Electrical Impedance TomographyElectrical Impedance Tomography

Myoung Hwan Choi Myoung Hwan Choi (1)

Gary J. Gary J. SaulnierSaulnier (2)

David Isaacson David Isaacson (2)

Jonathan C. Newell Jonathan C. Newell (2)

(2) Kangwon National UniversityKangwon National University(2) Rensselaer Polytechnic InstituteRensselaer Polytechnic Institute

What is What is Electrical Impedance Tomography Electrical Impedance Tomography

(EIT)(EIT)

??

2D Phantom Results2D Phantom Results

What is EIT?What is EIT?•• Technique for measuring the electrical Technique for measuring the electrical

impedance (conductivity and permittivity) inside impedance (conductivity and permittivity) inside a body from measurements made on its surface.a body from measurements made on its surface.

•• Most approaches apply currents and measure Most approaches apply currents and measure voltagesvoltages

•• The inverse problem of reconstructing images The inverse problem of reconstructing images from the measured data is illfrom the measured data is ill--posedposed–– Large impedance changes in the interior can produce Large impedance changes in the interior can produce

small changes in measurementssmall changes in measurements–– Requires highRequires high--precision measurementsprecision measurements

Some Possible ApplicationsSome Possible Applications•• Medical Medical

–– Continuous RealContinuous Real--Time MonitoringTime Monitoring•• Heart, LungHeart, Lung, Brain, Stomach, Temperature, Brain, Stomach, Temperature

–– ScreeningScreening•• Breast CancerBreast Cancer, Prostate Cancer, Prostate Cancer

–– Electrophysiological Data for Inverse ProblemsElectrophysiological Data for Inverse Problems•• Inverse Problem of Electrocardiography Inverse Problem of Electrocardiography •• EEG, EMGEEG, EMG

•• GeologicalGeological–– VadoseVadose Zone (collaboration with C. Zone (collaboration with C. CarriganCarrigan at LLNL)at LLNL)

Basis for Medical ApplicationsBasis for Medical Applications

500500.2.2Breast Breast CarcinomaCarcinoma

30003000.03.03Normal Normal BreastBreast

20002000.05.05LungLung

500500.2.2Cardiac Cardiac MuscleMuscle

150150.67.67BloodBlood

ResistivityResistivity(Ohm(Ohm--cm)cm)

Conductivity Conductivity (S/m)(S/m)

TISSUETISSUE

Some EIT SystemsSome EIT Systems•• Sheffield Applied Potential Tomography (APT) Sheffield Applied Potential Tomography (APT)

SystemSystem–– Single source systemSingle source system

•• Rensselaer Adaptive Current Tomography Rensselaer Adaptive Current Tomography (ACT) System(ACT) System–– Multiple source systemMultiple source system

•• TT--Scan Electrical Impedance Scanning SystemScan Electrical Impedance Scanning System–– Single source systemSingle source system–– Does not reconstruct imagesDoes not reconstruct images–– FDA approved as adjunct to mammographyFDA approved as adjunct to mammography

Single vs. Multiple SourcesSingle vs. Multiple Sources•• Some EIT systems use a Some EIT systems use a singlesingle current sourcecurrent source

–– Apply a current between a pair of electrodesApply a current between a pair of electrodes–– Measure the voltages on all the other electrodesMeasure the voltages on all the other electrodes–– Step the source through all pairs of adjacent Step the source through all pairs of adjacent

electrodeselectrodes

ACcurrentsource

Homogeneoustarget

Current Flow

wiresfrom

electrodes

Voltmeter

Multiplexer

electrodes

Multiple SourcesMultiple Sources•• In our system, we use a source for In our system, we use a source for eacheach

electrodeelectrode–– Apply Apply patternspatterns of currentof current–– Measure voltages on all electrodesMeasure voltages on all electrodes

•• For a homogeneous target, the best patterns are For a homogeneous target, the best patterns are spatial spatial sinessines and cosinesand cosines

-1.5-1

-0.50

0.51

1.5

1 3 5 7 9 11 13 15

electrode number

norm

aliz

ed c

urre

nt

cos(theta)

sin(theta)

