Novel characterization method of impedance cardiography signals using time-frequency distributions

Abstract

The purpose of this document is to describe a methodology to select the most adequate time-frequency distribution (TFD) kernel for the characterization of impedance cardiography signals (ICG). The predominant ICG beat was extracted from a patient and was synthetized using time-frequency variant Fourier approximations. These synthetized signals were used to optimize several TFD kernels according to a performance maximization. The optimized kernels were tested for noise resistance on a clinical database. The resulting optimized TFD kernels are presented with their performance calculated using newly proposed methods. The procedure explained in this work showcases a new method to select an appropriate kernel for ICG signals and compares the performance of different time-frequency kernels found in the literature for the case of ICG signals. We conclude that, for ICG signals, the performance (P) of the spectrogram with either Hanning or Hamming windows (P = 0.780) and the extended modified beta distribution (P = 0.765) provided similar results, higher than the rest of analyzed kernels. Graphical abstract Flowchart for the optimization of time-frequency distribution kernels for impedance cardiography signals.

Keywords: Impedance cardiography; Time-frequency distributions.

Graphical abstract

Flowchart for the optimization of time-frequency distribution kernels for impedance cardiography signals.

Fig. 1

Five most frequent patterns in an ICG recording calculated with a correlation threshold of 0.85

Fig. 2

Fourier model of the ICG pattern: original ICG template (dashed blue) and an approximation of two tones of the Fourier model (red). Characteristic points B, C, and X are marked on the ICG curve

Fig. 3

ICG signals with a constant IF (a) and a linear frequency variation (b) synthetized with two tones

Fig. 4

Periodograms of the synthetized ICG signals with no frequency variation (a) and with a linear frequency variation (b). Each instantaneous frequency is plotted individually (in color) and the total resulting spectra are also included (in black)

Fig. 5

Performance optimization results: the resulting performance P of the spectrograms (a), ZAM distribution (b), CWD (c), MBD (d), SM (e), and EMBD (f) for varying parameters is plotted. The SM is optimized for a rectangular (e1), Hamming (e2), Hanning (e3), and Bartlett (e4) windows

Fig. 6

a A time slice at t = 5 s of the TFD with the characteristic points $A_{s_1},A_x,A_2,A_{s2}$, and frequency bands V₁ and V₂ in red of the two tones and the cross tones for the calculation of the performance P. b The resulting optimized TFD. c Location of the resulting first (in blue) and second (in red) IFs, IF₁, and IF₂ against the theoretical results (in black), for each type of analyzed TFD: spectrogram with a Bartlett window (1), CWD (2), and EMBD (3)

Fig. 7

Results to noise tests. a and b show the performance P of several TFDs to different SNR rates and c shows the root mean square error (MSE) in the detection of the first instantaneous frequency

Fig. 8

Main ICG pattern for all patients in the data base. X-axis is normalized time and Y-axis is normalized ICG. Patterns have been normalized to the same time duration in the X-axes