Elastography for Breast Cancer Assessment By: Hatef Mehrabian.

Elastography for Breast Elastography for Breast Cancer Assessment Cancer Assessment

By: Hatef MehrabianBy: Hatef Mehrabian

Outline

• Applications• Breast cancer • Elastography (Linear & Hyperelastic)• Inverse problem • Numerical validation & results• Regularization techniques • Experimental validation & results• Summary and conclusion

Applications

• Cancer detection and Diagnosis– Breast cancer– Prostate cancer– Etc.

• Surgery simulation– Image guided surgery

• Modeling behavior of soft tissues

– Virtual reality environments• Training surgeons

Breast Cancer

• Worldwide, breast cancer is the fifth most Worldwide, breast cancer is the fifth most common cause of cancer deathcommon cause of cancer death

• ~ 1/4 million women will be diagnosed with ~ 1/4 million women will be diagnosed with breast cancer in the US within the next yearbreast cancer in the US within the next year

• statistics shows that one in 9 women is expected to develop breast cancer during her lifetime; one in 28 will die of it

• Symptoms:– pain in breast– Changes in the appearance or shape – Change in the mechanical behavior of breast tissues

Breast CancerBreast Cancer

• Detection method: – Self exam (palpation)– x-ray mammography– Breast Magnetic resonance imaging (MRI)– Ultrasound imaging

• Tissue Stiffness variation is associated with pathology Tissue Stiffness variation is associated with pathology (palpation)(palpation)– not reliable especially for

• small tumorsmall tumor• Tumors located deep in the tissueTumors located deep in the tissue

• Other methods: specificity problemOther methods: specificity problem

Breast Tissue Elasticity

ElastographyElastography

• ElastographyElastography– Noninvasive, abnormality detection and Noninvasive, abnormality detection and

assessmentassessment– Capable of detecting small tumorsCapable of detecting small tumors– Elastic behavior described by a number of Elastic behavior described by a number of

parametersparameters

• How?How?– Tissue undergo compressionTissue undergo compression– Image deformation (MRI, US, …)Image deformation (MRI, US, …)– Reconstruct elastic behaviorReconstruct elastic behavior

Elastography (Cont.)

Elastography (Cont.)

• Soft tissue– Anisotropic– Viscoelastic– non-linear

• Assumptions– isotropic– elastic– Linear

• Strain calculation• Uniform stress distribution • F=Kx - Hooke’s law

Linear Elastography

• Linear stress – strain relationship

• Not valid for wide range of strains

• Increase in compression

Strain hardening

Difficult to interpret

σ

ε

E1

E2

ε1 ε2

Non-linear ElastographyNon-linear Elastography

• Stiffness change by compressionStiffness change by compression non-linearity in behaviornon-linearity in behavior• Pros.Pros.

– Large deformations can be appliedLarge deformations can be applied– Wide range of strain is covered Wide range of strain is covered – Higher SNR of compressionHigher SNR of compression

• Cons.Cons.– Non-linearity (geometric & Intrinsic)Non-linearity (geometric & Intrinsic)– ComplexityComplexity

Inverse ProblemInverse Problem

• Forward Problem

• Governing Equations– Equilibrium (stress distribution)

– stress - deformation

0iji

j

fx

11 2 2

2[( ) . ]U U U

DEV I B B B pIJ I I I

• Strain energy functions : U = U (strain invariants)

– Polynomial (N=2)

– Yeoh

– Veronda-Westmann

1 2

1

3 3N i j

iji j

U C I I

3

101

3i

ii

U C I

13( 1)

21 1 2 3C I

U C C Ie

Inverse ProblemInverse Problem

Constrained ElastographyConstrained Elastography

• Stress – DeformationsStress – Deformations

• Rearranged equationRearranged equation

• Why Constrained Reconstruction ?• What is constrained reconstruction?

– Quasi – static loading– Geometry is known– Tissue homogeneity

1

1 2 2

2. ,

U U UDEV I B B B pI

J I I I

{ } [ ]{ }A C

Iterative Reconstruction Iterative Reconstruction ProcessProcess

Acquire Displacement

values

Calculate Deformation Gradient (F)

Calculate Strain Invariants (from F)

