG67c_a2w8/s1600/2015-07-12%2B17.21.24.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="266" src="http://4.bp.blogspot.com/-y2jxvj6hzAc/VdOCxdiGgrI/AAAAAAAAAu8/1OG67c_a2w8/s400/2015-07-12%2B17.21.24.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Poppies</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-wKuvGtKjQyk/VdODPoOyU-I/AAAAAAAAAxg/jAHXyAkLQ0M/s1600/2015-07-11%2B08.59.34.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="266" src="http://1.bp.blogspot.com/-wKuvGtKjQyk/VdODPoOyU-I/AAAAAAAAAxg/jAHXyAkLQ0M/s400/2015-07-11%2B08.59.34.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Unknown spider taking a walk on the clothes line</td></tr>
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<br />Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-68229923764553578072015-08-17T13:52:00.000+02:002015-08-17T13:52:12.857+02:00The evolution of carrying capacity in constrained and expanding tumour cell populations My position at Moffitt Cancer Center certainly payed off in terms of research output. Recently my second paper based on work done at the<a href="http://labpages.moffitt.org/imo/" target="_blank"> Integrated Mathematical Oncology</a> group was published. The paper investigates the dynamics of carrying capacity evolution in tumours and was written together with <a href="http://labpages.moffitt.org/andersona/" target="_blank">Sandy Anderson</a>. The paper is published in Physical Biology, and was chosen as a "featured article" and is therefore open access for a limited time.<br />
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A copy can be found <a href="http://iopscience.iop.org/1478-3975/12/5/056001/article" target="_blank">here</a>, and the arxiv-version <a href="http://arxiv.org/abs/1402.0757" target="_blank">here</a> (which will remain open access forever).<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxjHlf3tyRQkYsI14iADWzNPkhKjq9RZnpFHfKTBp4-EVva9MG6XetO7Xp94znaX83D35pM673xAXiSllOeI_Nd8AJSfKpd2np6c-LSrI0oKGJj7iKPr5-WS4Eqhtg6ZyQXZBFIY41gCo/s1600/fig1.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="303" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxjHlf3tyRQkYsI14iADWzNPkhKjq9RZnpFHfKTBp4-EVva9MG6XetO7Xp94znaX83D35pM673xAXiSllOeI_Nd8AJSfKpd2np6c-LSrI0oKGJj7iKPr5-WS4Eqhtg6ZyQXZBFIY41gCo/s400/fig1.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Illustrating the evolution of carrying capacity (A) and growth rate (B) in a constrained population of tumour cells. </td></tr>
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<br />Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-53601530112840313422015-06-29T12:30:00.000+02:002015-06-29T12:30:14.583+02:00Complexity and stability in growing cancer cell populationsMe and <a href="http://michorlab.dfci.harvard.edu/index.php/people/philipp-altrock" target="_blank">Philipp Altrock</a> recently published a comment on a recent paper by Archetti et al. in PNAS. <a href="http://intl.pnas.org/content/112/6/1833.abstract" target="_blank">Their paper</a> was about the dynamics of growth factor production in cancer cells. The study contained some beatiful experimental work, but we had some concerns about the theory presented to explain the data.<br />
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Read our comment <a href="http://intl.pnas.org/content/112/21/E2742.extract" target="_blank">here</a>, and the response by Archetti et al. <a href="http://intl.pnas.org/content/112/21/E2744.extract" target="_blank">here</a>, and judge for yourselves.Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-8075602627996297412015-06-29T12:24:00.000+02:002015-06-29T12:24:05.644+02:00Dynamics of tumor growth (1964)
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<span style="font-family: "Courier New",Courier,monospace;">[The tumor] grows as though it were a single organism, rather than as a population of dissociated individual cells, each the progenitor of an independent line of tumor cells, as presumably bacteria and other free cells do when inoculated into a new culture medium. This relation suggests further that the host plus tumor represents a new, integrated system of growth whose nature we do not as yet understand. </span></div>
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<span style="font-family: "Courier New",Courier,monospace;"> </span></div>
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<span style="font-family: "Courier New",Courier,monospace;">Anna Kane Laird, Dynamics of tumor growth, British Journal of Cancer (1964)</span></div>
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<span style="font-family: "Courier New",Courier,monospace;"><span style="font-family: Arial, Helvetica, sans-serif;">Now, 50 years on some people still think of cancer cells as independent beings that can be eradicated with toxic enough drugs. I think mathematical modeling can and will aid in pushing the above half-century old perspective on cancer.</span></span>
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</span>Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-79639535141173834812015-02-23T09:34:00.003+01:002015-02-23T09:34:36.336+01:00Back from the back burnerDuring my postdoc at the <a href="http://www.nbi.ku.dk/" target="_blank">Niels Bohr Institute</a> i started working on a manuscript about asymmetric mutations rates and its implications for the fitness landscape methaphor. I was never able to tie that paper together and it has been lying around for almost 5 years collecting dust. Recently I told <a href="https://twitter.com/d4n__" target="_blank">Dan Nichol</a> about my unfinished work, and after having read the draft asked me why I never tried to communicate the results. I didn't really have a good answer, so instead I sat down and cleaned up the draft and turned it into something readable.<br />