Current Flow for Current Flow for cos(cos(θθ) and sin() and sin(5

3 7

1115

1

5

3 7

1115

Homogeneoustarget

Homogeneoustarget

θθ))

1 9 9

13

cos(θ) and sin(θ) produce a uniform current density in a homogeneous

target

13cos(θ) sin(θ)

Image ReconstructionImage Reconstruction•• We generally use a single step of a We generally use a single step of a linearizedlinearized

iterative algorithmiterative algorithm–– Initially assume a homogeneous impedance Initially assume a homogeneous impedance

distribution in a known geometrydistribution in a known geometry–– Use analytical forward solverUse analytical forward solver–– Use differences between predicted (forward solver) Use differences between predicted (forward solver)

voltages and measured voltages to adapt impedance voltages and measured voltages to adapt impedance distributiondistribution

•• Additional iterations provide better results but Additional iterations provide better results but are very expensive computationallyare very expensive computationally–– Require a forward solverRequire a forward solver

•• Images have (LImages have (L--1)L/2 degrees of freedom1)L/2 degrees of freedom

ACT 3 InstrumentACT 3 Instrument•• In service since early to mid 1990In service since early to mid 1990’’ss•• Single frequency (28.8 kHz)Single frequency (28.8 kHz)•• 32 electrodes32 electrodes

–– Fully parallel architecture / 32 sources and metersFully parallel architecture / 32 sources and meters

•• Applies currents / measures voltagesApplies currents / measures voltages–– High output impedance current sources with 16 bit High output impedance current sources with 16 bit

amplitude controlamplitude control–– Digital phaseDigital phase--sensitive voltmetersensitive voltmeter

•• 7 frames/sec (16 bits) or 20 frames/sec (15 bits)7 frames/sec (16 bits) or 20 frames/sec (15 bits)•• Large enclosure with limited portabilityLarge enclosure with limited portability

ACT 3 SystemACT 3 SystemInstrument ControlInstrument Control

Display RealReal--TimeTimeImage DisplayDisplay Image Display

Instrument ControlInstrument ControlKeyboardKeyboard

32 Current Sources32 Current Sourcesand Voltmetersand Voltmeters

Cables toCables toElectrodesPower SuppliesPower Supplies Electrodes

2D Phantom Results2D Phantom Results

ACT 3 imaging blood as it leaves the heart ( blue) and fills the lungs (red) during systole.

2D Human Results2D Human Results

Changes with Changes with respiration

Changes with Changes with cardiac systole: cardiac systole:

Blood leaves heart Blood leaves heart and goes to lungs

respiration

and goes to lungs •• Difference images in permittivity Difference images in permittivity

displayed as displayed as ωεωε

3D Phantom Results3D Phantom Results•• An insulating target is An insulating target is

lowered through a lowered through a salinesaline--filled tank with 4 filled tank with 4 layers of 8 electrodes layers of 8 electrodes each.each.

•• A 3D A 3D reconstructorreconstructor is is usedused

3D Human Results3D Human Results

•• Images showing conductivity changes with Images showing conductivity changes with respirationrespiration

Chest Image Chest Image -- The MovieThe Movie•• Static image Static image

of the human of the human chestchest

•• Heart and Heart and lung regions lung regions are clearly are clearly evidentevident

Respiration Respiration –– The MovieThe Movie•• Difference Difference

images images showing showing increased increased impedance of impedance of lung regions lung regions with inspirationwith inspiration

Cardiac Cardiac –– The MovieThe Movie•• Blood moves from Blood moves from

heart to lungsheart to lungs

Research directions in RPIResearch directions in RPI•• Developing algorithms, instrumentation, and Developing algorithms, instrumentation, and

electrode arrays for breast imagingelectrode arrays for breast imaging–– Planar electrode arraysPlanar electrode arrays–– Reconstruction algorithms for planar arraysReconstruction algorithms for planar arrays–– ACT 4 ACT 4 –– 44thth generation systemgeneration system–– Reconstruction algorithm in mammogram geometry Reconstruction algorithm in mammogram geometry

