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Branching process models of cancer

Author: Richard Durrett
Publisher: Cham : Springer, [2015] ©2015
Series: Mathematical Biosciences Institute lecture series., Stochastics in biological systems ;, v. 1.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Richard Durrett
ISBN: 9783319160658 3319160656 3319160648 9783319160641
OCLC Number: 911386316
Description: 1 online resource (vii, 63 pages) : illustrations (some color).
Contents: 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.
Series Title: Mathematical Biosciences Institute lecture series., Stochastics in biological systems ;, v. 1.
Responsibility: Richard Durrett.

Abstract:

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  Read more...

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"It provides a survey of cancer modeling using multitypebranching processes. ... the text should be accessible for graduate students inmathematics and biology who are familiar with Poisson processes Read more...

 
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