Signals in bioimpedance measurement: Different waveforms for different tasks

Abstract

Alternatives to the traditional sine wave excitation are studied in the paper. Impedance measurements can be performed much
faster by using a broad bandwidth signal for excitation. Using of square wave pulses, Gaussian function and its derivative,
also modifications of sinc and chirp signals, is analysed. Carefully designed pulse wave excitation can become to an alternative
to established excitation waveforms, especially, when fast measurements with exact timing are required, and when the energy
consumption is important.

Full text

Hermann Scharfetter, Robert Merva (Eds.): ICEBI 2007, IFMBE Proceedings 17, pp. 181–184, 2007
www.springerlink.com © Springer-Verlag Berlin Heidelberg 2007
Signals in bioimpedance measurement: different waveforms for different tasks
M. Min1, U. Pliquett2, T. Nacke2, A. Barthel2, P. Annus1 and R. Land1
1 Tallinn University of Technology, Tallinn, Estonia
2 Institute of Bioprocessing and Analytical Measurement Techniques, Heilbad Heiligenstadt, Germany
Abstract— Alternatives to the traditional sine wave excita-
tion are studied in the paper. Impedance measurements can be
performed much faster by using a broad bandwidth signal for
excitation. Using of square wave pulses, Gaussian function and
its derivative, also modifications of sinc and chirp signals, is
analysed. Carefully designed pulse wave excitation can become
to an alternative to established excitation waveforms, espe-
cially, when fast measurements with exact timing are required,
and when the energy consumption is important.
Keywords— Broadband excitation, pulse wave signals, fast
measurement, time-frequency analysis, low power devices.
I. INTRODUCTION TO THE PROBLEM
Electrical bioimpedance [1] is a well recognised parame-
ter for tissue characterisation in implantable medical tech-
nology, e.g. in cardiac pacemakers and defibrillators [2].
Measurement systems are downsized to the nanoliter size
biotechnology in the lab-on-the-chip type devices [3].
The frequency domain analysis is commonly used in bioim-
pedance measurement practice.
Impedance measurements can be performed much faster
by using a broad bandwidth signal for excitation and calcu-
lating the spectrum by means of Fourier transform. If the
signal is partially transformed, windowing functions are
used to extract the spectrum at a defined time point. This
approach is advantageous in cardiac applications [2] or in
high throughput bioprocessing [3].
Here, the joint time-frequency measurement and analysis
is one of the aims for development of new impedance meas-
urement methods. A generalised approach for bioimpedance
measurement is the current excitation and monitoring of the
voltage developing across the object (Fig.1). An excitation
generator G generates an AC excitation current ie(t), which
is injected into the complex impedance Ż to be measured
and analysed. The response to the excitation – a voltage vr(t)
carries information about the impedance Ż. This informa-
tion will be analysed in an impedance analyser – classically
in frequency domain, but also in time domain, e.g. for ob-
taining time varying spectrum. As a result, both, the spectral
and time based parameters of the impedance behaviour will
be obtained – Ż (ω, t). Typically the sine wave excitation
with adjustable frequency is used. To accelerate both, the
measurement and analysis processes, simultaneous multi-
sine measurements have been introduced [4, 5].
v
r
(t)
i
e
(t)
Ż(ω,t)
G Ż
excitation
generator
impedance
Impedance
Analyzer
response
voltage
Fig.1 Typical impedance measurement system
Compared to other biosensors, the bioimpedance meas-
urement requires generation of the excitation signal, which
means significant energy consumption. This is rather impor-
tant for wearable and other battery powered instruments,
and can be crucial in implantable device. Here we pay spe-
cial attention to the generation of minimal-energy excitation
signals where a sufficiently broad spectrum can be meas-
ured. It is expected that optimal excitation waveforms en-
able us to achieve both of these aims – to provide the short-
term but accurate spectral analysis, and to focus the excita-
tion energy onto the desired frequency range at the prede-
termined time instant.
II. WAVEFORMS OF EXCITATION SIGNALS
Sine wave excitations are commonly used for impedance
measurements. For fast measurements, the multi-sine simul-
taneous measurement [5] or time domain based approaches
(application of square wave pulses) are used [6]. Such a
simple broadband signal, as a short rectangular pulse
(Fig.2a), is typically used for excitation while the analysis
employs the Fourier-transformed signal [7]. This yields a
spectrum of sinc(ωT)=sin(ωT)/ωT type spectrum, which is
almost constant up to the frequency fmax=1/2T.
In Fig.2a, the duration of pulse is T=50μs. As a result,
the first zero value of the spectrum takes place at the
frequency f10= 1/T= (1/50)106 =20kHz, see Fig.2a and 2b,
and the fmax is there about 10kHz.
With such a quick method even fast changes of the object
impedance can be monitored. There are, however, some
drawbacks. For instance, the distribution of spectral energy

