Stability Analysis of a Model of Interaction Between the Immune System and Cancer Cells in Chronic Myelogenous Leukemia

Besse, Apollos; Clapp, Geoffrey D.; Bernard, Samuel; Nicolini, Franck E.; Levy, Doron; Lepoutre, Thomas

doi:10.1007/s11538-017-0272-7

Cited by 30 publications

(35 citation statements)

References 20 publications

(43 reference statements)

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“…where r = r − µ and K = K 1 − µ r . However, the form of the first equation of (2.1) was motivated by the models in [15,32]. From the biological perspective, all the model parameters have to be positive, and accordingly, the initial condition for the system (2.1) is (C s (0), C m (0), T (0)) ∈ R 3 + .…”

Section: Deterministic Modelmentioning

confidence: 99%

A quantitative study on the role of TKI combined with Wnt/β-catenin signaling and IFN-α in the treatment of CML through deterministic and stochastic approaches

Pan

Raha

Chakrabarty

2020

Chaos, Solitons & Fractals

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We propose deterministic and stochastic models for studying the pharmacokinetics of chronic myeloid leukemia (CML), upon administration of IFN-α (the traditional treatment for CML), TKI (the current frontline medication for CML) and Wnt/β-catenin signaling (the state-of-the art therapeutic breakthrough for CML). To the best of our knowledge, no mathematical model incorporating all these three therapeutic protocols are available in literature. Further, this work introduces a stochastic approach in the study of CML dynamics.The key contributions of this work are: (1) Determination of the patient condition, contingent upon the patient specific model parameters, which leads to prediction of the appropriate patient specific therapeutic dosage. (2) Addressing the question of how the dual therapy of TKI and Wnt/β-catenin signaling or triple combination of all three, offers potentially improved therapeutic responses, particularly in terms of reduced side effects of TKI or IFN-α. (3) Prediction of the likelihood of CML extinction/remission based on the level of CML stem cells at detection.

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Section: Deterministic Modelmentioning

confidence: 99%

A quantitative study on the role of TKI combined with Wnt/β-catenin signaling and IFN-α in the treatment of CML through deterministic and stochastic approaches

Pan

Raha

Chakrabarty

2020

Chaos, Solitons & Fractals

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“…Cancer models based on differential equations form a vast body of literature: see, among others [9,11,12]. There exist models considering tumorigenesis in greater detail than is done here, for instance [4,7,34,36]; as concerns the interaction of cancer with the immune system, [3,9,20], modelling of therapies, [14,31] and more specifically on drug resistance to therapies, [5,15,21]. Extensive bibliographic references can be found in the review papers [2,10].…”

Section: The Modelmentioning

confidence: 99%

Efficiency of cancer treatments:in silico experiments

Piretto

Delitala

Ferraro

2020

Math. Model. Nat. Phenom.

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Despite the advances in the formulation of different therapies to fight cancer, the design of successful protocols is still a challenging problem. In order to provide some indications on the effectiveness of medical treatments, results from in silico experiments are presented based on a mathematical model comprising two cancer populations competing for resources and with different susceptibilities to the action of therapies. The focus is on the outcome of protocols in which the total dose can be administered with different time distributions. An efficiency index is proposed to quantify the effectiveness of different protocols. Simulations show that a standard dose chemotherapy is effective when the sensitive clone has a marked competitive advantage, whereas its outcome is much worse when a resistant clone emerges; obviously combinations of immune and chemotherapy work better. These results, in accord with previous finding reported in the literature, stress the importance to take into account competitive interactions among cancer clones to decide which therapeutic strategy should be adopted. However, it is not just the efficiency that changes in these different configurations of clonal composition and therapy timing. A general rule seems to emerge: when evolutionary pressures are strong, the best protocols entail and early starting of the treatment, whereas, on the contrary, when interactions among clones are weak, therapy should start later. Finally the model has been adapted to investigate the relative efficiency of different protocols, by using data reported in literature regarding experiments with breast cancer cells.

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“…Continuing the immune system theme, Besse et al (2017) present a 3-compartment ODE model for the immune response to chronic myelogenous leukemia (CML). This model, a simplification of their previously published model, is amenable to a very detailed mathematical analysis, and it is shown to fit patient data well.…”

Section: Special Issue On Mathematical Oncologymentioning

confidence: 99%

Mathematical Oncology

Anderson

Maini²

2018

Bull Math Biol

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Despite a huge amount of research effort, cancer continues to be a major killer. One of the main reasons for this is the immense complexity of the disease. Cancer is a multiscale process in which genetic mutations occurring at a subcellular level manifest themselves as functional changes at the cellular and tissue scale. Conversely, tissue level properties, such as blood flow, produce Darwinian selection forces that govern the local distribution of cellular phenotypes and genotypes. Changes in tissue lead to a disruption of organ form and function that can ultimately lead to failure and death (Fig. 1). This multiscale aspect of cancer has largely been neglected in the reductionist paradigm, which typically views cancer as "a disease of the genes". The reason for this is clear as the remarkable advances in molecular technology have greatly enhanced quantitative measurements at the genetic scale, while cellular-or tissue-scale properties remain the province of pathology and radiology, which generally lack such tools. The genomic revolution has led to the development of an extensive set of tools to measure and analyze gene expression and mutation. However, the mapping of these changes to in vivo structure and function of cancer cells and tissue remains limited. Furthermore, while tumor evolution is often viewed as a mutation-driven process, it is

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Stability Analysis of a Model of Interaction Between the Immune System and Cancer Cells in Chronic Myelogenous Leukemia

Cited by 30 publications

References 20 publications

A quantitative study on the role of TKI combined with Wnt/β-catenin signaling and IFN-α in the treatment of CML through deterministic and stochastic approaches

A quantitative study on the role of TKI combined with Wnt/β-catenin signaling and IFN-α in the treatment of CML through deterministic and stochastic approaches

Efficiency of cancer treatments:in silico experiments

Mathematical Oncology

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