Bioimpedance Measurement

Bioimpedance MeasurementDept. of Biomedical Engineering

2003200449YOUNHO HONG

Impedance measure

IR A v =1

V =R i

+

-

O U T

constantcurrentsource

i=0

i=0measured

knowni

VR

Z0II

+

-

IZ

V

V jXR Zimpedance resistance

reactance

Impedance measure(Example) 1000HzFreq. , ][ 4521 jZ

1

1

1+j

Re

Im

)}8000

1(10002sin{2

)4

10002sin(2)(452

)10002sin()( [mA] 01

t

ttV

tti

IZV

I

i V

t

1 You are given with i(t) = I sin(2πft)You measure v(t) = V sin(2πft+θ)

ZI

V

I

VZ

Impedance measure(Example)

R C Z

)()()1

(1

11

1

222

2

222wjXwR

CRw

CwRj

CRw

R

jwRC

R

jwCR

jwCR

Z )(tan 1 wRCR Z

Impedance measure

R

C

R 1 C

R 2

)()()1

(1

wjXwRwC

jRjwC

R

Z

)1

(tan1

21

222

RCwCwR Z

ZwjXwR

CRW

CwRj

CRw

RR

)()(

)1

(1 22

12

21

221

21

2Z

Impedance measure

I

D if f e re n t ia l A M P

+

-

O U TZ X

X

T

I dttVT 0

)(1

T

Q dttVT 0

)(1

?

?

sin(2πft)

cos(2πft)

phase-sensitive Demodulation

Impedance measure

)}22cos({cos2

)2sin()2sin()2sin()()(

ftV

ftftVfttVtVI

I

T

I

VV

TT

VdttV

T

2

1cos

2

)(cos1

2)(

10

In-phase Component

cosVVI

Impedance measure

Quadrature Component

}sin)22{sin(2

)2cos()2sin()2cos()()(

ftV

ftftVfttVtVQ

Q

T

Q

VV

TT

VdttV

T

2

1sin

2

)(sin1

2)(

10

sinVVQ

Impedance measure

2222222 cossin VVVVV QI

22QI VVV

tancos

sin

V

V

V

V

I

Q

I

O

V

V1tan

sincos jZZjXRZ Z

Vsin θ

Vcosθ Re

Im

V

θ

(In-phase Component)

(Quadrature Component)

V=VI+jVQ

Two-electrode Method

V

I

skin

electrodeequivalent circuit

R c

R sE h c

C c

i

E h 1 E h 2

V

ZC1 ZC2

Zb

Inject current and then measure voltage

2211 )( EhEh CbC IZZZV

Two-electrode Method)sin()sin()sin()( 221121 wtIZwtIZwtIZEhEhtV CbbC

Component) phase-(In coscoscos

sin)(1

2

2211

0

IZIZIZ

dtwttVT

V

CbbC

T

I

Component) e(Quadratur sinsinsin 2211 IZIZIZV CbbCQ

Re

Im

ZbcosθbZc1cosθ1Zc2cosθ2

Zc1sinθ1

Zc2sinθ2

Zbsinθb

impedance)body (contact

sincos

sincos

sincos

21

2222

1111

CbC

CC

bbbb

CC

QI

jZZ

jZZ

jZZI

jVV

ZZZ

Z

Four-electrode Method

V

I

skin

E1 E3 E4 E2

i

E h 1 E h 3E h 4

E h 2

ZC1 ZC3

Zb1 Zb2

ZC4 ZC2

Zb

0I IIZV b

sincos)(1

2

cossin)(1

2

)sin()(

0

0

IZdtwttVT

V

IZdtwttVT

V

wtIZtV

b

T

Q

b

T

I

bb

impedance)body (only

sincos

b

bbbb

QIm

jZZI

jVV

Z

Z

Three-electrode Method

V

I

skin

E1 E3 E2

i

E h 1 E h 3 E h 2

ZC1 ZC3 ZC2

Zb1 Zb

2

22

22

sinsin

coscos

Cb

CCbb

CCbb

QIm

jZjZ

ZZI

jVV

ZZ

Z

We can measure skin impedanceusing Three and Four electrode Method

2

)()(

C

mm MethodfourMethodthree

Z

ZZ

Noise Effect

)()sin()()()( tnwtZItntVtVm

coscos

sin)(2

sin)sin(2

sin)(1

2

00

0

f

TT

T

mmI

NZI

dtwttnT

dtwtwtZIT

dtwttVT

V

Spectrum AnalizertwAtwAtwAtV NN sin.....sinsin)( 2211

A1A3A2

f1

AN

f2 f3 fN…

…

X

X

1

01

1 Tdt

T

2

02

1 Tdt

T

sinw1t / cosw1tV(t)

X NT

N

dtT 0

1

…

…sinw2t / cosw2t

sinwNt / coswNt

2,

211 BA

2,

222 BA

2,

2NN BA

T

nn dttwtVA0

sin)(

“ DFT “

Bio Impedance Spectroscophy

Z

+

-

I

VZ b

Repeat measurement for many frequencies

Zb

f

θ f

Thank you.