Bioimpedance

Eung Je Woo

Department of Biomedical Engineering

Impedance Imaging Research Center (IIRC)

College of Medicine

Kyung Hee University

Korea

ejwoo@khu.ac.kr

2

Conductivity and Resistance

V

I

I

L

S

MobileIons

-+

e-

e-

V+_ V

I

I

-+

e-

e-

MobileIons

V+

_

𝐄 = −𝛻𝑢, 𝐅 = 𝑞𝐄 = 𝑚𝐚, 𝐯𝑑 = 𝜇𝐄

𝐼 = 𝑅𝑉, 𝑅 =𝑉

𝐼=

1

𝜎

𝐿

𝑆

𝐉 = 𝑐𝐯𝑑 = 𝑐𝜇𝐄 = 𝜎𝐄 = −𝜎𝛻𝑢

3

V+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

V-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-+

-+

-

+

-+

-+

-+

-+

-

+

-+

-+

-

+

-

+

-+

-+

-

+

-+

-+

-+

- - - - - - - - -

+ + + + + + + + +

+ + + + + + + + +

- - - - - - - - -+Q

-Q

L

S

PolarizationImmobile Polar Molecules

Permittivity and Capacitance

e-

e-

e-

e- +Q

-Q

𝑞 𝑡 = 𝐶𝑣 𝑡 = 𝜀𝑆

𝐿𝑣 𝑡 , 𝑖 𝑡 =

𝑑𝑞(𝑡)

𝑑𝑡= 𝐶

𝑑𝑣(𝑡)

𝑑𝑡

𝑣 𝑡 = 𝑉 cos𝜔𝑡 , 𝑖 𝑡 = −𝑉𝜔𝐶 sin𝜔𝑡

𝑣(𝑡) = 𝑅𝑒 𝑉𝑒𝑗𝜔𝑡 , 𝑖 𝑡 = 𝑅𝑒 𝑉𝜔𝐶𝑒𝑗 𝜔𝑡+90°, 𝐙 =

𝐕

𝐈=

1

𝑗𝜔𝐶

4

-Cl+Na

-Cl+Na

+Na -Cl

+ + + + + + +

+ + + + + + +

_ _ _ _ _ _ _

_ _ _ _ _ __

i(t)

+

v(t)

-

1 2

1 2

1 1R jX R R

j C j C Z

cos , sin

R jX Z

R Z X Z

Z

( ) sin and

( ) sin

m

m

i t I t

v t I Z t

i(t)

1

1

2

2

R

C

C

R

Cell Membrane

Extra-cellular Fluid

Intra-cellular Fluid

+

v(t)

-

Admittivity and Impedance (or Admittance)

, , ,j r r r

5

Extra-cellularFluid

Intra-cellularFluid

CellularMembrane

Tissue Model (Macroscopic Apparent Conductivity)

-+

+

-

+

-

-

+ +

- -

+

6

Tissue Conductivity (Tumor)

Haemmerich et al., Physiol. Meas., 2003.

Normal Tumor

Necrosis

Fibrosis

Liver Breast

Lobular Carcinoma Ductal Carcinoma

Normal

Normal tissue

Central part of tumor

Surowiec et al., IEEE Trans. Biomed. Eng., 1988.

7

Tissue Conductivity (Lung Ventilation and Perfusion)300 million alveoli

Ventilation

Perfusion

Z : 10 mW to 40 W

8

• Molecular composition of cells

• Shape and direction of cells

• Density and structure of cells

• Contents of extra-cellular matrix

• Concentration and mobility of ions

• Concentration and mobility of charge-carrying molecules

• Amounts of intra- and extra-cellular fluids

• Lung ventilation and perfusion

• Cardiac function and hemodynamics

• Sleep apnea

• Tumor

• Bleeding

• Gastric emptying

• Stoke

• Epilepsy

• Neural activity

• Temperature or ablation

Structure and Composition Function and Pathology

Tissue Conductivity

9

Tissue Conductivity (1 Hz – 1 MHz)

