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Computational and Mathematical Methods in Medicine
An Interdisciplinary Journal of Mathematical, Theoretical and Clinical Aspects of Medicine
Volume 11, 2010 - Issue 1
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Original Articles

A hypothetical-mathematical model of acute myeloid leukaemia pathogenesis

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Pages 49-65 | Received 04 Feb 2009, Accepted 16 Apr 2009, Published online: 05 Oct 2009
 

Abstract

Acute myeloid leukaemia is defined by the expansion of a mutated haematopoietic stem cell clone, with the inhibition of surrounding normal clones. Haematopoiesis can be seen as an evolutionary tree, starting with one cell that undergoes several divisions during the expansion phase, afterwards losing functional cells during the aging-related contraction phase. During divisions, offspring cells acquire ‘variations’, which can be either normal or abnormal. If an abnormal variation is present in more than 25% of the final cells, a monoclonal, leukemic pattern occurs. Such a pattern develops if: (A1) The abnormal variation occurs early, during the first or second divisions; (A2) The variation confers exceptional proliferative capacity; (B) A sizable proportion of the normal clones are destroyed and a previously non-significant abnormal clone gains relative dominance over a depleted environment; (C) The abnormal variation confers relative ‘immortality’, rendering it significant during the contraction phase. Combinations of these pathways further enhance the leukemic risk of the system. A simple mathematical model is used in order to characterize normal and leukemic states and to explain the above cellular processes generating monoclonal leukemic patterns.

AMS Subject Classification::

Acknowledgement

The authors would like to thank Professors Damian Trif and Marcel Serban for their help during the preparation of the manuscript. They are also grateful to the referee whose comments and suggestions have led to an improvement of the biology part of the paper.

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