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I'm <span style="font-size: small;">not</span> quite sure it reaches publication standards so for the moment I've uploaded it to bioarxiv.org. If you have any suggestions for where it can be submitted please let me know.<br />
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<a href="http://biorxiv.org/content/early/2015/02/20/015529" target="_blank"><span style="font-size: small;"><span style="font-weight: normal;">Directional variation in evolution: consequences for the fitness landscape metaphor.</span></span></a><br />Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-78963911779305615782015-01-19T13:35:00.001+01:002015-01-19T13:35:11.605+01:00Measuring frequency dependent fitnessIn a recent blog post at <a href="https://egtheory.wordpress.com/2014/12/01/is-cancer-really-a-game/" target="_blank">theEGG</a> me and Philipp Altrock argued for caution when applying game theoretic models to cancer. One of our concerns was the difficulty of measuring selective advantage, which is not constant, but changes with the frequency of the genotype. This problem has been partially addressed in a new paper by <a href="http://biorxiv.org/content/early/2014/12/16/012807" target="_blank">Ribeck & Lenski</a>. I have one reservation though: they only consider frequency dependence in one of two competing clones, which means that their approach cannot be applied to a general two-player game which has <a href="https://egtheory.wordpress.com/2012/03/14/uv-space/" target="_blank">two free parameters</a>. Also as a mathematician I would like to see a more rigorous comparison between the Monod model for cross-feeding and the proposed model for frequency dependence, but this paper is at least showing us the way forward.<br />
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<br />Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-1611324183015321072015-01-05T12:06:00.000+01:002015-01-05T12:06:16.313+01:00PhD-position in applied mathematicsA successful application to the Swedish Research Council (<a href="http://www.vr.se/" target="_blank">www.vr.se</a>) has made it possible for me to recruit a PhD-student. A link to the application can be found <a href="http://www.chalmers.se/en/about-chalmers/vacancies/Pages/default.aspx?rmpage=job&rmjob=2722" target="_blank">here</a>, and <a href="http://www.math.chalmers.se/~gerlee/phdposition.html" target="_blank">here's</a> more information about the position. Deadline is 15th February. Spread the word!Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-88305349612760371762014-12-01T10:01:00.003+01:002014-12-01T10:01:39.106+01:00Is cancer really a game?In response to a recent <a href="https://twitter.com/CancerConnector/status/531903056959770624" target="_blank">debate on Twitter</a>, I have, together with <a href="http://michorlab.dfci.harvard.edu/index.php/people/philipp-altrock" target="_blank">Philipp Altrock</a>, written a longer (i.e. more than 140 characters) piece on the limitations of evolutionary game theory as a tool to model cancer. It appears in the form of a guest post on <a href="https://egtheory.wordpress.com/" target="_blank">TheEGG</a>, a blog run by Artem Kaznatcheev.<br />
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Here's a link: <a href="https://egtheory.wordpress.com/2014/12/01/is-cancer-really-a-game/#more-6520" target="_blank">Is cancer really a game?</a>Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-39984284540370280122014-10-22T11:47:00.001+02:002014-10-22T11:47:29.583+02:004th IMO workshop on viruses in cancer<div class="separator" style="clear: both; text-align: center;">
<a href="http://labpages.moffitt.org/andersona/images/workshop/iv.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://labpages.moffitt.org/andersona/images/workshop/iv.jpg" height="256" width="320" /></a></div>
The 4th workshop on Intergrative Mathematical Oncology is being held at Moffitt Cancer Center in November. I attended the event last year and must say that it was a great experience (in part maybe because <a href="http://p-gerlee.blogspot.se/2013/11/imo-workshop.html" target="_blank">our team won it</a>). A lot of hard work (forcing mathematicians, experimentalist and clinicians to find a common language), and late nights, but in the end it was definitely worth it. The project that secured out victory last year is still very much active and a publication is planned early next year.<br /><br />Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-59982781408803849522014-10-17T14:26:00.002+02:002014-10-17T14:26:39.322+02:00Chalmers magasinThe latest issue of Chalmers magasin (aimed mainly at alumni of the university) features an interview with me. The main focus is the use of mathematics to aid cancer research.<br />
