Analysis of mathematical model of leukemia

Helal, Mohamed; Adimy, Mostafa; Lakmeche, Abdelkader; Praly, Laurent

doi:10.1051/itmconf/20150401005

Cited by 4 publications

(9 citation statements)

References 5 publications

(14 reference statements)

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“…There are extensive mathematical models for representing the dynamics of the CML patient's body. In (Moore & Li, 2004; Padhi & Kothari, 2007; Colijn & Mackey, 2005; Nanda et al, 2007; Aïnseba & Benosman, 2011; Zhang, Tanaka, Chen, & Aihara, 2012; Helal, Adimy, Lakmeche, & Pujo‐Menjouet, 2015; Rădulescu, Candea, & Halanay, 2015; Rădulescu, Candea, & Halanay, 2016; Abdelhafid, Chakir, & Mohamed, 2017), the mathematical models and their explanations are given. All these models follow a very similar mathematical structure and some of them are confronted with the real clinical data.…”

Section: Mathematical Modelmentioning

confidence: 99%

An intelligent control strategy for cancer cells reduction in patients with chronic myelogenous leukaemia using the reinforcement learning and considering side effects of the drug

2020

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Chronic Myelogenous Leukaemia (CML) is a haematopoietic stem cells disease with complex dynamical behaviour. One of the effective factors in treating patients is to determine the appropriate drug dosage. A physician should test the different drug dosages through trial and error in order to find its optimal value. This procedure is normally a time‐consuming and error‐prone task that can even be harmful. The contribution of this paper is to design an intelligent control strategy, which can be used to help physicians, by finding a drug treatment regimen to minimize the number of cancer cells for a CML patient. In this paper, the eligibility traces algorithm and Q‐learning approach are adopted as sub‐optimal methods for progressively reducing the population of cancer cells. In addition, the injected dosage of the drug has improved, compared with previous methods. More importantly, the proposed method is followed by the reduction in side effects of the drug. The advantage of the backward view and the previous states investigation are applied in the Eligibility Traces algorithm. These effects increase the learning procedure and decrease the growth rate of cancer cells and total dosage of the injected drug during the treatment period of time. The proposed strategy mitigates the side effects of the drug on the normal cells.

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Section: Mathematical Modelmentioning

confidence: 99%

An intelligent control strategy for cancer cells reduction in patients with chronic myelogenous leukaemia using the reinforcement learning and considering side effects of the drug

2020

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“…The authors established that the dynamics of the system is unstable around the tumor-free equilibrium and obtained the global stability conditions for the internal tumor equilibrium. A general model for CML to include normal, leukemic and resistant types of both stems cells and progenitor cells is considered in [30] and the global analysis for the disease free, healthy free and endemic equilibrium is discussed. Further, optimal control problems for several imatinib therapy scenarios and the suboptimal response in CML are studied.…”

Section: Introductionmentioning

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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“…The Ph-chromosome results from a reciprocal translocation between the long arms of chromosomes 9 and 22. In this paper, we study a mathematical model of chronic myeloid leukemia (CML) under treatment, the model studied here is inspired from [9] and [16]. Several recent works have been developed to study the dynamics of CML under chemotherapy treatment, see ( [14], [15], [16] and [17]).…”

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confidence: 99%

“…Several recent works have been developed to study the dynamics of CML under chemotherapy treatment, see ( [14], [15], [16] and [17]). More specifically, we consider the following mathematical model which is an extension of the model proposed in [9]. In our model, we assume that normal (resp.…”

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confidence: 99%

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Chronic myeloid leukemia model with periodic pulsed treatment

Helal

Lakmeche

Souna

2019

Revue Africaine De Recherche en Informatique Et Mathématiques Appliquées

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In this work we develop a mathematical model of chronic myeloid leukemia including treatment with instantaneous effects. Our analysis focuses on the values of growth rate γ which give either stability or instability of the disease free equilibrium. If the growth rate γ of sensitive leukemic stem cells is less than some threshold γ * , we obtain the stability of disease free equilibrium which means that the disease is eradicated for any period of treatment τ 0. Otherwise, for γ great than γ * , the period of treatment must be less than some specific value τ * 0. In the critical case when the period of treatment is equal to τ * 0 , we observe a persistence of the tumor, which means that the disease is viable. Dans ce travail, nous développons un modèle mathématique de la leucémie myéloïde chronique avec un traitement à effets instantanés. Notre analyse se focalise sur les valeurs du taux de croissance γ pour avoir la stabilité ou l'instabilité de l'équilibre sans maladie. Si le taux de croissance γ des cellules souches leucémiques sensibles est inférieur à un seuil γ * , nous obtenons la stabilité d'un équilibre sans maladie, ce qui signifie que la maladie sera éradiquée pour toute période de traitement τ 0. Sinon, pour γ supérieur à γ * , la durée du traitement doit être inférieure à une valeur spécifique τ * 0. Dans le cas critique où la période de traitement est égale à τ * 0 , nous observons une persistance de la tumeur, ce qui signifie que la maladie est viable.

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Analysis of mathematical model of leukemia

Cited by 4 publications

References 5 publications

An intelligent control strategy for cancer cells reduction in patients with chronic myelogenous leukaemia using the reinforcement learning and considering side effects of the drug

An intelligent control strategy for cancer cells reduction in patients with chronic myelogenous leukaemia using the reinforcement learning and considering side effects of the drug

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

Chronic myeloid leukemia model with periodic pulsed treatment

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