IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010 Eung Je Woo Impedance Imaging Research Center (IIRC) Department of Biomedical Engineering, Kyung Hee University KOREA http://iirc.khu.ac.kr Basics of Basics of Bioimpedance and Bioimpedance and Admittivity Imaging Admittivity Imaging
Basics of Bioimpedance and Admittivity Imaging. Eung Je Woo Impedance Imaging Research Center (IIRC) Department of Biomedical Engineering, Kyung Hee University KOREA http://iirc.khu.ac.kr. Fundamental Quantity. Length (dimension or size) in meter (m) - PowerPoint PPT Presentation
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IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Eung Je Woo
Impedance Imaging Research Center (IIRC)
Department of Biomedical Engineering, Kyung Hee University
KOREA
http://iirc.khu.ac.kr
Basics of Bioimpedance Basics of Bioimpedance and Admittivity Imagingand Admittivity Imaging
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Fundamental QuantityFundamental Quantity•Length (dimension or size) in meter (m)•Time (sequence or duration or interval) in second (s)•Mass in kilogram (kg)•Charge in coulomb (C)•Temperature in kelvin (K)•Amount of substance in mole (mol)•Luminous intensity in candela (cd)
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Charged Particle and Charge DensityCharged Particle and Charge Density• Free electron and hole are mobile• Unbounded ion and molecule are mobile• Bounded atom and molecule are immobile but may vibrate• Polar molecule has no net charge but dipole moment and may
rotate
•Mass•Charge•Size•Position
, , ,m Q dr
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
FieldField• Space with nothing
Qx
y
z
0
Qrr
• Space with a single charged particle• Space with two charged particles• Space with multiple charged particles• Space with a charge density distribution
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Potential or VoltagePotential or Voltage• Space with electric field E(r)
Qrr1
• Put a point charge at r1 from the infinity (a reference point)• Move the point charge from r1 to r2
E(r)
Qrr2
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Conductivity and ResistanceConductivity and Resistance
V -Cl
-e
-e
+Na
I
I
V
-eI
-eI
-Cl+Na
v dcJ vd v E vc u J E Eu E q m F E a
l
S
, ,
1 1,
V V VE J E I JS S
l l ll l l l
V I I RI RS S S S
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Permittivity and CapacitancePermittivity and Capacitance
V+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
V-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-e
-e- - - - - - - - -
+ + + + + + + + +
-e
-e+ + + + + + + + +
- - - - - - - - -+Q
-Q +Q
-Q
l
S
( ) ( )( )
dQ t dv ti t C
dt dt
( ) sin( ), ( ) cos( )
10, 90 ,
mm
mm
Ii t I t v t t
CI
IC j C
V
I V ZI
0, S
Q CV Cl
( ) cos , ( ) sinmm
Ii t I t v t t
C
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Polarization, Permittivity and Polarization, Permittivity and CapacitanceCapacitance
V+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
V-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-e
-e- - - - - - - - -
+ + + + + + + + +
-e
-e+ + + + + + + + +
- - - - - - - - -+Q
-Q +Q
-Q
l
S
( ) ( )( )
dQ t dv ti t C
dt dt
0 r
SQ CV
l ( ) sin( ), ( ) cos( )
10, 90 ,
mm
mm
Ii t I t v t t
CI
IC j C
V
I V ZI
( ) cos , ( ) sinmm
Ii t I t v t t
C
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Cell and Bio-impedanceCell and Bio-impedance
VV
1
1
2
2
R
C
C
R
1 21 2
1 1R jX R R
j C j C Z
-Cl+Na
-Cl+Na
+Na -Cl
+ + + + + + +
+ + + + + + +
_ _ _ _ _ _ _
_ _ _ _ _ _ _
Cell Membrane
Extra-cellularFluid
Intra-cellularFluid
cos , sin
R jX Z
R Z X Z
Z
( ) cos
( ) cos
m
m
i t I t
v t I Z t
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Conductivity and Permittivity of TissuesConductivity and Permittivity of TissuesExtra-cellular
Fluid
Intra-cellularFluid
CellMembrane
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Conductivity and Permittivity of TissuesConductivity and Permittivity of Tissues
• Tissues themselves
– Molecular composition of cells
– Shape and density of cells
– Direction of cells
– Concentration and mobility of ions
– Amounts of intra- and extra-cellular fluids
• Amplitude and frequency of current
• Temperature
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
D. Haemmerich, S. T. Staelin, J. Z. Tsai, S. Tungjitkusolmun, D. M. Mahvi and J. G. Webster, “In vivo electrical conductivity of hepatic tumours,” Physiol. Meas., vol. 24, pp. 251–260, 2003.