182 M. Min, U. Pliquett, T. Nacke, A. Barthel, P. Annus and R. Land
__________________________________________ IFMBE Proceedings Vol. 17 ___________________________________________
time
amplitude
log
f
1/2T
lin
f
lin magnlog magn
10kHz 20kHz 40kHz
T=50μs
20kHz 40kHz
10kHz
1/2T
(1)
(
2
)
a
)
b
)
c
)
Fig.2 Rectangular pulse excitations (a) with a DC component (1) and
without it (2), and their spectra in linear (b) and log (c) scales
is not adjustable, meaning that energy is wasted in fre-
quency regions without interest. The “wasted” energy can
reach about 40% of the useful one. As a result, the spectral
density of useful excitation remains low at the actual level
of energy consumption.
Our aim is to find waveforms for excitation pulses with
the energy concentrated in the frequency range of interest.
The measurement process must be fast at the predetermined
or precisely registered moment.
Therefore, there is an urgent need to find more effective
waveforms for the excitation pulses than the simplest rec-
tangular ones, having the two discrete values (+1 and 0, or
+1 and –1, see Fig.2a), see [6]. Min et al [8] proposed the
modified rectangular pulses with three discrete values
(+A, -A, and 0). However, these waveforms are no real
improvement to established waveforms in the present case
of application.
If only a limited bandwidth is required, excitation signals
like Gaussian function (see Fig.3a)
2
5.0
0
)(
⎟
⎠
⎞
⎜
⎝
⎛
−
=
σ
t
eAtG (1)
and preferably its derivatives, which do not contain any DC
component (Fig.4a), have an advantage due to the higher
energy density within the desired range of the spectrum
(Fig.3b and 3c). Anyway, the spectra of Gaussian pulse and
its first derivative (Figs 3 and 4) are not simply rectangle.
time
amplitude
log
f
lin
f
lin magnlog magn
10kHz 20kHz
20kHz
10kHz
(1)
(
2
)
a
)
b
)
c
)
2T=100μs
Fig.3 Gaussian (1) and windowed sinc (2) excitation pulses (a), and their
spectra in linear (b) and log (c) scales
Much better results gives the more complicated sinc(ωt)
type excitation pulse, especially when the windowing of the
pulse function is taken into use (Hanning window in Fig.3).
Some modification of sinc function, e.g. haversinc(ωt)=
=sin2(ωt)/ωt, is more preferred in biological systems,
because it does not contain the DC component, see Fig.4.
A difference of two sinc(ωt) type pulses as Asinc(ωt)-
-Bsinc(nωt) enables to shift the excitation bandwidth to the
desired higher frequency range from about ω to nω.
III. COMPARISON OF SINC AND GAUSSIAN PULSES
A shortened (duration 1ms) and windowed by Hanning
sinc function sin(ωt)/(ωt) in Fig.3a has a near to rectangular
spectrum with a bandwidth, which is proportional to the
frequency f = ω/2π of the sine function sin(ωt), see Fig.3b
and 3c. In principle, the sinc function has the perfectly rec-
tangular spectrum when its duration extends to infinity.
However, the practical case in Fig.3 is fully acceptable,
though not ideal. Less than 10% of the excitation energy
drops outside the bandwidth of interest. Thanks to certain
important properties of Gaussian function (simple wave-
form, smooth transient response, the spectrum is also the
Gaussian function without any side lobes), these pulses
(see Fig.3a) are of interest. Since the spectrum is not flat
(Fig.3b and 3c), the data processing requires as response as
well as the excitation signal.

