Age-structured and two-delay models for erythropoiesis

Bélair, Jacques; Mackey, Michael C.; Mahaffy, Joseph M.

doi:10.1016/0025-5564(94)00078-e

Cited by 167 publications

(183 citation statements)

References 42 publications

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“…In 1995, Bélair et al (1995) proposed a modification of Mackey's model to consider the influence of growth factors on stem cell differentiation. The authors focused on erythropoiesis and assumed that erythropoietin (EPO) -a growth factor known to play a crucial role in erythropoiesis regulation -acted only on introduction of HSC in cycle.…”

Section: Introductionmentioning

confidence: 99%

Adding self-renewal in committed erythroid progenitors improves the biological relevance of a mathematical model of erythropoiesis

Crauste¹,

Praly²,

Génieys³

et al. 2008

Journal of Theoretical Biology

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Section: Introductionmentioning

confidence: 99%

Adding self-renewal in committed erythroid progenitors improves the biological relevance of a mathematical model of erythropoiesis

Crauste¹,

Praly²,

Génieys³

et al. 2008

Journal of Theoretical Biology

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“…Though the preliminary estimates of ' r value, there is quite a difference between the other preliminary parameter estimates and the actual values that were arrived at in the fit. The origin of this discrepancy is primarily due to the fact that the actual value of  as given ranges from about 2 to 5, values well below the previously estimated values of [8][9][10][11][12][13][14][15][16]. Though we have no data that would allow us to estimate the value of  in normal dogs, if they have hematopoietic systems similar to humans and the mouse, the low values of  calculated here would suggest that the ANC (Absolute Neutophil Count) has much less available in their neutrophil control system to respond to increased demands for neutrophils.…”

Section: Introductionmentioning

confidence: 76%

G-CSF Reduction: The Equilibrium Solution for the DDE and a Sufficient Condition for the Global Stability

Balamuralitharan¹,

Rajasekaran²

2012

IJCA

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In this paper, we introduce delay differential equation (DDE) models of the hematopoietic system designed for the study of the effects of Granulocyte-Colony Stimulating Factor (G-CSF) administration. G-CSF is used clinically for treating subjects presenting low numbers of white blood cells, a condition referred to as Neutropenia that can result from different causes. The aim of this paper is to study alternative treatment that would minimize the use of G-CSF drug using a mathematical modeling.We propose is a parameter estimation model that considers G-CSF administration for Cyclical Neutropenia (CN), a dynamical disorder characterized by oscillations in the circulating neutrophil count. The model develops the dynamics of circulating blood cells before and after the G-CSF treatment. The model develops the equilibrium solution for the DDE and a sufficient condition for the global stability. The model focuses on the effects of two compartments forms of G-CSF for the treatment of CN (Fast Fourier Transform simulations). For each model, we use a combination of mathematical analysis and numerical simulations (linear chain trick) to study alternative G-CSF treatment that would be efficient while reducing the amount of drug. This reduces the quantity of G-CSF required for potential maintenance. This model gives us good result in treatment. The changes would be analytical and reduce the risk side as well as the cost of treatment in G-CSF.

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“…Strong collaborations kept on being fruitful. For instance, Mackey produced several works mostly theoretical with Lasota [176], [177] on stability studies for cell replication, work with Milton [200] on feedbacks and delays, Bélair and Mahaffy on two delay models [54] and state dependent delay models with moving boundary contitions [204]. New collaborations started on the same spirit as Lasota, mainly with Rudnicki [202], [203] on theoretical study of an age-maturity model.…”

Section: The 1990's: Continuitymentioning

confidence: 99%

“…Other general cyclic hematopoietic diseases were studied [264], some with chemotherapy modeling attempts [270], [163] or treatments [142] and other hematotoxic products [260]. Few works were focused on erythropoiesis, besides some theoretical approaches from Bélair et al [54], [202], [254], [256] and some attempts to fit experimental data for anemia [189], or erythropoietin (EPO) effect [98], [101].…”

Section: The 1990's: Continuitymentioning

confidence: 99%

Blood Cell Dynamics: Half of a Century of Modelling

Praly

2016

Math. Model. Nat. Phenom.

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Abstract. The objective of this paper is to give a review of the main works dealing with mathematical modeling of blood cell formation, disorders and treatments within the past fifty years. From the first models to the most recent ones, this research field has inspired many leading experts in mathematics, biology, physics, physiology and computer sciences. Each contribution was a step further to the understanding of these complex processes. This work summarizes the key ones and tries to show not only the evolution of the interest for this problem but also the different research trends throughout the decades up to the latest models of the past years.

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Age-structured and two-delay models for erythropoiesis

Cited by 167 publications

References 42 publications

Adding self-renewal in committed erythroid progenitors improves the biological relevance of a mathematical model of erythropoiesis

Adding self-renewal in committed erythroid progenitors improves the biological relevance of a mathematical model of erythropoiesis

G-CSF Reduction: The Equilibrium Solution for the DDE and a Sufficient Condition for the Global Stability

Blood Cell Dynamics: Half of a Century of Modelling

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