Analysis of HR using principal dynamic modes

The PDM is a non-linear method which is designed to extract only the principal dynamic components of the signal via eigen decomposition. The PDMs are calculated using the Volterra-Wiener kernels based on expansion of Laguerre polynomials (Marmarelis, 1993). Among all possible choices of expansion bases, some require the minimum number of basis functions to achieve a given mean-square approximation of the system output. This minimum set of basis functions is termed the PDMs of the non-linear system. PDM specifically accounts for the inherent non-linear dynamics of HR control, which the PSD does not. A minimum set of basis functions is determined using a method widely known as principal component analysis, in which the dominant eigenvectors and eigenvalues are retained as they relate more closely to the true characteristics of the signal, and non-dominant eigenvectors and eigenvalues are considered to represent noise or non-essential characteristics. Thus, principal component analysis separates only the essential dynamic characteristics from a signal that is likely to be corrupted by noise and non-system related dynamics. In the case of the HR signal, the dominant eigenvectors and eigenvalues should reflect the dynamics of the sympathetic and parasympathetic systems. We have modified the PDM technique to be used with even a single output signal of HRV data, whereas the original PDM required both input and output data. A detailed summary of the procedure has been presented in our previous study (Zhong et al., 2004), and comparisons between the PDM and PSD have been made using the same data (Zhong et al., 2004, 2006).

While the PDM is a time-domain representation, we convert it to the frequency domain via the Fast Fourier Transform (FFT) to facilitate interpretation of the two ANS activities, as they are usually illustrated in the frequency domain. Therefore, hereafter we will describe the PDMs' dynamic characteristics in the frequency domain. For this study, we used 8 Laguerre functions with a memory length of 60. The detailed steps involved in the calculation of PDMs as well as determining the Laguerre functions and the memory lengths have been previously described (Zhong et al., 2004). Henceforth, the derived PDMs' two main dynamics will be termed the PDMsymp and PDMpara. The frequency bands of PDMsymp and PDMpara are within the same bands of LF and HF derived from PSD.