Elastography for Breast Cancer Assessment

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Elastography for Breast Cancer Assessment

• By Hatef Mehrabian

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Outline

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

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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

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Breast Cancer

• Worldwide, breast cancer is the fifth most common
  cause of cancer death
• 1/4 million women will be diagnosed with breast
  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

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Breast Cancer

• Detection method
• Self exam (palpation)
• x-ray mammography
• Breast Magnetic resonance imaging (MRI)
• Ultrasound imaging
• Tissue Stiffness variation is associated with
  pathology (palpation)
• not reliable especially for
• small tumor
• Tumors located deep in the tissue
• Other methods specificity problem

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Breast Tissue Elasticity
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Elastography

• Elastography
• Noninvasive, abnormality detection and assessment
• Capable of detecting small tumors
• Elastic behavior described by a number of
  parameters
• How?
• Tissue undergo compression
• Image deformation (MRI, US, )
• Reconstruct elastic behavior

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Elastography (Cont.)
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Elastography (Cont.)

• Soft tissue
• Anisotropic
• Viscoelastic
• non-linear
• Assumptions
• isotropic
• elastic
• Linear
• Strain calculation
• Uniform stress distribution
• FKx - Hookes law

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Linear Elastography

• Linear stress strain relationship
• Not valid for wide range of strains
• Increase in compression
• Strain
  hardening
• Difficult to interpret

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Non-linear Elastography

• Stiffness change by compression
• non-linearity in behavior
• Pros.
• Large deformations can be applied
• Wide range of strain is covered
• Higher SNR of compression
• Cons.
• Non-linearity (geometric Intrinsic)
• Complexity

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Inverse Problem

• Forward Problem
• Governing Equations
• Equilibrium (stress distribution)
• stress - deformation

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Inverse Problem

• Strain energy functions U U (strain
  invariants)
• Polynomial (N2)
• Yeoh
• Veronda-Westmann

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Constrained Elastography

• Stress Deformations
• Rearranged equation
• Why Constrained Reconstruction ?
• What is constrained reconstruction?
• Quasi static loading
• Geometry is known
• Tissue homogeneity

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Iterative Reconstruction Process
Acquire Displacement values
Initialize Parameters
Calculate Deformation Gradient (F)
Stress Calculation Using FEM
Update Parameters
Calculate Strain Invariants (from F)
No
Strain Tensor
Parameter Updating and Averaging
Convergence
Yes
End
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Numerical Validation

• Cylinder Hemisphere
• Three tissue types
• Simulated in ABAQUS
• Three strain energy functions
• Yeoh
• Polynomial
• Veronda-Westmann

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Polynomial Model

• Convergence
  Stress-Strain Relationship

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Regularization
Over-determined

• Polynomial System is ill-conditioning
• Regularization techniques to solve the problem
• Truncated SVD
• Tikhonov reg.
• Wiener filtering

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3
1
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Results (Polynomial)
Initial Guess True Value Calculated Value Iteration Number 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
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Phantom Study

• Block shape Phantom
• Three tissue types
• Materials
• Polyvinyl Alcohol (PVA)
• Freeze and thaw
• Hyperelasic
• Gelatin
• Linear
• 30 compression

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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

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Results
Parameter Initial Guess (MPa) True Value (MPa) Calculated Value (MPa) Iteration Number Tolerance (tol ) Error ()
Youngs Modulus (tumor) 1 0.23 0.2261 6 0.69 1.72

• E1110 kPa
• E2120 kPa
• E3230 kPa

• Reconstructed
• E3226.1 kPa

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PVA Phantom

• Tumor 10 PVA,
• 5 FTCs, 0.02 biocide
• Fibroglandular tissue 5 PVA,
• 3 FTCs, 0.02 biocide
• Fat 5 PVA,
• 2 FTCs, 0.02 biocide
• Cylindrical Samples

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Uniaxial Test

• The electromechanical setup

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Relative vs. Absolute Reconstruction

• Force information is missing
• The ratios can be reconstructed

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Uniaxial v.s Reconstructed

• Polynomial Model

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Relative Reconstruction
Reconstruction Results for Polynomial Model
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
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
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Summary 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

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Summary 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

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Thank You

• Questions
• (?)