TY  - BOOK
AU  - Durrett,Richard
ED  - SpringerLink (Online service)
TI  - Branching Process Models of Cancer
T2  - Mathematical Biosciences Institute Lecture Series
SN  - 9783319160658
AV  - QA273.A1-274.9 
U1  - 519.2 23
PY  - 2015///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Mathematics
KW  - Cancer research
KW  - Probabilities
KW  - Biomathematics
KW  - Probability Theory and Stochastic Processes
KW  - Mathematical and Computational Biology
KW  - Cancer Research
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-319-16065-8
ER  -