D. Haemmerich, S. T. Staelin, J. Z. Tsai, S. Tungjitkusolmun, D. M. Mahvi and J. G. Webster, “In vivo electrical conductivity of hepatic tumours,” Physiol. Meas., vol. 24, pp. 251–260, 2003.
Normal Cells Tumor
NecrosisFibrosis
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Breast Tumor ConductivityBreast Tumor Conductivity
A. J. Surowiec, S. S. Stuchly, J. R. Barr, and A. Swarup, ”Dielectric properties of breast carcinoma and the surrounding tissues,” IEEE Trans. Biomed. Eng., vol. 35, no. 4, pp. 257–263, 1988.
A. J. Surowiec, S. S. Stuchly, J. R. Barr, and A. Swarup, ”Dielectric properties of breast carcinoma and the surrounding tissues,” IEEE Trans. Biomed. Eng., vol. 35, no. 4, pp. 257–263, 1988.
NormalTissue
NormalTissue
LobularCarcinoma
LobularCarcinoma
DuctalCarcinoma
DuctalCarcinoma
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Conductivity and Neural ActivityConductivity and Neural Activity• Cole K S and Curtis H J 1939 Electrical impedance of the squid giant axon during
activity J. Gen. Physiol. 22 649-670 • Cole K S 1949 Dynamic electrical characteristics of squid axon membrane Arch.
Sci. Physiol. 3 253-258 • Adey W, Kado R and Didio J 1962 Impedance measurements in brain tissue of
animals using microvolt signals Exp. Neruol. 5 47-66 • Van-Harreveld A and Schade J 1962 Changes in the electrical conductivity of
cerebral cortex during seizure activity Exp. Neurol. 5 383-400 • Rank J B 1963 Specific impedance of rabbit cerebral cortex Exp. Neurol. 7 144-
152 • Aladjolova N A 1964 Slow electrical processes in the brain Prog. Brain Res. 7 155-
237 • Geddes L A and Baker L E 1967 The specific resistance of biological material: a
compendium of data for the biomedical engineer and physiologist Med. Biol. Eng. 5 271-293
• Meister M, Pine J, Baylor, DA 1994 Multi-neuronal signals from the retina: acquisition and analysis J. Neurosci. Meth. 51 95-106
Neural activity produces 3-5% local conductivity changes at low frequency.
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Bio-electric Signal and Source ImagingBio-electric Signal and Source Imaging
Medical Instrumentation: Application and Design, 3rd ed., by J. G. Webster
ECG
Amplifier
( ; ) ( ; ) ( ; )t V t f t r r r
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Bio-magnetic Signal and Source ImagingBio-magnetic Signal and Source Imaging
( ; ) ( ; ) ( ; )t t V t J r r r
( ; ) ( ; ) ( ; )t V t f t r r r
f(r;t)J(r;t)
MEG
03
'( ; ) ( '; ) '
4 't t dv
r r
B r J rr r
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Defibrillation and CardioversionDefibrillation and Cardioversion
R. S. Yoon, T. P. DeMonte, and M. L. G. Joy, “Measurement of thoracic current flow in pigs for the study of defibrillation and cardioversion,” IEEE Trans. Biomed. Eng., vol. 50, no. 10, pp. 1167-1173, 2003.
R. S. Yoon, T. P. DeMonte, and M. L. G. Joy, “Measurement of thoracic current flow in pigs for the study of defibrillation and cardioversion,” IEEE Trans. Biomed. Eng., vol. 50, no. 10, pp. 1167-1173, 2003.
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
M. L. G. Joy,V. P. Lebedev, and J. S. Gati, “Imaging of current density and current pathways in rabbit brain during transcranial electrostimulation,” IEEE Trans. Biomed. Eng., vol. 46, no. 9, pp. 1138-1148, 1999.
M. L. G. Joy,V. P. Lebedev, and J. S. Gati, “Imaging of current density and current pathways in rabbit brain during transcranial electrostimulation,” IEEE Trans. Biomed. Eng., vol. 46, no. 9, pp. 1138-1148, 1999.
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Motivation and GoalMotivation and Goal• Physiological functions and pathological changes
alter conductivity and permittivity values.
• Neural activity induces changes in conductivity.
• Source imaging needs conductivity values.
• Electromagnetic stimulations need conductivity values.
