Breath waves filtration in bioimpedance cardiography

EuroConference BIOSIGNAL 2000
Brno, Czech Republic



K.Beliaev, N.Kuzminyh
Faculty of Biomedical Technology,
Moscow State Technical University n/a Bauman
2nd Baumanskaya, 5, 107004, Moscow, Russia

Summary: We have elaborated and tested the new method for adaptive filtration of breath waves in bioimpedance cardiography, that is close to optimal Viener filtration.

The interest to bioimpedance cardiography as method for Cardiac Output (CO) monitoring has considerably increased for the last 15 years. This method is based on analysis of electrical impedance changes of the patient’s chest during heart beat [1]. It is fast, cheap and noninvasive, so it does not require sterile environment and can be used anywhere. However, there is a number of problems that affect the precision of this method, one of them – so called “breath waves”.

Thorax bioimpedance signal generally includes waves from two sources: “fast” heart signal and “slow” breath signal (Figure 1). The last component seriously complicates the CO determination. Hence, it must be removed from the signal with minimum distortion of heart component.

Figure 1 Bioimpedance signal (top), breath signal – spirogram (medium) and ECG (bottom)

Breath signal is usually shaped as a square wave with exponential fronts, and includes at least 5 frequency harmonics with main frequency at 0.1 ¸  1 Hz. Cardiosignal looks like two successive waves and includes more than 6 harmonics with main frequency at 0.5 ¸  4 Hz. Ratio between main frequencies of two components is in range 2 ¸  8, so power spectrums of breath and heart signals essentially overlap each other. Due to this reason ordinary high frequency filters are not effective, even if adaptive algorithms are used for cut-off frequency adjustment.

The best linear filtration (by criteria of mean square error, MSE) may be achieved with optimal Viener’s filter, which spectral characteristic is given by:


where Ps(w ) and Pn(w ) – are power spectrum density (PSD) of the signal and noise respectively. Unfortanutely, in practice the PSDs of noise and signal are unknown and formula (1) cannot be used. We have suggested [2] the way to overcome this difficulty and perform filtration, close to optimal.

The main idea is to locate the harmonics in spectrum, that corresponds heart signal and suppress all others. This location can be done with the help of electrocardiogram signal (ECG), that gives us the heart rate (HR), and hence the frequency of main cardiosignal harmonic. Positions of other cardiosignal harmonics can be found as multiples of main harmonic frequency, because cardiosignal is close to periodic. The next question is to determine width of each spectral peak. As a simple decision, we look for local minimums, closest to each peak position and regard them as peak borders. We found, that decreasing amplitude of spectrum components below the first cardiosignal harmonic and between first and second ones (marked in grey on Figure 2) gives the substantial suppression of breath waves with small distortion of heart component.

Figure 2 Breath waves suppression algorithm

For testing purpose we recorded pure heart signal during apnea, pure breath signal with spirograph and produce a set of mixed signals with different amplitudes and frequency ratios. We considered two situations: patient with stable shape of heart signal and patient with serious ishemic disease, hence unstable heart signal (Figure 3).

Figure 3 Stable (above) and ustable (bottom) cardiosignals

The filtration quality was estimated as the mean square error (MSE) between the filtered and the original heart signal, normalized for heart signal amplitude in percentage. The results are presented at Figure 4. Vertical axis denotes the ratio between heart rate (HR) and breath rate (BrR). Horizontal axis shows ratio between breath (Abr) and heart (Arheo) signal amplitudes. Lines denote the levels with the same MSE.

Previously we have found that MSE greater than 15 ¸  20 % corresponds to unacceptable distortions of heart signal. Analysis of Figure 4 gives the range of frequency and amplitude ratios where elaborated algorithm can be used. For stable cardiosignal these ranges are: heart rate – breath rate ratio is greater than 2.5 ¸  4 and breath – heart signal amplitude ratio is less than 1.5 ¸  3. For unstable cardiosignal we have found very small working area. Heart rate – breath rate ratio must be greater than 5 and breath – heart signal amplitude ratio must be less than 0.5.

Figure 4 Results of algorithm testing: stable cardiosignal (left), unstable cardiosignal (right)

There are 2 explanations for algorithm failure with unstable signal. First, the unstable signal has wide spectral peaks, so a lot of breath harmonics are incise peaks of cardiosignal and cannot be removed. Second, we use very simple algorithm for peak borders search, and some parts of wide peaks may be regarded as “noise” and suppressed.

Conclusions: The proposed method gives promising results with stable cardiosignal, but without further refinement it cannot be used for analysis of the data from seriously ill patients with unstable heart rate.

As an interesting evolution of current method, it can be suggested the autoregressive estimation and further decomposition [3,4] of power spectrum. The resulting “decomposed” PSDs can be used as estimations for Ps(w ) and Pn(w ) in formula (1) for filter construction.


[1] Barin E, Haryadi DG, Schookin SI, Westenskow DR, Zubenko VG, Beliaev KR, Morozov AA.: Evaluation of a thoracic bioimpedance cardiac output monitor during cardiac catheterization. Crit Care Med., Vol.28(3), p.698-702, 2000

[2] Beliaev K.R.: Biotehnicheskaja sistema dlja diagnostiki i biosinhronizirovannoi electromagnitnoi terapii serdechno-sosudistoi sistemy. PhD Thesis, Moscow State Technical University n/a Bauman, 1996

[3] Kay S.M., Marple, S.L.Jr.: Spectrum Analysis – a modern perspective. Proc. IEEE, Vol. 69, p.1380–1419, 1981.

[4] Isaksson A., Wennberg A., Zetterberg L.H.: Computer analysis of EEG signals with parametric models. Proc. IEEE, Vol.69, p.451–61, 1981