1. ICEBI ’07
August 29th – September 2nd in GRAZ, AUSTRIA
Simultaneous multi-frequency bio-impedance measurement applying synchronised uniform or non-uniform sampling –––––––––––––––––––––––––––––––––––––––––––––––––––– by
Ants Ronk, Mart Min, and Toomas Parve
Department of Electronics
Tallinn University of Technology, Tallinn, Estonia
TUT

2. *** In this paper the possibilities to perform
ICEBI ’07
August 29th – September 2nd in GRAZ, AUSTRIA
Simultaneous multi-frequency bio-impedance measurement applying synchronised uniform or non-uniform sampling
A. Ronk, M. Min and T. Parve 2
***
In this paper
the possibilities to perform
multi-frequency bio-impedance measurement
simultaneously for several tissue channels
are discussed, and
a method of synchronous signal sampling
by applying uniform or non-uniform sampling,
together with digital signal processing
is presented.
TUT

3.    
ICEBI ’07
August 29th – September 2nd in GRAZ, AUSTRIA
Simultaneous multi-frequency bio-impedance measurement applying synchronised uniform or non-uniform sampling
A. Ronk, M. Min and T. Parve 3
I. INTRODUCTION    
Measurement of electrical bio-impedance enables to characterise a state of tissues/organs, to get diagnostic images, to find hemodynamical parameters, etc.
Simultaneous multichannel and multifrequency measurements are needed.
Why multichannel ? Why multifrequency ? Why simultaneous ?
Some examples of electrical bioimpedance measurement from cardiography
a noninvasive b multielectrode invasive estimation c intracardiac impedance measured
plethysmography of the ventricular volume for pacing control
TUT

4. 4 What is so specific in the bioimpedance (EBI) I. INTRODUCTION
ICEBI ’07
August 29th – September 2nd in GRAZ, AUSTRIA
Simultaneous multi-frequency bio-impedance measurement applying synchronised uniform or non-uniform sampling
A. Ronk, M. Min and T. Parve
    4
I. INTRODUCTION
Complex bioimpedance Ż=R+jX is found as Ż = V/ I
from the measured voltage response V to the sine wave excitation current I passed through the bio-object, commonly. .
Explanation of the EBI Simple 3-element equivalent Phasor diagram for a frequency f.
What is so specific in the bioimpedance (EBI)
The phasor diagramme of the static EBI (▬), and of its 3-element equivalent (▬), and the phasors of the static EBI for 2 frequencies, low ωl and high ωh.

5. II. M E A S U R E M E N T S Y S T E M : SIGNALS AND ALGORITHMS
ICEBI ’07
August 29th – September 2nd in GRAZ, AUSTRIA
Simultaneous multi-frequency bio-impedance measurement applying synchronised uniform or non-uniform sampling
A. Ronk, M. Min and T. Parve 5
II. M E A S U R E M E N T S Y S T E M :               SIGNALS AND ALGORITHMS        
Simultaneous multifrequency EBI measurement system . . . .
VZ = Iexcit Z = If1 Z(f1) + If2 Z(f2)
Sampling pulses
Fig.1 A system for simultaneous two-frequency bio-impedance measurement applying synchronised sampling
TUT

6. Multi-site EBI measurement using synchronous sampling
ICEBI ’07
August 29th – September 2nd in GRAZ, AUSTRIA
Simultaneous multi-frequency bio-impedance measurement applying synchronised uniform or non-uniform sampling
A. Ronk, M. Min and T. Parve 6
II. MEASUREMENT SYSTEM: SIGNALS AND ALGORITHMS
Multi-site EBI measurement using synchronous sampling
Re+
Im–
Im+
Re–
fsampling = 4 · fsignal
The real Re and imaginary Im parts of the phasor Ż are determined as
Re = (Re+ – Re–) ∕ 2
and
Im = (Im+ – Im–) ∕ 2
Synchronous sampling of a single sine wave response.
Real part samples Re+ are designated as filled red dots ● and Re– as unfilled red ones ○,
imaginary part samples Im+ as filled green squares ■, and Im– as unfilled green squares □
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7. non-uniform synchronous sampling
ICEBI ’07
August 29th – September 2nd in GRAZ, AUSTRIA
Simultaneous multi-frequency bio-impedance measurement applying synchronised uniform or non-uniform sampling
A. Ronk, M. Min and T. Parve 7
II. MEASUREMENT SYSTEM: SIGNALS AND ALGORITHMS
Two typical cases of multifrequency measurement
Multi-site Multi-frequency
a)  Two different impedances are measured  b)  The same impedance is measured
      at a slightly differing frequency at (two) essentially different frequencies
non-uniform synchronous sampling
TUT
Fig. 3. Simultaneous measurement of responses to two excitations
Note: Only the Re+ samples are shown for the response signal.

