Branching Process Models of Cancer

Häftad, Engelska, 2015

Del 1 i serien Mathematical Biosciences Institute Lecture Series

333 kr

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Beskrivning

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 applications, the author evaluate ovarian cancer screening strategies and give rigorous proofs for results of Heano and Michor concerning tumor metastasis.

Produktinformation

Utgivningsdatum:2015-07-06
Mått:155 x 235 x 9 mm
Vikt:152 g
Format:Häftad
Språk:Engelska
Serie:Mathematical Biosciences Institute Lecture Series
Antal sidor:63
Förlag:Springer International Publishing AG
ISBN:9783319160641

Utforska kategorier

Matematisk statistik inom Naturvetenskap och teknik
Onkologi inom Medicin
Biovetenskap inom Naturvetenskap och teknik

Mer om författaren

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.

Recensioner i media

"It provides a survey of cancer modeling using multitype branching processes. ... the text should be accessible for graduate students in mathematics and biology who are familiar with Poisson processes and continuous-time Markov chains." (Matthias Meiners, zbMATH 1328.92004, 2016)

Innehållsförteckning

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.