•• We have demonstrated experimentally that our We have demonstrated experimentally that our ““Optimal PatternsOptimal Patterns”” detect detect inhomogenietiesinhomogenieties at at greater greater depthdepth than Tthan T--Scan for planar arrays Scan for planar arrays

•• Our approach images in 3D and fast enough for Our approach images in 3D and fast enough for cardiaccardiac--related variationsrelated variations

Planar Electrode ArrayPlanar Electrode Array•• 64 element planar array64 element planar array

–– Platinum/Iridium electrodesPlatinum/Iridium electrodes

ACT 4 DesignACT 4 Design•• Maximize digital processing / minimize analog Maximize digital processing / minimize analog

processingprocessing•• Support for 64 electrodes / expandable to 256Support for 64 electrodes / expandable to 256

–– Channels are added in increments of 8Channels are added in increments of 8•• Can apply and measure either currents or Can apply and measure either currents or

voltages over a broad frequency rangevoltages over a broad frequency range–– 100 Hz to 1 MHz100 Hz to 1 MHz

•• Software and firmware upgradeableSoftware and firmware upgradeable–– DSPDSP-- and FPGAand FPGA--based processingbased processing–– Arbitrary excitation waveform capable Arbitrary excitation waveform capable

•• Relatively compact and portableRelatively compact and portable

ACT 3 (1993)ACT 3 (1993)•• 32 Current sources 32 Current sources

•• 32 Voltmeters32 Voltmeters

•• 32 Electrodes32 Electrodes•• 30 kHz30 kHz•• 20 Frames / Sec20 Frames / Sec•• Accuracy > .01%Accuracy > .01%•• ReconstructedReconstructed

VoxelsVoxels = 496 = 496 •• Resolution = Resolution = 1 1 –– 3 cm3 cm

ACT 4 (2004)ACT 4 (2004)•• 64 Current sources64 Current sources•• 64 Voltage sources64 Voltage sources•• 64 Voltmeters64 Voltmeters•• 64 Current meters64 Current meters•• 64 Electrodes64 Electrodes•• 100 Hz 100 Hz –– 1 MHz1 MHz•• 30 Frames / Sec30 Frames / Sec•• Accuracy > .002%Accuracy > .002%•• ReconstructedReconstructed

VoxelsVoxels = 2016= 2016•• Resolution = Resolution = .3 .3 –– 1 cm1 cm

Performance SummaryPerformance Summary

How Can one Increase the How Can one Increase the Sensitivity and Specificity?Sensitivity and Specificity?

Use Use MathematicsMathematicsandand

ElectromagneticElectromagnetic theorytheoryto design system to design system

to reconstruct and display to reconstruct and display conductivity inside the body conductivity inside the body

in 3Din 3D

What are the Equations?What are the Equations?

MaxwellMaxwell’’s Equations Equation

tBEtDJH

∂−∂=∇∂∂+=∇

/x/x

AssumeAssume

ti

ti

ti

ti

ti

exJtxJexBtxBexDtxDexHtxHexEtxE

ω

ω

ω

ω

ω

)(),()(),()(),()(),()(),(

=

=

=

=

=

Constitutive RelationsConstitutive Relations

EJHBED

σµε

===

ThusThus

HiEEiH

µωεωσ

−=∇+=∇

x)(x

⇓

HiEEiH

µωεωσ

−=∇=+⋅∇=∇⋅∇

x0)(x

0x0

0 Assume

=∇=⋅∇

⇓

=

EEσ

ω

0

0x

=∇⋅∇

−∇=⇒=∇

UThus

UEE

σ

Main EquationMain Equation

0=∇⋅∇ Uσ

Main Equation Main Equation with boundary conditionwith boundary condition

Bυ

σ

Bin 0=∇⋅∇ Uσ

Son / jU =∂∂ νσS

Forward Problem:Forward Problem:

Given Given conductivity conductivity σσ(p(p) and ) and current density j on S, current density j on S,

Find Find V = UV = U on S.