8. f1 ⁄ f2 = 6 ⁄ 5 tmeas = 6 ⁄ f1 = 5 ⁄ f2 An example: 8
ICEBI ’07
August 29th – September 2nd in GRAZ, AUSTRIA
Simultaneous multi-frequency bio-impedance measurement applying synchronised uniform or non-uniform sampling
A. Ronk, M. Min and T. Parve 8
II. MEASUREMENT SYSTEM: SIGNALS AND ALGORITHMS f1 f2
fSP,1 = f1
fSP,2 = f2
fSP
6 A1= ΣAi ⁄ 6
i=1 6
Σ Ai = 0 5
A2= Σ Ai ⁄ 5
non-uniform sampling
Using the non-uniform sampling at simultaneous measurement
An example:
f1  ⁄  f2  = 6 ⁄ 5
tmeas = 6 ⁄  f1  = 5 ⁄  f2
Convergence of results in the case of simultaneous measurement of the responses to two excitations with near (slightly differing) frequencies f1 and f2 

9. Simultaneous multifrequency measurement using uniform sampling
ICEBI ’07
August 29th – September 2nd in GRAZ, AUSTRIA
Simultaneous multi-frequency bio-impedance measurement applying synchronised uniform or non-uniform sampling
A. Ronk, M. Min and T. Parve 9
II. MEASUREMENT SYSTEM: SIGNALS AND ALGORITHMS
Simultaneous multifrequency measurement using uniform sampling
Timing and weighting of the samples usable for determining the real and the imaginary part of the components of the VZ signal in the case of two-frequency operation
f2 = 2 f1
TUT

10. ICEBI ’07
August 29th – September 2nd in GRAZ, AUSTRIA
Simultaneous multi-frequency bio-impedance measurement applying synchronised uniform or non-uniform sampling
A. Ronk, M. Min and T. Parve 10
II. MEASUREMENT SYSTEM: SIGNALS AND ALGORITHMS
Timing and weighting of the samples usable for determining the real part of the VZ signal in the case of two-frequency operation
f2 = 3 f1
TUT

11. ICEBI ’07
August 29th – September 2nd in GRAZ, AUSTRIA
Simultaneous multi-frequency bio-impedance measurement applying synchronised uniform or non-uniform sampling
A. Ronk, M. Min and T. Parve 11
II. MEASUREMENT SYSTEM: SIGNALS AND ALGORITHMS
Timing and weighting of the samples usable for determining the real part of the VZ signal in the case of two-frequency operation
f2 = 6 f1
TUT

12. Example 1 – Decade distances
ICEBI ’07
August 29th – September 2nd in GRAZ, AUSTRIA
Simultaneous multi-frequency bio-impedance measurement applying synchronised uniform or non-uniform sampling
A. Ronk, M. Min and T. Parve 12
II. MEASUREMENT SYSTEM: SIGNALS AND ALGORITHMS
Choice of frequencies (Examples for some more general cases)
Example 1 – Decade distances 2n 1 2 4 8 16 32 64
128 fs
256
512 k 11 5 25 13 63 33
157 79 f 10
100
104
1008
1056
10048
10112
Example 2 – Half decade distances 2n 1 2 4 8 16 32 64
128 fs
256
512 k 3 5 25
125
625 f 10
100
1000
1008
320
3200
TUT
k = 2i + 1
i = 0, 1, 2, ….

13. Weighting patterns for νc1(t)
ICEBI ’07
August 29th – September 2nd in GRAZ, AUSTRIA
Simultaneous multi-frequency bio-impedance measurement applying synchronised uniform or non-uniform sampling
A. Ronk, M. Min and T. Parve 13
II. MEASUREMENT SYSTEM: SIGNALS AND ALGORITHMS
Processing of one component of a 4-component multi-sine response with 2 pairs of close frequencies.
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1 -4 -2 2 4
ν(t)
The signal ν(t) , its four components and 32 samples taken per its period (measurement interval)
wRe1
wIm1
Weighting patterns for νc1(t) 5 10 15 20 25 30 -1
-0.5
0.5 1
=>real part
=>imag. part
=>modulus
1.0
0.5
–0.5
–1.0 Z1
ReŻ1=R1
νc1(t)
ImŻ1=X1
Convergence of results to real and imaginary parts and module for νc1(t)
Main text

14. Thank you for your attention !
ICEBI ’07
August 29th – September 2nd in GRAZ, AUSTRIA
Simultaneous multi-frequency bio-impedance measurement applying synchronised uniform or non-uniform sampling
A. Ronk, M. Min and T. Parve 14
CONCLUSIONS
The presented measurement signal system(s) and digital signal processing method enable to measure bioimpedance and to demodulate bio-modulations of components of a multi-sine measurement signal, which covers a wide frequency range (from kHz up to several MHz) simultaneously.
The same can be done applying Fourier transformation but the proposed approach is significantly simpler and suits well for microelectronic implementation (e.g. in FPGA).
Thus it looks promising for applications in portable/wearable bioimpedance measurement systems of low power consumption.
Thank you for your attention !
ACKNOWLEDGMENT
Estonian Science Foundation supported this work under the grants 7243 and 7212.
Address of the corresponding author:
Ants Ronk, Tallinn University of Technology, Ehitajate tee 5, Tallinn, Estonia
TUT