1
2
Outline
Ultrasound
Elasticity Imaging
•
•
•
•
•
•
•
Stanislav (Stas) Emelianov
emelian@mail.utexas.edu
Department of Biomedical Engineering
Introduction
Mechanical properties of tissue
Approaches in elasticity imaging
Elasticity imaging systems
Applications
Challenges, advantages and limitations
Future developments
3
Notations
X=(x1,x2,x3)=(x,y,z) – coordinate system
U=(u1,u2,u3) – displacement vector
εij – strain tensor
i=1,2,3
σij – stress tensor
j=1,2,3
δij – Kronecker delta
(1 for i=j, 0 otherwise)
Einstein summation convention –
summation is implied over the repeated index,
for example:
aii =
3
aii = a11 + a22 + a33
i =1
j = 1 → ai bi1 =
ai bij =
3
aibij
i =1
j = 2 → aibi 2 =
j = 3 → ai bi 3 =
3
ai bi1 = a1b11 + a2b21 + a3b31
i =1
3
i =1
3
ai bi 2 = a1b12 + a2b22 + a3b32
ai bi 3 = a1b13 + a2b23 + a3b33
4
Elasticity Imaging – Goal
ρ – density (kg/m3)
ν – Poisson’s ratio
E – Young’s modulus
λ, µ – Lame coefficients
G – shear modulus
K – bulk modulus
η – shear viscosity
ξ – bulk viscosity
ct – shear wave speed
cl – longitudinal wave speed
ct =
µ
λ + 2µ
, cl =
ρ
ρ
Remote
non-invasive (or adjunct to invasive)
imaging (or sensing) of
mechanical properties of
tissue for
clinical applications
i =1
1
5
Hippocrates, circa 460-377 B.C.
Tissue Elasticity
Ultrasound
MRI
Oestreicher, 1951
6
Mechanical Properties of Tissue
(i.e., Why Bother)
Elasticity Imaging – Glance at History
Other methods
Frank et al, 1948
Biomechanics
(muscle, skin, ...)
Sarvazyan et al, 1975
Frizzell et al, 1976
Fung, 1981
Elasticity (e.g., bulk and shear moduli)
Thompson et al, 1981
Wilson and Robinson, 1982
Dickinson and Hill, 1982
Eisensher et al, 1983
Tristam et al, 1986
Sarvazyan et al, 1984
Viscosity (e.g., bulk and shear viscosities)
Krouskop, (Le)vinson, 1987
Lerner and Parker, 1988
Yamakoshi et al, 1988
Adler et al, 1989
Meunier and Bertrand, 1989
Duck, 1990
Parker et al, 1990
Ophir et al, 1991
Sarvazyan and Skovoroda, 1991
Avalanche of papers
Krouskop et al, 1998
Erkamp et al, 1998
Pereira et al, 1990
Nonlinearity (e.g., strain hardening)
DeJong et al, 1990
Fowlkes et al, 1992
Sarvazyan et al, 1995
Fowlkes et al, 1995
Muthupillai et al, 1995
Plewes et al, 1995
Chenevert et al, 1998
Other (e.g., anisotropy, pseudoelasticity)
Many papers
7
8
Which Elastic Moduli?
Elasticity
Changes in tissue elasticity are related to pathological changes
… Such swellings as are soft, free from pain, and yield to the finger, ...
and are less dangerous than the others.
... then, as are painful, hard, and large, indicate danger of speedy death;
but such as are soft, free of pain, and yield when pressed with the finger,
are more chronic than these.
THE BOOK OF PROGNOSTICS, Hippocrates, 400 B.C.
Hippocrates
It is the business of the physician to know, in the first place, things similar
and things dissimilar; … which are to be seen, touched, and heard; which
are to be perceived in the sight, and the touch, and the hearing, … which
are to be known by all the means we know other things.
ON THE SURGERY, Hippocrates, 400 B.C.
=
=
Poisson’s ratio (ν)
Bulk modulus (K)
Shear modulus (µ=G)
Young’s modulus (E)
Most soft tissues are incompressible, i.e.,
deformation produces no volume change
ct =
G
ρ
< cl =
K + 23 G
ρ
G << K
G
→0
K
ν→
1
2
Hippocrates, 400 B.C.
2
9
Elasticity
10
Human sense of touch – what do we feel?
R
Incompressible material
Relations between various elastic constants
x2
F1
Constant
λ
µ
E
ν
Κ
G
λ, µ
Rigid circular die
Common Pair
E, ν
λ
µ
µ (3λ + 2 µ )
(λ + µ )
λ + 23 µ
µ
F1 = 3µε 0
K − 23 G
W
G
Semi-infinite elastic medium
K – bulk modulus
µ – shear modulus
9 KG
3K + G
3K − 2G
6 K + 2G
E
λ
µ
= 0.5 −
2(λ + µ )
2(λ + µ )
x3
F
K, G
νE
(1 +ν )(1 − 2ν )
E
2(1 +ν )
ν
E
3(1 − 2ν )
E
2(1 +ν )
x1
G
F = 8 RWG 1 + K
G
1+
3K
K
G
−1

G → 8 RWµ
K
→0
Static deformation of
(nearly) incompressible material is
primarily determined by
shear or Young’s modulus (!!!),
and boundary conditions (?!?)
