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Elastography for Breast Cancer Assessment

Elastography for Breast Cancer Assessment . By: Hatef Mehrabian. Outline . Applications Breast cancer Elastography (Linear & Hyperelastic) Inverse problem Numerical validation & results Regularization techniques Experimental validation & results Summary and conclusion .

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Elastography for Breast Cancer Assessment

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  1. Elastography for Breast Cancer Assessment By: HatefMehrabian

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

  3. 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

  4. 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

  5. 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

  6. Breast Tissue Elasticity

  7. 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

  8. Elastography (Cont.)

  9. Elastography (Cont.) • Soft tissue • Anisotropic • Viscoelastic • non-linear • Assumptions • isotropic • elastic • Linear • Strain calculation • Uniform stress distribution • F=Kx - Hooke’s law

  10. σ E2 E1 ε ε1 ε2 Linear Elastography • Linear stress – strain relationship • Not valid for wide range of strains • Increase in compression Strain hardening Difficult to interpret

  11. 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

  12. Inverse Problem Forward Problem Governing Equations Equilibrium (stress distribution) stress - deformation

  13. Inverse Problem • Strain energy functions : U = U (strain invariants) • Polynomial (N=2) • Yeoh • Veronda-Westmann

  14. Constrained Elastography Stress – Deformations Rearranged equation Why Constrained Reconstruction ? What is constrained reconstruction? Quasi – static loading Geometry is known Tissue homogeneity

  15. Iterative Reconstruction Process Initialize Parameters Acquire Displacement values 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

  16. Numerical Validation Cylinder + Hemisphere Three tissue types Simulated in ABAQUS Three strain energy functions: Yeoh Polynomial Veronda-Westmann

  17. Polynomial Model Convergence Stress-Strain Relationship

  18. Regularization Polynomial: System is ill-conditioning Regularization techniques to solve the problem Truncated SVD Tikhonov reg. Wiener filtering Over-determined 2 3 1

  19. Results (Polynomial)

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

  21. 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%

  22. Results • E1=110 kPa • E2=120 kPa • E3=230 kPa • Reconstructed • E3=226.1 kPa

  23. 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

  24. Uniaxial Test • The electromechanical setup

  25. Relative vs. Absolute Reconstruction Force information is missing The ratios can be reconstructed

  26. Uniaxial v.s Reconstructed • Polynomial Model

  27. Relative Reconstruction Reconstruction Results for Polynomial Model

  28. 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

  29. 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

  30. Thank You Questions (?)

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