A mathematical model of chemotherapy with variable infusion

Abdulrashid, Ismail; Han, Xiaoying

doi:10.3934/cpaa.2020082

Cited by 4 publications

(2 citation statements)

References 18 publications

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“…For example, we assume a constant dose of drug throughout the simulation. In reality, chemotherapy is not a continuous infusion, but is more accurately modeled by a time-dependent pharmacodynamic model [67]. Additionally, cancer cells are known to develop resistance to chemotherapy [68] which will also change measured IC 50 and ε max values.…”

Section: Discussionmentioning

confidence: 99%

Understanding the effect of measurement time on drug characterization

2020

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In order to determine correct dosage of chemotherapy drugs, the effect of the drug must be properly quantified. There are two important values that characterize the effect of the drug: ε max is the maximum possible effect of a drug, and IC 50 is the drug concentration where the effect diminishes by half. There is currently a problem with the way these values are measured because they are time-dependent measurements. We use mathematical models to determine how the ε max and IC 50 values depend on measurement time and model choice. Seven ordinary differential equation models (ODE) are used for the mathematical analysis; the exponential, Mendelsohn, logistic, linear, surface, Bertalanffy, and Gompertz models. We use the models to simulate tumor growth in the presence and absence of treatment with a known IC 50 and ε max. Using traditional methods, we then calculate the IC 50 and ε max values over fifty days to show the time-dependence of these values for all seven mathematical models. The general trend found is that the measured IC 50 value decreases and the measured ε max increases with increasing measurement day for most mathematical models. Unfortunately, the measured values of IC 50 and ε max rarely matched the values used to generate the data. Our results show that there is no optimal measurement time since models predict that IC 50 estimates become more accurate at later measurement times while ε max is more accurate at early measurement times.

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Section: Discussionmentioning

confidence: 99%

Understanding the effect of measurement time on drug characterization

2020

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“…This is the reason why many scientists are trying to develop accurate mathematical models for tumor growth under different conditions. [1][2][3] Meanwhile, for early diagnosis of cancerous tissues, infrared thermography can be used. 4,5 One of the most effective methods of cancer treatment is chemotherapy.…”

Section: Introductionmentioning

confidence: 99%

Adaptive fuzzy control of drug delivery in cancer treatment using combination of chemotherapy and antiangiogenic therapy

Ghasemabad

Mirhadi

Zarandi

et al. 2023

Proc Inst Mech Eng H

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This paper introduces the adaptive fuzzy control scheme as a promising control technique for cancer treatment from a theoretical point of view. A mathematical model describing the dynamics of tumor growth under the drug interventions of chemotherapy and antiangiogenic therapy is considered. The model incorporates the effects of normal cells, cancer cells, and endothelial cells. Then, the control goals in cancer treatment are discussed and the desired trajectory for a typical patient is derived using the optimal control theory. Since the dynamic model of tumor growth is not accurate and also varies from patient to patient, an adaptive fuzzy controller is designed to make the outputs of the dynamic model track the desired trajectory. The proposed control system is model–independent and identifies the dynamic model of tumor growth over time. The performance of the designed controller is assessed by several numerical simulations. Finally, a hardware–in–the–loop simulation is conducted to validate the results.

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Predicting the effectiveness of chemotherapy using stochastic ODE models of tumor growth

Sharpe

Dobrovolny

2021

Communications in Nonlinear Science and Numerical Simulation

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A mathematical model of chemotherapy with variable infusion

Cited by 4 publications

References 18 publications

Understanding the effect of measurement time on drug characterization

Understanding the effect of measurement time on drug characterization

Adaptive fuzzy control of drug delivery in cancer treatment using combination of chemotherapy and antiangiogenic therapy

Predicting the effectiveness of chemotherapy using stochastic ODE models of tumor growth

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