Bσ

υ

on S.S

)(σRjRV )(σ=

: Neumann to Dirichlet mapping

Inverse Problem:Inverse Problem:

Bσ

Vj,Given υ

)(pσFind

jRV )(σ= S

How can we reconstruct useful How can we reconstruct useful images?images?

Reconstruction Algorithms:Reconstruction Algorithms:1. Linearization1. Linearization2. Optimization2. Optimization3. Direct methods:3. Direct methods:

LinearizationsLinearizations

NOSER (NOSER (S.SimskeS.Simske,,……))FNOSER(P.EdicFNOSER(P.Edic,,……))

TODDLER(R.Blue,TODDLER(R.Blue,……))

nnmm

nm

juju

uu

000

00

//

00

=∂∂=∂∂

=∇⋅∇=∇⋅∇

νσνσ

σσ

dpuudSuuuu

dpuuuu

uuuu

nm

BS

nmmn

B

nmmn

nmmn

00000

000

000

)(

0

00

∇⋅∇−=∂−∂

⇓

=∇⋅∇−∇⋅∇

=∇⋅∇=∇⋅∇

∫∫

∫

σσσσ

σσ

σσ

νν

)(

)(),(

)( then If

)( m)Data(n,

200

00

000

00

0000

δσδσ

σσ

σδσσσδσ

σσ

σσ νν

Odxuu

dxuumnData

Ouu

dxuu

dSjujudSuuuu

nm

B

nm

B

mm

nm

B

S

nmmn

S

nmmn

+∇⋅∇=

∇⋅∇−=

+=<<−≡

∇⋅∇−=

=−=∂−∂

∫

∫

∫

∫∫

MCD

CMnmData

dpuupCnmData

pCpp

dpuumnData

kk

knm

nm

Bkk

kk

k

nm

B

=

=

∇⋅∇=

=

∇⋅∇≈

∑

∫∑

∑

∫

,

00k

k

00

),(

)(),(

solve; toneedonly Thus

)()()},({, basis Choose

),(

ψ

ψδσ

ψ

δσ

Compute C

Introduce planar arrays:Introduce planar arrays:3x3 Electrode Array Tank3x3 Electrode Array Tank

5x5 Electrode Array Tank5x5 Electrode Array Tank

Geological Impedance ImagingGeological Impedance Imaging

Salt Water TankElectrode Arrays

ACT4 under developmentACT4 under development•• Circuit boards in testCircuit boards in test

Breast Cancer Imaging Breast Cancer Imaging by by

Electrical Impedance Electrical Impedance TomographyTomography

Breast Cancer in the United StatesBreast Cancer in the United Statesin 2003in 2003

•• In the United States alone, In the United States alone, –– breast cancer is responsible for over 40,000 deaths breast cancer is responsible for over 40,000 deaths

annually, andannually, and–– over 180,000 new cases are diagnosed (Newman over 180,000 new cases are diagnosed (Newman

1999).1999).

Breast Tissues Breast Tissues ––How to distinguish between them?How to distinguish between them?

•• SkinSkin•• Adipose (fatty) tissueAdipose (fatty) tissue•• Glandular tissueGlandular tissue

•• CystsCysts•• Scar TissueScar Tissue•• CalcificationsCalcifications•• Benign tumors Benign tumors •• Malignant tumors (cancer)Malignant tumors (cancer)

Normal Tissues

Inhomogeneities

Difficulties with ExistingDifficulties with ExistingScreening TechniquesScreening Techniques

•• ““Gold StandardGold Standard”” : X: X--ray mammography.ray mammography.•• XX--ray mammography ray mammography

–– misses between 2% and 18% of cancers, misses between 2% and 18% of cancers, –– incorrectly reports the presence of cancer between incorrectly reports the presence of cancer between

12% and 32% of the time. (Kolb 2002).12% and 32% of the time. (Kolb 2002).•• XX--ray mammography has demonstrated limited ray mammography has demonstrated limited

effectiveness in women effectiveness in women –– with dense breast tissue (women < 40y, with dense breast tissue (women < 40y, –– breasts with surgical scars, etc.)breasts with surgical scars, etc.)

