Mathematical Oncology 2013 PDF
Preview Mathematical Oncology 2013
Modeling and Simulation in Science, Engineering and Technology Alberto d'Onofrio Alberto Gandolfi Editors Mathematical Oncology 2013 ModelingandSimulationinScience,EngineeringandTechnology SeriesEditor NicolaBellomo PolitecnicodiTorino Torino,Italy EditorialAdvisoryBoard K.J.Bathe P.Koumoutsakos DepartmentofMechanicalEngineering ComputationalScience&Engineering MassachusettsInstituteofTechnology Laboratory Cambridge,MA,USA ETHZürich Zürich,Switzerland M.Chaplain H.G.Othmer DivisionofMathematics DepartmentofMathematics UniversityofDundee UniversityofMinnesota Dundee,Scotland,UK Minneapolis,MN,USA P.Degond K.R.Rajagopal DepartmentofMathematics, DepartmentofMechanicalEngineering ImperialCollegeLondon, TexasA&MUniversity London,UnitedKingdom CollegeStation,TX,USA A.Deutsch T.E.Tezduyar CenterforInformationServices DepartmentofMechanicalEngineering& MaterialsScience andHigh-PerformanceComputing RiceUniversity TechnischeUniversitätDresden Houston,TX,USA Dresden,Germany A.Tosin M.A.Herrero IstitutoperleApplicazionidelCalcolo DepartamentodeMatematicaAplicada “M.Picone” UniversidadComplutensedeMadrid ConsiglioNazionaledelleRicerche Madrid,Spain Roma,Italy Moreinformationaboutthisseriesathttp://www.springer.com/series/4960 Alberto d’Onofrio (cid:129) Alberto Gandolfi Editors Mathematical Oncology 2013 Albertod’Onofrio AlbertoGandolfi InternationalPreventionResearchInstitute IstitutodiAnalisideiSistemied Lyon,France Informatica“AntonioRuberti”—CNR Rome,Italy DepartmentofExperimentalOncology EuropeanInstituteofOncology Milano,Italy ISSN2164-3679 ISSN2164-3725(electronic) ISBN978-1-4939-0457-0 ISBN978-1-4939-0458-7(eBook) DOI10.1007/978-1-4939-0458-7 SpringerNewYorkHeidelbergDordrechtLondon LibraryofCongressControlNumber:2014951354 Mathematics Subject Classification (2010): 92-XX, 92B05, 97M60, 37N25, 35Q92, 00A69, 92C37, 92B99 ©SpringerScience+BusinessMediaNewYork2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.birkhauser-science.com) Preface Aftera longincubationperiodinwhichonlysporadicinvestigationsweredevoted totheapplicationsofmathematicsandphysicstothestudyoftumors(see,e.g.,the workofDollandArmitageontumorigenesisinthe1950s),intheearly1970s,the papersbyNortonandSimonandbyGreenspanwereaturningpointinthescientific interestontumormodeling. In this first phase, the majority of models were essentially population-based models. Although many important results were established—for example, the possibleonsetofadynamicequilibriumbetweenatumorandtheimmunesystem, only recently experimentally confirmed—the majority of studies did not directly rouse the attention of the oncology world, with the remarkable exception of the papers by Goldie and Coldman on the Darwinian emergence of resistance to chemotherapyandoftheabove-mentionedworksbyNortonandSimon. ThepioneeringworkbyGreenspan,wherethemodelingalsoinvolvedphysico- chemical aspects of tumor growth, remained almost isolated for two decades. Finally, in the 1990s, a large number of mathematical models were devoted to describing the spatial growth of tumors, with approaches ranging from simple diffusivemodelstocomplexmultiphasemechanicalmodels.Later,theinteractions ofthetumorwiththeimmunesystemandwiththeangiogenesisprocessalsobecame theobjectofextensivetheoreticalresearch. The follow-up in the medical world, however, remained rather scarce. This is due mainly to the limited number of joint works between biomedical and biomathematical researchers, although there have been some isolated cases of theoreticalscientists—forexample,R.Jain—whohavebeensodeeplyinvolvedin biologicalresearchastobecomeinfluentialbiomedicalresearchleaders. Things are, however, rapidly changing. In recent years, two major phenomena havegivengreatmomentumtoresearchinmathematicaloncology. The first is of a technical nature—that is, the birth of multiscale modeling— where microstructures such as individual cells can be explicitly represented. v