A mathematical model of hematopoiesis: II. Cyclical neutropenia

Abstract

Cyclical neutropenia is a dynamical disease of the hematopoietic system marked by an oscillation in circulating leukocyte (e.g. neutrophil) numbers to near zero levels and then back to normal. This oscillation is also mirrored in the platelets and reticulocytes which oscillate with the same period. Cyclical neutropenia has an animal counterpart in the grey collie. Using the mathematical model of the hematopoietic system of Colijn and Mackey [A mathematical model of hematopoiesis: I. Periodic chronic myelogenous leukemia. Companion paper to the present paper.] we have determined what parameters are necessary to mimic laboratory and clinical data on untreated grey collies and humans, and also what changes in these parameters are necessary to fit data during treatment with granulocyte colony stimulating factor (G-CSF). Compared to the normal steady-state values, we found that the major parameter changes that mimic untreated cyclical neutropenia correspond to a decreased amplification (increased apoptosis) within the proliferating neutrophil precursor compartment, and a decrease in the maximal rate of re-entry into the proliferative phase of the stem cell compartment. For the data obtained during G-CSF treatment, good fits were obtained only when parameters were altered that would imply that G-CSF led to higher amplification (lower rate of apoptosis) in the proliferating neutrophil precursors, and a elevated rate of differentiation into the neutrophil line.

Introduction

All blood cells originate from the hematopoietic stem cells (HSC) in the bone marrow. These stem cells differentiate and proliferate, forming the three major cell lines: the leukocytes, the platelets, and the erythrocytes. The known peripheral regulatory loops all have a negative feedback nature and are mediated by a variety of cytokines including erythropoietin (EPO), which mediates the regulation of erythrocyte production; thrombopoietin (TPO), which plays the same role in the platelet line (but may also affect other lines); and granulocyte colony-stimulating factor (G-CSF), which regulates leukocyte numbers.

In Colijn and Mackey (2004), we have presented a comprehensive mathematical model of the regulation of hematopoiesis by linking together models for the regulation of the HSC and the differentiated cells (leukocytes, platelets and erythrocytes) in which the cell numbers are regulated by negative feedback loops mimicking the actions of these cytokines. This modelling was motivated by the existence of several hematological diseases that display a highly dynamic nature characterized by oscillations in one or more of the circulating progeny of the HSC (Haurie et al., 1998b). These include, but are not limited to, cyclical neutropenia (CN), periodic chronic myelogenous leukemia (PCML), cyclical thrombocytopenia, and periodic hemolytic anemia. Of particular interest in this paper is cyclical neutropenia, while periodic chronic myelogenous leukemia was dealt with in the previous paper (Colijn and Mackey, 2004). In both of these diseases, the oscillations in peripheral blood cell counts all occur at the same period in a given patient.

Cyclical neutropenia is characterized by oscillations that are most prominent in the neutrophils. Neutrophil numbers fall from normal or above normal levels to almost zero, and rise again, with a period of about 19–21 days in humans (Guerry et al., 1973, Haurie et al., 1998b, Hammond et al., 1989). The disease also occurs in grey collies, with a shorter period of 11–16 days (Haurie et al., 1999b). Interestingly, the platelet numbers typically oscillate as well, with the same period as the neutrophils, but with a mean around the normal platelet level. Reticulocyte levels may also oscillate, again with the same period as the neutrophils and platelets.

The origins of oscillations in cyclical neutropenia are unclear. While many have modelled CN as arising from oscillations in peripheral control loops that regulate neutrophil numbers (for example, King-Smith and Morley, 1970, Morley et al., 1969), the work of Hearn et al. (1998) cast doubt on this explanation. As an alternative, Mackey (1978) and Haurie et al. (1998b) have suggested that the oscillations originate in a loss of stability in the hematopoietic stem cells, but Bernard et al. (2003) suggests that the origin of CN lies in a destabilization of the combined HSC and peripheral neutrophil control system. The matter remains unresolved, and the model results presented here offer some insight into this question.

The hypothesis that oscillations originate in the stem cells is related to the fact that these oscillations occur in more than one cell line. However, in many earlier models, only one cell line, or one line coupled to the stem cells, was represented. In this context it is not possible to examine the effects of a destabilization in one line or in the stem cell compartment on the other lines. In the work of Bernard et al. (2003), they were able to duplicate various features of CN. However, since their model included neither erythrocyte nor platelet control, it is unknown if their hypothesis would be consistent with observed platelet and reticulocyte data.

The present model provides a framework in which these questions can be addressed. Specifically, we wish to use a comprehensive model for the regulation of hematopoiesis to deduce what must be different in the model parameters to explain the dynamic behaviour seen in CN as manifested in the grey collie and in humans. To do this, we take a $G_0$ model for the stem cell compartment, based on Mackey (1978) and Pujo-Menjouet et al. (2001), and couple it to a leukocyte model based on the work of Bernard et al. (2003), as well as to two simplified models representing the control of platelet and erythrocyte production. Our model is presented in some detail in the preceding paper (Colijn and Mackey, 2004), along with a detailed discussion of the relevant parameter estimation. Therefore, in Section 2.1, we give only a summary of the mathematical formulation, and in Section 2.2, we present the normal steady-state parameters without the detailed discussion in Colijn and Mackey (2004). In Section 4, the simulations generated by the model are compared with observed dog and human neutropenia data.