The first model includes chemotherapy effect on logistic tumor proliferation, while the second one demonstrates radiotherapy effect on exponential tumor increasing, whereas the third one models the effects of the combination of chemotherapy and radiotherapy on Gompertzian tumor growth.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:This paper aims to control partial differential equations, modeling cancer chemotherapy and or radiotherapy, so in order to asymptotically stabilize the tumor density.
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Temel Bulgular & Veri:Viability kernel of general model on set of initial condition is used to solve the control problem, and characterize the control solution as regulation law of regulation map.
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Sonuç & Katkı:The first model includes chemotherapy effect on logistic tumor proliferation, while the second one demonstrates radiotherapy effect on exponential tumor increasing, whereas the third one models the effects of the combination of chemotherapy and radiotherapy on Gompertzian tumor growth.
This paper aims to control partial differential equations, modeling cancer chemotherapy and or radiotherapy, so in order to asymptotically stabilize the tumor density. Viability kernel of general model on set of initial condition is used to solve the control problem, and characterize the control solution as regulation law of regulation map. Three models from the literature are considered to simulate the results. The first model includes chemotherapy effect on logistic tumor proliferation, while the second one demonstrates radiotherapy effect on exponential tumor increasing, whereas the third one models the effects of the combination of chemotherapy and radiotherapy on Gompertzian tumor growth.
MOUSTAFİD, A. (2023). Set-Valued Stabilization of Reaction-Diffusion Model by Chemotherapy and or Radiotherapy. Fundamental Journal of Mathematics and Applications, Cilt: 6 Sayı: 3, 147–156. https://ajindex.com/articles/964187
V. Noviantri, T. Tomy, A. Chowanda, Linear and nonlinear model of brain tumor growth simulation using finite difference method, Procedia Comput. Sci., 179 (2021), 297-304
F. Mohd, H. Sulaiman, N. A. Alias, Modified Swanson’s equation to detect the growth of glioblastomas multiforme (GBM) tumour, Int. J. Adv. Res. Eng. Innıv., 3(1) (2021), 1-18
Y. Zhang, P. X. Liu, W. Hou, Modeling of glioma growth using modified reaction-diffusion equation on brain MR images, Comput. Methods Programs Biomed., 227 (2022), 107233
N. Henscheid, Generating patient-specific virtual tumor populations with reaction-diffusion models and molecular imaging data, Math. Biosci. Eng., 17(6) (2020), 6531-6556
A. K. Y. Tam, M. J. Simpson, Pattern formation and front stability for a moving-boundary model of biological invasion and recession, Phys. D: Nonlinear Phenom., 444 (2023), 133593
V. A. Khoa, Convergence of a spectral regularization of a time-reversed reaction-diffusion problem with high-order Sobolev-Gevrey smoothness, J. Math. Anal. Appl., 518(1) (2023), 126666
B. Liang, L. Lozenski, U. Villa, D. Faghihi, PDE-constrained optimization formulation for tumor growth model calibration, ArXiv Preprint ArXiv:2302.06445, (2023)
K. N. Soltanov, Behavior of solutions nonlinear reaction-diffusion PDE’s relation to dynamics of propagation of cancer, ArXiv Preprint ArXiv:2108.03023, (2021)
N. A. Nayied, F. A. Shah, K. S. Nisar, M. A. Khanday, S. Habeeb, Numerical assessment of the brain tumor growth model via fibonacci and haar wavelets, Fractals, 31(2) (2023), 2340017
R. Everett, K. B. Flores, N. Henscheid, J. Lagergren, K. Larripa, D. Li, T. J. Nardini, P.T.T. Nguyen, E. B. Pitman, E. M. Rutter, A tutorial review of mathematical techniques for quantifying tumor heterogeneity, Math. Biosci. Eng., 17(4) (2020), 3660-3709
I. Mazari, The bang-bang property in some parabolic bilinear optimal control problems via two-scale asymptotic expansions, J. Funct. Anal., 284(10) (2023), 109855
N. Moshtaghi-Kashanian, H. Niroomand-Oscuii, N. Meghdadi, Simulating glioblastoma growth consisting both visible and invisible parts of the tumor using a diffusion–reaction model followed by resection and radiotherapy, Acta Neurol. Belg., 120 (2020), 629-637
M. S. Iqbal, N. Ahmed, R. Naeem, A. Akg¨ul, A. Razzaque, M. Inc, H. Khurshid, Dynamical behavior of cancer cell densities in two dimensional domain by the representation theory of solitons, Phys