Transcript Document 7207614

Elastography for Breast
Cancer Assessment
By: Hatef Mehrabian
Outline
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•
•
•
•
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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 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
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
Breast Tissue Elasticity
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
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
σ
E2
Difficult to interpret
E1
ε1
ε2
ε
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
Inverse Problem
• Forward Problem
• Governing Equations
– Equilibrium (stress distribution)
 ij
x j
 fi  0
– stress - deformation
2
U
U
U
  DEV [(
 I1
)B 
B.B ]  pI
J
I1
I 2
I 2
Inverse Problem
• Strain energy functions : U = U (strain invariants)
– Polynomial (N=2)
U
– Yeoh
 C I
N
i  j 1
ij
1
3

3
 I
i
U   Ci 0 I 1  3
i 1

2
3

j
i
– Veronda-Westmann
U  C1
e
C 3( I1 1)

 1  C 2  I 2  3
Constrained Elastography
• Stress – Deformations
 U

2
U 
U
  DEV 
 I1
B.B   pI ,
B
J
 I2 
 I2
  I1

• Rearranged equation
{ }  [ A]{C}
• Why Constrained Reconstruction ?
• What is constrained reconstruction?
– Quasi – static loading
– Geometry is known
– Tissue homogeneity
Iterative Reconstruction
Process
Acquire
Displacement
values

Initialize
Parameters
 U

2
U 
U
DEV 
 I1
B.B   pI ,
B
J
 I2 
 I2

  I1
{ }  [ A]{C}
Calculate
Deformation
Gradient (F)
Calculate Strain
Invariants (from F)
Stress
Calculation
Using FEM
Strain Tensor
Parameter Updating and Averaging
Update
Parameters
No
Convergence
Yes
End
Numerical Validation
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Cylinder + Hemisphere
Three tissue types
Simulated in ABAQUS
Three strain energy
functions:
• Yeoh
• Polynomial
• Veronda-Westmann
Polynomial Model
Convergence
Stress-Strain Relationship
Regularization
{ }  [ A]{C}
Over-determined
• Polynomial: System
is ill-conditioning
• Regularization
techniques to solve
the problem
– Truncated SVD
– Tikhonov reg.
– Wiener filtering
C  ( A A) A 
T
1
T
2
1
3
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
Phantom Study
• Block shape Phantom
• Three tissue types
• Materials
– Polyvinyl Alcohol (PVA)
• Freeze and thaw
• Hyperelasic
5%, 3 cycle PVA, Yeoh Model
1.8
– Gelatin
1.6
1.4
• Linear
Force (N)
• 30% compression
1.2
1
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
Deformation (mm)
2
2.5
3
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
Parameter
Initial
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
• E1=110 kPa
• E2=120 kPa
• E3=230 kPa

Reconstructed
E3=226.1 kPa

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
Fs1 =k1 x1 =F
Fs2 =k 2 x 2 =F
 k1 x1 =k 2 x 2
k1 x 2
 =
k 2 x1
Uniaxial v.s Reconstructed
• Polynomial Model
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
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
(?)