Sarvazyan et al, 1995
11
How to (Directly) Measure
Tissue Elasticity
12
Direct Elasticity Measurements
2-D
Positioning
System
R
•
Sample preparation
Tissue
Rotational stage
•
Deformation method
–
–
•
Static
Oscillatory (low frequency)
F = 8 RWµ
F
Scale
Rigid
circular
die
Load – Displacement Tests
Preconditioning of the tissue
W
Load – Displacement measurements
•
Strain – Stress calculations
•
Elastic modulus evaluation
30
Semi-infinite elastic medium
x2
x2
F
F
x1
x3
Stress (kPa)
•
F = 3µε 11
x1
x3
Scale
Scale
15
0
10
20
Strain (%)
Erkamp et al, 1998
3
13
14
Direct Elasticity Measurements
Krouskop T.A., Wheeler T.M., Kallel F., Garra B.S., Hall T.J.,
"The elastic moduli of breast and prostate tissues under
compression,“ Ultrasonic Imaging, 20:260-274, 1998.
Artann Laboratories, NJ
www.artannlabs.com
Deformation piston
Fi
F0 (force)
H0
Wellman P.S., Howe R.D., Dalton E., Kern K.A., “Breast Tissue
Stiffness in Compression is Correlated to Histological Diagnosis,”
Harvard BioRobotics Laboratory, Technical Report, 1999
Hi
Tissue sample
Nava A., Mazza E., Haefner O., and Bajka M.
“Experimental Observation and Modeling of
Preconditioning in Soft Biological Tissues,” in
Proceedings of Medical Simulation
International Symposium, 2004 Cambridge.
Rigid support plane
Artann Laboratories, NJ
Xie et al. 2004
15
Breast Tissue Elasticity and Pathology
Skovoroda et al., 1995,
Breast Tissue Elasticity and Pathology
Wellman et al., 1999,
Biophysics, 40(6):1359-1364.
Breast Tissue
Type
Normal
gland
Infiltrative ductal
cancer with alveolar
tissue predominating.
Fibroadenomas of
glandular origin
Infiltrative ductal cancer
with fibrous tissue
predominating.
Ductal
fibroadenoma
Young’s
Modulus (kPa)
0.5-1.5
1.0-1.5
1.5-2.5
2.0-3.0
8.0-12.0
Samani A., Bishop J., Luginbuhl C. and Plewes D.B.,
“Measuring the elastic modulus of ex vivo small tissue samples,”
Physics in Medicine and Biology, 48, pp.2183-2198, 2003.
16
Harvard BioRobotics Laboratory Technical Report.
Krouskop et al., 1998, Ultrasonic Imaging, 20:260-274.
Samani et al., 2003, Physics in Medicine and Biology, 48:2183-2198
.
4
17
Elastic Properties of Arteries
Sarvazyan A.P., 2001,” In: Handbook of Elastic Properties of Solids, Liquids and Gases.
Type of soft tissue
E, kPa
Comments
18
Elastic Properties of Prostate Gland
Aglyamov S.R. and Skovoroda A.R., 2000, Biophysics,
2000, 45(6).
Reference
Artery
human, in vitro
Thoracic aorta
Abdominal aorta
Iliac artery
Femoral artery
300-940
980-1,420
1,100-3,500
1,230-5,500
For normal physiological conditions of longitudinal
tension and distending blood pressure, below 200 mm
Hg.
Ascending aorta
183-582
M-mode echocardiography in different age groups.
Alessandri et al., 1995
Coronary artery
1,060-4,110
Represents values for various ages (0-80 y.o.) and
atherosclerosis conditions in right and left arteries.
Ozolanta et al., 1998
100-1,500
Equilibrated at intraluminal pressure of 45 mmHg,
media thickness and lumen diameter were measured in
the applied 3 -140 mmHg intraluminal pressure range.
Intengan et al., 1998
700-1,600
Range includes measurements for normal vs
spontaneously hypertensive animals.
rat, in vitro
mesenteric small arteries
aortic wall
porcine, in vitro
thoracic aorta
intima-medial layer
adventitia layer
ascending aorta
intima-medial layer
adventitia layer
descending aorta
intima-medial layer
adventitia layer
McDonald, 1974
Marque et al., 1999
43
4.7
447
112
Bending experiments were used to impose various
strains on different layers of tested blood vessels.
Fung, 1993
248
69
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20
Strain hardening
Contrast in Elasticity Imaging
•
•
All Soft Tissues
•
•
Bone
102 103 104 105 106 107 108 109 1010 Bulk Modulus (Pa)
Glandular Tissue of Breast
Liver
Relaxed Muscle
Fat
40
Bone
Stress (kPa)
Dermis
Connective Tissue
Contracted Muscle
Palpable Nodules
30
Collagen
20
10
Epidermis
Cartilage
Cornea
Strain hardening in kidney samples
(Erkamp et al, 1998)
Vessel Composition (Fung, 1988):
muscle (soft), elastin (soft), collagen (hard)
Shear Modulus (Pa)
Blood
Vitreous Humor
Most soft tissues exhibit strain hardening
Tissues of organs with primary “mechanical” functions (muscle, skin,
tendon, etc.)
Other tissues (kidney, brain, blood clot, etc.)
Strain hardening vs. strain softening (strain energy density function)
Elastin
0
1.0
1.1
1.2
Stretch ratio (L/L0)
80
Young's modulus [kPa]
Liquids
1.3
40
0
5
10
15
Strain [%]
Sarvazyan et al, 1995
5
21
Strain hardening
22
Strain hardening
This and other graphs as well as other literature data suggest that tissue
strain hardening (or nonlinearity in stress-strain relations) can be used for
tissue analysis including composition, differentiation, etc.
Krouskop et al, 1998
Ophir et al., 2001
Wellman et al., 1999
23
24
Viscosity
Anisotropy
• Shear viscosity: shear waves
• Bulk viscosity: longitudinal ultrasound waves
• Viscoelastic models:
Maxwell, Voigt, Kelvin, KVFD, etc.
