03799nam 22006615 450 991029977560332120200704120952.03-319-16065-610.1007/978-3-319-16065-8(CKB)3710000000434400(EBL)2096172(SSID)ssj0001524817(PQKBManifestationID)11869177(PQKBTitleCode)TC0001524817(PQKBWorkID)11484924(PQKB)10067254(DE-He213)978-3-319-16065-8(MiAaPQ)EBC2096172(PPN)186399030(EXLCZ)99371000000043440020150620d2015 u| 0engur|n|---|||||txtccrBranching Process Models of Cancer[electronic resource] /by Richard Durrett1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (73 p.)Stochastics in Biological Systems,2364-2297 ;1.1Description based upon print version of record.3-319-16064-8 Includes bibliographical references.Multistage Theory of Cancer -- Mathematical Overview -- Branching Process Results -- Time for Z_0 to Reach Size M -- Time Until the First Type 1 -- Mutation Before Detection? -- Accumulation of Neutral Mutations -- Properties of the Gamma Function -- Growth of Z_1(t) -- Movements of Z_1(t) -- Luria-Delbruck Distributions -- Number of Type 1's at Time T_M -- Gwoth of Z_k(t) -- Transitions Between Waves -- Time to the First Type \tau_k, k \ge 2 -- Application: Metastasis -- Application: Ovarian Cancer -- Application: Intratumor Heterogeneity.This volume develops results on continuous time branching processes and applies them to study rate of tumor growth, extending classic work on the Luria-Delbruck distribution. As a consequence, the authors calculate the probability that mutations that confer resistance to treatment are present at detection and quantify the extent of tumor heterogeneity. As applications, the authors evaluate ovarian cancer screening strategies and give rigorous proofs for results of Heano and Michor concerning tumor metastasis. These notes should be accessible to students who are familiar with Poisson processes and continuous time. Richard Durrett is mathematics professor at Duke University, USA. He is the author of 8 books, over 200 journal articles, and has supervised more than 40 Ph.D. students. Most of his current research concerns the applications of probability to biology: ecology, genetics, and most recently cancer.Stochastics in Biological Systems,2364-2297 ;1.1ProbabilitiesBiomathematicsCancer researchProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Mathematical and Computational Biologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M31000Cancer Researchhttps://scigraph.springernature.com/ontologies/product-market-codes/B11001Probabilities.Biomathematics.Cancer research.Probability Theory and Stochastic Processes.Mathematical and Computational Biology.Cancer Research.614.5999Durrett Richardauthttp://id.loc.gov/vocabulary/relators/aut55577MiAaPQMiAaPQMiAaPQBOOK9910299775603321Branching process models of cancer1522586UNINA