Abstract
A pseudohyperbolic problem of optimal control of intratumoral drug distribution is formulated. It takes into account the heterogeneity of tumor tissues and effects of convection diffusion in a fissured porous medium. A mathematical model constructed and the corresponding optimal control problem are shown to be correct.
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References
R. K. Jain, “Transport of molecules, particles, and cells in solid tumors,” Annu. Rev. Biomed. Eng., 1, 241–263 (1999).
S. H. Jang, M. G. Wientjes, D. Lu, and J. L. S. Au, “Drug delivery and transport in solid tumors,” Pharm. Res., 20, 1337–1350 (2003).
L. T. Baxter and R. K. Jain, “Transport of fluid and macromolecules in tumors. I. Role of interstitial pressure and convection,” Microvasc. Res., 37, 77–104 (1989).
L. T. Baxter and R. K. Jain, “Transport of fluid and macromolecules in tumors. II. Role of heterogeneous perfusion and lymphatics,” Microvasc. Res., 40, 246–263 (1990).
L. T. Baxter and R. K. Jain, “Transport of fluid and macromolecules in tumors. III. Role of binding and metabolism,” Microvasc. Res., 41, 5–23 (1991).
J. Lankelma, R. F. Luque, H. Dekker, W. Schinkel, and H.M. Pinedo, “A mathematical model of drug transport in human breast cancer,” Microvasc. Res., 59, 149–161 (1999).
E. P. Goldberg, A. R. Hadba, B. A. Almond, and J. S. Marotta, “Intratumoral cancer chemotherapy and immunotherapy: Opportunities for nonsystemic preoperative drug delivery,” J. Pharm. Pharmacol., 54, 159–180 (2002).
J. P. Ward and J. R. King, “Mathematical modelling of drug transport in tumor multicell spheroids and monolayer cultures,” Math. Biosciences, 181, No. 2, 177–207 (2003).
A. R. Tzafriri, E. I. Lerner, M. Flashner-Barak, M. Hinchckiffe, E. Ratner, and H. Parnas, “Mathematical modeling and optimization of drug delivery from intratumorally injected microspheres,” Clinical Cancer Res., 11, 826–834 (2005).
W. Kaowumpai, W. Koolpiruck, and K. Viravaidya, “Development of a mathematical model for doxorubicin controlled release system using Pluronic gel for breast cancer,” in: Abstracts 2nd Intern. Symp. on Biomed. Eng. (Bangkok, Thailand, November 8–10, 2006) (2006), pp. 65–70.
Y. M. F. Goh, H. L. Kong, and C.-H. Wang, “Simulation of the Delivery of Doxorubicin to Hepatoma,” Pharmaceutical Res., 18, No. 6, 761–770 (2001).
O. A. Plumb and S. Whitaker, “Dispersion in heterogeneous porous media. Parts 1 and 2,” Water Resour. Res., 24, No. 7, 913–938 (1988).
S. I. Lyashko, Generalized Control of Linear Systems [in Russian], Naukova Dumka, Kiev (1998).
S. I. Lyashko, D. F. Nomirovskii, and T. I. Sergienko, “Trajectory and final controllability in hyperbolic and pseudohyperbolic systems with generalized actions,” Cybernetics and Systems Analysis, No. 5, 157–166 (2001).
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Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 147–154, November–December 2007.
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Klyushin, D.A., Lyashko, N.I. & Onopchuk, Y.N. Mathematical modeling and optimization of intratumor drug transport. Cybern Syst Anal 43, 886–892 (2007). https://doi.org/10.1007/s10559-007-0113-z
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DOI: https://doi.org/10.1007/s10559-007-0113-z