Strain Tensor

Parameter Updating and Averaging

Initialize Parameters

Stress Calculation Using FEM

Convergence

No

Update Parameters

Yes End

1

1 2 2

2. ,

U U UDEV I B B B pI

J I I I

{ } [ ]{ }A C

Numerical ValidationNumerical Validation

• Cylinder + Hemisphere Cylinder + Hemisphere • Three tissue typesThree tissue types• Simulated in ABAQUSSimulated in ABAQUS• Three strain energy Three strain energy

functions: functions: • Yeoh Yeoh • PolynomialPolynomial

• Veronda-WestmannVeronda-Westmann

Polynomial ModelPolynomial Model

Convergence Stress-Strain RelationshipConvergence Stress-Strain Relationship

RegularizationRegularization

• Polynomial: System Polynomial: System is ill-conditioning is ill-conditioning

• Regularization Regularization techniques to solve techniques to solve the problemthe problem– Truncated SVDTruncated SVD– Tikhonov reg.Tikhonov reg.– Wiener filteringWiener filtering

1

2

3

1( )T TC A A A { } [ ]{ }A C Over-determined

Results (Polynomial)

InitialGuess

True Value CalculatedValue

IterationNumber

Tolerance(tol %)

Error(%)

C10 (Polynomial) 0.01 0.00085 0.000849 60 0.04 0.038

C01 (Polynomial) 0.01 0.0008 0.000799 60 0.04 0.016

C20 (Polynomial) 0.01 0.004 0.004065 60 0.04 1.630

C11 (Polynomial) 0.01 0.006 0.005883 60 0.04 1.950

C02(Polynomial) 0.01 0.008 0.008051 60 0.04 0.648

Phantom StudyPhantom Study

• Block shape Phantom• Three tissue types• Materials

– Polyvinyl Alcohol (PVA)• Freeze and thaw• Hyperelasic

– Gelatin• Linear

• 30% compression

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Deformation (mm)

For

ce (

N)

5%, 3 cycle PVA, Yeoh Model

Assumption

– Plane stress assumption– Use the deformation of

the surface– Perform a 2-D analysis– Mean Error (Y-axis): 3.57% – Largest error (Y-axis) : 5.3%– Mean Error (X-axis): 0.36%– Largest Error (X-axis):

2.68%

ResultsResults

• E1=110 kPa• E2=120 kPa• E3=230 kPa

Reconstructed E3=226.1 kPa

ParameterInitial Guess (MPa)

True Value (MPa)

Calculated Value (MPa)

Iteration Number

Tolerance (tol %)

Error(%)

Young’s Modulus (tumor) 1 0.23 0.2261 6 0.69 1.72

PVA Phantom

• Tumor: 10% PVA,

5 FTC’s, 0.02% biocide

• Fibroglandular tissue: 5% PVA,

3 FTC’s, 0.02% biocide

• Fat: 5% PVA,

2 FTC’s, 0.02% biocide

Cylindrical Samples

Uniaxial Test

• The electromechanical setup

Relative vs. Absolute Reconstruction

• Force information is missing

• The ratios can be reconstructed

s1 1 1F =k x =F

s2 2 2F =k x =F

1 1 2 2k x =k x

1 2

2 1

k x=

k x

Uniaxial v.s Reconstructed

• Polynomial Model

Reconstruction Results for Polynomial Model

Relative Reconstruction

C10_t/C10_n2(Polynomial)

C01_t/C01_n2(Polynomial)

C20_t/C20_n2(Polynomial)

C11_t/C11_n2(Polynomial)

C02_t/C02_n2(Polynomial)

Reconstructed 2.725945178 2.145333277 2.516019376 2.51733066 2.481142409

Uniaxial test 2.982905983 2.050012345 2.956818182 2.782742681 2.936363636

Error (%) 8.614445325 4.650403756 14.9078766 9.537785251 15.50289009

C10_t/C10_n1(Polynomial)

C01_t/C01_n1(Polynomial)

C20_t/C20_n1(Polynomial)

C11_t/C11_n1(Polynomial)

C02_t/C02_n1(Polynomial)

Reconstructed 3.170368027 3.545108429 11.60866449 11.5544369 10.97304134

Uniaxial test 3.56122449 3.84375 11.02542373 10.75 11.13793103

Error (%) 10.97533908 7.769536807 5.289962311 7.483133953 1.48043375

Summary & ConclusionSummary & Conclusion

• Non-linear behavior must be considered to avoid discrepancy

• Tissue nonlinear behavior can be characterized by hyperelastic parameters

• Novel iterative technique presented for tissue hyperelstic parameter reconstruction

• Highly ill-conditioned system• Regularization technique was developed

Summary & ConclusionSummary & Conclusion

• Three different hyperelstic models were examined and their parameters were reconstructed accurately

• Linear Phantom study led to encouraging results• Absolute reconstruction required force

information• Relative reconstruction resulted in acceptable

values• This can be used for breast cancer classification

Thank You

Questions

(?)