• Is there a characteristic time?
Across
fibers
4
0
5
10
15
20
Strain (%)
Creep
Constant Load
Creep
Stress Relaxation
Deformation
0
Stress
8
Time
12
Constant Deformation
Force (N)
Along
fibers
12
Load
•
16
Deformation
•
Arterial wall: orthotropic material – 9 constants
two orthogonal planes of symmetry
Muscle: transversely isotropic – 5 constants
axis of symmetry
Isotropic – 2 constants
Stress (kPa)
•
8
Cornea
4
Stress Relaxation
Time
0
30
60
90
Time (min)
6
25
Viscosity
• Hysteresis loops:
independent of the rate of loading (most soft tissues)
• Pseudoelastic material:
elastic after preconditioning (with hysteresis)
•
Duck, F.A. Physical properties of tissues. Academic press; New York, 1990
•
Fung YC. Biomechanics – mechanical properties of living tissues. SpringerVerlag; New York, 1981
•
Krouskop TA, Wheeler TM, Kallel F, Garra BS, Hall TJ, “The elastic moduli
of breast and prostate tissues under compression,” Ultrasonic Imaging vol. 20
pp. 260-274, 1998
•
Aglyamov SR, Skovoroda AR, “Mechanical properties of soft biological
tissues,” Biophysics, Pergamon, 45(6):1103-1111, 2000.
•
Sarvazyan AP, “Elastic properties of soft tissues,” In: Handbook of Elastic
Properties of Solids, Liquids and Gases, Volume III, Chapter 5, 107-127, eds.
Levy, Bass and Stern, Academic Press, 2001
•
Other text books and archival publications
Loading Cycles
Stress
1st cycle
Load
5th
Strain
26
Mechanical Properties of Tissue:
References
>10th cycle
Elongation
27
Phantoms for Elasticity Imaging
•
Tissue-mimicking phantoms
•
Gelatin and Gelatin/Agar-agar
– Gelatin gels
– Easy to prepare
– Agar-agar and gelatin mixtures
– E ~ Cn, C – concentration, n=[1-2]
•
PVA (poly-vinyl alcohol) tissuemimicking phantom
•
Background:
8% PVA solution
1% silica (40µm diameter)
1 freeze/thaw cycle
– Short shelf life
– Rubber (plastisol, silicone)
materials
– Additives are possible
•
– PVA (poly-vinyl alcohol)
– Polyacrilamyde gels
28
Phantoms for Elasticity Imaging: Preparation
•
Plastisol
– Time-stable phantoms
•
– Requires excessive heating during
preparation
Tissue-containing phantoms
– Gelatin gels
– Agar-agar and gelatin gels
•
•
Imaging:
SONIX RP imaging system
(Ultrasonix, Inc.)
5-7 MHz, 40 mm linear probe
•
Deformations
manual
0.3%
PVA
– Freeze-thaw cycles to vary
elasticity
– Polyacrilamyde gels
– Time-stable
Hall et al., 1997
Other papers
Inclusion:
10% PVA solution
2% silica particles
3 freeze/thaw cycles
50mm
10mm
50mm
50mm
Park et al., 2007
7
Phantoms for Elasticity Imaging:
References
29
30
Elasticity Imaging using ...?
Madsen EL, Frank GR, Krouskop TA, Varghese T, Kallel F, Ophir J,
“Tissue-mimicking oil-in-gelatin dispersions for use in heterogeneous
elastography phantoms,” Ultrasonic Imaging vol. 25 pp. 17-38, 2003
Computerized Tomography:
•
Madsen EL, Hobson MA, Frank GR, Shi H, Jiang J, Hall TJ, Varghese T,
Doyley MM, Weaver JB, “Anthropomorphic breast phantoms for testing
elastography systems,” Ultrasound Med Biol. vol. 32 pp. 857-874, 2006
MRI:
•
Hall TJ, Bilgen M, Insana MF, Krouskop TA, “Phantom materials for
elastography,” IEEE Trans. UFFC, vol. 44 pp. 1355-1365, 1997
•
Surry KJM, Austin HJB, Fenster A, Peters TM, “Poly(vinly alcohol) cryogel
phantoms for use in ultrasound and MR imaging,” Phys. Med. Biol., vol. 49
pp. 5529-5546, 2004
•
Other text books and archival publications
•
Where to buy
ATS Laboratories, Inc. (http://www.atslabs.com/)
spatial distribution of the absorption (density)
proton spin density and relaxation time constants
Ultrasound Imaging:
variation in acoustical impedance
(bulk modulus and density)
Optical Imaging:
refraction index
31
Elasticity Imaging – Approaches
32
How … Static Elasticity Imaging?
Displacement
Strain
Static (strain-based, or reconstructive)
Soft
imaging internal motion under static deformation
Dynamic (wave-based)
Hard
imaging shear wave propagation
Mechanical (stress-based, also reconstructive)
measuring tissue response at the surface
Range
•
8
33
34
Elasticity Imaging – Main Components
How … Static Elasticity Imaging?