Signals in bioimpedance measurement: different waveforms for different tasks 183
__________________________________________ IFMBE Proceedings Vol. 17 ___________________________________________
IV. COMPARISON OF HAVERSINC PULSE AND
THE DERIVATIVE OF GAUSSIAN FUNCTION
Any DC-application to biological structures should be
avoided. Therefore, the windowed haversinc pulse
sin2(ωt)/ωt and the first derivative of Gaussian function
dG(t)/dt are preferred for excitation (see Fig.4) instead of
original sinc and Gaussian pulses (Fig.3). Their spectra in
Fig.4a and 4b are similar to those of the original functions
in Fig.3b and 3c, only the DC component is absent and low
frequency parts are suppressed, the other properties are
almost the same.
The amplitude coefficient
(2)
of the n-th derivative (i = 1, 2, 3…, n) ensures equal ener-
gies for all the derivatives taking the values of amplitudes as
(3)
V. USING OF CHIRP PULSES
The chirp pulses or chirplets can be expressed mathe-
matically as
(4)
where 0< t ≤ T, B/T is a chirp rate, and T is duration of
the chirp pulse. These functions describe the radio impulse
with linearly increasing frequency and the bandwidth B
extending from ω/2π to (ω/2π +B) in Hz. In the simplest
case ω=0 (see Fig.5a), and the spectrum covers the range
from DC to B (see graphs 1 in Fig.5b and 5c, where
B=1MHz). The DC component is an average value over
time T, and it depends on the final value of the chirp signal
at the moment tfin=T. The DC component can be set to zero
choosing the “right” value for the final moment tfin.
The excitation spectrum approaches the ideal one by in-
creasing the time interval T.
We do not have any possibility to use the standard
windowing procedures for chirp function, but applying
some of their modifications can essentially improve the
shape of its spectrum [9].
A response spectrum of the β-region impedance
(frequency range from 10kHz to 1MHz) of a skeleton
muscle flap is given by graphs 2 in Fig. 5b and 5c.
time
amplitude
log
f
lin
f
lin magnlog magn
10kHz 20kHz
20kHz
10kHz
(1)
(
2
)
a
)
b
)
c
)
2T=100μs
Fig.4 Derivative of the Gaussian pulse (1) and haversinc (2) function (a),
and their spectra in linear (b) and log (c) scales
amplitude
log
f
lin
f
lin magnlog magn
1MHz
1MHz
a
)
b
)
c
)
time
100
μ
s
(1)
(
2
)
Fig.5 Initial 100μs part of the chirp pulse (a) and its spectrum (1) in linear
(b) and log (c) scale, and the response (2) of the impedance (β region) of
skeleton muscle flap to the chirp excitation
∏
=−
=
n
i
ni
C
15.0
σ
nn CAA ×= 0
)2/)/(2sin()( 2
tTBttch
πω
+=Ω

