Basics of Bioimpedance and Admittivity Imaging
description
Transcript of Basics of Bioimpedance and Admittivity Imaging
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)
•Mechanics•Electromagnetics •Optics•Thermodynamics•Chemistry
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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
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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
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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
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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
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Permittivity and CapacitancePermittivity and Capacitance
V+-
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V-+
-+
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-+
-+
-+
-+
-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
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Polarization, Permittivity and Polarization, Permittivity and CapacitanceCapacitance
V+-
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V-+
-+
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-+
-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
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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
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Conductivity and Permittivity of TissuesConductivity and Permittivity of TissuesExtra-cellular
Fluid
Intra-cellularFluid
CellMembrane
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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
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Hepatic Tumor ConductivityHepatic Tumor Conductivity
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
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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
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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.
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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
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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
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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.
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Transcranial Electrical StimulationTranscranial Electrical Stimulation
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.
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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
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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)
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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
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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.
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KHU Mark2 mfEIT SystemKHU Mark2 mfEIT System
• Multiple current sources
• Multiple voltmeters
• No pre-determined electrode configuration
• Wide bandwidth
• Compact design
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Boundary Current and VoltageBoundary Current and Voltage
cos( )mI t
cos( )pq mZ I t
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Contact ImpedanceContact Impedance
Two-electrode Method Four-electrode Method
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Data Collection ProtocolData Collection Protocol
Neighboring Method
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ReciprocityReciprocity
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Neumann-to-Dirichlet DataNeumann-to-Dirichlet Data
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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
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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
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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
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Multi-frequency Data CollectionMulti-frequency Data Collectionjth Current
ji
V
j
j+1
k
k+1
kth Voltage
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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
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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]
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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
+
-
+
-
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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
+
-
+
-
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Equipotential Lines at 100 kHzEquipotential Lines at 100 kHz
v (real part) h (imaginary part)
Saline
Banana
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Voltage and Current DensityVoltage and Current Density
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EIT using Boundary MeasurementsEIT using Boundary MeasurementsNeumann
(Boundary Current)
Dirichlet
(Boundary Voltage)
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Problem Definition in EITProblem Definition in EIT
V ZI
( ; ; ; )V f I G E
S
IL
( ) ( ) 0u r r on u
Jn
j
or
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tdEIT Imaging: Human ThoraxtdEIT Imaging: Human Thorax
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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
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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.