• Capture data during
externally or internally applied
tissue motion or deformation
• Capture data during deformation
• Evaluate tissue response
(displacement, strain, stress)
• Estimate displacements
• Compute strain tensor
• Reconstruct elastic modulus based on
theory of elasticity
• Reconstruct mechanical properties
Theory of elasticity is common part in
all approaches in Elasticity Imaging
35
L0
F
F
S0
S
Theory of Elasticity
(Static Approach)
L=L0+∆L
• Strain
ε ij =
L − L0
ε11 =
L0
• Stress
σ 11 =
General (3-D) case
1 ∂ui ∂u j ∂u k ∂u k
+
+
2 ∂x j ∂xi ∂xi ∂x j
ε 11 ε12 ε 13
ε 21 ε 22 ε 23
ε 31 ε 32 ε 33
F
S
σ 11 σ 12 σ 13
σ 21 σ 22 σ 23
σ 31 σ 32 σ 33
36
Equations of Equilibrium
Small deformations of linear, isotropic (i.e., Hookean) material
∂
∂u ∂u ∂u
∂
∂u
∂
∂u ∂u
∂
∂u ∂u
(λ ( 1 + 2 + 3 )) +
( 2µ 1 ) +
(µ ( 1 + 2 )) +
( µ ( 1 + 3 )) + f1 = 0
∂x1
∂x1 ∂x2 ∂x3
∂x1
∂x1 ∂x2
∂x2 ∂x1
∂x3
∂x3 ∂x1
∂
∂u ∂u ∂u
∂
∂u ∂u
∂
∂u
∂
∂u ∂u
(λ ( 1 + 2 + 3 )) +
( µ ( 2 + 1 )) +
( 2µ 2 ) +
( µ ( 2 + 3 )) + f 2 = 0
∂x2
∂x1 ∂x2 ∂x3
∂x1
∂x1 ∂x2
∂x2
∂x2
∂x3
∂x3 ∂x2
∂
∂u ∂u ∂u
∂
∂u ∂u
∂
∂u ∂u
∂
∂u
(λ ( 1 + 2 + 3 )) +
( µ ( 3 + 1 )) +
( µ ( 3 + 2 )) +
(2µ 3 ) + f3 = 0
∂x2
∂x2 ∂x3
∂x3
∂x3
∂x3
∂x1 ∂x2 ∂x3
∂x1
∂x1 ∂x3
Examples (incompressible material)
x2
• Constitutive relationships
σ 11 = Eε11
E – Young’s modulus
R
σ ij = λε iiδ ij + 2µε ij
F1
x1
x3
• Equations of equilibrium
∂σ 11
=0
∂x1
∂σ ij
i
∂x j
+ fi = 0
F = 8RWµ
F
Rigid
circular
die
F1 = 3µε 0
W
Semi-infinite elastic medium
9
37
38
Image during Deformation
References
• Landau LD and Lifshitz EM. Theory of elasticity. Pergamon
Press; New York, 1986
• Externally or internally induced deformation
• Continuous deformation while imaging
• Saada AS. Elasticity Theory and Applications. Krieger
Publishing Company; Malabar, Florida, 1993
• Nowazki W. Dynamics of elastic systems. Wiley;
New York, 1963
Transducer
1-D Motion axis
Phantom
• Constrained or free-hand transducer
Deformation
plate
• Various imaging techniques
• Deformation, not translation
• Nowazki W. Thermoelasticity. Pergamon Press;
New York, 1983
• Other text books and archival publications
Beware: most (soft) tissues are (nearly) incompressible
39
Displacements
1-D, 2-D (3-D) Correlation Tracking
Kernel Size
Normalized Correlation Coefficient
• Speckle motion
Tissue motion
Speckle tracking
• Ultrasound Imaging (2-D → 3-D)
ρˆ (l ) =
B-Scan
Axial (u2) displacement
40
s (t ) ⋅ s2 (t + l ) dt
*
1
Before
Deformation
s (t )dt ⋅ s (t + l ) dt
2
1
2
2
Lag
• Displacement vector: U=(u1,u2,u3)
u1 – lateral component
u2 – axial (along the ultrasound beam)
u3 – elevational (out-of-plane) component
• Various speckle tracking techniques
• “Anisotropy” in displacement measurements
1
1-D
0.5
0
-0.5
-1
Correlation Lag
Axial lag
Correlation coefficient
After
Deformation
2-D
Lateral lag
Before
Deformation
After
Deformation
Correlation coefficient
10
41
Strains
• Displacement vector → Strain tensor
Static or Reconstructive
Ultrasound Elasticity Imaging
42
• Displacement derivatives
ε ij =
1 ∂ui ∂u j ∂uk ∂uk
+
+
2 ∂x j ∂xi ∂xi ∂x j
Axial (u2) displacement
Normal axial (ε22) strain
B-Scan
Displacements
Strains
Elasticity
Deform and image
Track internal motion
Evaluate deformations
Reconstruct
Young’s or shear
elastic modulus
• Six (3-D) or three (2-D)
independent components
ε 11 ε12 ε 13
ε 21 ε 22 ε 23
ε 31 ε 32 ε 33
• Sources of error
• Improvement and Optimization
• Effect of strain hardening, anisotropy, etc.
43
Deformation: Challenges
Deformation vs. rotation and translation
translation – no information about tissue elasticity
rotation – no information about tissue elasticity and speckle tracking difficulties
deformation – consider “anisotropy” in displacement measurements (example 1)
Volumetric deformation vs. 1-D or 2-D US imaging
deformation – control the deformation state (i.e., plane strain) if possible
Deformation vs. temporal and spatial sampling
control deformation rate and/or frame rate and spatial sampling
44
Strain Imaging: Challenges
Sources of error in strain images
ultrasound imaging system (electronic SNR, etc.)
interpolation
strain induced decorrelation
other sources (out-of-plane motion, peak hopping, etc.)
Optimal SNR and CNR in strain images
short-time correlation, companding, temporal stretching, strain filter, etc.
adaptive strain imaging for large deformations, multi-compression, etc.
