On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach

Urszula Ledzewicz; Shuo Wang; Heinz Schättler; Nicolas André; Marie Amélie Heng; Eddy Pasquier; Urszula Ledzewicz; Shuo Wang; Heinz Schättler; Nicolas André; Marie Amélie Heng; Eddy Pasquier

doi:10.3934/mbe.2017014

Mathematical Biosciences and Engineering

2017, Volume 14, Issue 1: 217-235. doi: 10.3934/mbe.2017014

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On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach

1.
Institute of Mathematics, Lodz University of Technology, 90-924 Lodz, Poland
2.
Dept. of Mathematics and Statistics, Southern Illinois University, Edwardsville, Il, 62026-1653, USA
3.
Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Mo, 63130, USA
4.
Service d'hématologie et Oncologie Pédiatrique, Centre Hospitalo-Universitaire Timone Enfants, AP-HM, Marseille, UMR S_911 CRO2 Aix Marseille Université, Marseille, France
5.
Metronomics Global Health Initiative, Marseille, France
6.
Childrens Cancer Institute Australia, Lowy Cancer Research Centre, University of New South Wales, Randwick, NSW, Australia

Received: 01 December 2015 Accepted: 30 June 2016 Published: 01 February 2017
MSC : Primary: 49K15, 92B05; Secondary: 93C95

Effects that tumor heterogeneity and drug resistance have on the structure of chemotherapy protocols are discussed from a mathematical modeling and optimal control point of view. In the case when two compartments consisting of sensitive and resistant cells are considered, optimal protocols consist of full dose chemotherapy as long as the relative proportion of sensitive cells is high. When resistant cells become more dominant, optimal controls switch to lower dose regimens defined by so-called singular controls. The role that singular controls play in the structure of optimal therapy protocols for cell populations with a large number of traits is explored in mathematical models.
- Cancer chemotherapy,
- tumor heterogeneity,
- drug resistance,
- optimal control,
- singular controls,
- metronomic chemotherapy
Citation: Urszula Ledzewicz, Shuo Wang, Heinz Schättler, Nicolas André, Marie Amélie Heng, Eddy Pasquier. On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach[J]. Mathematical Biosciences and Engineering, 2017, 14(1): 217-235. doi: 10.3934/mbe.2017014

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Abstract

Effects that tumor heterogeneity and drug resistance have on the structure of chemotherapy protocols are discussed from a mathematical modeling and optimal control point of view. In the case when two compartments consisting of sensitive and resistant cells are considered, optimal protocols consist of full dose chemotherapy as long as the relative proportion of sensitive cells is high. When resistant cells become more dominant, optimal controls switch to lower dose regimens defined by so-called singular controls. The role that singular controls play in the structure of optimal therapy protocols for cell populations with a large number of traits is explored in mathematical models.

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