Transcript Bioimpedance Measurement

Bioimpedance Measurement
Dept. of Biomedical Engineering
2003200449
YOUNHO HONG
Impedance measure
i=0
+
I
R
Av =1
R 
OUT
V
i
V=Ri
measured
known
i=0
constant
current
source
+
I  I 0
reactance
V  V
Z
 Z I
-
Z  R  jX
impedance
resistance
Impedance measure
(Example) Z  1  j 
2  45  [  ] , Freq.  1000Hz
Im
1
I  1 0  [mA]  i ( t )  sin( 2   1000 t )
1+j
V  Z I 
1
2 sin( 2   1000 t 
2  45   V ( t ) 

)
4
Re
2 sin{ 2   1000 ( t 

1
8000
i V
You are given with i(t) = I sin(2πft)
You measure v(t) = V sin(2πft+θ)
1
t
Z 
V
I

V
I
  Z
)}
Impedance measure
(Example)
R
R
Z 
R
Z
C
1
jwC
1

Z  R   tan
R
1  jwRC
jwC

2
R
1 w R C
2
2
2
 j(
wR C
1 w R C
2
2
2
)  R ( w )  jX ( w )
1
( wRC )
Impedance measure
R
Z R
C
Z 
1
 R  j(
jwC
1
R 
2
  tan
2
2
R2
R1
C
)  R ( w )  jX ( w )
wC
w C
Z  R2 
1
2
1  w R1  C
1
(
2
)
w RC
2
R1
2
1
2
 j(
 R ( w )  jX ( w )  Z  
wR 1 C
2
1  W R1 C
2
2
)
Impedance measure
Dif f erential AMP
phase-sensitive Demodulation
+
I
Z
OUT
X
sin(2πft)
1

T
T
1
T
0
V I ( t )  dt
?
V Q ( t )  dt
?
X

T
0
cos(2πft)
Impedance measure
In-phase Component
V I ( t )  V ( t )  sin( 2  ft )  V sin( 2  ft   )  sin( 2  ft )

V
{cos   cos( 2   2 ft   )}
2
1
T

T
0
V I ( t )  dt 

V
2
V
2

1
(cos  )T
T
cos  
1
2
VI
V I  V cos 
Impedance measure
Quadrature Component
V Q ( t )  V ( t )  cos( 2  ft )  V sin( 2  ft   )  cos( 2  ft )

V
{sin( 2   2 ft   )  sin  }
2
1
T

T
0
V Q ( t )  dt 

V
V
2
2

1
(sin  )T
T
sin  
1
2
VQ
V Q  V sin 
Impedance measure
V I  V Q  V sin   V cos   V
2
2
2
2
V  V I  VQ
2
2
2
VQ
VI

2
V sin 
V cos 
2
 tan 
  tan
Z  Z    R  jX  Z cos   jZ sin 
Im
Vsin θ
V=VI+jVQ
V
(Quadrature
Component)
θ
Vcosθ
(In-phase Component)
Re
1
VO
VI
Two-electrode Method
Rc
V
equivalent circuit
I
electrode
skin
Ehc
Rs
Cc
V
Inject current
and then measure voltage
i
Eh1
Eh2
ZC1
ZC2
Zb
V  Eh 1  ( Z C 1  Z b  Z C 2 ) I  Eh 2
Two-electrode Method
V ( t )  Eh 1  Eh 2  Z C 1 I sin( wt   1 )  Z b I sin( wt   b )  Z C 2 I sin( wt   2 )
VI  2
1
T

T
V ( t ) sin wt  dt
0
 Z C 1 I cos  1  Z b I cos  b  Z C 2 I cos  2 (In - phase Component)
V Q  Z C 1 I sin  1  Z b I sin  b  Z C 2 I sin  2 (Quadratur e Component)
Im
Z 
Zc1sinθ1
V I  jV Q
I
 Z C 1 cos  1  jZ C 1 sin  1
Zc2sinθ2
 Z b cos  b  jZ b sin  b
Zbsinθb
Zbcosθb Zc1cosθ1 Zc2cosθ2
Re
 Z C 2 cos  2  jZ C 2 sin  2
 Z C 1  Z b  Z C 2 (contact  body impedance)
Four-electrode Method
I
V  Zb I
V
E1
E3
E4
I  I 0 
E2
V ( t )  Z b I sin( wt   b )
skin
i
VI  2
Eh1
Eh3
Eh2
VQ  2
Eh4
ZC1
ZC3
ZC4
ZC2
Zm 
1
T
1
T

T
0

V ( t ) sin wt  dt  Z b I cos 
T
0
V ( t ) cos wt  dt  Z b I sin 
V I  jV Q
I
 Z b cos  b  jZ b sin  b
Zb1
Zb
Zb2
 Z b (only body impedance)
Three-electrode Method
I
Zm 
V
E1
E3
E2
skin
V I  jV Q
I
 Z b cos  b  Z C 2 cos  C 2
 jZ b sin  b  jZ C 2 sin  C 2
i
 Zb  ZC2
Eh1
Eh3
ZC1
ZC3
Eh2
ZC2
We can measure skin impedance
using Three and Four electrode Method
Z m ( three  Method )  Z m ( four  Method )
 ZC2
Zb1
Zb
Noise Effect
V m ( t )  V ( t )  n ( t )  ZI sin( wt   )  n ( t )
V I m  2

2
T
1

T
T
0

T
V m ( t ) sin wt  dt
ZI sin( wt   ) sin wt  dt 
0
 ZI cos   N f cos 
2
T

T
0
n ( t ) sin wt  dt
Spectrum Analizer
V ( t )  A1 sin w1t  A2 sin w 2 t  .....  A N sin w N t
A1
A2 A3
f1 f2 f3
V(t)
X
sinw1t / cosw1t
X
sinw2t / cosw2t
AN
…
…
fN
1
T1
1
T2


T2
 dt
0
A1 B1
,
2 2
A2 B 2
,
2 2
1
TN

TN
0
 dt
An 

T
0
V ( t ) sin w n t  dt
“ DFT “
…
sinwNt / coswNt
 dt
0
…
X
T1
AN
2
,
BN
2
Bio Impedance Spectroscophy
+
Zb 
Z
V
I
-
Repeat measurement for many frequencies
θ
Zb
f
f
Thank you.