Clinical study and numerical simulation of brain cancer dynamics under radiotherapy

Nawrocki, Sergiusz; Zubik‐Kowal, Barbara

doi:10.1016/j.cnsns.2014.08.001

Cited by 14 publications

(2 citation statements)

References 25 publications

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“…This suggests that γ(P ) should be a monotonically decreasing function of P . We illustrate most of our analysis using γ(P ) = r(1 − P/K), which corresponds to a logistic growth [28][29][30], even though Gompertzian growth γ(P ) = r log(K/P ) is tested as well [31].…”

Section: Tumor Growth In the Presence Of Chemotherapeutic Drugsmentioning

confidence: 99%

Nonlinear cancer chemotherapy: Modelling the Norton-Simon hypothesis

López

Iarosz

Batista

et al. 2019

Communications in Nonlinear Science and Numerical Simulation

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A fundamental model of tumor growth in the presence of cytotoxic chemotherapeutic agents is formulated. The model allows to study the role of the Norton-Simon hypothesis in the context of dose-dense chemotherapy. Dose-dense protocols aim at reducing the period between courses of chemotherapy from three weeks to two weeks, in order to avoid tumor regrowth between cycles. We address the conditions under which these protocols might be more or less beneficial in comparison to less dense settings, depending on the sensitivity of the tumor cells to the cytotoxic drugs. The effects of varying other parameters of the protocol, as for example the duration of each continuous drug infusion, are also inspected. We believe that the present model might serve as a foundation for the development of more sophisticated models for cancer chemotherapy.

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Section: Tumor Growth In the Presence Of Chemotherapeutic Drugsmentioning

confidence: 99%

Nonlinear cancer chemotherapy: Modelling the Norton-Simon hypothesis

López

Iarosz

Batista

et al. 2019

Communications in Nonlinear Science and Numerical Simulation

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“…The simulation of the normal and cancer cells' population changes was done with the improved cancer treatment model. The improved model couples the Caputo-Fabrizio fractional cancer treatment model (1) with the linear-quadratic model (2,3). The parameters for the cells population dynamics include the proliferation rates, carrying capacities and competitive coefficients.…”

Section: A T E R I a L S A N D M E T H O D Smentioning

confidence: 99%

Population Dynamics of Normal and Cancer Cells Under Radiotherapy

2019

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The use of the improved cancer treatment model predicted the population changes in the normal and cancer cells during radiotherapy. The simulated radiation doses are 15 Gy, 18 Gy, 20 Gy and 24 Gy administered 5 times for each dose. The population of the cancer cells reduced from 40 % of the carrying capacity to 10.72%, 23.25 %, 1.61 % and 3.72 % of the carrying capacity for the respective doses. The population of the normal cells reduced from 70% of the carrying capacity to 65.50%, 62.48%, 68.49% and 67.59% of the carrying capacity for the respective doses. During the no treatment stage (0 Gy), the model predicted an increase in the population of cancer cells and a decrease in the population of normal cells.

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Fast Parameter Estimation for Cancer Cell Progression and Response to Therapy

Stpiczyński

Zubik‐Kowal

2017

Integral Methods in Science and Engineering, Volume 2

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Clinical study and numerical simulation of brain cancer dynamics under radiotherapy

Cited by 14 publications

References 25 publications

Nonlinear cancer chemotherapy: Modelling the Norton-Simon hypothesis

Nonlinear cancer chemotherapy: Modelling the Norton-Simon hypothesis

Population Dynamics of Normal and Cancer Cells Under Radiotherapy

Fast Parameter Estimation for Cancer Cell Progression and Response to Therapy

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