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Publications about 'chemotherapy'
Articles in journal or book chapters
  1. J.M. Greene, J.L. Gevertz, and E. D. Sontag. A mathematical approach to distinguish spontaneous from induced evolution of drug resistance during cancer treatment. JCO Clinical Cancer Informatics, DOI: 10.1200/CCI.18.00087:1-20, 2019. [PDF] Keyword(s): cancer heterogeneity, phenotypic variation, nonlinear systems, epigenetics.
    Abstract:
    Resistance to chemotherapy is a major impediment to the successful treatment of cancer. Classically, resistance has been thought to arise primarily through random genetic mutations, after which mutated cells expand via Darwinian selection. However, recent experimental evidence suggests that the progression to resistance need not occur randomly, but instead may be induced by the therapeutic agent itself.This process of resistance induction can be a result of genetic changes, or can occur through epigenetic alterations that cause otherwise drug-sensitive cancer cells to undergo ``phenotype switching''. This relatively novel notion of resistance further complicates the already challenging task of designing treatment protocols that minimize the risk of evolving resistance. In an effort to better understand treatment resistance, we have developed a mathematical modeling framework that incorporates both random and drug-induced resistance. Our model demonstrates that the ability (or lack thereof) of a drug to induce resistance can result in qualitatively different responses to the same drug dose and delivery schedule. The importance of induced resistance in treatment response led us to ask if, in our model, one can determine the resistance induction rate of a drug for a given treatment protocol. Not only could we prove that the induction parameter in our model is theoretically identifiable, we have also proposed a possible in vitro experiment which could practically be used to determine a treatment's propensity to induce resistance.


Conference articles
  1. J.M. Greene, C. Sanchez-Tapia, and E.D. Sontag. Control structures of drug resistance in cancer chemotherapy. In Proc. 2018 IEEE Conf. Decision and Control, pages 5195-5200, 2018. [PDF]
    Abstract:
    The primary factor limiting the success of chemotherapy in cancer treatment is the phenomenon of drug resistance. This work extends the work reported in "A mathematical approach to distinguish spontaneous from induced evolution of drug resistance during cancer treatment" by introducing a time-optimal control problem that is analyzed utilizing differential-geometric techniques: we seek a treatment protocol which maximizes the time of treatment until a critical tumor size is reached. The general optimal control structure is determined as a combination of both bang-bang and path-constrained arcs. Numerical results are presented which demonstrate decreasing treatment efficacy as a function of the ability of the drug to induce resistance. Thus, drug-induced resistance may dramatically effect the outcome of chemotherapy, implying that factors besides cytotoxicity should be considered when designing treatment regimens.


Internal reports
  1. J.M. Greene, C. Sanchez-Tapia, and E.D. Sontag. Mathematical details on a cancer resistance model. Technical report, bioRxiv 2018/475533, 2018. [PDF] Keyword(s): drug resistance, chemotherapy, optimal control theory, singular controls.
    Abstract:
    The primary factor limiting the success of chemotherapy in cancer treatment is the phenomenon of drug resistance. We have recently introduced a framework for quantifying the effects of induced and non-induced resistance to cancer chemotherapy . In this work, the control structure is precisely characterized as a concatenation of bang-bang and path-constrained arcs via the Pontryagin Maximum Principle and differential Lie techniques. A structural identfiability analysis is also presented, demonstrating that patient-specfic parameters may be measured and thus utilized in the design of optimal therapies prior to the commencement of therapy.



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Last modified: Wed Aug 7 15:28:02 2019
Author: sontag.


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