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Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy

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Abstract

A minimally parameterized mathematical model for low-dose metronomic chemotherapy is formulated that takes into account angiogenic signaling between the tumor and its vasculature and tumor inhibiting effects of tumor-immune system interactions. The dynamical equations combine a model for tumor development under angiogenic signaling formulated by Hahnfeldt et al. with a model for tumor-immune system interactions by Stepanova. The dynamical properties of the model are analyzed. Depending on the parameter values, the system encompasses a variety of medically realistic scenarios that range from cases when (i) low-dose metronomic chemotherapy is able to eradicate the tumor (all trajectories converge to a tumor-free equilibrium point) to situations when (ii) tumor dormancy is induced (a unique, globally asymptotically stable benign equilibrium point exists) to (iii) multi-stable situations that have both persistent benign and malignant behaviors separated by the stable manifold of an unstable equilibrium point and finally to (iv) situations when tumor growth cannot be overcome by low-dose metronomic chemotherapy. The model forms a basis for a more general study of chemotherapy when the main components of a tumor’s microenvironment are taken into account.

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Acknowledgments

This material is based upon work supported by the National Science Foundation under collaborative research Grants Nos. DMS 1311729/1311733. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Authors and Affiliations

  1. Department of Electrical and Systems Engineering, Washington University, St. Louis, MO, 63130, USA

    Heinz Schättler

  2. Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, IL, 62025, USA

    Urszula Ledzewicz & Behrooz Amini

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  1. Heinz Schättler
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  2. Urszula Ledzewicz
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  3. Behrooz Amini
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Correspondence to Urszula Ledzewicz.

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Schättler, H., Ledzewicz, U. & Amini, B. Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy. J. Math. Biol. 72, 1255–1280 (2016). https://doi.org/10.1007/s00285-015-0907-y

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  • DOI: https://doi.org/10.1007/s00285-015-0907-y

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