Monte Carlo Methods for Radiation Transport: Fundamentals and Advanced Topics PDF
Preview Monte Carlo Methods for Radiation Transport: Fundamentals and Advanced Topics
Biological and Medical Physics, Biomedical Engineering Oleg N. Vassiliev Monte Carlo Methods for Radiation Transport Fundamentals and Advanced Topics BIOLOGICAL AND MEDICAL PHYSICS, BIOMEDICAL ENGINEERING BIOLOGICAL AND MEDICAL PHYSICS, BIOMEDICAL ENGINEERING The fields of biological and medical physics and biomedical engineering are broad, multidisciplinary and dynamic.Theylieatthe crossroadsof frontier researchinphysics,biology, chemistry,andmedicine.The BiologicalandMedicalPhysics,BiomedicalEngineeringSeriesisintendedtobecomprehensive,coveringa broadrangeoftopicsimportanttothestudyofthephysical,chemicalandbiologicalsciences.Itsgoalisto providescientistsandengineerswithtextbooks,monographs,andreferenceworkstoaddressthegrowingneed forinformation. 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Vassiliev Monte Carlo Methods for Radiation Transport Fundamentals and Advanced Topics 123 OlegN.Vassiliev DepartmentofRadiationPhysics TheUniversityofTexas MDAndersonCancerCenter Houston,TX,USA ISSN1618-7210 ISSN2197-5647 (electronic) BiologicalandMedicalPhysics,BiomedicalEngineering ISBN978-3-319-44140-5 ISBN978-3-319-44141-2 (eBook) DOI10.1007/978-3-319-44141-2 LibraryofCongressControlNumber:2016954643 ©SpringerInternationalPublishingSwitzerland2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Inmemoryofmyparents Thenareyousocertainthatyourrouletteplayingwillgetus outofourdifficulties? F.Dostoevsky,“TheGambler” Preface This book is intended as an introductory graduate-level text on the application of the Monte Carlo method to radiation transport problems. The target audience is radiation medical physicists: students, faculty members, and researchers special- izing in radiotherapy physics, medical imaging, or nuclear medicine. The book should be of interest to clinicians as well, because Monte Carlo-based software, no longer confined to the research environment, is gradually finding its way into routineclinicalpractice. The types of problems that are important in the field of medical physics determined the material that was selected for the book. Rather than focusing on the practical application of Monte Carlo techniques, however, the book focuses on the fundamentals of the method: its mathematical foundations, the numerical techniques on which it relies, its optimization strategies, and the statistical aspect of its calculations. With this approach, most of the information is quite general, andpartsshouldbeusefultoabroadaudience.Moreadvancedtopicsareincluded as well, such as the adjoint formulation of the transport problem, the transport of charged particles in an external magnetic field, microdosimetry, elements of stochastictransporttheory,andgrid-basedsolvers.Inclusionofthesetopicsmakes the text more complete and extends the book into areas of recent significant developments. An important objective of this book is to introduce the basic concepts, termi- nology, and formalism of radiation transport theory. This material, of course, is necessary to understand how transport problems are solved with the Monte Carlo method. It is also of significant interest in its own right because it is the basis for methods other than Monte Carlo, analytical and numerical, that have been used extensively in radiation medical physics. Several such methods are covered in the book. OurdidacticapproachreflectstheviewexpressedbyN.MetropolisandS.Ulam in their seminal paper “The Monte Carlo method” (1949) that Monte Carlo is a “statistical approach to the study of differential equations, or more generally, of integro-differential equations.” The equation that we study in this book is the ix x Preface Boltzmanntransportequation.Forthisreason,wededicateanentirechaptertothe equationanditsvariousforms.Onlyaftertheequationisexplaineddoweintroduce algorithmsforsolvingit. Thechaptersandappendixofthebookcanbesummarizedasfollows: • Chapters 1 and 2 present a general introduction to the Monte Carlo method with an emphasis on sampling techniques, an essential element of any Monte Carloalgorithm.Samplingtechniquesareusedtogeneraterandomnumbersand vectorsthathavedistributionsrequiredbythealgorithm. • Chapter 3 begins with definitions of the fundamental quantities of radiation transport theory, such as cross sections, free path, and fluence. Next is a rather elementaryintroductiontotheBoltzmannequationfollowedbyexamplesofits various forms. We conclude the chapter with more advanced topics: a general algorithmforsolvingtheBoltzmannequationwiththeMonteCarlomethodand the related topic of biasing techniques, which together form the mathematical basisforalgorithmoptimization. • Chapter 4 discusses three main components of a Monte Carlo algorithm for radiation transport problems: generation of a particle trajectory, tallying, and variance reduction. Tallying is the process of deriving a numerical estimate of a quantity of interest from information contained in particle trajectories. Here, andthroughoutthebook,thewordestimateisusedinsteadofcalculatebecause MonteCarloisastatisticalmethod.Thisbynomeansimpliespooraccuracyof theresult.Variancereductionisabroadtermreferringtoavarietyofoptimization methodsthatreducestatisticaluncertaintieswithoutintroducingsystematicerror orbias. • Chapter 5 is dedicated to the transport of charged particles such as electrons, protons,andheavyions.MostMonteCarloalgorithmsforchargedparticlesrely on multiple scattering models. We cover all the classic models for energy loss fluctuations (energy straggling), angular distribution, and transverse and longi- tudinalspatialdisplacements.Thischapteralsoincludessectionsontransportin magneticfieldsandthechargeexchangeprocess,whichisparticularlyimportant neartheendofaheavyiontrack. • Inthelasttwochapters,Chaps.6and7,wepresenttwoadvancedtopics:micro- dosimetry with elements of stochastic transport theory and grid-based solvers of the Boltzmann equation. The calculation of microdosimetric characteristics is a problem fundamentally different from more conventional problems, such as the dose calculation, because the Boltzmann equation is not applicable in this case. For this reason, in this chapter, we introduce another equation, the stochastic transport equation, and discuss algorithms for solving it. Grid-based Boltzmann equation solvers are deterministic algorithms that present a viable alternative to Monte Carlo. The best-known algorithm of this type is Acuros (Vassiliev et al. 2010), which was translated into the clinic almost instantly, for treatment planning for radiotherapy of cancer. The grid-based Boltzmann equation solver, however, remains a relatively new technology and has the potentialforimprovementandforuseinnewapplications.InChap.7,weexplain step-by-stephowanalgorithmofthistypeworks.
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