Measurement of Cell Distribution in Organs
with Lissajous of Impedance
Shigehiro Hashimoto, Nobumichi Nagano,
Yoshinori Murashige and Satoshi Yamauchi

Department of Electronics, Information and Communication Engineering,Osaka Institute of Technology
5-16-1, Ohmiya, Asahi-ku, Osaka, 535-8585, Japane-mail: hasimoto@elc.oit.ac.jp

ABSTRACTThe relations between Lissajous' figure of impedance
and the cell distribution in the biological tissues wereexperimentally investigated with the micro-electrode.
The micro-electrode of concentric cylinders wasmanufactured with the stainless steel needles: thediameter of outer needle is 1.20 mm. The electrode wasstuck into the normal bovine tissues: the heart, thelever, the kidney, the fatty tissue, or the intestinal
mucous membrane. The sinusoidal alternating currentof the frequency between one to 1000 kHz wasintroduced to the circuit with an oscillator. The output
voltage was measured at the series resistance. The
phase shift between the voltage and the current throughthe biological tissue was calculated from the effective
values of the input voltage, the output voltage, and thephase shift, which was measured at Lissajous' figure
between the input and output voltages. The capacitanceof the tissue was calculated with an electrical model of
one parallel pair of capacitance and resistance. The cell
distribution in the tissue was observed with amicroscope. The results show that the capacitanceincreases with the density of cells. This study
demonstrates the effectiveness of the Lissajous' figure
measurement on the cell distribution in biologicaltissue.
Keywords: Bio-measurement, Impedance, Microelectrode, Phase Shift, Lissajous' Figure, BiologicalTissue, Cell Distributionof the cells, which act as capacitance. The highfrequency signals pass straight through cells, while thelow frequency signals go round between cells. The cell
distribution was also studied for the detection of thetumor [1].
Various methods have been used to measure biological
impedance. The electric current pathway depends on
the shape of two electrodes and on the position
between them. Capacitance causes the phase shift
between current and voltage. Lissajous' figure is often
used to measure the phase shift between two sinewaves. The present study has investigated thereferences between Lissajous' figure of impedance andthe cell distribution in the biological organs by themeasurement with the micro-electrode of concentric
cylinders.

2. METHODS
Micro electrodeTo keep stable position between two electrodes, themicro-electrode of concentric cylinders was selected(Fig. 1). That was manufactured by the stainlessneedles: the outer needle of 1.20 mm diameter, 38 mm
length; the inner needle of 0.60 mm diameter, 32 mm
length. Both cylinders were insulated with silicone
grease and with a cylinder of vinyl chloride each other.

outer needle1. INTRODUCTION
Many electrical models on impedance of the biologicaltissue have been proposed in the previous studies.
Impedance on the tissue changes with the frequency ofelectric signals. This change relates to the distribution

inner needle
Fig. 1. Micro-electrode.

JRxZ

V2
A

V2

V3

J
B
V3

V1

V1

Fig. 4. Relation among phasevectors V1, V2, and V3.

Fig. 2. Electric circuit.
The angle of the electrode end to stick into the tissues
is 45 degree.
Materials
The fresh normal bovine tissues were used to measure
impedance: the heart, the lever, the kidney, the fatty
tissue, or the intestinal mucous membrane. The
electrode was stuck into the tissues perpendicularly
with the depth of 1.2 mm.
Electric circuit
The load of the electric resistance (Rx) of 985 ohm wasconnected in series to the electrical circuit including
the biological tissue (Z) (Fig. 2). The alternating
current in sine wave of the frequency between one to1000 kHz was introduced to the circuit by an oscillator.
Lissajous' figure
The phase shift angle (A) is calculated from Lissajous'figure between the input voltage and the output voltage(Fig. 3). The output voltage was measured at theconnected load of resistance (Rx).
sin(A) = Q / P(1)where P is the amplitude of output voltage, and Q is
the intercept of output voltage on the center line at theinput voltage equals zero.
Phase shift at the biological tissue
The effective value of voltage loaded on the biologicaltissue (V3) is calculated from Eq. (2).
V32 = V12 + V22 - 2V1V2 cos(A)(2)