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Here's a link to the online version: http://chalmeriana.lib.chalmers.se/chalmersmagasin/cm14_3/Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-10929933459693443992014-09-24T09:17:00.000+02:002014-09-24T13:47:51.341+02:00Anything goes I have never received any formal training in the scientific method. This might sound a bit surprising given that I make a living as a scientist. Instead I have picked up bits and pieces ever since my undergraduate training in physics and throughout my scientific career. This intensified during the research that I did for a <a href="https://www.studentlitteratur.se/#9789144074207/Vetenskapliga+modeller" target="_blank">textbook on scientific modelling</a> (currently only in Swedish, but an English version is under way), and I read extensively about the scientific revolution, empiricism, logical positivism and Thomas Kuhn's ideas on paradigm shifts.<br />
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My latest foray into philosophy of science is the book/extended essay <i>Against Method</i> by Paul Feyerabend. It was first published in 1975 and has ever since been both celebrated and strongly disliked by philosophers and scientists alike (but for different reasons that I will get back to). The main thesis is that there is no coherent scientific method and never has been. Instead Feyerabend proposes theoretical anarchy in which <i>anything goes.</i> For example he shows that introduction of hypotheses that contradict established theories is sometimes a sensible way forward, a move that would be strongly disliked by any philosopher of rationalist creed. He delves specifically into the Copernican revolution and suggests that Galileo used a great deal of propaganda and smoke and mirrors to expound the heliocentric world-view. For example telescopic observations, which are often cited as supporting evidence, were at the time highly speculative and required the development of auxiliary sciences (e.g. optics and meteorology) before they could be considered as solid evidence. Also, the Copernican model of the solar system was no better at explaining empirical observations than was the prevailing Ptolemaic model. Despite this (and hence in contradiction to reason) the Copernican world-view gained followers and was later supported by numerous independent evidence. <br />
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I find Feyerabends account quite convincing and also supported by my own experience of 'doing science'. Most of the models, theories and hypothesis investigated in the field of mathematical biology wouldn't stand much of a chance if they were exposed to the rigour of proper science (i.e. as defined by philosopher of science). In many cases the models aren't even falsifiable since their connection to actual phenomena is at best vague. Not to speak of the field of Artificial Life where models aren't even aimed at resembling any real phenomena. Rather they serve as means to aid and guide our feeble thinking. Much of my own work (devising and analysing mathematical models) has the goal of connecting with biology, not right now, but at some point in the future. But this doesn't render the research useless. It is speculative (in relation to existing knowledge, the models themselves are logically consistent), but it is heading somewhere.<br />
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This resonates with another conclusions drawn by Feyerabend, which is that the transition from one theory to the next entails a decrease in empirical content. We take a step back, speculate, and slowly approach the empirical facts and observations. My feeling is that mathematical (cancer) biology is in precisely this situation: we are exploring new concepts and ideas (i.e. developing or extending our ontology). And to me this makes perfect sense, and is something that should be encouraged.<br />
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My feeling is that philosophers of science dislike this book because it essentially makes them unemployed. If anything goes then there's no point devising or even describing a scientific method. Let the scientists have a go at it. Let anarchy rule. The cool reception from scientists I think has less to do with methodological anarchy (which most of us are quite familiar with) but rather with the perceived anti-scientism that Feyerabend has been accused of. If science does not rely on a specific method (not even reason or adherence to empirical fact) then it should be viewed as any other human activity such as religion or the arts. This is were many scientists (including me) start getting a bit uncomfortable. What I think he is trying to say is that there are many facets to human life and that science cannot and never will provide the full picture. There are always other views/stories/perspectives that inform us about the human condition.<br />
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EDIT: I think this quote by physisct Max Born sums up Feyerabend's thesis in a nice way:<br />
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<i>"I believe there is no philosophical high-road in science, with
epistemological signposts. No, we are in a jungle and find our way by
trial and error, building our road behind us as we proceed."</i> <br />
