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SDE-driven modeling of phenotypically heterogeneous tumors: The influence of cancer cell stemness

  • We deduce cell population models describing the evolution of a tumor (possibly interacting with its environment of healthy cells) with the aid of differential equations. Thereby, different subpopulations of cancer cells allow accounting for the tumor heterogeneity. In our settings these include cancer stem cells known to be less sensitive to treatment and differentiated cancer cells having a higher sensitivity towards chemo- and radiotherapy. Our approach relies on stochastic differential equations in order to account for randomness in the system, arising e.g., by the therapy-induced decreasing number of clonogens, which renders a pure deterministic model arguable. The equations are deduced relying on transition probabilities characterizing innovations of the two cancer cell subpopulations, and similarly extended to also account for the evolution of normal tissue. Several therapy approaches are introduced and compared by way of tumor control probability (TCP) and uncomplicated tumor control probability (UTCP). A PDE approach allows to assess the evolution of tumor and normal tissue with respect to time and to cell population densities which can vary continuously in a given set of states. Analytical approximations of solutions to the obtained PDE system are provided as well.

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Metadaten
Author:Julia Kroos, Christian Stinner, Christina Surulescu, Nicolae Surulescu
URN (permanent link):urn:nbn:de:hbz:386-kluedo-54262
Document Type:Preprint
Language of publication:English
Publication Date:2018/12/03
Year of Publication:2018
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2018/12/05
Number of page:31
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 500 Naturwissenschaften
MSC-Classification (mathematics):34-XX ORDINARY DIFFERENTIAL EQUATIONS
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K61 Nonlinear initial-boundary value problems for nonlinear parabolic equations
92-XX BIOLOGY AND OTHER NATURAL SCIENCES
Licence (German):Creative Commons 4.0 - Namensnennung (CC BY 4.0)