Bulletin of Mathematical Biology

, Volume 73, Issue 12, pp 2983–3007

A Model of Oscillatory Blood Cell Counts in Chronic Myelogenous Leukaemia

Original Article

DOI: 10.1007/s11538-011-9656-2

Cite this article as:
Drobnjak, I. & Fowler, A.C. Bull Math Biol (2011) 73: 2983. doi:10.1007/s11538-011-9656-2


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 SA 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.


Chronic myelogenous leukaemiaCMLChronic phaseOscillationsDelay equationsBlast crisis

Copyright information

© Society for Mathematical Biology 2011

Authors and Affiliations

  1. 1.Centre for Medical Image Computing, Department of Computer ScienceUniversity College LondonLondonUK
  2. 2.MACSIUniversity of LimerickLimerickIreland