184 M. Min, U. Pliquett, T. Nacke, A. Barthel, P. Annus and R. Land
__________________________________________ IFMBE Proceedings Vol. 17 ___________________________________________
VI. DISCUSSIONS
Every excitation mode has its advantages and drawbacks
for practical applications. The Gaussian pulse and its
derivative are simple. The sinc function has a nice flat
spectrum, but the signal waveform is more complex.
The chirp excitation is the most favourable when the small
crest-factor (the peak value divided by the RMS value)
is required. The chirp pulse has a crest-factor about 1.4,
which is almost the same as of a single sine wave. Such the
signals as chirp and haversinc pulses and the derivatives of
Gaussian function might be preferred due to the absence of
the DC component. All the pulse wave excitations have a
wide frequency spectrum; therefore the noise level can be
relatively high in the response signal. The amplitude of
excitation pulses must be relatively high to obtain the inten-
sive broadband spectrum. Therefore, nonlinearity problems
can be more apparent than in the case of the periodic excita-
tion.
VII. CONCLUSIONS
Carefully designed pulse wave excitation can become to
an alternative to established excitation waveforms, espe-
cially, when fast measurements with exact timing are
required, and when the energy consumption is important
(implantable and wearable devices, laboratories on the
chip). The theoretical expectations were verified using an
electrical phantom of bioimpedance, an arbitrary waveform
generator AFG3252 as the excitation source, and a digital
oscilloscope DPO4104 with spectral analysis for measure-
ment and analysis (both from Tektronix).
The results were compared in different cases using both,
computer simulations and electrical experiments. For the
experiments, an arbitrary function generator, matched with
special amplifiers to the electrode system, and a digital high
speed oscilloscope for tracing the signals, were used.
The experiments were performed with RC-combination,
mimicking the biological object. All the above described
excitation waveforms can be used, but the most interesting
can give sinc and chirp pulses. The experiments show that
combining two pulses with different parameters, e.g. using
Asinc(x)-Bsinc(nx), we can get a smooth power spectrum
within the desired bandwidth, even when only a simple
windowing has been used. Simulation suggests a reasonable
outcome at even two or three full periods. Using of chirp
pulses can be the most informative, only the complicated
windowing problem needs to be solved before practical
implementations.
The results confirm that the described measurement
methods can become alternatives to the established ones,
e.g. to the multi-frequency simultaneous measurement.
ACKNOWLEDGMENT
The work was carried out in frames of the FP6 Marie
Curie Fellowship ToK project 29857 InFluEMP and
supported by grants no. 7212 and 7243 of Estonian Science
Foundation, and also by Enterprise Estonia through the
Competence Centre ELIKO.
REFERENCES
1. Grimnes S, Martinsen O.G (2000) Bioimpedance and Bioelectricity
Basics. Academic Press, London
2. Webster J.G (Ed.) (1995) Design of Cardiac Pacemakers. IEEE Press,
New York
3. Cheung K, Gawad S, Renaud P (2005) Impedance Spectroscopy Flow
Cytometry: On-chip Label-Free Cell Differentiation. Cytometry,
Part A, 65A:124-132
4. Gordon R, Land R, Min M, Parve T, Salo R W (2005) A virtual
system for simultaneous multi-frequency measurement of electrical
bioimpedance. Int J Bioelectromagnetism 7(2):243-246
5. Bragos R, Blanco-Enrich R, Casas O, Rosell J (2001) Characterisa-
tion of Dynamic Biologic Systems using Multisine based Impedance
Spectroscopy, Proc. IEEE Instrum. and Measurement Tech. Conf.
Budapest, Hungary, 2001, Vol.1, pp 44-47
6. Pliquett U, Gersing E, Pliquett F (2000) Evaluation of Time-domain
based Impedance Measurements on Biological Tissue. Biomediz-
inische Technik 45(1-2):6-13
7. Howie M B, Dzwonczyk R, McSweeney T D (2001) An Evaluation
of a new Two-Electrode Myocardial Electrical Impedance Monitor
for Detecting Myocardial Ischemia. Anesth Analg 92:12-18
8. Min M, Kink A, Land R, Parve T, Rätsep I (2004) Modification of
pulse wave signals in electrical bioimpedance analyzer for implant-
able medical devices, Proc. IEEE EMBS 26 International Conference,
San Francisco, California, 2004, pp 2263-2266
9. Xu F (2007) The Imaginary Part: A Source of Creativity in Instru-
mentation and Measurement. IEEE Instrumentation and Measurement
Magazine 10(1):29-33
Address of the corresponding author:
Author: Mart Min
Institute: Tallinn University of Technology
Street: Ehitajate tee 5
City: Tallinn
Country: Estonia
Email: min@elin.ttu.ee