Anisotropy in displacement measurements
incompressibility processing
other approaches (phase sensitive interpolation, grid slopes, etc.)
Deformation vs. distribution and symmetries of elasticity
spatial symmetries (if any) must be considered to assist
displacement estimation
imaging of strain and interpretation (example 1 and 2)
elasticity reconstruction (example 1 and 2)
Effect of tissue strain hardening on strain images
utilize as independent parameter of tissue differentiation
11
A fundamental limit on delay estimation
0.5
0
-0.5
time
distance
(via sound velocity)
-1
Correlation Lag
True
displacement
3
2 f π T B 3 + 12 B
3
0
2
(
f0 – center frequency
T – the observation time
B – fractional bandwidth
)
1
ρ
2
1+
1
SNR 2
2
−1
SNR – root mean squared signal-to-noise ratio
ρ – correlation coefficient
στ – root mean squared time delay estimate error
Walker and Trahey, 1995
Walker and Trahey, 1995
47
48
Interpolation Error
Correlation Coefficient
46
False Peak
1
στ ≥
Strain
Complex
RF
1
0.5
0
• Correlation peak position of
complex baseband signal
• Phase zero-crossing of
analytic signal correlation
-0.5
-1
Decorrelation
Displacement error ~ 1 / Kernel Size
(Kernel size
Observation time
Strain decorrelation
Reduce kernel size
Filter correlation functions
−π
3
2
1
0
40
50
Time (µsec)
60
h(t)
Some other approaches are discussed in:
Cespedes et al, 1995
Cohn et al, 1997
Pesavento et al, 1999
Geiman et al, 2000
−π/2
Window size)
Strain Error
T = 0.35 µsec (with filter)
True strain
T = 1.3 µsec
4
^
ρ(t0+ ξ1 , t0 + ξ1 +τ)
π/2
0
Displacement Error
Spatial resolution vs. error
Analytic
Baseband
π
Strain Decorrelation
No strain
Two-step approach
(computationally efficient)
Correlation Lag
Correlation Phase
A fundamental limit on delay estimation
Strain (%)
Correlation coefficient
Jitter
45
Correlation Lag
O’Donnell et al, 1993
Lubinski et al, 1999
t
^
ρ(t0, t0 +τ)
^
ρ(t0- ξ1 , t0 - ξ1 +τ)
τ
h(0)
h(+ξ1)
τ
h(-ξ1)
t
^ρF(t0, t0 +τ)
Σ
τ
τ
Correlation Coefficient
Functions
Correlation Filter
Filtered Correlation
Coefficient Function
Lubinski et al, 1999
12
49
Time Delay Estimation and
Interpolation Techniques
50
Kernel size vs. resolution and SNR
Resolution
SNR
Kernel 0.86 mm
Time Delay Estimation
Doppler-based techniques
Optical Flow
Normalized Covariance
Normalized Cross-correlation
Hybrid-sign Correlation
Polarity-coincidence Correlation
Cross-correlation
Sum of Squared Differences (SSD)
Sum of Absolute Differences (SAD)
Mutual Information
Many, many other algorithms
Interpolation
Parabolic
Phase zero crossing
Cosine
Spline
Grid slopes
Autocorrelation
Kernel 0.43 mm
•
Correlation window is longer than pulse length:
the axial resolution of elasticity imaging is
determined by the correlation window.
Correlation window decreases to pulse length and
below: spatial resolution is ultimately limited by
the bandwidth of the ultrasonic imaging system.
•
Formula for optimal kernel size:
B – bandwidth
s – strain
f0 – center frequency
Liu et al., 2003
Varghese et al., 1998
Lubinski et al, 1999
51
Elasticity Imaging – Approaches
52
L0
F
F
S0
S
Theory of Elasticity
(Dynamic Approach)
L=L0+∆L
Static (strain-based, or reconstructive)
imaging internal motion under static deformation
Dynamic (wave-based)
imaging shear wave propagation
• Strain
ε11 =
General (3-D) case
ε ij =
L − L0
L0
• Stress
1 ∂ui ∂u j ∂u k ∂u k
+
+
2 ∂x j ∂xi ∂xi ∂x j
σ 11 σ 12 σ 13
σ 21 σ 22 σ 23
σ 31 σ 32 σ 33
ε 11 ε12 ε 13
ε 21 ε 22 ε 23
ε 31 ε 32 ε 33
F
σ 11 =
S
• Constitutive relationships
Mechanical (stress-based, also reconstructive)
σ 11 = Eε11
E – Young’s modulus
σ ij = λε iiδ ij + 2µε ij + ξ
measuring tissue response at the surface
• Equations of motion
∂σ 11
∂ 2u
= ρ 21
∂x1
∂t
∂σ ij
i
∂x j
+ fi = ρ
∂ε
∂ε ii
δ ij + 2η ij
∂t
∂t
∂ 2 ui
∂t 2
13
53
54
Example: plane waves
Transient Elastography
• Infinite homogeneous (λ,µ=const) elastic medium (i.e., ignore bulk and shear
viscosities), no body forces (fi=0)
The displacement vector is not always orthogonal to the propagation vector:
finite medium, finite size vibrator