JcCpJRRpJFig. 5. Electrical circuit model forbiological tissue.

where V1 is the effective value of the input voltage, V2
is that of output voltage (Fig. 4). The phase shift angle(B) between the voltage (V3) and the current (J)through the biological tissue (Z) is calculated from Eq.
(3).
V12 = V22 + V32 + 2V2V3 cos(B)(3)

Electrical model
An electrical circuit model (Fig. 5) for the biologicaltissue with one parallel pair of capacitance (C) andresistance (R) introduces the value of capacitance (Cp)of the tissue from these calculated values at a given
frequency (f) (Fig. 6).
Jc = J sin(B)J = V2 / Rx(4)(5)

V2PQJO

V1JcBJRFig. 3. Lissajous' figure between theinput voltage (V1) and the output voltage (V2).

V3

Fig. 6. Relation between phase vectors Jand Jc.

where Jc is the current at capacitance, and J is the total
current at the circuit.
Cp = Jc / (6.28 f V3)(6)

Cell distribution
These tissues were fixed, dehydrated, embedded, sliced
and stained with hematoxylin-eosin staining method.
The cell distribution in the tissue was observed with amicroscope.

3. RESULTS
The calculated Cp is shown in relation to frequency ofelectric current in the lever (Fig. 7). The results showthat capacitance decreases with the increase offrequency.

Fig. 8. (a) Cell distribution (kidney). Scale from rightto Left : 0.5 mm.

Typical cell distribution in each tissue was shown inFig. 8. Cell distribution is high in the kidney, while nocell is observed in the fatty tissue. The relation
between Cp at 10 kHz and density of cells was shownin Fig. 9. The results show that capacitance increases
with density of cells.

Fig. 8. (b) Cell distribution (lever).

12Capasitane [nF]10864200200400600

800

1000

Frequency [kHz]Fig. 7. The relation between Cp andfrequency

Fig. 8. (c) Cell distribution (intestinal mucousmembrane).

4. DISCUSSION
Previous studies about the biological tissue evaluatedcomplex models of impedance, which consists ofseveral elements of resistance and of capacitance.
Electric model should include a parallel capacitanceaccordingtothefrequency
characteristic.
Three-dimensional internal structure of biologicaltissue was also tried to estimate with equivalent
electric circuit [2].
To stabilize electric current pathway through biologicaltissue, both the shape and position of electrodes isimportant. The micro-electrode of concentric cylinders,which is introduced in the present study, has enoughstability to measure impedance of biological tissue.

Fig. 8. (d) Cell distribution (heart).

The measurement of local impedance was also applied
to detect tumor [1]. The distribution of cells in tumor
might be different from that in normal tissue.

5. CONCLUSION
The results show that the capacitance increases withthe density of cells. This study demonstrates theeffectiveness of the Lissajous' figure to estimate thecharacteristic of biological tissues from the impedance
measurement with the micro-electrode of concentric
cylinders.

6. ACKNOWLEDGMENT
Fig. 8. (e) Cell distribution (fatty tissue).

Cp, [nF]

This work was supported in part by a Grant-in-Aid for
Scientific Research from the Japanese Ministry ofEducation, Science, Sports and Culture.
20181614121086420

7. REFERENCES[1] S. Kimura, T. Morimoto, T. Uyama, Y. Monden, Y.
Kinouchi and T. Iritani, "Application of Electrical
Impedance Analysis for Diagnosis of a Pulmonary
Mass", Chest, Vol. 105, 1994, pp. 1679-1682.

01000

2000

3000
2Density of cells, [1/mm ]Fig. 9. The relation between Cp anddensity of cells

4000[2] N. Momose, Y. Kinouchi, T. Iritani, et al., "Three
Dimensional Analysis of Local Tissue Impedance
by a Finite Element Method", World Congress on
Medical Physics and Biomedical Engineering, 1997,
p. 347.