ICEBI ’07 August 29th – September 2nd 2007 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

*** In this paper the possibilities to perform ICEBI ’07 August 29th – September 2nd 2007 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

    ICEBI ’07 August 29th – September 2nd 2007 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 What is so specific in the bioimpedance (EBI) I. INTRODUCTION ICEBI ’07 August 29th – September 2nd 2007 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.

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 2007 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

Multi-site EBI measurement using synchronous sampling ICEBI ’07 August 29th – September 2nd 2007 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 □ TUT

non-uniform synchronous sampling ICEBI ’07 August 29th – September 2nd 2007 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.

f1 ⁄ f2 = 6 ⁄ 5 tmeas = 6 ⁄ f1 = 5 ⁄ f2 An example: 8 ICEBI ’07 August 29th – September 2nd 2007 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 

Simultaneous multifrequency measurement using uniform sampling ICEBI ’07 August 29th – September 2nd 2007 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

ICEBI ’07 August 29th – September 2nd 2007 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

ICEBI ’07 August 29th – September 2nd 2007 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

Example 1 – Decade distances ICEBI ’07 August 29th – September 2nd 2007 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, ….

Weighting patterns for νc1(t) ICEBI ’07 August 29th – September 2nd 2007 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

Thank you for your attention ! ICEBI ’07 August 29th – September 2nd 2007 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, 19086 Tallinn, Estonia Email: ronk@ttu.ee TUT