Limiting the development of anti-cancer drug resistance in a spatial model of micrometastases

Ami B.  Shah; Katarzyna A.  Rejniak; Jana L.  Gevertz

doi:10.3934/mbe.2016038

Article Contents

2016, Volume 13, Issue 6: 1185-1206. Doi: 10.3934/mbe.2016038

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Limiting the development of anti-cancer drug resistance in a spatial model of micrometastases

1.
Department of Biology, The College of New Jersey, Ewing, NJ
2.
Integrated Mathematical Oncology Department and Center of Excellence in Cancer Imaging and Technology, H. Lee Mott Cancer Center and Research Institute, Department of Oncologic Sciences, University of South Florida, Tampa, FL
3.
Department of Mathematics and Statistics, The College of New Jersey, Ewing, NJ

Received: September 30, 2015

Revised: April 30, 2016

Published: July 2016

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Abstract

While chemoresistance in primary tumors is well-studied, much less is known about the influence of systemic chemotherapy on the development of drug resistance at metastatic sites. In this work, we use a hybrid spatial model of tumor response to a DNA damaging drug to study how the development of chemoresistance in micrometastases depends on the drug dosing schedule. We separately consider cell populations that harbor pre-existing resistance to the drug, and those that acquire resistance during the course of treatment. For each of these independent scenarios, we consider one hypothetical cell line that is responsive to metronomic chemotherapy, and another that with high probability cannot be eradicated by a metronomic protocol. Motivated by experimental work on ovarian cancer xenografts, we consider all possible combinations of a one week treatment protocol, repeated for three weeks, and constrained by the total weekly drug dose. Simulations reveal a small number of fractionated-dose protocols that are at least as effective as metronomic therapy in eradicating micrometastases with acquired resistance (weak or strong), while also being at least as effective on those that harbor weakly pre-existing resistant cells. Given the responsiveness of very different theoretical cell lines to these few fractionated-dose protocols, these may represent more effective ways to schedule chemotherapy with the goal of limiting metastatic tumor progression.

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Mathematics Subject Classification: Primary: 92C50; Secondary: 37N25.

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