In most hormonal systems (as well as many physiological systems more generally), the chemical signals from the brain, which drive much of the dynamics, can not 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 aging. 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: (1) 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, (2) 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.

中文翻译：

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多维激素系统的非线性时间动力学建模

在大多数荷尔蒙系统（以及更普遍的许多生理系统）中，无法在人类中观察到来自大脑的化学信号，这些信号驱动了大部分动态。当分子到达外周血时，它们已被稀释到无法检测。不可能侵入性（手术）测量大脑中的这些药物。这在评估动态是否因疾病或衰老而改变方面造成了困难。此外，大多数生物前馈和反馈相互作用发生在时间延迟之后，需要正确估计时间延迟。我们解决以下两个问题：（1）是否有可能设计出临床实验的组合，通过外源输入，荷尔蒙系统可以被扰乱到新的稳态，从而可以确定有关未观察到的成分的信息；以及，(2) 能否设计出比传统方法更稳健的方法来估计（可能是随时间变化的）多维非线性时间序列分量之间的时间延迟？我们使用压力（ACTH-皮质醇）激素系统作为原型，提出了解决这两个问题的方法，但该方法的适用范围更广。