Branching Process Models of Cancer

• Main Author: Durrett, Richard (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Series: Mathematical Biosciences Institute Lecture Series ; 1.1
• Subjects: Mathematics.; Cancer research.; Probabilities.; Biomathematics.; Probability Theory and Stochastic Processes.; Mathematical and Computational Biology.; Cancer Research.

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 det...

Table of 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.