Optimization of an in vitro chemotherapy to avoid resistant tumours.

Chemotherapy use against solid tumours often results in the resistance of the cancer cells to the molecule used. In this paper, we will set up and analyse an ODE model for heterogeneous in vitro tumours, consisting of cells that are sensitive or resistant to a certain drug. We will then use this model to develop different protocols, that aim at reducing the tumour volume while preserving its heterogeneity. These drug administration schedules are determined through analysis of the system dynamics, and optimal control theory.

[1]  J H Goldie,et al.  A stochastic model for the origin and treatment of tumors containing drug-resistant cells. , 1986, Bulletin of mathematical biology.

[2]  M. Chyba,et al.  Singular Trajectories and Their Role in Control Theory , 2003, IEEE Transactions on Automatic Control.

[3]  A. Deutsch,et al.  Studying the emergence of invasiveness in tumours using game theory , 2008, 0810.4724.

[4]  Robert A Gatenby,et al.  Application of quantitative models from population biology and evolutionary game theory to tumor therapeutic strategies. , 2003, Molecular cancer therapeutics.

[5]  R. Gillies,et al.  Exploiting evolutionary principles to prolong tumor control in preclinical models of breast cancer , 2016, Science Translational Medicine.

[6]  P. Hahnfeldt,et al.  Minimizing long-term tumor burden: the logic for metronomic chemotherapeutic dosing and its antiangiogenic basis. , 2003, Journal of theoretical biology.

[7]  Urszula Ledzewicz,et al.  Drug resistance in cancer chemotherapy as an optimal control problem , 2005 .

[8]  Philip Hahnfeldt,et al.  Maximum tolerated dose versus metronomic scheduling in the treatment of metastatic cancers. , 2013, Journal of theoretical biology.

[9]  B. G. Birkhead,et al.  A mathematical model of the effects of drug resistance in cancer chemotherapy , 1984 .

[10]  H. Schättler,et al.  On optimal delivery of combination therapy for tumors. , 2009, Mathematical biosciences.

[11]  J. Leith,et al.  Tumor micro-ecology and competitive interactions. , 1987, Journal of theoretical biology.

[12]  Florence Hubert,et al.  MATHEMATICAL MODEL OF CANCER GROWTH CONTROLED BY METRONOMIC CHEMOTHERAPIES , 2013 .

[13]  B. Frieden,et al.  Adaptive therapy. , 2009, Cancer research.

[14]  B. Perthame,et al.  Modeling the Effects of Space Structure and Combination Therapies on Phenotypic Heterogeneity and Drug Resistance in Solid Tumors , 2014, Bulletin of Mathematical Biology.

[15]  John Carl Panetta,et al.  A mathematical model of periodically pulsed chemotherapy: Tumor recurrence and metastasis in a competitive environment , 1996 .

[16]  T van Doorn,et al.  Tumour resistance to cisplatin: a modelling approach , 2005, Physics in medicine and biology.

[17]  Robert A Gatenby,et al.  A theoretical quantitative model for evolution of cancer chemotherapy resistance , 2010, Biology Direct.

[18]  Richard Bellman,et al.  Introduction to the mathematical theory of control processes , 1967 .

[19]  Urszula Ledzewicz,et al.  An Optimal Control Approach to Cancer Chemotherapy with Tumor–Immune System Interactions , 2014 .

[20]  S Gallivan,et al.  A mathematical model of the development of drug resistance to cancer chemotherapy. , 1987, European journal of cancer & clinical oncology.