Branching Process Models of Cancer

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Durrett, Richard (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2015.
Edición:1st ed. 2015.
Colección:Stochastics in Biological Systems, 1.1
Temas:
Probabilities.
Biomathematics.
Cancer.
Probability Theory.
Mathematical and Computational Biology.
Cancer Biology.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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