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Controlling a model for bone marrow dynamics in cancer chemotherapy

Urszula Ledzewicz, Heinz Schättler
2004 Mathematical Biosciences and Engineering  
This paper analyzes a mathematical model for the growth of bone marrow cells under cell-cycle-specific cancer chemotherapy originally proposed by Fister and Panetta [8] .  ...  We apply the Maximum Principle, followed by high-order necessary conditions for optimality of singular arcs and give sufficient conditions for optimality based on the method of characteristics.  ...  In this paper we analyzed a model for cancer chemotherapy proposed earlier by Fister and Panetta [19, 8] , which aims at minimizing the damage to bone marrow cells during chemotherapy with an objective  ... 
doi:10.3934/mbe.2004.1.95 pmid:20369962 fatcat:jbepsca43bfnno4nlhifiduzla

Scheduling the adjuvant endocrine therapy for early stage breast cancer

Sera Kahruman, Elif Ulusal, Sergiy Butenko, Illya V. Hicks, Kathleen M. Diehl
2010 Annals of Operations Research  
Based on the data available through published trial results, we build a mixed integer nonlinear programming (MINLP) model in order to find an optimal treatment plan for a given Hr+ early stage breast cancer  ...  used in the constraints for the risks of several side effects, including endometrial cancer, thromboembolic events, cardiovascular diseases, bone fractures, hot flushes, and vaginal bleeding.  ...  ) , Fister and Panetta (2000) .  ... 
doi:10.1007/s10479-010-0741-y fatcat:noe3ostxtndcvhasnofjm5wuue

Understanding the antiangiogenic effect of metronomic chemotherapy through a simple mathematical model

Diego S. Rodrigues, Paulo F.A. Mancera, Suani T.R. Pinho
2016 Physica A: Statistical Mechanics and its Applications  
to be more effective in eliminating tumour cells. a b s t r a c t Despite the current and increasingly successful fight against cancer, there are some important questions concerning the efficiency of  ...  The in silico approach may be very useful for providing a comparative analysis of these two kinds of protocols.  ...  In order to improve and clarify how chemotherapy works, one can use mathematical modelling, for example, to design oncologic chemotherapy protocols (Panetta & Fister [1] ).  ... 
doi:10.1016/j.physa.2016.07.076 fatcat:e2ugxhkhknaxtegz6itgpqkdii