Optimizing drug regimens in cancer chemotherapy: a simulation study using a PK-PD model

In cancer chemotherapy, it is important to design treatment strategies for drug protocols that ensure a desired rate of tumor cell kill without overdosing the host. Mathematical modeling was used for optimization in which we minimize the end value of the tumor cells while limiting toxicity by always maintaining the white blood cell count beyond a limit. The optimal solution for this is a mixture of an initial bolus application of drug followed by no drug and then continuous infusion that keeps the normal cell population at its lower limit while decreasing the tumor cell population.

[1]  J. Goldie,et al.  A model for the resistance of tumor cells to cancer chemotherapeutic agents , 1983 .

[2]  F L Pereira,et al.  A new optimization based approach to experimental combination chemotherapy. , 1995, Frontiers of medical and biological engineering : the international journal of the Japan Society of Medical Electronics and Biological Engineering.

[3]  J. M. Murray,et al.  Some optimal control problems in cancer chemotherapy with a toxicity limit. , 1990, Mathematical biosciences.

[4]  R. B. Martin,et al.  Optimal control drug scheduling of cancer chemotherapy , 1992, Autom..

[5]  T. Vincent,et al.  Optimal control analysis in the chemotherapy of IgG multiple myeloma. , 1977, Bulletin of mathematical biology.

[6]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[7]  M E Fisher,et al.  A mathematical model of cancer chemotherapy with an optimal selection of parameters. , 1990, Mathematical biosciences.

[8]  C. Nicolini,et al.  Mathematical approaches to optimization of cancer chemotherapy. , 1979, Bulletin of mathematical biology.

[9]  A Iliadis,et al.  Pharmacokinetics and pharmacodynamics of nitrosourea fotemustine: a French cancer centre multicentric study. , 1996, European journal of cancer.

[10]  B. Chabner,et al.  Potential roles for preclinical pharmacology in phase I clinical trials. , 1986, Cancer treatment reports.

[11]  J. M. Murray,et al.  Optimal drug regimens in cancer chemotherapy for single drugs that block progression through the cell cycle. , 1994, Mathematical biosciences.

[12]  L. Sheiner,et al.  Understanding the Dose-Effect Relationship , 1981, Clinical pharmacokinetics.

[13]  Mark J. Ratain,et al.  Principles of Antineoplastic Drug Development and Pharmacology , 1996 .

[14]  A Iliadis,et al.  Dynamical dosage regimen calculations in linear pharmacokinetics. , 1988, Computers and biomedical research, an international journal.

[15]  V. Oliverio,et al.  Clinical pharmacology of anticancer drugs. , 1977, Seminars in oncology.

[16]  Richard Bellman,et al.  Differential-Difference Equations , 1967 .

[17]  L B Sheiner,et al.  Kinetics of pharmacologic response. , 1982, Pharmacology & therapeutics.

[18]  Lawrence M. Fagan,et al.  Combining Physiologic Models and Symbolic Methods to Interpret Time-Varying Patient Data* , 1991, Methods of Information in Medicine.

[19]  A Swierniak,et al.  Optimal control problems arising in cell‐cycle‐specific cancer chemotherapy , 1996, Cell proliferation.

[20]  M A Woodbury,et al.  A new model for tumor growth analysis based on a postulated inhibitory substance. , 1980, Computers and biomedical research, an international journal.

[21]  A. Papoulis Signal Analysis , 1977 .

[22]  John G. Wagner,et al.  Fundamentals of Clinical Pharmacokinetics , 1975 .

[23]  George W. Swan,et al.  Applications of Optimal Control Theory in Biomedicine , 1984 .

[24]  G. W. Swan Role of optimal control theory in cancer chemotherapy. , 1990, Mathematical biosciences.

[25]  Malur K. Sundareshan,et al.  Periodic optimization of a class of bilinear systems with application to control of cell proliferation and cancer therapy , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[26]  Nicholas H. G. Holford,et al.  The Population Approach: Rationale, Methods, and Applications in Clinical Pharmacology and Drug Development , 1994 .

[27]  D. F. Rufer Implementation and Properties of a Method for the Identification of Nonlinear Continuous Time Models , 1978 .

[28]  J. M. Murray,et al.  Optimal control for a cancer chemotherapy problem with general growth and loss functions. , 1990, Mathematical biosciences.