Experimental Validation of a Mathematical Model to Describe the Drug Cytotoxicity of Leukemic Cells
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Department of Mathematics, Ariel University, Ariel 4070000, Israel
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Department of Chemical Engineering, Ariel University, Ariel 4070000, Israel
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Adelson School of Medicine, Ariel University, Ariel 4070000, Israel
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Ariel Center for Applied Cancer Research, Ariel University, Ariel 4070000, Israel
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Author to whom correspondence should be addressed.
Academic Editor: Mariano Torrisi
Symmetry 2021, 13(10), 1760; https://doi.org/10.3390/sym13101760
Received: 12 August 2021
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Revised: 14 September 2021
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Accepted: 15 September 2021
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Published: 22 September 2021
(This article belongs to the Special Issue Mathematical Models: Methods and Applications)
Chlorambucil (Chl), Melphalan (Mel), and Cytarabine (Cyt) are recognized drugs used in the chemotherapy of patients with advanced Chronic Lymphocytic Leukemia (CLL). The optimal treatment schedule and timing of Chl, Mel, and Cyt administration remains unknown and has traditionally been decided empirically and independently of preclinical in vitro efficacy studies. As a first step toward mathematical prediction of in vivo drug efficacy from in vitro cytotoxicity studies, we used murine A20 leukemic cells as a test case of CLL. We first found that logistic growth best described the proliferation of the cells in vitro. Then, we tested in vitro the cytotoxic efficacy of Chl, Mel, and Cyt against A20 cells. On the basis of these experimental data, we found the parameters for cancer cell death rates that were dependent on the concentration of the respective drugs and developed a mathematical model involving nonlinear ordinary differential equations. For the proposed mathematical model, three equilibrium states were analyzed using the general method of Lyapunov, with only one equilibrium being stable. We obtained a very good symmetry between the experimental results and numerical simulations of the model. Our novel model can be used as a general tool to study the cytotoxic activity of various drugs with different doses and modes of action by appropriate adjustment of the values for the selected parameters.
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Keywords:
A20 cells; cytotoxicity rate; in vitro experiments; logistic cancer growth rate; stability analysis; tumor doubling time
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MDPI and ACS Style
Guzev, E.; Luboshits, G.; Bunimovich-Mendrazitsky, S.; Firer, M.A. Experimental Validation of a Mathematical Model to Describe the Drug Cytotoxicity of Leukemic Cells. Symmetry 2021, 13, 1760. https://doi.org/10.3390/sym13101760
AMA Style
Guzev E, Luboshits G, Bunimovich-Mendrazitsky S, Firer MA. Experimental Validation of a Mathematical Model to Describe the Drug Cytotoxicity of Leukemic Cells. Symmetry. 2021; 13(10):1760. https://doi.org/10.3390/sym13101760
Chicago/Turabian StyleGuzev, Ekaterina, Galia Luboshits, Svetlana Bunimovich-Mendrazitsky, and Michael A. Firer. 2021. "Experimental Validation of a Mathematical Model to Describe the Drug Cytotoxicity of Leukemic Cells" Symmetry 13, no. 10: 1760. https://doi.org/10.3390/sym13101760
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