A mathematical model of the acute myeloblastic leukemic state in man

Rubinow, S. I.; Lebowitz, Joel L.

doi:10.1016/s0006-3495(76)85740-2

Cited by 55 publications

(34 citation statements)

References 27 publications

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“…The first mathematical models of CML date back to 1969 and are due to Vincent et al (1969), and Rubinow and Lebowitz (1976a, 1976b, 1977. A pioneering work originating from the hematopoietic system is due to Fokas et al (1991).…”

Section: Introductionmentioning

confidence: 99%

Modeling Imatinib-Treated Chronic Myelogenous Leukemia: Reducing the Complexity of Agent-Based Models

2007

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We develop a model for describing the dynamics of imatinib-treated chronic myelogenous leukemia. Our model is based on replacing the recent agent-based model of Roeder et al. (Nat. Med. 12(10):1181-1184, 2006) by a system of deterministic difference equations. These difference equations describe the time-evolution of clusters of individual agents that are grouped by discretizing the state space. Hence, unlike standard agent-base models, the complexity of our model is independent of the number of agents, which allows to conduct simulation studies with a realistic number of cells. This approach also allows to directly evaluate the expected steady states of the system. The results of our numerical simulations show that our model replicates the averaged behavior of the original Roeder model with a significantly reduced computational cost. Our general approach can be used to simplify other similar agent-based models. In particular, due to the reduced computational complexity of our technique, one can use it to conduct sensitivity studies of the parameters in large agent-based systems.

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Section: Introductionmentioning

confidence: 99%

Modeling Imatinib-Treated Chronic Myelogenous Leukemia: Reducing the Complexity of Agent-Based Models

2007

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“…In 1975, Rubinow and Lebowitz published some of the first papers on mathematical modeling of neutrophil production in man and applications to acute myeloblastic leukemia. [77][78][79] Based on partial and delay differential equations, Adimy and Crauste developed an age-structured model of hematopoiesis and applied it to chronic myeloid leukemia (CML). 80 The equations describe the rates of change of the densities of the populations of proliferating and nonproliferating cells, and their dependence on the concentration of intercellular growth factors, one that influences apoptosis and another that affects stem cell proliferative capacity.…”

Section: Stress and Disease As Systemic Perturbationsmentioning

confidence: 99%

Hematopoiesis and its disorders: a systems biology approach

Whichard

Sarkar

Kimmel

et al. 2010

Blood

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Scientists have traditionally studied complex biologic systems by reducing them to simple building blocks. Genome sequencing, high-throughput screening, and proteomics have, however, generated large datasets, revealing a high level of complexity in components and interactions. Systems biology embraces this complexity with a combination of mathematical, engineering, and computational tools for constructing and validating models of biologic phenomena. The validity of mathematical modeling in hematopoiesis was established early by the pioneering work of Till and McCulloch. In reviewing more recent papers, we highlight deterministic, stochastic, statistical, and network-based models that have been used to better understand a range of topics in hematopoiesis, including blood cell production, the periodicity of cyclical neutropenia, stem cell production in response to cytokine administration, and the emergence of imatinib resistance in chronic myeloid leukemia. Future advances require technologic improvements in computing power, imaging, and proteomics as well as greater collaboration between experimentalists and modelers. Altogether, systems biology will improve our understanding of normal and abnormal hematopoiesis, better define stem cells and their daughter cells, and potentially lead to more effective therapies. (Blood. 2010;115:2339-2347) IntroductionDespite advances made in identifying genes, epigenetic modifiers, lipids, proteins, and their posttranslational processing, much remains unknown about the precise roles these components play in health and disease. That biologic processes are complex and dynamic has been clearly established, albeit underappreciated. 1 One obstacle to a more complete understanding is that reductionism dominates biologists' thinking. Reductionism states that a problem can be solved by decomposing it into building blocks and studying them one at a time. 2 Large datasets of genes, lipids, metabolites, and proteins have made it impossible for one to intuit, reinforcing the appeal of reductionism. Yet, by breaking down a system one may lose properties that emerge only by virtue of the system's complexity. Systems biology approaches embrace this complexity, using engineering principles and computational methods to build and validate models using experimental data (Table 1). 3 Using these and other approaches, systems biology seeks to explain and predict the complex properties underlying normal and abnormal physiology.Biologic systems are multiscalar, functioning at the molecular, cellular, tissue, and organismismal levels. To perform their specialized functions, highly differentiated blood cells are continuously produced by stem cells. A combination of more than a dozen growth and stromal factors drive cells to divide asymmetrically, undergo differentiation, and carry out their end-cell functions. More than 10 000 genes are expressed in a B-cell lymphocyte. 4 A simple erythrocyte, enucleated and without mitochondria, contains more than 750 proteins, ignoring posttranslational modifications...

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“…We suppose that A is controlled by a similar equation to that of S, but with different parameters, as described below. A model of essentially this type was introduced by Rubinow and Lebowitz (1976) in modelling acute myeloblastic leukaemia. However, they considered the precursor cells to be myeloblasts rather than stem cells, so that although the model was quite similar to that given here, the appropriate parameter choice was quite different.…”

Section: A Competitive G 0 Modelmentioning

confidence: 99%

“…A mathematical model of this has been proposed by Rubinow and Lebowitz (1976). This is in contrast to the Dowding hypothesis, which suggests that leukemic stem cell proliferation alone can explain the expansion (Gordon et al 1987).…”

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confidence: 99%

A Model of Oscillatory Blood Cell Counts in Chronic Myelogenous Leukaemia

Drobnjak

Fowler

2011

Bull Math Biol

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In certain blood diseases, oscillations are found in blood cell counts. Particularly, such oscillations are sometimes found in chronic myelogenous leukaemia, and then occur in all the derived blood cell types: red blood cells, white blood cells, and platelets. It has been suggested that such oscillations arise because of an instability in the pluri-potential stem cell population, associated with its regulatory control system. In this paper, we consider how such oscillations can arise in a model of competition between normal (S) and genetically altered abnormal (A) stem cells, as the latter population grows at the expense of the former. We use an analytic model of long period oscillations to describe regions of oscillatory behaviour in the S-A phase plane, and give parametric criteria to describe when such oscillations will occur. We also describe a mechanism which can explain dynamically how the transformation from chronic phase to acute phase and blast crisis can occur.

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A mathematical model of the acute myeloblastic leukemic state in man

Cited by 55 publications

References 27 publications

Modeling Imatinib-Treated Chronic Myelogenous Leukemia: Reducing the Complexity of Agent-Based Models

Modeling Imatinib-Treated Chronic Myelogenous Leukemia: Reducing the Complexity of Agent-Based Models

Hematopoiesis and its disorders: a systems biology approach

A Model of Oscillatory Blood Cell Counts in Chronic Myelogenous Leukaemia

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