Papadimitriou S, Bezerianos A
Department of Medical Physics, School of Medicine, University of Patras, Greece.
Int J Med Inform. 1999 Jan;53(1):43-60. doi: 10.1016/s1386-5056(98)00102-6.
Many studies on the physiology of the cardiovascular system revealed that nonlinear chaotic dynamics govern the generation of the heart rate signal. This is also valid for the fetal heart rate (FHR) variability, where however the variability is affected by many more factors and is significantly more complicated than for the adult case. Recently an adaptive wavelet denoising method for the Doppler ultrasound FHR recordings has been introduced. In this paper the performance and reliability of that method is confirmed by the observation that for the wavelet denoised FHR signal, a deterministic nonlinear structure, which was concealed by the noise, becomes apparent. It provides strong evidence that the denoising process removes actual noise components and can therefore be utilized for the improvement of the signal quality. Hence by observing after denoising a significant improvement of the 'chaoticity' of the FHR signal we obtain strong evidence for the reliability and efficiency of the wavelet based denoising method. The estimation of the chaoticity of the FHR signal before and after the denoising is approached with three nonlinear analysis methods. First, the rescaled scale analysis (RSA) technique reveals that the denoising process increases the Hurst exponent parameter as happens when additive noise is removed from a chaotic signal. Second, the nonlinear prediction error evaluated with radial basis function (RBF) prediction networks is significantly lower at the denoised signal. The significant gain in predictability can be attributed to the drastic reduction of the additive noise from the signal by the denoising algorithm. Moreover, the evaluation of the correlation coefficient between actual and neural network predicted values as a function of the prediction time displays characteristics of chaos only for the denoised signal. Third, a chaotic attractor, reconstructed with the embedding dimension technique, becomes evident for the denoised signal, while it is completely obscured for the original signals. The correlation dimension of the reconstructed attractor for the denoised signal tends to reach a value independent of the embedding dimension, a sign of deterministic chaotic signal. In contrast for the original signal the correlation dimension increases steadily with the embedding dimension, a fact that indicates strong contribution of noise.
许多关于心血管系统生理学的研究表明，非线性混沌动力学支配着心率信号的产生。这对于胎儿心率（FHR）变异性同样适用，不过胎儿心率变异性受到更多因素的影响，并且比成人情况要复杂得多。最近，一种针对多普勒超声FHR记录的自适应小波去噪方法被提出。在本文中，通过观察发现，对于经小波去噪的FHR信号，一个被噪声掩盖的确定性非线性结构变得明显，从而证实了该方法的性能和可靠性。这提供了有力证据，表明去噪过程去除了实际的噪声成分，因此可用于提高信号质量。因此，通过观察去噪后FHR信号“混沌性”的显著改善，我们获得了基于小波的去噪方法可靠性和有效性的有力证据。采用三种非线性分析方法来评估去噪前后FHR信号的混沌性。首先，重标度分析（RSA）技术表明，去噪过程会增加赫斯特指数参数，这与从混沌信号中去除加性噪声时的情况相同。其次，用径向基函数（RBF）预测网络评估的非线性预测误差在去噪信号处显著更低。预测性的显著提高可归因于去噪算法使信号中的加性噪声大幅减少。此外，实际值与神经网络预测值之间的相关系数作为预测时间的函数进行评估时，仅对于去噪信号显示出混沌特征。第三，用嵌入维数技术重构的混沌吸引子对于去噪信号变得明显，而对于原始信号则完全被掩盖。去噪信号重构吸引子的关联维数趋于达到一个与嵌入维数无关的值，这是确定性混沌信号的一个标志。相比之下，对于原始信号，关联维数随着嵌入维数稳步增加，这一事实表明噪声的影响很大。
