Implication of the nonlinear dynamics in cortisol secretion processes

As we have already mentioned (cf. Chapter 3), one of the most important features of nonlinear dynamics is the sensitivity to initial conditions. A measure to verify the chaotic nature of a dynamic system is the Lyapunov exponent [32], 

Cortisol Suppression by Corticosteroids The model presented here allows the consideration of external corticosteroid administration as a perturbation of the cortisol secretion system. As a matter of fact, corticosteroids cause a temporary diminution of plasma cortisol levels [522]. Assuming that the drug follows one-compartment model disposition with first-order input and output, the effect-site [525] concentration is described by the following equation [417]  

The effect-site concentration of the corticosteroids can be considered to affect one or more parameters of the model described by (11.12). This must be implemented so that the presence of y (t) suppresses the cortisol secretion in accordance with the experimental data. Instead of g (t), the parameter describing the circadian rhythm, a new parameter g (t) was introduced to include the effect of corticosteroid administration following a receptor reduction  

The solid and dashed lines represent simulations for two individuals with significantly different profiles corresponding to different initial conditions, c (0) = 90/igml-1 (solid) and c(0) = 150/rgml-1 (dashed). Parameter values were set to 

These values were selected in order to generate qualitatively similar profiles to the experimental data and were not optimized since fitting is not well established for chaotic systems. In parallel, the sensitive dependence of the detailed final profile from the exact values of the concentration y (t) should be emphasized, since y (t) directly affects one of the parameters of the chaotic oscillator (11.15). 

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