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


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


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


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


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


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


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


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


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


Conductivity and Permittivity of TissuesConductivity and Permittivity of TissuesExtra-cellular

Fluid

Intra-cellularFluid

CellMembrane


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


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


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


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.


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


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


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.


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.


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


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)


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


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.


KHU Mark2 mfEIT SystemKHU Mark2 mfEIT System

• Multiple current sources

• Multiple voltmeters

• No pre-determined electrode configuration

• Wide bandwidth

• Compact design


Boundary Current and VoltageBoundary Current and Voltage

cos( )mI t

cos( )pq mZ I t


Contact ImpedanceContact Impedance

Two-electrode Method Four-electrode Method


Data Collection ProtocolData Collection Protocol

Neighboring Method


ReciprocityReciprocity


Neumann-to-Dirichlet DataNeumann-to-Dirichlet Data


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


Complex Conductivity ProblemComplex Conductivity Problem

p

q

i

V

j

( ) cos( )p mi t I t


, , , cos ,u t U t r r r

,, ju U e rr r


Complex Conductivity ProblemComplex Conductivity Problem

0, j u u r jx

r x

x r

( ) cos( )p mi t I t


Ip=Im0

Vq=ZpqIm

Zpq=Zpqp

q

i

V

j


Multi-frequency Data CollectionMulti-frequency Data Collectionjth Current

ji

V

j

j+1

k

k+1

kth Voltage


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


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]


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

+

-

+

-


Equipotential Lines at 100 kHzEquipotential Lines at 100 kHz

v (real part) h (imaginary part)

Saline

Banana


Voltage and Current DensityVoltage and Current Density


EIT using Boundary MeasurementsEIT using Boundary MeasurementsNeumann

(Boundary Current)

Dirichlet

(Boundary Voltage)


Problem Definition in EITProblem Definition in EIT

V ZI

( ; ; ; )V f I G E

S

IL

( ) ( ) 0u r r on u

Jn

j

or


tdEIT Imaging: Human ThoraxtdEIT Imaging: Human Thorax


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


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.


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


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


tdEIT AlgorithmtdEIT Algorithm Linearization

Misfit Functional

Algorithm


fdEIT AlgorithmfdEIT Algorithm

: homogeneous complex conductivity at 1 and 2 : complex voltage with

: frequency-difference image between 1 and 2


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


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


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


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


Experimental Results: tdEIT and fdEITExperimental Results: tdEIT and fdEIT

BananaPerspex TX151 BananaMetal Banana

16-Channel mfEIT(IIRC KHU Mark1)

Imaging Objects


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


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


Time-difference with homogeneous phantom data as reference

Frequency-difference with 100Hz data as reference


tdEIT and fdEIT: Stainless Steel (Conductor)tdEIT and fdEIT: Stainless Steel (Conductor)

Real Part

Real Part

Imaginary Part

Imaginary Part





tdEIT and fdEIT: TX151tdEIT and fdEIT: TX151


Real Part

Real Part

Imaginary Part

Imaginary Part





tdEIT and fdEIT: BananatdEIT and fdEIT: Banana


Real Part

Real Part

Imaginary Part

Imaginary Part





tdEIT and fdEIT: CucumbertdEIT and fdEIT: Cucumber


Real Part

Real Part

Imaginary Part

Imaginary Part





tdEIT and fdEIT: Perspex and BananatdEIT and fdEIT: Perspex and Banana


Real Part

Real Part

Imaginary Part

Imaginary Part





tdEIT and fdEIT: Stainless Steel and BananatdEIT and fdEIT: Stainless Steel and Banana


Real Part

Real Part

Imaginary Part

Imaginary Part





tdEIT and fdEIT: TX151 and BananatdEIT and fdEIT: TX151 and Banana


Real Part

Real Part

Imaginary Part

Imaginary Part





Time-difference Imaging: Animal ThoraxTime-difference Imaging: Animal Thorax

<Inhale> <Exhale>


Time-difference Imaging: Human ThoraxTime-difference Imaging: Human Thorax


tdEIT: Human Thorax tdEIT: Human Thorax

At 1kHz

At 100kHz

At 250kHz


fdEIT between 1 and 100 kHz: fdEIT between 1 and 100 kHz: Human ThoraxHuman Thorax


Images of Air Distributions in LungsImages of Air Distributions in Lungs

Sitting

R

X

Right Lateral Left Lateral

Sitting

RightLateral

LeftLateral


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


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.


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

Basics of Bioimpedance and Admittivity Imaging

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