vi Preface The second, and most important from a “sociological” point of view, is that a largenumberofbiomedicalscientistsarebecomingdirectlyinvolvedinquantitative research due to the need to decipher an ever larger mass of “omics” data (mainly fromgenomicsandproteomics). The increasing number of modeling papers published in journals devoted to oncology, and in particular the opening of the new section on mathematical oncologyinCancerResearch,oneofthemostimportantbasicresearchjournalson cancer, is the most important evidence that tumor modeling is slowly but signifi- cantlyimpactingtheoncologyworld. Moreover,thefactthatintheseyearsanumberofresearchgroups—oftenledby biomedicalscientists turnedto computationalsciences—are being “embedded”in researchmedicalcentersisfurtherevidenceofthescientificinterestofthetopic. On the other hand, from the point of view of mathematicians, there is an increasingawarenessthattheapplicationsofbothclassicalmechanicsandnonlinear analysistothestudyoftumorgrowthtranslateintonewchallengingproblemsatthe frontierofcontemporarymathematics. Thisismirroredbytheincreasingnumberofpapersonmathematicaloncology thatarepublishedinmathematicaljournals. This book is entirely composed of in-depth contributions reviewing personal researchresults of outstandingscientists in the field. It is aimed atprovidingboth experienced researchers and the increasing number of newcomers with a careful selectionofstate-of-the-artresults. Manynewresearcherswhoareenteringthefieldofmathematicaloncologyoften experiencesignificantdifficulties.Startingworkinmathematicalcancermodeling, indeed,isaslowanddifficultprocessthatrequirestheacquisitionofaspecialforma mentis that goes well beyond that of the usual applications of mathematics and physics,wherethelearningcanbelimitedtotheacquisitionofbasicconceptsand methodsofthedomainofapplication.Intumors,onthecontrary,manyapparently differentphenomenaare interrelated,and all of them are strictly linked to clinical issues. We believe that in the chapters of this book the authors have successfully transferrednotonlytheirresultsbutalso,mostimportantly,theirwayofseeingand approachingproblems. In order to cope with the state of the art, the book covers different biological subjectsandmathematicalapproaches. As far as the tumor onset and early phases of tumor growth are concerned, Bortolusso and Kimmel investigate the interplay of spatiality and stochasticity in the process of tumorigenesis by stressing some exquisitely stochastic spa- tiotemporal phenomena without deterministic counterpart and the role of cellular cooperation.Fasano,Bertuzzi,andSinisgallifocusonthe roleoftheconservation laws of mathematical physics to decipher the dynamics of the early phases of neoplasias by means of the analysis of some free-boundary problems for partial differential equations. Techniques of nonlinear mathematical physics and statis- tical mechanics, as well as WKB approximations, are used by Ben Amar to treat two typical features of melanomas: morphological instabilities and phase Preface vii segregation. In her contribution, Ben Amar also provides an overview of the historicaldevelopmentof“mathematicalbiophysics”oftumors. With regard to the intercellular interplay between tumor cells and other cells in the environment, Dyson and Webb extend their models that include the “cell cycle age” of tumor cells by also including the cell-to-cell adhesion theory by Painterand Sherratandprovidea completemathematicalanalysisof the resulting model by using the theory of semigroups. Lachowitz, Dolfin, and Szymanska, in the framework of the kinetic theories of tumor-immune system interplay, provide a theoreticalframeworkfor the constructionof micro- andmeso-modelsthat may be related to macroscopic models and that are able to take into account various additionalaspects ofthe microscopicscale. Kareva,Wilkie, andHahnfeldtreview the role of the interplay of tumors with their microenvironment: This includes