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Publications about 'drug resistance'
Articles in journal or book chapters
  1. J. M. Greene, C. Sanchez-Tapia, and E.D. Sontag. Mathematical details on a cancer resistance model. Frontiers in Bioengineering and Biotechnology, 8:501: 1-27, 2020. [PDF] [doi:10.3389/fbioe.2020.00501] Keyword(s): drug resistance, chemotherapy, phenotype, optimal control, singular controls.
    Abstract:
    One of the most important factors 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, we expound on the details relating to an optimal control problem outlined in our previous paper (Greene et al., 2018). The control structure is precisely characterized as a concatenation of bang-bang and path-constrained arcs via the Pontryagin Maximum Principle and differential Lie algebraic techniques. A structural identifiability analysis is also presented, demonstrating that patient-specific parameters may be measured and thus utilized in the design of optimal therapies prior to the commencement of therapy. For completeness, a detailed analysis of existence results is also included.


  2. A.P. Tran, M. Ali Al-Radhawi, I. Kareva, J. Wu, D.J. Waxman, and E.D. Sontag. Delicate balances in cancer chemotherapy: Modeling immune recruitment and emergence of systemic drug resistance. Frontiers in Immunology, 11:1376-, 2020. [PDF] [doi:10.3389/fimmu.2020.01376] Keyword(s): metronomic chemotherapy, cyclophosphamide, mathematical modeling, immune recruitment, cancer resistance, immunology.
    Abstract:
    Metronomic chemotherapy can drastically enhance immunogenic tumor cell death. However, the responsible mechanisms are still incompletely understood. Here, we develop a mathematical model to elucidate the underlying complex interactions between tumor growth, immune system activation, and therapy-mediated immunogenic cell death. Our model is conceptually simple, yet it provides a surprisingly excellent fit to empirical data obtained from a GL261 mouse glioma model treated with cyclophosphamide on a metronomic schedule. The model includes terms representing immune recruitment as well as the emergence of drug resistance during prolonged metronomic treatments. Strikingly, a fixed set of parameters, not adjusted for individuals nor for drug schedule, excellently recapitulates experimental data across various drug regimens, including treatments administered at intervals ranging from 6 to 12 days. Additionally, the model predicts peak immune activation times, rediscovering experimental data that had not been used in parameter fitting or in model construction. The validated model was then used to make predictions about expected tumor-immune dynamics for novel drug administration schedules. Notably, the validated model suggests that immunostimulatory and immunosuppressive intermediates are responsible for the observed phenomena of resistance and immune cell recruitment, and thus for variation of responses with respect to different schedules of drug administration.


  3. 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.L. Gevertz, J.M. Greene, and E.D. Sontag. Validation of a mathematical model of cancer incorporating spontaneous and induced evolution to drug resistance. Technical report, Cold Spring Harbor Laboratory, 2019. Note: BioRxiv preprint 10.1101/2019.12.27.889444. Keyword(s): cancer heterogeneity, phenotypic variation, nonlinear systems, epigenetics, optimal control theory.
    Abstract:
    This paper continues the study of a model which was introduced in earlier work by the authors to study spontaneous and induced evolution to drug resistance under chemotherapy. The model is fit to existing experimental data, and is then validated on additional data that had not been used when fitting. In addition, an optimal control problem is studied numerically.


  2. A. P. Tran, M. A. Al-Radhawi, I. Kareva, J. Wu, D. J. Waxman, and E. D. Sontag. Delicate balances in cancer chemotherapy: modeling immune recruitment and emergence of systemic drug resistance. Technical report, Cold Spring Harbor Laboratory, 2019. Note: BioRxiv 2019.12.12.874891. Keyword(s): chemotherapy, immunology, immune system, cancer, tumors, metronomic.
    Abstract:
    Metronomic chemotherapy can drastically enhance immunogenic tumor cell death. However, the responsible mechanisms are still incompletely understood. Here, we develop a mathematical model to elucidate the underlying complex interactions between tumor growth, immune system activation, and therapy-mediated immunogenic cell death. Our model is conceptually simple, yet it provides a surprisingly excellent fit to empirical data obtained from a GL261 mouse glioma model treated with cyclophosphamide on a metronomic schedule. The model includes terms representing immune recruitment as well as the emergence of drug resistance during prolonged metronomic treatments. Strikingly, a fixed set of parameters, not adjusted for individuals nor for drug schedule, excellently recapitulates experimental data across various drug regimens, including treatments administered at intervals ranging from 6 to 12 days. Additionally, the model predicts peak immune activation times, rediscovering experimental data that had not been used in parameter fitting or in model construction. The validated model was then used to make predictions about expected tumor-immune dynamics for novel drug administration schedules. Notably, the validated model suggests that immunostimulatory and immunosuppressive intermediates are responsible for the observed phenomena of resistance and immune cell recruitment, and thus for variation of responses with respect to different schedules of drug administration.


  3. 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): identifiability, 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: Tue Jun 30 22:40:29 2020
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