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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
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tdEIT AlgorithmtdEIT Algorithm Linearization
Misfit Functional
Algorithm
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fdEIT AlgorithmfdEIT Algorithm
: homogeneous complex conductivity at 1 and 2 : complex voltage with
: frequency-difference image between 1 and 2
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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 ,
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
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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 ,
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
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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
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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
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Experimental Results: tdEIT and fdEITExperimental Results: tdEIT and fdEIT
BananaPerspex TX151 BananaMetal Banana
16-Channel mfEIT(IIRC KHU Mark1)
Imaging Objects
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Preliminary Experiment: tdEITPreliminary Experiment: tdEIT
Pink object : 0.391 S/mGreen object : 0.171 S/mBackground : 0.137 S/m
4 cm
3 cm 3 cm
Sponge conductivity : 0.02 S/mBackground conductivity : 0.0217S/m
Sponge
Tx151
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tdEIT and fdEIT: Perspex (Insulator)tdEIT and fdEIT: Perspex (Insulator)
5kHz 100Hz 1kHz 10kHz 50kHz 100kHz 250kHz 50Hz
Real Part
Real Part
Imaginary Part
Imaginary Part
5kHz 50Hz 1kHz 10kHz 50kHz 100kHz 250kHz 10Hz
Time-difference with homogeneous phantom data as reference
Frequency-difference with 100Hz data as reference
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tdEIT and fdEIT: Stainless Steel (Conductor)tdEIT and fdEIT: Stainless Steel (Conductor)
Real Part
Real Part
Imaginary Part
Imaginary Part
5kHz 50Hz 1kHz 10kHz 50kHz 100kHz 250kHz 10Hz
Time-difference with homogeneous phantom data as reference
Frequency-difference with 100Hz data as reference
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tdEIT and fdEIT: TX151tdEIT and fdEIT: TX151
5kHz 100Hz 1kHz 10kHz 50kHz 100kHz 250kHz 50Hz
Real Part
Real Part
Imaginary Part
Imaginary Part
5kHz 50Hz 1kHz 10kHz 50kHz 100kHz 250kHz 10Hz
Time-difference with homogeneous phantom data as reference
Frequency-difference with 100Hz data as reference
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tdEIT and fdEIT: BananatdEIT and fdEIT: Banana
5kHz 100Hz 1kHz 10kHz 50kHz 100kHz 250kHz 50Hz
Real Part
Real Part
Imaginary Part
Imaginary Part
5kHz 50Hz 1kHz 10kHz 50kHz 100kHz 250kHz 10Hz
Time-difference with homogeneous phantom data as reference
Frequency-difference with 100Hz data as reference
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tdEIT and fdEIT: CucumbertdEIT and fdEIT: Cucumber
5kHz 100Hz 1kHz 10kHz 50kHz 100kHz 250kHz 50Hz
Real Part
Real Part
Imaginary Part
Imaginary Part
5kHz 50Hz 1kHz 10kHz 50kHz 100kHz 250kHz 10Hz
Time-difference with homogeneous phantom data as reference
Frequency-difference with 100Hz data as reference
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tdEIT and fdEIT: Perspex and BananatdEIT and fdEIT: Perspex and Banana
5kHz 100Hz 1kHz 10kHz 50kHz 100kHz 250kHz 50Hz
Real Part
Real Part
Imaginary Part
Imaginary Part
5kHz 50Hz 1kHz 10kHz 50kHz 100kHz 250kHz 10Hz
Time-difference with homogeneous phantom data as reference
Frequency-difference with 100Hz data as reference
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
tdEIT and fdEIT: Stainless Steel and BananatdEIT and fdEIT: Stainless Steel and Banana
5kHz 100Hz 1kHz 10kHz 50kHz 100kHz 250kHz 50Hz
Real Part
Real Part
Imaginary Part
Imaginary Part
5kHz 50Hz 1kHz 10kHz 50kHz 100kHz 250kHz 10Hz
Time-difference with homogeneous phantom data as reference
Frequency-difference with 100Hz data as reference
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
tdEIT and fdEIT: TX151 and BananatdEIT and fdEIT: TX151 and Banana
5kHz 100Hz 1kHz 10kHz 50kHz 100kHz 250kHz 50Hz
Real Part
Real Part
Imaginary Part
Imaginary Part
5kHz 50Hz 1kHz 10kHz 50kHz 100kHz 250kHz 10Hz
Time-difference with homogeneous phantom data as reference
Frequency-difference with 100Hz data as reference
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Time-difference Imaging: Animal ThoraxTime-difference Imaging: Animal Thorax
<Inhale> <Exhale>
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Time-difference Imaging: Human ThoraxTime-difference Imaging: Human Thorax
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
tdEIT: Human Thorax tdEIT: Human Thorax
At 1kHz
At 100kHz
At 250kHz
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
fdEIT between 1 and 100 kHz: fdEIT between 1 and 100 kHz: Human ThoraxHuman Thorax
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Images of Air Distributions in LungsImages of Air Distributions in Lungs
Sitting
R
X
Right Lateral Left Lateral
Sitting
RightLateral
LeftLateral
IIRC: Impedance Imaging Research Center, Korea (http://iirc.khu.ac.kr) January 2010
Images of Stomach MotilityImages of Stomach Motility
Filling
Emptying
0s 35s 45s 56s 1m 3s 1m 33s 1m 48s 1m 54s20s (Intake)
15m 20m 22m 29s 25m 32m 30s 35m 50m 52m 29s
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
• Time-difference imaging– Pulmonary function– Cardiac function– Gastric emptying– Fracture healing– Epilepsy imaging
• Frequency-difference imaging– Tumor imaging– Stoke imaging– Neural activity imaging