shear wave is not purely transverse
• Assume that u1=u1(x1,t), u2=u2(x1,t), and u3=u3(x1,t)
Transmit low frequency shear waves
mechanical vibration parallel to ultrasound beam
∂
∂u ∂u ∂u
∂
∂u
∂
∂u ∂u
∂
∂u ∂u
∂ 2u
(λ ( 1 + 2 + 3 )) +
( 2µ 1 ) +
( µ ( 1 + 2 )) +
(µ ( 1 + 3 )) = ρ 21
∂x1
∂x1 ∂x2 ∂x3
∂x1
∂x1 ∂x2
∂x2 ∂x1
∂x3
∂x3 ∂x1
∂t
∂
∂u ∂u ∂u
∂
∂u ∂u
∂
∂u
∂
∂u ∂u
∂ 2u
(λ ( 1 + 2 + 3 )) +
( µ ( 2 + 1 )) +
(2 µ 2 ) +
( µ ( 2 + 3 )) = ρ 22
∂x2
∂x2
∂x3
∂x3 ∂x2
∂t
∂x2
∂x1 ∂x2 ∂x3
∂x1
∂x1 ∂x2
∂
∂u
∂ 2u
∂
∂u ∂u ∂u
∂
∂u ∂u
∂
∂u ∂u
(λ ( 1 + 2 + 3 )) +
( µ ( 3 + 1 )) +
(µ ( 3 + 2 )) +
(2 µ 3 ) = ρ 23
∂x2
∂x2 ∂x3
∂x3
∂x3
∂t
∂x3
∂x1 ∂x2 ∂x3
∂x1
∂x1 ∂x3
(λ + 2µ ) ∂ u21 − ρ ∂ u21 = 0
2
2
∂x1
∂ u 2 ( 3)
2
µ
∂x12
∂t
∂ u 2 ( 3)
→
2
−ρ
∂t 2
=0 →
∂ 2u1 1 ∂ 2u1
λ + 2µ
−
= 0 where c l =
∂x12 cl2 ∂t 2
ρ
∂ 2u 2 ( 3)
∂x12
2
1 ∂ u 2 (3)
− 2
= 0 where c t =
ct ∂t 2
µ
ρ
Longitudinal wave
(ultrasound)
Ima
are ge
a
y
x
Shear wave
z
Catheline, Fink et al. 1999
Laboratoire Ondes et Acoustique, France
http://www.loa.espci.fr/
55
Transient Elastography
Transient Elastography
Image shear waves and measure its velocity using ultrafast imaging and motion tracking
Conventional
Imaging
56
Ultrafast
Imaging
Evaluate shear modulus from shear wave velocity
Isotropic, homogeneous, elastic medium
ρ
r
r r r
rr
∂ 2u
= (λ + µ )∇ ∇.u + µ∆ u
2
∂t
( )
Active
elements
compression
Shear wave propagation equation
75 mm
Transmit
beam profile
Transmit
wave front
t beam ≥
2⋅ R
cl
Time needed to acquire 1 frame:
t frame
ρ
∂ 2 ui
= µ∆ ui , i = x, y, z
∂t 2
Local inversion algorithm
250 beams
2 ⋅ 75 mm
= tbeam ⋅# beams =
⋅ 256 ≈ 25 ms
1.5 mm/µm
shear
t frame
2 ⋅ 75 mm
= tbeam =
≈ 100 µs
1.5 mm/µm
Vs ( x , z ) =
1
N
∂ 2 u ( x , z , t ) ∂ 2 u ( x, z , t ) ∂ 2 u ( x, z , t )
+
∂t 2
∂x 2
∂z 2
n =1
N
−1
14
57
Transient Elastography
58
Acoustic Radiation Force Imaging
Ultrasound Image
Transducer
10
1.
Focused Acoustic Radiation
Force generates localized,
impulsive (<0.1 ms) tissue
excitation
2.
Track tissue response with
same ultrasonic transducer used
for force generation
3.
Repeat in multiple locations
throughout 2D FOV
4.
Generate images of relative
tissue response within the
region of excitation
(displacement after force
removal, recovery time, etc) to
assess structural information
about tissue
20
40
50
-20
0
20
Shear velocity map
5
10
4
20
3
30
Radiation
Force
F=
2
40
2αI ta
c
1
50
Bercoff et al. 2003
Direction of Wave
Propagation
30
m/s
-20
0
Nightingale, Trahey et al.
Duke University
20
59
Supersonic
Shear Wave Imaging
60
Shear Wave
Imaging
Bercoff et al. 2004
Bercoff et al. 2004
15
61
Elasticity Imaging Systems
(Static
/
Dynamic)
• Siemens/Acuson Antares
• Supersonic Imaging, Inc.
• Hitachi Imaging System
• Siemens
• Sonic RP by Ultrasonix
Medical, Inc.
• Echosens
• Volcano Therapeutics IVUS
Imaging
62
Siemens Sonoline Elegra and Acuson Antares systems
• Other systems
eSie Touch elasticity imaging
• Improves border delineation of this biopsy-proven
invasive ductal carcinoma. Live dual imaging
provides real time comparison of elastogram to
standard 2D imaging.
• Winprobe Research Platform
eSie Touch elasticity imaging
• Provides additional qualitative information by
demonstrating the typical internal characteristics
pattern of three cysts.
• Other systems
www.siemens.com
63
64
Hall et al, 2006
www.engr.wisc.edu/bme/faculty/hall_timothy.html
www.medphysics.wisc.edu/medphys_docs/people/hall/hall.html
Hall, Zhu et al, 2003
Fibroadenoma:
changing contrast
equal lesion size ratio
IDC:
constant contrast
large lesion size ratio
16
65
Lesion size comparison technique
Lesion size comparison technique
66
Invasive ductal carcinoma
Benign fibroadenoma
WR - size ratios for width
AR - size ratios for area
A, B, C, D, E – five observers
Regner et al. 2006
67
Lesion size comparison technique
WR - size ratios for width
AR - size ratios for area
A, B, C, D, E – five observers
Lesion size comparison technique
Regner et al. 2006
68
Potential problems: for some lesions it is difficult to distinguish from the
surrounding breast tissue on B-mode images.