Tissue Conductivity [S/m] Anisotropy

Lung 0.05 – 0.6 Local

Whole blood 0.7 Flow dependent

Bone 0.005 – 0.06 Strong

Muscle 0.05 – 0.6 Strong

Fat 0.02 – 0.05 Small

Liver 0.2 – 0.3 Unknown

Saline, 0.9% 2 None

Sea water 5 None

Low- and high-frequency current paths in biological tissue

Grimnes and Martinsen, 2008

10

Body as a Passive Volume Conductor

Malmivuo and Plonsey, 1995

Conductivity Voltage

Injection Current

⋅ 𝜎 𝐫, 𝑡 𝑢 𝐫, 𝑡 = 0 in Ω

−𝜎 𝐫, 𝑡 𝑢 𝐫, 𝑡 ⋅ 𝐧 = 𝑔 on 𝜕Ω

Current Density

𝐉 𝐫, 𝑡 = −𝜎 𝐫, 𝑡 𝑢 𝐫, 𝑡

u

, r

11

Homogeneous Conductivity (Toy Problem)

22

2

0

0

, 0z L z

uu

z

u V u

V

u z zL

z

Vz u z

L

- -J a

zS

VI z dxdy S

L

- J a

1 [ ]

VR

I

L

S W

V

0 z = 0

z = LS

J

V

0

I

12

Geometrical Effect (Toy Problem)

Grimnes and Martinsen, 2008

2

2

0

10

, 0

ur

r r r

u r a V u r

0aVu r

r

0

2 r

aVr u r

r

- J a

2002Half sphere

2 2aV

I r d r a Vr

J r

0 1 [ ]

2

VR

I a W

V0

a

13

Geometrical Effect (Toy Problem)

2

2

0

10

, 0

ur

r r r

u r a V u r b

0 1aV b

u rb a r

-

-

0

2 r

abVr u r

b a r

-

-J a

20 0

2Half sphere2 2

abV ab VI r d r

b a r b a

- - J r

0 1 1 1 [ ]

2 b

V

I aR

- W

a

b

V0

0

14

Current Flow and Conductivity

Grimnes and Martinsen, 2008

E and J are parallel

E and J are not parallel

Isotropic Conductivity Anomaly

Anisotropic Conductivity Anomaly

15

Current in Body

Grimnes and Martinsen, 2008

• Voltage, current density and magnetic flux density distributions are generated.

• Electrode position, body shape, body size and conductivity determine them.

16

Current in Body

Skin

Bone

Skin

CSF

GM

WM

0.25[A/m2]

0

17

Electrode and Contact Impedance

Skin

Electrode-Electrolyte-Skin Interface

Amplifier

John G. Webster, Medical Instrumentation: Application and Design, 3rd. ed.

Underneath the Skin

Electrode Surface

18

Two and Four-Electrodes (Simplified View)

ZB

ZC1 ZC2

i

v

ZB

ZC1 ZC2

i

v

ZC3 ZC4

1 2C B CV Z Z Z I BV Z I

V3

V3

V4

V4

19

Impedance Measurement

( ) sin( )i t I t

cos , sin

R jX Z

R Z X Z

Z

( ) sin( ) cos sin( ) sin cos( )v t ZI t ZI t ZI t

Real Part (In-phase Component)

Imaginary Part(Quadrature Component)

Phase

Amplitude

Z 0I ZI V

+

_

20

Phase-sensitive Demodulation

( ) sin( )i t I t

cos , sin

R jX Z

R Z X Z

Z

( ) sin( ) cos sin( ) sin cos( )v t ZI t ZI t ZI t

Real Part (In-phase Component)

Imaginary Part(Quadrature Component)

( )v t

sin( )t

cos( )t

0

1 T

dtT

0

1 T

dtT

1cos

2ZI

1sin

2ZI

Z 0I ZI V

+

_

21

IMM (Impedance Measurement Module)

