Modelling the nonlinear time dynamics of multidimensional hormonal systems
Article first published online: 21 JUN 2012
© 2012 Blackwell Publishing Ltd
Journal of Time Series Analysis
Special Issue: Time Series Analysis in the Biological Sciences
Volume 33, Issue 5, pages 779–796, September 2012
How to Cite
Keenan , D. M., Wang, X., Pincus, S. M. and Veldhuis, J. D. (2012), Modelling the nonlinear time dynamics of multidimensional hormonal systems. Journal of Time Series Analysis, 33: 779–796. doi: 10.1111/j.1467-9892.2012.00795.x
The first two authors are joint first authors.
- Issue published online: 29 AUG 2012
- Article first published online: 21 JUN 2012
- Final version received February 2012
- Time series;
- nonlinear dynamics;
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.