A Planning Algorithm for Correction Therapies After Allogeneic Stem Cell Transplantation

Precup, Radu; Şerban, Marcel-Adrian; Trif, Damian; Cucuianu, Andrei

doi:10.1007/s10852-012-9187-3

Cited by 7 publications

(6 citation statements)

References 12 publications

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“…In this way, from a mathematical point of view, the transition from one hematological state to another occurs as the result of a change of the basic leukemic cell parameters cumulated by D. The transition is progressive as the disease gets worse, and regressive as a result of treatment. For the last case, our analysis could be a guide to the improvement of therapeutic agents and strategies, as suggested in Precup et al [41].…”

Section: Introductionmentioning

confidence: 90%

A Mathematical Model of the Transition from the Normal Hematopoiesis to the Chronic and Accelerated Acute Stages in Myeloid Leukemia

Parajdi¹,

Precup²,

Bonci³

et al. 2020

Preprint

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A mathematical model given by a two - dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

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Section: Introductionmentioning

confidence: 90%

A Mathematical Model of the Transition from the Normal Hematopoiesis to the Chronic and Accelerated Acute Stages in Myeloid Leukemia

Parajdi¹,

Precup²,

Bonci³

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this way, from a mathematical point of view, the transition from one hematological state to another occurs as the result of a change of the basic leukemic cell parameters accumulated by D. The transition is progressive as the disease gets worse, and regressive as a result of treatment. For the last case, our analysis could be a guide to the improvement of therapeutic agents and strategies, as suggested in Precup et al [41].…”

Section: Introductionmentioning

confidence: 90%

A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia

et al. 2020

Self Cite

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A mathematical model given by a two-dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated-acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated-acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

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“…In the paper by Precup et al (2013), the equilibria of system (5) are found and their stability is established in terms of the system parameters. According to the main result of Precup et al (2013) the system has, as the numerical simulations by Precup et al (2012) suggested, only two asymptotically stable equilibria, namely the 'bad' equilibrium P 2 (0, D, 0) and the 'good' one P 3 (0, 0, d) . The 'good' equilibrium is reached when the transplant succeeds.…”

Section: Control Of Cell Evolution After Bone Marrow Transplantationmentioning

confidence: 99%

“…The source of parameters is the paper by Precup et al (2012). The values are reasonable estimates, as the actual cell kinetics within the stem cell niche are largely inaccessible.…”

Section: Control Of Cell Evolution After Bone Marrow Transplantationmentioning

confidence: 99%

A method of lower and upper solutions for control problems and application to a model of bone marrow transplantation

Parajdi,

Precup,

Haplea

2023

International Journal of Applied Mathematics and Computer Scien

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A Planning Algorithm for Correction Therapies After Allogeneic Stem Cell Transplantation

Cited by 7 publications

References 12 publications

A Mathematical Model of the Transition from the Normal Hematopoiesis to the Chronic and Accelerated Acute Stages in Myeloid Leukemia

A Mathematical Model of the Transition from the Normal Hematopoiesis to the Chronic and Accelerated Acute Stages in Myeloid Leukemia

A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia

A method of lower and upper solutions for control problems and application to a model of bone marrow transplantation

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