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

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 common cause of cancer deathWorldwide, 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~ 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

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)Tissue Stiffness variation is associated with pathology (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

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

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 E1E1 E2E2 ε1ε1 ε2ε2

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

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

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

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

Iterative Reconstruction Process 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

Numerical Validation Cylinder + HemisphereCylinder + Hemisphere Three tissue typesThree tissue types Simulated in ABAQUSSimulated in ABAQUS Three strain energy functions:Three strain energy functions: YeohYeoh PolynomialPolynomial Veronda-WestmannVeronda-Westmann

Polynomial Model Convergence Stress-Strain Relationship Convergence Stress-Strain Relationship

Regularization Polynomial: System is ill-conditioningPolynomial: System is ill-conditioning Regularization techniques to solve the problemRegularization techniques to solve the problem –Truncated SVD –Tikhonov reg. –Wiener filtering Over-determined

Results (Polynomial) Initial Guess True Value Calculated Value Iteration Number Tolerance (tol %) Error (%) C10 (Polynomial) C01 (Polynomial) C20 (Polynomial) C11 (Polynomial) C02(Polynomial)

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

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%

Results E1=110 kPa E2=120 kPa E3=230 kPa Reconstructed E3=226.1 kPa Parameter Initial Guess (MPa) True Value (MPa) Calculated Value (MPa) Iteration Number Tolerance (tol %) Error (%) Young’s Modulus (tumor)

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

Uniaxial v.s Reconstructed Polynomial Model

Reconstruction Results for Polynomial Model Relative Reconstruction C 10 _t/C 10 _n2 (Polynomial) C 01 _t/C 01 _n2 (Polynomial) C 20 _t/C 20 _n2 (Polynomial) C 11 _t/C 11 _n2 (Polynomial) C 02 _t/C 02 _n2 (Polynomial) Reconstructed Uniaxial test Error (%) C 10 _t/C 10 _n1 (Polynomial) C 01 _t/C 01 _n1 (Polynomial) C 20 _t/C 20 _n1 (Polynomial) C 11 _t/C 11 _n1 (Polynomial) C 02 _t/C 02 _n1 (Polynomial) Reconstructed Uniaxial test Error (%)

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

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

Thank You Questions (?)