Benign fat necrosis
WR - size ratios for width
AR - size ratios for area
A, B, C, D, E – five observers
Regner et al. 2006
Regner et al. 2006
17
Hitachi HI Vision 8500/900
systems
69
70
Acoustic Radiation Force Imaging:
Breast
Nonscirrhous type invasive ductal carcinoma in 29-year-old
woman
ARFI image of an in-vivo breast lesion (an infected lymph node) showing differences in displacement
and recovery response of different tissues to radiation force excitation
Fibroadenoma with in 39-year-old woman
Itoh et al. 2006
In vivo Breast Lymph Node (Reactive, Benign)
B-mode
Nightingale, Trahey et al.
In Vivo Breast Lesions
IDAC
Max. Disp. (~5µm)
Fibroadenoma
ARFI Displacement
(~6.5 µm)
B-mode
ARFI Displacement
(~1.8 µm)
Depth (mm)
B-mode
Lateral Position (mm)
IDAC
Lateral Position (mm)
B-mode
Lateral Position (mm)
Fat Necrosis
Combined
ARFI Image
B-mode
ARFI Displacement
(~5.1 µm)
Typical Lymph Node Histology
Reproduced from Wheater’s Functional
Histology, 4th Ed.
Nightingale et al.; Trahey et al.
Duke University
Lateral Position (mm)
Lateral Position (mm)
Nightingale et al.; Trahey et al.
18
Supersonic Imagine:
Elasticity Imaging of Breast
73
Elasticity Imaging of Prostate cancer
Gray-scale transrectal
ultrasonography
74
Real-time
elastography
Color Doppler ultrasonography
T2-weighted image
Dynamic contrast-enhanced image
Histopathology
Sumura et al., 2007
75
Real-time (30 fps) Strain Imaging of Prostate:
Digital System, 7.5 MHz
Ruhr Center of Competence for Medical Engineering
Bochum, Germany (http://www.hf.ruhr-uni-bochum.de)
Elastography of Thermal Lesions in the Liver
after RF Ablation
76
Varghese et al. 2002
19
Monitoring liver stiffness after RF ablation
77
Before RF Ablation
Canine liver tissue in vitro
normal liver
Ex Vivo RF Liver Ablation
After RF Ablation
liver with a lesion
after RF ablation
Bharat et al., 2005
Staging of Liver Fibrosis with Radiation Force
Nightingale et al.; Trahey et al.
80
Fibroscan
Key clinical question is degree to which liver fibrosis has occurred
Biopsy? Imaging?
Quantitative measure of liver stiffness is needed
SWEI: new shear wave speed estimation approach
eliminates 2nd order differentiation
Nightingale et al.; Trahey et al.
http://www.echosens.com
20
Non-invasive staging of liver fibrosis
81
82
SuperSonic Imagine:
ShearWave Elastography
In vivo assessment of Young’s modulus in a healthy volunteer
A. Real-time elastography; B. Aspartate transaminase-to-platelet ratio index; C. Elasticity- laboratory combination values
Friedrich-Rust et al. 2007
Ulrasonix Sonix RP
Imaging System
83
Deffieux at al. 2007
84
Winprobe Elasticity Imaging System
(FPGA-based solution)
-2%
-1%
www.ultrasonix.com
www.winprobe.com
21
Characterizing lesions - Palpograms
85
86
In vivo acquisition scheme
Intra-coronary
pressure [mmHg]
140
120
100
80
60
40
0
20
40
60
80
100
120
Frame no.
Strain [%]
1.0
0.0
Cespedes, De Korte et al./Ultrasound in Med. & Biol., Vol. 26, No. 3, pp. 385–396, 2000
de Korte, Mastik and van der Steen
Erasmus Medical Center, Rotterdam
http://www.eur.nl/fgg/thorax/elasto/
Eur Heart J 23(5): 405-413 (2002)
87
88
Vascular Strain Imaging using
Arterial Pressure Equalization
3 Dimensional Elastography:
feasibility in a human coronary
Pressure (mmHg)
120
80
40
}
Pulse Pressure
MAP
}
Strain(%)
de Korte, Mastik and van der Steen
Erasmus Medical Center, Rotterdam
http://www.eur.nl/fgg/thorax/elasto/
Kim et al, Weitzel et al
University of Michigan
http://bul.eecs.umich.edu/
22
91
Cardiac
Strain and Strain Rate
Imaging
12
1.5
Strain Rate (Hz)
Strain (%)
6
0
healthy
0
0.5
healthy
diseased
8
60
30
1.0
0
diseased
Strain Rate (Hz)
Physiologic
Pressure
Pressure
Equalization
Kim et al, Weitzel et al
University of Michigan
http://bul.eecs.umich.edu/
90
Clinical Data: 5 healthy, 5 diseased arteries
Strain (%)
89
Vascular Strain Imaging using
Arterial Pressure Equalization
4
0
Kim et al, Weitzel et al
Cardiac Strain and Strain Rate Imaging
92
• Cross-correlation method
high sensitivity
high accuracy
2-D or 2.5-D
computationally intensive
• Gradient velocity method
fast
1-D (axial)
aliasing
• Real-time implementation is
required
D’hooge et al. 2000
Different parametric imaging in 3-/4D display, all from a normal subject. Left to right: The red-blue display of tissue velocity, the colored bands of tissue
tracking and the yellow-blue display of strain rate. In tissue velocity, lighter color represents higher velocities, showing clearly the velocity gradient from base to
apex both in systole and diastole. In tissue tracking, each color represents an interval of 2 mm displacement, as shown by the legend. This means that red
represents 2 – 4 mm displacement, increasing to magenta showing >14 mm at the base. Strain rate shows shortening in yellow to red, lengthening in blue, darker
color represents more deformation. Some inhomogeneity is visible due to noise and dropouts. Top to bottom: Bull's eye display both in systole and diastole (except
tissue tracking), M-mode array from all six walls with apex on top and base at the bottom with ECG and a 3D surface reconstruction, velocity and strain rate in
systole and diastole. The bull's eye projection shows all of the surface, but the area is distorted; the apex is progressively diminished, while the base is overrepresented, the 3D figure shows a representation of the true area, but has to be rotated to see all of the surface. Reconstruction is done from three separate cineloops, synchronized by means of ECG. The ECG at the left is inverted, but is from the same patient, as may be seen by the end of the cycle, where there is noise in
the ECG signal. The aortic annulus and location of the imaging planes are added for orientation.