interplaywithendothelialcellsintheprocessofangiogenesisandwiththeimmune system,aswellastheroleofrecyclingofnutrients. Finally,asfarasthemodelingofantitumortherapiesisconcerned,dePillisand Radunskayareviewtheirmodelsoftumor-immunesystemsandimmunotherapies, as well as the effect of chemotherapies on normal, tumor, and immune cells. A varietyofapproachesareusedbydePillisandRadunskaya,rangingfromordinary differential equations to cellular automata. A hybrid multiscale framework—also including cell cycle dynamics of individual cells—is adopted by Powathil and Chaplaintomodelthespatiotemporalresponseoftumorstochemotherapyaloneor incombinationwithradiotherapy.Clairambaultreviewsthechronobiologyoftumor growth and antitumor therapies, i.e., he focuses on how to “exploit” the influence ofcircadianrhythmsontheproliferationoftumorsinordertomaximizetheeffects ofchemotherapies.Methodsandtoolsofoptimalcontroltheoriesareintroducedby LedzewiczandSchaettlerinthefinalchapter,whichreviewstheapplicationofthese theories to optimize antitumor treatments under various biologically meaningful conditions. We end the preface with a brief consideration. The field of mathematical modelingoftumorgrowthandofrelatedtherapieshasinrecentyearsbeennamed “mathematicaloncology.”From the pointof view of both a layman and of a pure mathematician, this could seem bizarre or as an overstatement. However, as we hope this book will demonstrate, this term is not an exaggeration as all major mathematical tools of analytical and computational mathematics can be fruitfully “exploited” in order to investigate the many problems of oncological interest— methods ranging from ordinary differentialequations to the statistical mechanics of phase transitions, from the theoryof semigroupsto Gillespie’s algorithm,from cellularautomatatothegeometrictheoryofoptimalcontrol,etc. However, it is not only a question of adopting analytical theories or computa- tional tools to tackle biological problems from a physical-mathematical point of view.No!Thefirstchallengeinmathematicaloncologyisforbiologicalproblemsto provideanimpetustodeveloporsubstantiallyimprovenewmathematicaltheories and computational algorithms. This is exactly what happened to other related or unrelatedbranchesofmathematicalbiology,asmaybe seenbytakinga historical perspective of the developments of dynamical systems theory and computational viii Preface sciences,aswellasclassicalandcomputationalstatistics.Thesecondchallengeis, of course, to develop and increment the collaboration with biomedical scientists. This point has been considered several times in the past but here we want to also stress that a major effort is needed from the didactic point of view. Indeed, a differentand more integrated approachto mathematical oncologymight lead to a newgenerationoftheoreticalbiologistswithbackgroundsequallydividedbetween quantitativesciencesandbiomedicine. Lyon,France Albertod’Onofrio Rome,Italy AlbertoGandolfi Jan15,2014 Contents PartI CancerOnsetandEarlyGrowth Modeling Spatial Effects in Carcinogenesis: Stochastic andDeterministicReaction-Diffusion ......................................... 3 RobertoBertolussoandMarekKimmel ConservationLawsinCancerModeling ...................................... 27 AntonioFasano,AlessandroBertuzzi,andCarmelaSinisgalli AvascularTumorGrowthModelling:PhysicalInsightstoSkinCancer... 63 MartinaBenAmar PartII TumorandInter-CellularInteractions ACellPopulationModelStructuredbyCellAgeIncorporating Cell–CellAdhesion............................................................... 109 JanetDysonandGlennF.Webb AGeneralFrameworkforMultiscaleModeling ofTumor–ImmuneSystemInteractions....................................... 151 MarinaDolfin,MirosławLachowicz,andZuzannaSzyman´ska The Power of the Tumor Microenvironment:A Systemic ApproachforaSystemicDisease............................................... 181 IrinaKareva,KathleenP.Wilkie,andPhilipHahnfeldt ix
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