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<br />Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-29545132341226482762014-09-16T08:40:00.000+02:002014-09-16T08:40:04.082+02:00Back homeAfter almost a year in Tampa at the <a href="http://moffitt.org/research--clinical-trials/research-disciplines/departments/integrated-mathematical-oncology" target="_blank">Intergrated Mathematical Oncology</a> department I've now returned to Sweden and a position as assistant professor. The position is in the Mathematical Sciences at Chalmers University of Technology and besides teaching I will continue my work on cancer modelling, focusing in particular on brain tumour growth (which was the focus during my post-doc at the Sahlgrenska Cancer Center). This time around my work will be more theoretical with the aim of connecting microscopic cell-level dynamics with macroscopic outcomes. Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-82274184454311265092014-05-13T20:07:00.002+02:002014-05-13T20:07:27.840+02:00Pint of ScienceNext week on Wednesday the 21st of May I'm giving a popular science talk at the <a href="http://www.pintofscience.us/" target="_blank">Pint of Science festival</a> in <a href="http://www.pintofscience.us/#!tampa/c1mkc" target="_blank">Tampa</a>. The title of my talk is "When small things are a big deal", and will be about the emergence of complex phenomena out of simple microscopic rules. If you're in Tampa be sure to join me at the <a href="http://www.pintofscience.us/#!datz/cqze" target="_blank">Dough</a> for my presentation, and also the one given by <a href="http://moffitt.org/research--clinical-trials/individual-researchers/julio-m--pow-sang-md" target="_blank">Julio Powsang</a>. <br />
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<br />Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0tag:blogger.com,1999:blog-3475596854533063127.post-50920290035973822772014-02-24T21:01:00.001+01:002014-02-24T21:01:31.670+01:00Forecasting tumour growthThe concept of personalised oncology is often compared to weather prediction. The idea being that with increased amounts of data from patients (genetic sequencing, phenotypic characterisation of cancer cells, imaging etc.) and more advanced mathematical models, we will be able predict tumour progression and responses to therapy in individual patients with increased accuracy. <br />
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When making this comparison, the patient data is analogous to the current state of the atmosphere (temperature, air pressure, wind speed and direction etc.) used as input to fluid dynamics models, which can for example be used in order to predict the future course of a hurricane (or in terms of cancer predict the rate of growth under different therapies). <br />
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The current state of personalised medicine is however falling short on both accounts: the data acquired from patients is meager (although microarray data is 'big' it's pretty useless as input to computational models), and our present-day theoretical understanding of tumour growth is limited. Even if we had all the data we could dream of it would most likely be useless because of our ignorance.<br />
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Although the analogy seems to fall short it actually sheds some light on our inability to predict tumour growth, the reason being that meteorology was in a similar situation roughly a century ago. Before the advent of digital computers, weather prediction was a difficult business based on previous experience and certain rules of thumb. Or in the words of Lew Fry Richardson in the preface of "<a href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CC0QFjAA&url=https%3A%2F%2Farchive.org%2Fdetails%2Fweatherpredictio00richrich&ei=MIMHU9WqK-ezsQSfjoDwDA&usg=AFQjCNEzA0_eRr9EqpsrzMULRL0lWB0iZQ&sig2=SKZY1qDWXIG05rSIt6_NnQ&bvm=bv.61725948,d.cWc&cad=rja" target="_blank">Weather prediction by numerical process</a>" (1922):<br />
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<i>The process of forecasting, which has been carried on in London for many years, maybe typified by one of its latest developments, namely Col. E. Gold's Index of Weather Maps. It would be difficult to imagine anything more immediately practical. The observing stations telegraph the elements of present weather. At the head office these particulars are set in their places upon a large-scale map. The index then enables the forecaster to find a number of previous maps which resemble the present one. The forecast is based on the supposition that what the atmosphere did then, it will do again now. There is no troublesome calculation, with its possibilities of theoretical or arithmetical error. The past history of the atmosphere is used, so to speak, as a full-scale working model of its present self.</i><br />
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This process of manually predicting the weather is similar to the way clinicians in the present day decide upon different cancer therapies. Treatment choices are based on sparse data and previous experience of similar patients. <br />
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The seminal work of Vilhelm Bjerknes and the above quoted book lay the foundation of quantitative weather prediction. What was still lacking was however the computational power, which held back large scale weather forecasting by another 30 years. The situation in mathematical oncology today is however reversed. We have all the computational power we need, but still lack the appropriate theoretical understanding. Hope fully one day that will change.Philip Gerleehttp://www.blogger.com/profile/16507348301981322638noreply@blogger.com0