2022
DOI: 10.1088/1742-6596/2287/1/012013
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Mathematical Model for Combined Radiotherapy and Chemotherapy that Fits with Experimental Data

Abstract: One of the most challenges to effective treatment of cancer is radiation resistance. Published data from a notably experiment performed to examine the ability of a compound therapy to overcome radiation resistance is utilized. The chemotherapeutic drug used was vinblastine. The experiment included control tumors and tumors which were treated with radiation, chemotherapy, or both. In this paper a mathematical model is developed. The model fits with the data reported from the mentioned experiment. Starting with … Show more

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Cited by 4 publications
(7 citation statements)
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“…(e α 1 t −1) of the dynamics (21) in the absence of therapy (v I (t), v M (t), h m (t)) = (0, 0, 0), see Fig. 1, is reversed to an upper exponential decreasing y(t) ≤ y 0 e −αt (11) with α > α 1 , towards null limit (7), see Fig. 2, by the therapy (v I (t), v M (t), h m (t)) = u(t, x) solution to the minimization problem (20), which is numerically solved in the Section 4 by Uzawa method (26-27) of parameter (λ, σ), to get numerical solution (y, x) of discretized model (25) by Euler method of step h, see Fig.…”
Section: Discussionmentioning
confidence: 95%
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“…(e α 1 t −1) of the dynamics (21) in the absence of therapy (v I (t), v M (t), h m (t)) = (0, 0, 0), see Fig. 1, is reversed to an upper exponential decreasing y(t) ≤ y 0 e −αt (11) with α > α 1 , towards null limit (7), see Fig. 2, by the therapy (v I (t), v M (t), h m (t)) = u(t, x) solution to the minimization problem (20), which is numerically solved in the Section 4 by Uzawa method (26-27) of parameter (λ, σ), to get numerical solution (y, x) of discretized model (25) by Euler method of step h, see Fig.…”
Section: Discussionmentioning
confidence: 95%
“…Remark 2. In addition to the asymptotic stability (7), the tumor size y is a decreasing function, since the derivative ẏ is strictly negative as (10), and the Graph(y) is convex which rends the decreasing more considerable, however large values of the parameter α may decrease further the tumor size y.…”
Section: The Problemmentioning
confidence: 99%
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“…The two aspects described above are related to the administration scheduling that has an effect on tumor progression, regression, and the evolution of resistant cells. To determine the optimal chemotherapy schedule, mathematical models have been employed for personalized cancer treatment [30,[229][230][231][232][233][234][235][236][237][238][239].…”
Section: Tumor Modeling With Chemotherapy Treatmentmentioning
confidence: 99%
“…Also, there are many mathematical models suggested for treating cancer by chemotherapy [11,12,27]. Furthermore, there are several studies that provide mathematical models to simulate the effects of combined radiotherapy and chemotherapy [28][29][30][31][32]. Ghaffari et.…”
Section: Introductionmentioning
confidence: 99%