Numerical analysis of critical parameter values for remission during imatinib treatment of chronic myelogenous leukemia

Dana Paquin; Lizzy Gross; Avery Stewart; Giovani Thai; Dana Paquin; Lizzy Gross; Avery Stewart; Giovani Thai

doi:10.3934/mbe.2025057

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 6: 1551-1571. doi: 10.3934/mbe.2025057

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Numerical analysis of critical parameter values for remission during imatinib treatment of chronic myelogenous leukemia

Department of Mathematics, California Polytechnic State University, 1 Grand Ave, San Luis Obispo, CA 93407, USA

Academic Editor: Bapan Ghosh

Received: 12 December 2024 Revised: 08 April 2025 Accepted: 14 April 2025 Published: 15 May 2025

Chronic myelogenous leukemia (CML) is a cancer of the white blood cells that results from uncontrolled growth of myeloid cells in the bone marrow and the accumulation of these cells in the blood. The most common form of treatment for CML is imatinib, a tyrosine kinase inhibitor. Although imatinib is an effective treatment for CML and most patients treated with imatinib do attain some form of remission, imatinib does not completely eradicate all leukemia cells, and if treatment is stopped, all patients eventually relapse. Kim et al. constructed a system of delay differential equations to mathematically model the dynamics of anti-leukemia T-cell responses to CML during imatinib treatment, and demonstrated the usefulness of the mathematical model for studying novel treatment regimes to enhance imatinib therapy. Paquin et al. demonstrated numerically using this DDE model that strategic treatment interruptions (STIs) may have the potential to completely eradicate CML in certain cases. We conducted a comprehensive numerical study of the model parameters to identify the mathematical and numerical significance of the individual parameter values on the efficacy of imatinib treatment of CML. In particular, we analyzed the effects of the numerical values of the model parameters on the behavior of the system, revealing critical threshold values that impact the ability of imatinib treatment to achieve remission and/or elimination. We also showed that STIs provide improvements to these critical values, categorizing this change as it relates to parameters inherent to either CML growth or immune response.
- chronic myelogenous leukemia,
- imatinib,
- mathematical model,
- parameter analysis,
- strategic treatment interruptions,
- delay differential equations
Citation: Dana Paquin, Lizzy Gross, Avery Stewart, Giovani Thai. Numerical analysis of critical parameter values for remission during imatinib treatment of chronic myelogenous leukemia[J]. Mathematical Biosciences and Engineering, 2025, 22(6): 1551-1571. doi: 10.3934/mbe.2025057

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Abstract

Chronic myelogenous leukemia (CML) is a cancer of the white blood cells that results from uncontrolled growth of myeloid cells in the bone marrow and the accumulation of these cells in the blood. The most common form of treatment for CML is imatinib, a tyrosine kinase inhibitor. Although imatinib is an effective treatment for CML and most patients treated with imatinib do attain some form of remission, imatinib does not completely eradicate all leukemia cells, and if treatment is stopped, all patients eventually relapse. Kim et al. constructed a system of delay differential equations to mathematically model the dynamics of anti-leukemia T-cell responses to CML during imatinib treatment, and demonstrated the usefulness of the mathematical model for studying novel treatment regimes to enhance imatinib therapy. Paquin et al. demonstrated numerically using this DDE model that strategic treatment interruptions (STIs) may have the potential to completely eradicate CML in certain cases. We conducted a comprehensive numerical study of the model parameters to identify the mathematical and numerical significance of the individual parameter values on the efficacy of imatinib treatment of CML. In particular, we analyzed the effects of the numerical values of the model parameters on the behavior of the system, revealing critical threshold values that impact the ability of imatinib treatment to achieve remission and/or elimination. We also showed that STIs provide improvements to these critical values, categorizing this change as it relates to parameters inherent to either CML growth or immune response.

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