Støylen, 2003
23
93
Deep Vein Thrombosis (DVT) and
Pulmonary Embolism (PE)
94
Triplex Ultrasound: Grayscale, Doppler, Elasticity
• SpragueSprague-Dawley rats (300 g)
• Surgically induced clots in IVC
• Imaging studies clots at
2-day (acute)
6-day (sub(sub-acute)
9-day (chronic)
• Siemens Sonoline Elegra
9-13 MHz center frequency
• 2-D correlation and strain imaging
Softer
Harder
-0.10
-0.55
Emelianov, Rubin et al, 2000 and 2002
95
2
96
Elasticity Imaging to Age DVT
Can elasticity
imaging age
DVT ?
1.5
1
17 mm
0.5
2
4
6
8
Age (day)
10
• Fitting of data from the first set of
experiments
ε=e(aD+b)
ε – normalized strain
D – age of the clot (day)
• Can first data set predict the age of the
clot in the second set of experiments ?
Xie et al 2004
Second Set of Experiments
(4 rats)
12
12
Estimated age (day)
0
10
11 mm
First Set of Experiments
(learning set, 10 rats)
22 mm
Normalized Strain
2.5
Acute DVT
-20 %
Chronic DVT
0%
-60 %
-6 %
Estimation error:
± 0.8 day
Strain magnitude
8
Ultrasound backscatter
6
4
2
2
4
6
8
True age (day)
10
12
Rubin et al., 2006
24
97
98
3-D Strain
Imaging
3-D Strain
Imaging
• Deformation
3-D motion
• Ultrasound
imaging: 2-D
• 3-D tracking is
needed
• Results:
• Deformation
3-D motion
• Ultrasound
imaging: 2-D
• 3-D tracking is
needed
• Results:
2-D linear array
Siemens Antares
5:1 contrast
1.5% deformation
–
–
–
–
2-D linear array
Siemens Antares
5:1 contrast
1.5% deformation
Hall et al, 2006
Hall et al, 2006
99
Non-linearity in stress-strain relations
100
Imaging of Tissue Non-linearity
90
Elastic Modulus (kPa)
–
–
–
–
Cortex and Medulla
Collective System
60
∂µ
≈ 13
∂ε
40 kPa
30
20 kPa
0
0
5
∂µ
≈3
∂ε
10
Strain (%)
15
Emelianov et al, 1998
Erkamp et al, 1998, 1999
Emelianov et al, 1997
Erkamp et al, 1999
25
101
102
Young’s Modulus (kPa)
Young’s Modulus (E/E0)
Viscoelasticity
Imaging
Remote (i.e., Elasticity Imaging)
6
5
4
3
2
1
0
0
10
20
30
60
Direct (i.e., tissue sample)
50
40
30
20
10
0
0
4
8
12
Strain
Strain (%)
Strain(%)
Elasticity
Creep
Viscosity
Emelianov et al, 1997; Erkamp et al, 1998
103
104
Retardance Time Imaging, T1
Fibroadenoma
ε 0 (x)
In Vivo Patient Studies
strain image sequence ε (x) + ε (x)
0
1
10mm Sonogram
TT11:1
Strain
8
(sec)
10
20
8
40
6
5
60
4
4
80
2
3
100
0
7
6
-2
(sec)
x
T1(x)
strain
Gelatin phantom
with inclusion
having twice the
collagen density
ε ( x, k∆t ) = ε 0 ( x ) + ε 1 ( x ) × (1 − exp( − k∆ t / T1 ( x )))
0
∆t
2∆t
N∆t
time
Michael F. Insana et al. University of Illinois at Urbana-Champaign
http://ultrasonics.bioen.uiuc.edu
IDC
10mm
Sonogram
Strain
8
20
6
4
TT11:4
40
60
10
8
0
6
0
4
0
2
0
Two patients with 1-cm, non-palpable lesions detected mammographically. With the
retardance time image, malignant and benign lesions can be differentiated because of
differences in the collagen ultrastructure between the two lesion types.
Sridhar M, Liu J, Insana MF, “Elasticity imaging of polymeric media,” ASME J Biomechan Eng (in press)
Insana MF, Pellot-Barakat C, Sridhar M, Lindfors K, “Viscoelastic imaging of breast tumor microenvironment with ultrasound,”
J Mammary Gland Biol Neoplasia. 9: 393-404, 2004
Insana MF, “Elasticity imaging,” In: Wiley Encyclopedia of Biomedical Engineering, M Akay, ed., ISBN: 0-471-24967-X, Hoboken: John
Wiley & Sons, Inc., 2006
26
105
Acknowledgements
All who contributed to
the field of Elasticity Imaging and
to this presentation
27