elastography for breast cancer assessment by: hatef mehrabian
TRANSCRIPT
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
(?)