Cross-sectional Imaging of
Conductivity, Permittivity and
Current Density Distribution
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Trans-resistanceTrans-resistance( ) cos( ) cos(2 )p m mi t I t I ft
( ) cos( ) cos(2 )q pq m pq mv t R I t R I ft
p
q
i
V
Ip=Im0
Vq=RpqIm0
Zpq=Rpq0
Rpq depends on
(1)electrode configuration
(2)conductivity distribution, (3)geometry (boundary shape and size)
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Trans-impedanceTrans-impedance( ) cos( ) cos(2 )p m mi t I t I ft
( ) cos( )q pq mv t Z I t
Zpq depends on
(1)electrode configuration
(2)complex conductivity distribution, +j(3)geometry (boundary shape and size)
p
q
i
V
j
Ip=Im0 Vq=ZpqImZpq=Zpq
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
KHU Mark1 mfEIT SystemKHU Mark1 mfEIT System
32-Channel System16-Channel SystemT. I. Oh, E. J. Woo, and D. Holder, “ Multi-frequency EIT system with radially symmetric architecture: KHU Mark1,” Physiol.
Meas., 28, pp. S183-96, 2007.T. I. Oh, K. H. Lee, S. M. Kim, W. Koo, E. J. Woo, and D. Holder, “Calibration methods for a multi-channel multi-frequency EIT
system,” Physiol. Meas., 28, pp. 1175-88, 2007.T. I. Oh, W. Koo, K. H. Lee, S. M. Kim, J. Lee, S. W. Kim, J. K. Seo, and E. J. Woo, “Validation of a multi-frequency electrical
impedance tomography (mfEIT) system KHU Mark1: impedance spectroscopy and time-difference imaging,” Physiol. Meas., 29, pp. 295-307, 2008.
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
KHU Mark2 mfEIT SystemKHU Mark2 mfEIT System
• Multiple current sources
• Multiple voltmeters
• No pre-determined electrode configuration
• Wide bandwidth
• Compact design
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Boundary Current and VoltageBoundary Current and Voltage
cos( )mI t
cos( )pq mZ I t
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Contact ImpedanceContact Impedance
Two-electrode Method Four-electrode Method
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Data Collection ProtocolData Collection Protocol
Neighboring Method
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
ReciprocityReciprocity
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Neumann-to-Dirichlet DataNeumann-to-Dirichlet Data
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
1. Linearity between current and voltage for a fixed
2. Linearity between voltage and c for a fixed
3. What are nonlinear?
Linearity and NonlinearityLinearity and Nonlinearity
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Complex Conductivity ProblemComplex Conductivity Problem
p
q
i
V
j
( ) cos( )p mi t I t
( ) cos( )q pq mv t Z I t
, , , cos ,u t U t r r r
,, ju U e rr r
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Complex Conductivity ProblemComplex Conductivity Problem
0, j u u r jx
r x
x r
( ) cos( )p mi t I t
( ) cos( )q pq mv t Z I t
Ip=Im0
Vq=ZpqIm
Zpq=Zpqp
q
i
V
j
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Multi-frequency Data CollectionMulti-frequency Data Collectionjth Current
ji
V
j
j+1
k
k+1
kth Voltage
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
1) Injection current, voltage and complex conductivity
2) Current density
3) Magnetic flux density
Mathematical ExpressionsMathematical Expressions
03
'( ; ; ) ( '; ; ) '
4 't t dv
r r
B r J rr r
( ; ; ) ( ; ; ) ( ; ; ) ( ; ; )t t j t u t J r r r r
( ; ; ) ( ; ; ) ( ; ; ) 0t j t u t r r r
on u
j gn
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Forward Solver: Example using FEMForward Solver: Example using FEM
B. I. Lee, S. H. Oh, E. J. Woo, S. Y. Lee, M. H. Cho, O. Kwon, J. K. Seo, J. Lee, and W. S. Baek, “Three-dimensional forward solver and its performance analysis for MREIT using recessed electrodes," Phys. Med. Biol., vol. 48, 1972-1986, 2003.
u
1E
2E
yx
yx
[ mV]
[S/m]
Bx
By
Bz
yx
yx
yx
[ Tesla]
[ Tesla]
[ Tesla]
Jx
Jy
Jz
yx
yx
yx
[mA/mm2]
[mA/mm2]
[mA/mm2]
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Forward Solver: Example using FEMForward Solver: Example using FEM• White lines are current stream lines.• Black lines are equipotential lines.
u J u f 0 on u
n
+
-
+
-
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Forward Solver: Example using FEMForward Solver: Example using FEM• White lines are current stream lines.• Black lines are equipotential lines.
u J u f 0 on u
n
+
-
+
-
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Equipotential Lines at 100 kHzEquipotential Lines at 100 kHz
v (real part) h (imaginary part)
Saline
Banana
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Voltage and Current DensityVoltage and Current Density
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
EIT using Boundary MeasurementsEIT using Boundary MeasurementsNeumann
(Boundary Current)
Dirichlet
(Boundary Voltage)
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Problem Definition in EITProblem Definition in EIT
V ZI
( ; ; ; )V f I G E
S
IL
( ) ( ) 0u r r on u
Jn
j
or
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
tdEIT Imaging: Human ThoraxtdEIT Imaging: Human Thorax
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Static Imaging in EITStatic Imaging in EIT
Image Reconstruction
Algorithm
Data Acquisition
System
Measured Boundary Voltage
Forward Solver
Computed Boundary Voltage
Injection
Current
Subject
ComputerModel
k
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Static Imaging in EITStatic Imaging in EIT
Image of absolute value of complex conductivity ( + i)
Must overcome the following problems– Geometry is unknown and varying.
