EuroConference BIOSIGNAL 2000

Brno, Czech Republic

**
**BREATH WAVES FILTRATION IN BIOIMPEDANCE CARDIOGRAPHY

K.Beliaev, N.Kuzminyh

Faculty of Biomedical Technology,

Moscow State Technical University n/a Bauman

2^{nd} Baumanskaya, 5, 107004, Moscow, Russia

e-mail: konstbel@gmail.com

*
*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 P_{s}(w
) and P_{n}(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 P_{s}(w
) and P_{n}(w
) in formula (1) for filter construction.

References:

[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