Huang W, Shen Z, Huang N E, Fung Y C
Department of Bioengineering, University of California, San Diego, La Jolla, CA 92093-0412, USA.
Proc Natl Acad Sci U S A. 1998 Oct 27;95(22):12766-71. doi: 10.1073/pnas.95.22.12766.
Recently, a new method to analyze biological nonstationary stochastic variables has been presented. The method is especially suitable to analyze the variation of one biological variable with respect to changes of another variable. Here, it is illustrated by the change of the pulmonary blood pressure in response to a step change of oxygen concentration in the gas that an animal breathes. The pressure signal is resolved into the sum of a set of oscillatory intrinsic mode functions, which have zero "local mean," and a final nonoscillatory mode. With this device, we obtain a set of "mean trends," each of which represents a "mean" in a definitive sense, and together they represent the mean trend systematically with different degrees of oscillatory content. Correspondingly, the oscillatory content of the signal about any mean trend can be represented by a set of partial sums of intrinsic mode functions. When the concept of "indicial response function" is used to describe the change of one variable in response to a step change of another variable, we now have a set of indicial response functions of the mean trends and another set of indicial response functions to describe the energy or intensity of oscillations about each mean trend. Each of these can be represented by an analytic function whose coefficients can be determined by a least-squares curve-fitting procedure. In this way, experimental results are stated sharply by analytic functions.
最近，提出了一种分析生物非平稳随机变量的新方法。该方法特别适用于分析一个生物变量相对于另一个变量变化的情况。在此，通过动物呼吸气体中氧气浓度的阶跃变化所引起的肺血压变化来说明这一点。压力信号被分解为一组具有零“局部均值”的振荡本征模函数与一个最终的非振荡模之和。利用这种方法，我们得到一组“平均趋势”，其中每一个都在确定的意义上代表一个“均值”，并且它们一起系统地代表了具有不同振荡含量程度的平均趋势。相应地，关于任何平均趋势的信号振荡含量可以由一组本征模函数的部分和来表示。当用“阶跃响应函数”的概念来描述一个变量对另一个变量阶跃变化的响应时，我们现在有了一组平均趋势的阶跃响应函数以及另一组用于描述围绕每个平均趋势的振荡能量或强度的阶跃响应函数。这些都可以由一个解析函数表示，其系数可以通过最小二乘曲线拟合程序来确定。通过这种方式，实验结果可以用解析函数清晰地表述出来。