– Electrode positions are unknown and varying.
– Very accurate forward model is needed.
– Higher degree of measurement accuracy is needed.
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Difference Imaging in EITDifference Imaging in EIT
Image of change in complex conductivity with respect to time and/or frequency
Common systematic errors can be cancelled out– Unknown boundary geometry– Uncertainty in electrode position– Systematic artifacts
Applications are limited but there are enough of them
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
If conductivity changes as
boundary voltage changes accordingly as
When is small,
Then, a difference image of is obtained as
Difference Imaging in EITDifference Imaging in EIT
2 1T Tu u u
2 1 ,
2 1.u u u
.u S
† .u S
Time-difference (tdEIT)
2 1T T 2 1u u u
Frequency-difference (fdEIT)
2 1
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
tdEIT AlgorithmtdEIT Algorithm Linearization
Misfit Functional
Algorithm
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
fdEIT AlgorithmfdEIT Algorithm
: homogeneous complex conductivity at 1 and 2 : complex voltage with
: frequency-difference image between 1 and 2
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Perturbation and SensitivityPerturbation and Sensitivity
j
qth Pixel
1,10,0
1,0,02,1
0,0
0,0 2,0,0
,10,0
,0,0
E
E
E
E E
f
f
f
f
f
f
f
1,10,
1,0,2,1
0,
0, 2,0,
,10,
,0,
q
Eq
q
q Eq
Eq
E Eq
f
f
f
f
f
f
f
qin q
2
1,1 1,11,0, 0,0
1, 1,,0, 0,0
2,1 2,11,0, 0,0
0, 0, 0, 0,0 2, 2,2 ,0, 0,0
,1 ,1( 1) 1,0, 0,0
, ,0, 0,0 ,
qq
E EE qq
E qq
q q q E EE qq
E EE E qq
E E E Eq E q
sf f
sf fsf f
Ssf f
sf f
sf f
f s f f
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Sensitivity and LinearizationSensitivity and Linearization
22
1,1,
,,
1,1,
0,( , ) 0,02 ,2 ,
( 1) 1,( 1) 1,
,,
yx
E yE x
E yE x
x y x yE yE x
E E yE E x
E yE x
ss
ss
ss
ss
ss
ss
f f
2
1,1 1,11,0, 0,0
1, 1,,0, 0,0
2,1 2,11,0, 0,0
0, 0, 0, 0,0 2, 2,2 ,0, 0,0
,1 ,1( 1) 1,0, 0,0
, ,0, 0,0 ,
qq
E EE qq
E qq
q q q E EE qq
E EE E qq
E E E Eq E q
sf f
sf fsf f
Ssf f
sf f
sf f
f s f f
xin x
yin y
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Sensitivity Matrix and LineariztionSensitivity Matrix and Lineariztion
22 2
1,1,1 1,2
,,1 ,2
1,1,1 1,2 1
2
02 ,2 ,1 2 ,2
( 1) 1,( 1) 1,1 ( 1) 1,2
,,1 ,2
Q
E QE E
E QE E
E QE E
Q
E E QE E E E
E QE E
ss s
ss s
ss s
ss s
ss s
ss s
f f Sr
- E electrodes- Q pixels
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Complex Sensitivity Matrix Complex Sensitivity Matrix and TSVDand TSVD
22 2
1,1,1 1,2
,,1 ,2
1,1,1 1,2 1
2
2 ,2 ,1 2 ,2
( 1) 1,( 1) 1,1 ( 1) 1,2
,,1 ,2
1 1
Q
E QE E
E QE E
l Rm m l R l
E QE Em m m m
Q
E E QE E E E
E QE E
ss s
ss s
ss s
ss sI I
ss s
ss s
f f
lmR
Sg
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Experimental Results: tdEIT and fdEITExperimental Results: tdEIT and fdEIT
BananaPerspex TX151 BananaMetal Banana
16-Channel mfEIT(IIRC KHU Mark1)
Imaging Objects
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Brain ImagingBrain Imaging
A. T. Tidswell, A. Gibson, R. H. Bayford, and D. S. Holder, “Three-dimensional electrical impedance tomography of human brain activity,” NeuroImage, vol. 13, pp. 283-294, 2001.
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Time- and Frequency-difference ImagingTime- and Frequency-difference Imaging