signal processing in impedance spectroscopy
TRANSCRIPT
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CEBE IAB meeting, May 19, 2015
Signal Processing in Impedance Spectroscopy
Mart Min
Thomas Johann Seebeck Department of Electronics Centre for Research Excellence CEBE
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Henry Cavendish born in Nice (Nizza) 1731-1810 ______________________________________________________________________________
Oliver Heaviside introduced the terms: -impedance in July 1886 -admittance in Dec 1887
Ohm's law 1826
The concept of electrical impedance generalizes Ohm's law to AC circuit analysis. Unlike electrical resistance, the impedance of an electric circuit can be a complex number: Z = V/I, where Z = R + jX, and R is a real part and X is an imaginary part.
Electrical impedance (or simply impedance) is a measure of opposition to sinusoidal electric current
Arthur Edwin Kennelly
innovator and engineer A paper “Impedance“ in 1893:
complex numbers to Ohm’s law for AC
Electrical Impedance
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Complex Impedance characterises structures and electric properties of materials, substances, devices, constructions
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Ż = V / I
Low and high frequency current components
Current flow I
Voltage V on the impedance Ż
C C R
r
High frequency current, only
Currentflow I
Z(jω) = R + X(jω)
xc(jω) = 1/ jωC = - j (1 / ωC)
xL(jω) = + jωL, ω = 2πf x
X C = 1,
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Complex Impedance depends also on dielectric properties of material: complex permittivity versus frequency
ε (jω)= ε’(ω) + jε’’(ω), ω = 2πf
Imaginary capacitive impedance Xc= 1/ jωC, the capacitance C = εA/d depends on ε (jω)
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Introduction to Impedance Spectroscopy
Excitation amplitude is severly limited! safety regulations nonlinearities of object Impact on the object parameters energy consumption
The best accuracy of time-frequency domain spectral analysis is the aim
In most cases the impedance spectrum of biological objects must be measured fast. Examples: flowing cells in microfluidic devices, cardiovascular system, beating heart, breathing lungs, pulsating blood, …
The question to be answered: how to perform the fast impedance spectroscopy within the needed frequency range (from f1 to f2) during a required short time interval (from t1 to t2) with minimum dynamic uncertainty and the lowest noise level.
(t)
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Spectrally rich excitation is required (microfluidic cytometry as an example)
effect of the interfacial double-layer
frequency range of interest
≤ ∓ 50 mV (to avoid nonlinearities)
Since the shape of impedance spectrum is smooth, it is not reasonable to spread the excitation energy over all the frequency range but to concentrate it onto limited number of discrete frequencies (frequency bins). Spectrally sparce excitation is recommended in this case.
Equivalent circuit
Simplified electrical model
Cdl = 2 nF Cm = 1 pF Cs = 20 pF Rs = 10k Rcy = 100k
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Spectrally rich but sparse excitation: a multisine signal
Sum of 4 sine wave components (k = 4) with frequencies 1f1, 3f1, 5f1, 7f1 and Ai = 1
Sum of 4 sine waves Φi = 0°, CF = 2.08
Sum of 4 sine waves Φi = 90° , CF = 2.83
Sum of 4 sine waves Φi = optimized, CF = 1.45
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4 3
2
-2 -3 -4
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Crest Factor (CF) – an important parameter for the excitation signal
Peak value of the excitation signal s(t)
RMS value of the excitation signal s(t)
T denotes the observation time of the multicomponent signal s(t)
RMS value does not depend on initial phases Φ(i) of separate components. The CF minimization problem reduces to finding the best set of phases, which ensures the minimum peak value for the excitation.
Result – the best packaging of energy into a signal with limited amplitude!
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CFs of the optimized multisines: consecutive frequency distribution (4, 5, 6, ... , 20)
Recent results of the CF optimisation using the developed new method by J.Ojarand, M. Min and P. Annus, Physiol. Meas. vol. 35 pp. 1019–1033, 2014.
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CF of a single sine wave
A world record level !
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Enhanced optimisation: minimization of the crest factors of both - excitation (CFE) and response (CFR)
Crest factor CFR of the response signal depends on the crest factor CFE of the excitation signal, but not directly.
1. CFE of the multisine excitation depends on initial phases of its components that are freely adjustable and can be optimized, therefore. 2. Phases of the response signal components will not remain the same as of the excitation has. They depend also on the phase shifts in object or the sample under test (SUT).
The idea for enhanced optimization of the excitation signal: Parameters of the excitation signal components (initial phases Φ(i)opt and amplitudes A(i)opt) should be modified so that the product CFER = CFE x CFR of crest factors of the excitation signal (CFE) and the response signal (CFR) will be minimal.
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Enhanced optimization of the excitation signal: one experimental case
A multisine signal containing 10 frequency components was used as an excitation voltage. RMS magnitudes of all the spectral components of the response current were equalized to 10 μA using the magnitudes of complex impedance Z (jω). More than 30% higher signal-to-noise ratio has been achieved in comparison of the optimisation of excitation signal only.
