Branching Process Models of Cancer

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Beschreibung

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 author calculate the probability that mutations that confer resistance to treatment are present at detection and quantify the extent of tumor heterogeneity. As applications, the author 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 Markov chains.
Richard Durrett is a 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.

Über den Autor

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.

Zusammenfassung

The first volume published in the new series Mathematical Biosciences Institute

Concise and easy to understand for graduate students familiar with Poisson processes and continuous time Markov chains

Includes examples and theorems throughout

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2015
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Stochastics in Biological Systems
Inhalt:	vii 63 S. 4 s/w Illustr. 2 farbige Illustr. 63 p. 6 illus. 2 illus. in color.
ISBN-13:	9783319160641
ISBN-10:	3319160648
Sprache:	Englisch
Herstellernummer:	978-3-319-16064-1
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Durrett, Richard
Hersteller:	Springer Nature Switzerland Springer International Publishing Springer International Publishing AG Stochastics in Biological Systems
Maße:	235 x 155 x 5 mm
Von/Mit:	Richard Durrett
Erscheinungsdatum:	06.07.2015
Gewicht:	0,138 kg

Artikel-ID: 104898107