Are there other properties of breast Are there other properties of breast tissues which can be exploited?tissues which can be exploited?

Electrical properties of tumorsElectrical properties of tumors

• Conductivity of tumors differs by up to 4:1 from normal of tumors differs by up to 4:1 from normal tissue (Jossinet 1996).tissue (Jossinet 1996).

• Permittivity of tumors differs by up to 10:1 from normal of tumors differs by up to 10:1 from normal tissue (Jossinet 1996, Surowiec 1988).tissue (Jossinet 1996, Surowiec 1988).

Electrical Conductivity and Electrical Conductivity and PermittivityPermittivity

• Electrical Conductivity, , σσ::–– Measure of how easily charge carriers (electrons or Measure of how easily charge carriers (electrons or

free ions) travel through a material.free ions) travel through a material.–– Resistance is a function of Resistance is a function of resistivityresistivity and and

measurement geometry.measurement geometry.• Electrical Permittivity, , εε::

–– A measure of how easily bound charges realign A measure of how easily bound charges realign themselves in the presence of an electric field.themselves in the presence of an electric field.

–– Capacitance is a function of permittivity and Capacitance is a function of permittivity and measurement geometry.measurement geometry.

Existing StudiesExisting Studies

• TransScan: T: T--scanscanTM , Reduced the X, Reduced the X--ray mammography ray mammography error rate by half.error rate by half.

• Dartmouth College: Published results from numerous : Published results from numerous clinical trials. Performed an initial study of EIT exam clinical trials. Performed an initial study of EIT exam consistency.consistency.

• Centillion System: Able to resolve tumors in 3: Able to resolve tumors in 3--D spatial D spatial coordinate system. Presently being studied for investigation coordinate system. Presently being studied for investigation use.use.

Conclusions : EIT may be a viable method of breast cancer Conclusions : EIT may be a viable method of breast cancer detection, and that further study is warranted.detection, and that further study is warranted.

TT--Scan SystemScan System•• 1 V 1 V –– 2.5 V applied to 2.5 V applied to

handhand--held wandheld wand•• Low frequency (few Low frequency (few

hundred Hertz)hundred Hertz)•• Measure currents at Measure currents at

grounded electrodes on grounded electrodes on scanning probescanning probe

•• 64 (normal resolution) or 64 (normal resolution) or 256 (high resolution) 256 (high resolution) electrodeselectrodes

•• Display current valuesDisplay current values•• No depth informationNo depth information

•• TT--Scan has Scan has FDA ApprovalFDA Approval

•• Adjunctive use of TAdjunctive use of T--Scan Scan IncreasesIncreases Sensitivity Sensitivity by by 22%22% and and SpecificitySpecificity by by 16%16% over Xover X--Ray Ray MammographyMammography

SensitivitySensitivity = # predicted to = # predicted to have have cancer cancer // # who # who havehave cancer cancer SpecificitySpecificity = # predicted = # predicted notnot to have cancer to have cancer / / # # freefree of cancerof cancer

Breast Imaging at Dartmouth CollegeBreast Imaging at Dartmouth CollegeABSOLUTE PERMITTIVITY IMAGES:

Patient with electrode array Coronal View Normal Breast at 125 kHz

Malignant tumor at 750 kHz Coronal View Breast with CYST at 125 kHz

Breast Imaging by Breast Imaging by CentillionCentillion SystemSystem

Currently undergoing clinical test for FDA approval

Breast Imaging by Breast Imaging by CentillionCentillion SystemSystem

EIT image of the normal breast, the slice is on 1.2 cm depth, the nipple is in the center

EIT image of the breast with large carcinoma, the slice is on 1.2 cm depth

EIT in Mammogram GeometryEIT in Mammogram Geometryat RPIat RPI

X-rayelectrode array

(4x4)

chestbreast

Mammogram geometry Mammogram geometry model

Mammogram geometry phantomMammogram geometry phantom

Electrode arrays in prototypeElectrode arrays in prototypemammographymammography

An array of 32 radiolucent electrodes That electrode array and an ACR phantom on a Tomosynthesis machine in