Digital waveform generator

Phase-sensitive demodulator

DAC

ADC

BPF & Amp

BPF & Amp

DC offset

HCP+

BPF & Amp

IA

I / V12 or 16 bit

16 bit Currentoutput

Voltageoutput

Differentialvoltage input

Currentinput

GIC x 4

FPGA

22

BCA (Body Composition Analysis)

1 H HR

S S

2HV SH

R

2

1 2 3

HTBW W

R Total Body Water (TBW):

H

S

Fat Free Mass (FFM): 0.73

TBWFFM

2

1 2

HTBW

R

Body Fat (BF): 2( ) 1

(%) 100 (1 ) 100W FFM H

BFW W R

-

-

2

1 2 3 4

1(%)

HBF A S

W R

H: heightW: weightR: resistanceA: ageS: sex

23

BCA (Body Composition Analysis)

x1 + x2 = r1x1 + x3 + x4 = r2

x2 + x3 + x5 = r3x4 + x5 = r4

x1 + x3 + x5 = r5x2 + x3 + x4 = r6

01 1 0 0 11

01 0 1 1 22

10 1 1 0 33

1 40 0 0 14

1 51 0 1 05

0 60 1 1 1

rx

rx

rx

rx

rx

r

Ax r

1( )T T-x A A A r

11 0.5 0.25 0.25 0 0.25 0.25

22 0.5 0.25 0.25 0 0.25 0.25

33 0.5 0.25 0.25 0.5 0.25 0.25

44 0 0.25 0.25 0.5 0.25 0.25

55 0 0.25 0.25 0.5 0.25 0.25

6

rx

rx

rx

rx

rx

r

- -

- - - - - - - -

x1 x2

x3

x4 x5

2

1 2 3 4 5 6

1 1 1(%) ( )

arm trunk leg

HBF A S

W R R R

1 2

1 2

arm

x xR

x x

4 5

4 5

leg

x xR

x x

3trunkR x

Grimnes and Martinsen, 2008

24

• ECIS- Real-time, label-free, non-invasive monitoring for live-cell- Functional and morphological change detection using impedance

for the activities of cells

• Culture ware

- Gold film electrodes with an insulating film

- Several electrodes at the base in the well

• Oxygen plasma process

- Clean the electrode and sterilize the chamber

- Improve the adhesion of cells due to hydrophilic

• Diameter of electrode(s): 15 – 500 μm

• Electrodes per well: 1 – 40

• Well volume : 100 – 600 μL

Wegener J, Keese C R and Giaever I, 2000, Electric cell-substrate impedance sensing(ECIS) as a noninvasive means to monitor the kinetics of cell spreading to artificial surfaces, Cell Research, 259, 158-166, www.biophysics.com

ECIS (Electric Cell-substrate Impedance Sensing)

25

S. Reitinger et al, 2012 Biosens Bioelectron. Vol. 34 Issue 1 pages 63-69

Inter-digitatedelectrodes

Inter-digitatedmicrosensor electrodes

Inter-digitatedelectrodes

Microelectrode array

E. Sarro et al, 2011 Biosens Bioelectron. Vol. 31 Issue 1 pages 257-263

K. Heileman et al, 2011 Biosens Bioelectron. Vol. 49 pages 348-359

• Impedance spectroscopy for cellular bio-sensing

• Observation of cells

• Measurement of physiological properties of cells

• Non-invasive and real time

Bioimpedance Sensors for Cells

26

E. Sarro et al, 2011, Biosens Bioelectron,vol. 31, Issue 1, pp. 257-263.

Monitoring of Cellular ConcentrationP.O. Bagnaninchi et al, 2011, PNAS 108, pp. 6462–6467.

Monitoring of Cell Differentiation

D. Opp et al, 2009 Biosens Bioelectron, vol. 24, Issue 8, pp. 2625-2629.

Cytotoxicity and Cell Death

Bioimpedance Signals from Cells

27

Lead (one or two pairs of electrodes) Design

• How to determine electrode positions for BCA?

• What is a best electrode configuration for bioimpedance

measurement using a wrist band?

28

Lead Field, Sensitivity and Transimpedance

Grimnes and Martinsen, 2008

EOD