A Model of Oscillatory Blood Cell Counts in Chronic Myelogenous Leukaemia

Abstract

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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“…Oscillations can arise in a model of competition between normal and genetically damaged abnormal stem cells as suggested in chronic myelogenous leukemia. 6 Cell cycle dependent oscillatory expression of estrogen receptor-alpha implicates Pol II elongation with malignant tumor genesis. 7 The dynamics of transformation in carcinogenesis are analogous to the emergence of chemotherapeutic agent resistance and within the frameworks of ongoing progression for transformation.…”

A study on stability and medical implications for a complex delay model for CML with cell competition and treatment

“…The following density dependence terms are introduced: 1 1 þ p x ðx 1 þ y 1 Þ and 1 1 þ p y ðx 1 þ y 1 Þ in the stem cell production rate (these functions introduce competition within the stem cell compartment), where p x , p y are dimensionless parameters that simulate the crowding effect that is seen in the bone marrow microenvironment. Another model with competition which has its grounds on the Mackey model is the Drobnjak and Fowler (2011) model. In this work, the competition is introduced through a "crowding factor" in the self-renew rate.…”

Optimal control analysis of a leukemia model under imatinib treatment

“…Moore and Li [36] modeled the interaction between the immune system (naive T cells and effector T cells) and CML cancer cells, using a system of ordinary differential equations. More recently, Drobnjak and Fowler [16] used the G 0 model, and focused on the approach described by Fowler and Mackey [17], where they analyzed a class of stem cell population models. Moreover, models involving the treatment of CML were developed.…”