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Selected Topics in Cancer ModelingDynamic Irregular Patterns and Invasive Wavefronts The Control of Tumour Growth by Cytotoxic T Lymphocytes

Selected Topics in Cancer Modeling: Dynamic Irregular Patterns and Invasive Wavefronts The... Dynamic Irregular Patterns and Invasive Wavefronts: The Control of Tumour Growth by Cytotoxic T-Lymphocytes Anastasios Matzavinos Department of Mathematics, Ohio State University, Columbus, OH 43210, USA tasos@math.ohio-state.edu 16.1 Introduction “Cancer dormancy” is an operational term used to describe the phenomenon of a prolonged quiescent state in which tumour cells are present, but tu- mour progression is not clinically apparent [42, 49, 53]. As a condition, cancer dormancy is often observed in breast cancers, neuroblastomas, melanomas, osteogenic sarcomas, and in several types of lymphomas, and is often found “accidentally” in tissue samples of healthy individuals who have died suddenly [1, 10]. In some cases, cancer dormancy has been found in cancer patients af- ter several years of front-line therapy and clinical remission. The presence of these cancer cells in the body determines, finally, the outcome of the dis- ease. In particular, age, stress factors, infections, the act of treatment itself or other alterations in the host can provoke the initiation of uncontrolled growth of initially dormant cancer cells and subsequent waves of metastases [25, 49]. Recently, some molecular targets for the induction of cancer dormancy and the re-growth of a dormant tumour have been identified [23, 48]. However, the precise http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Selected Topics in Cancer ModelingDynamic Irregular Patterns and Invasive Wavefronts The Control of Tumour Growth by Cytotoxic T Lymphocytes

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Publisher
Birkhäuser Boston
Copyright
© Birkhäuser Boston 2008
ISBN
978-0-8176-4712-4
Pages
1 –30
DOI
10.1007/978-0-8176-4713-1_16
Publisher site
See Chapter on Publisher Site

Abstract

Dynamic Irregular Patterns and Invasive Wavefronts: The Control of Tumour Growth by Cytotoxic T-Lymphocytes Anastasios Matzavinos Department of Mathematics, Ohio State University, Columbus, OH 43210, USA tasos@math.ohio-state.edu 16.1 Introduction “Cancer dormancy” is an operational term used to describe the phenomenon of a prolonged quiescent state in which tumour cells are present, but tu- mour progression is not clinically apparent [42, 49, 53]. As a condition, cancer dormancy is often observed in breast cancers, neuroblastomas, melanomas, osteogenic sarcomas, and in several types of lymphomas, and is often found “accidentally” in tissue samples of healthy individuals who have died suddenly [1, 10]. In some cases, cancer dormancy has been found in cancer patients af- ter several years of front-line therapy and clinical remission. The presence of these cancer cells in the body determines, finally, the outcome of the dis- ease. In particular, age, stress factors, infections, the act of treatment itself or other alterations in the host can provoke the initiation of uncontrolled growth of initially dormant cancer cells and subsequent waves of metastases [25, 49]. Recently, some molecular targets for the induction of cancer dormancy and the re-growth of a dormant tumour have been identified [23, 48]. However, the precise

Published: Aug 21, 2008

Keywords: Hopf Bifurcation; Travel Wave Solution; Random Motility; Stable Limit Cycle; Numerical Continuation

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