Simulation of the neutrophil count kinetics

Recently, Bernard et al. [499] studied oscillations in cyclical neutropenia, a rare disorder characterized by oscillatory production of blood cells. As above, they developed a physiologically realistic model including a second homeostatic control on the production of the committed stem cells that undergo apoptosis at their proliferative phase. By using the same approach, they found a local supercritical Hopf bifurcation and a saddle-node bifurcation of limit cycles as critical parameters (i.e., the amplification parameter) are varied. Numerical simulations are consistent with experimental data and they indicate that regulated apoptosis may be a powerful control mechanism for the production of blood cells. The loss of control over apoptosis can have significant negative effects on the dynamic properties of hemopoiesis. 

In the previous analysis, delayed negative feedback mechanisms were considered only for neutrophil regulation. However, if over a wide range of circulating neutrophil levels, the neutrophil production rate decreases as the number of neutrophils increases (i.e., negative feedback), in the range of low neutrophil numbers the production rate must increase as neutrophil number increases (i.e., positive feedback). This type of feedback was reported as mixed feedback [472], 

Although the detailed features of the interactions involved in cortisol secretion are still unknown, some observations indicate that the irregular behavior of cortisol levels originates from the underlying dynamics of the hypothalamic-pituitary-adrenal process. Indeed, Ilias et al. [514], using time series analysis, have shown that the reconstructed phase space of cortisol concentrations of healthy individuals has an attractor of fractal dimension dj = 2.65 0.03. This value indicates that at least three state variables control cortisol secretion [515]. A nonlinear model of cortisol secretion with three state variables that takes into account the simultaneous changes of adrenocorticotropic hormone and corticotropin-releasing hormone has been proposed [516]. 

The Model These observations prompted us to model cortisol plasma levels [517] relying on the well-established erratic secretion rate [518] and the circadian rhythm, while other factors controlling cortisol secretion are also considered but not expressed explicitly  

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Figure 11.9 Simulation of the neutrophil count kinetics for t° = 5 (solid line) and 15d (dashed line). The dotted line indicates the minimum allowed neutrophil level.

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