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30 kHz 300 kHz
3 MHz
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Electronics used in microfluidic experiments
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Making generation simpler: a multifrequency binary sequence as an excitation ( 4 frequences – 1, 3, 5, 7f )
Equal-level components
Growing-level components !
Decreasing levels: usual case! A simple
rectangular waveform
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QUADRATM TECHNOLOGY FOR IMPEDANCE SPECTROSCOPY
Basic solution – proof-of-concept prototype, hard & software.
CEBE partner: Th. J. Seebeck Department of Electronics.
Cooperation: ELIKO Competence Centre.
IP: Patent EE05668B1 (Estonia), Patent Applications EP2565654A2 (EU), and US2013/0054178 A1 (USA); Utility Model Application U201300075 (Estonia).
Operation principle: expandable multi-channel device generates a spectrally rich binary excitation containing 15 spectral lines to the system under study. The multi-frequency response signal is digitized and processed in parallel using time-frequency domain DFT.
Specifications: • Impedance measurement range: 10 Ω to 100 kΩ; • Frequency range: selectable from 1 kHz to 350 kHz, resolution 1 kHz; • Number of the frequency components: selectable from 4 to 15; • Measurement time: selectable, min 1ms.
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Practical case: 1ms cycle based binary excitation with the spectrum from 1kHz to 350 kHz, 15 spectral lines
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(b) initial 0.3 ms time interval zoomed out from the 1ms cycle.
time
+3V
-3V
Time interval 0.3 ms
time
High +3V
Lo w -3V
Time interval 1 ms
(a) a full 1 ms cycle of binary excitation
0
0 1.0 0.3 ms
0.3
0.3 ms
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Spectrum of the used binary sequence
0.70
0.00
0.10
0.20
0.30
0.40
0.50
0.60
1M1k 10k 100k 500k
The spectrum contains 15 equal-amplitude frequency components (a log frequency presentation)
VRMS
f, Hz
fNyquist =500kHz
fsampling
1 kHz 2 3 7 11 17 23 31 43 61 87 127 177 247 349 kHz
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The complete spectrogram of the impedance magnitude in the 10 second time interval containing cardiac and respiratory variations
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Spectrogram of the time-variant impedance
0 s 3.0 s 6.7 s
Cardiac variations, fast
Respiratory variations, slow
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110
80
85
90
95
100
105
100 1 2 3 4 5 6 7 8 9
Impedance, Ω
Impedance magnitude variations at 1 kHz frequency, including changes of cardiac and respiratory components
Time interval 10 s Time, s
3.0 s
6.7 s
0.0 s
Variations of the impedance magnitude in time
Cardiac components
Respiration period
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Impedance measurement for pacing rate control (St Jude Medical, USA, and Smartimplant OÜ, Estonia, owned the patents)
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A device for controlling of syringe needles in the body for the point-of-care medicine (cure, electronic biopsy) Injeq Oy, Finland, bought a licence for using the impedance spectroscopy
technology (binary multifrequency)
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1,75
-1,5
-1,25
-1
-0,75
-0,5
-0,25
0
0,25
0,5
0,75
1
1,25
1,5
Samples1000 10 20 30 40 50 60 70 80 90
BP Signal 2 004-02.aort
2,5
-2
-1,5
-1
-0,5
0
0,5
1
1,5
2
Samples1000 10 20 30 40 50 60 70 80 90
EBI Signal 2 004-02.aort
The CAP waveform
(normalized)
Radial EBI waveform
(normalized)
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Monitoring of Central Aortic Pressure (CAP) of blood: recording of waveforms and finding parametres as Augmentation Index
(about 100 human experiments in East-Tallinn Central Hospital)
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Aorta
artery
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Smart clothes, textile electrodes (LADE OÜ, Estonia): breathing and heart beating analysis
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Impedance spectroscopy sensing in lifejackets
Partners: MarinePool (Germany) and LADE OÜ (Estonia). For the use in Nordic and Polar seas: wireless monitoring of breathing and heart beating,
both rate and volume, in a salty cold water.
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Assessment and control of the meat cooking process (Electrolux Italy, 2012)
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Meat quality assessment (Carometec A/S, Denmark)
CAROMETEC bought a license to use the impedance spectroscopy method (binary multifrequency) for meat quality assessment
Carometec is a world leader in production of meat quality estimation equipment for the food industry
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Medical diagnosing in reconstructive surgery (Estonia) in Estonian private clinic
Electrical bioimpedance of transplanted muscle flaps “Bioimpedance measurement
is a key tool to avoid irreversible muscle damage postoperatively (25% cases)”
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Impedance of electrochemical cells: monitoring the health of batteries
Joint project by:
Department of Measurement and Automation, University of Bundeswehr Munich
TJ Seebeck Institute of Electronics at Tallinn University of Technology
Texas Instruments, USA
0 0.02 0.06 0.1 0.14 0.18
-0.08
-0.04
0
[Re(Z) - min(Re(Z))] in Ω
Im(Z
) in
Ω cycle 0-200
charge transfer reaction diffusion
porosity
inductivity
f
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