Dr. Kopans’ lab. , Harvard Medical School

Equations for the mammogram Equations for the mammogram geometrygeometry

Forward solutionelectrode array

Solve

B

SBin 02 =∇ U

Son / jU =∂∂ νσ

Equations for the mammogram Equations for the mammogram geometrygeometry

Forward solution

+= ∑ ∑

∞

=

∞

≠+=0

00 3,3,,

)(,,

,0, )sinh(

)0cosh()tanh(

1n

mnm mn

Bnm

mn

Tnm

mn

Tmn

TT

hj

hjC

aV

γγγσ

βα

βαβα

++

−= ∑ ∑

∞

=

∞

≠+=0

00 3,3,,

)(,,

)(,00

0,03, )tanh()sinh(

)0cosh(1n

mnm mn

Bnm

mn

Tnm

mn

Bmn

B

TB

hj

hj

Ca

jhV

γγγσσ

βα

βαβα

βα

α ββα

,0,0

1

0

1

0,

210,0

1 CIhh

jA B

T ∑∑−

=

−

=

=∑∑−

=

−

=

=1

0

1

0

,,,

,21,

4 A B

mnT

mn CIahh

jα β

βαβα

βα

∑∑−

=

−

=

=1

0

1

0

,0,,

,210,

2 A B

nTn CI

ahhj

α β

βαβα

βα∑∑−

=

−

=

=1

0

1

0

,,0,

,21,0

2 A B

mT

m CIahh

jα β

βαβα

βα

∆

∆=

22

2

11

1,, 2

sincos2

2sincos

2h

ymhym

mh

hxn

hxn

nh

C ccmn

πππ

πππ

βαβα

22

2,,0 2

sincos2h

ymhym

mxhC c

m∆∆

=ππ

πββα

1,0,0 =βαC

Verification of the model by experimentVerification of the model by experiment

Reconstruction EquationsReconstruction Equations

+

+

+= ∑ ∑

≠+

smn

mn

mnsmn

mn

mn

nmn

m mn

T

jhz

jh

hzh

ymh

xnzj

zyxU ,3,

,,

3,

3,

021,00

0,0

sinhcosh

sinh)(cosh

coscos11),,(γγ

γγππ

γσσ

MCD

CMnmData

dxdydzUUpCdSjuju

kk

knm

nm

Bkk

S

nmmn

=

=

∇⋅∇=−

∑

∫∑∫

,

00k

0

),(

)(ψ

Solve the linear equation for C

)()(k

pCp kkψδσ ∑=Display )( pδσ

New Planar Algorithms for Mammogram New Planar Algorithms for Mammogram GeometryGeometry

–– Tested analytically and experimentallyTested analytically and experimentally

Reconstructed images4 x 4 x 4 mesh with

target in second layerTarget

AnalyticModel

Experimentin phantom

Using Voltage Sources to generate Using Voltage Sources to generate currentscurrents

•• Applying currents and measuring voltages has Applying currents and measuring voltages has better noise tolerancebetter noise tolerance

•• Building high precision current sources is Building high precision current sources is –– difficult, expensive, difficult, expensive, –– llarge hardwarearge hardware

•• We can use voltage sources to generate We can use voltage sources to generate currents, but can we achieve the required currents, but can we achieve the required accuracy ?accuracy ?

•• An iterative algorithm is being studied.An iterative algorithm is being studied.

Future plansFuture plans

•• CComplete ACT4 developmentomplete ACT4 development•• Clinical test in Mass. General HospitalClinical test in Mass. General Hospital•• Improve mammogram geometryImprove mammogram geometry•• Refine reconstruction algorithmsRefine reconstruction algorithms•• Use voltage sources instead of current sourcesUse voltage sources instead of current sources

–– Needs to be tested in the experiment, when ACT4 is Needs to be tested in the experiment, when ACT4 is readyready

–– Reduce the cost, size, Reduce the cost, size, ……

•• …………