Biomedical Engineering Reference
In-Depth Information
Chapter 9
Non-linear Effects in the Respiratory Impedance
9.1 The Principles of Detection of Non-linear Distortions
in a Non-linear System
This section addresses two problems: (i) the problem of breathing interference with
the excitation signal and (ii) the detection of non-linear contributions in the mea-
sured signals. The common solution to these problems is the optimization of the
excitation signal, further detailed hereafter.
9.1.1 Reducing the Breathing Interference
In the standard use of the FOT, the excitation signal (i.e. with frequencies from
4 Hz to 48 Hz) lies well above the breathing frequency (i.e. around 0.3 Hz), which
enables high-pass filtering as a separation technique for the useful signals to be pro-
cessed. Also, harmonics of the breathing frequency become small in amplitude as
the frequency increases, such that the estimation of the impedance using standard
estimation methods as explained in Chap.
3
poses no problem. However, when fre-
quencies closer to the breathing are used in the excitation signal, the breathing of
the patient must be modeled in order to provide a good separation of the overlap-
ping frequencies. The challenges in this modeling step are manifold: the breathing
is a non-stationary, time varying signal, whose frequency and amplitude may vary
in time. In addition, the corresponding harmonics are overlapping with the excited
frequencies. In the remainder of this work, it is assumed that the breathing fre-
quency
F
0
remains fixed during the measurement time, which is in fact a reasonable
assumption.
The following is an algorithm which estimates the breathing of the patient from
measured offline data [
170
]. Consider that the real breathing signal
b(t)
has the
following form (
i
denotes here the harmonics of the breathing frequency
F
0
, going
