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Erschienen in:
Cancer and Tumor Development: Biomedical Background Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

2. Cell Cycle Specific Cancer Chemotherapy for Homogeneous Tumors

verfasst von : Heinz Schättler, Urszula Ledzewicz

Erschienen in: Optimal Control for Mathematical Models of Cancer Therapies

Verlag: Springer New York

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Abstract

In this chapter, we analyze a class of cell cycle specific compartmental models for cancer chemotherapy. Besides drug resistance, cell cycle specificity of drugs is viewed as one of the major obstacles against successful chemotherapy [83, 52]. By considering the phases of the cell cycle separately, it is possible to appropriately model the different actions of various drugs involved. A first such model was introduced for leukemia in the work of Kimmel and Swierniak [150] and later has been expanded greatly in the work by Swierniak and his co-workers (e.g., see [313, 321, 322, 323, 324] and many more).

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Vorheriges Kapitel Cancer and Tumor Development: Biomedical Background
Nächstes Kapitel Cancer Chemotherapy for Heterogeneous Tumor Cell Populations and Drug Resistance
Fußnoten
1
Even if we just consider the problem of minimizing a function f, it is not possible to determine the local optimality of a critical point x ∗ (i.e., \(f^{{\prime}}(x_{{\ast}}) = 0\)) from just the knowledge of the critical point itself, but we need to understand the behavior of the function f over a neighborhood of x ∗, as, for example, it can be gained from the fact that the second derivative \(f^{{\prime\prime}}(x_{{\ast}})\) does not vanish. The construction of a family of extremals serves this purpose.
 
2
The ω-limit set of a positive semi-trajectory \((x(t; x_{0},z_{0}),z(t; x_{0},z_{0}))\) is the set of all accumulation points of this trajectory as \(t \rightarrow \infty\).
 
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Metadaten
Titel
Cell Cycle Specific Cancer Chemotherapy for Homogeneous Tumors
verfasst von
Heinz Schättler
Urszula Ledzewicz
Copyright-Jahr
2015
Verlag
Springer New York
Buch
Optimal Control for Mathematical Models of Cancer Therapies

Print ISBN: 978-1-4939-2971-9

Electronic ISBN: 978-1-4939-2972-6

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-1-4939-2972-6_2

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