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Keywords:

  • Time series;
  • biomathematical;
  • endocrinology;
  • feedback;
  • nonlinear dynamics;
  • reconstruction
  • 92C50;
  • 60H10;
  • 92C30;
  • 62M09;
  • 93E03

In most hormonal systems (as well as many physiological systems more generally), the chemical signals from the brain, which drive much of the dynamics, cannot be observed in humans. By the time the molecules reach peripheral blood, they have been so diluted so as to not be assayable. It is not possible to invasively (surgically) measure these agents in the brain. This creates a difficult situation in terms of assessing whether or not the dynamics may have changed due to disease or ageing. Moreover, most biological feedforward and feedback interactions occur after time delays, and the time delays need to be properly estimated. We address the following two questions: (i) Is it possible to devise a combination of clinical experiments by which, via exogenous inputs, the hormonal system can be perturbed to new steady-states in such a way that information about the unobserved components can be ascertained; and (ii) Can one devise methods to estimate (possibly, time-varying) time delays between components of a multidimensional nonlinear time series, which are more robust than traditional methods? We present methods for both questions, using the Stress (ACTH–cortisol) hormonal system as a prototype, but the approach is more broadly applicable.