Transcript Ultrasonic Elasticity Imaging

Ultrasonic Elasticity Imaging
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Elasticity Imaging
• Image contrast is based on tissue elasticity
(typically Young’s modulus or shear
modulus).
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Clinical Values
• Remote palpation.
• Quantitative measurement of tissue elastic
properties.
• Differentiation of pathological processes.
• Sensitive monitoring of pathological states.
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Clinical Examples
• Tumor detection by palpation: breast, liver
and prostate (limited).
• Characterization of elastic vessels.
• Monitoring fetal lung development.
• Measurements of intraocular pressure.
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General Method
static force
vibration
object with different
elastic properties
object with different
elastic properties
• Static or dynamic deformation due to
externally applied forces.
• Measurement of internal motion.
• Estimation of tissue elasticity.
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Static Approaches
static force
object with different
elastic properties
• Equation of equilibrium:
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 ij
j 1
x j

 f i  0, i  1,2,3
where ij is the second order stress tensor, f i is the
body force per unit volume in the xi direction.
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Dynamic Approaches
• Wave equation with harmonic excitation:


 2U

2
x
 c 2

 2U
t 2
• Doppler spectrum of a vibrating target:
s (t )  A cos( x t )
 x   0   m cos( L t )
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Nomenclature
• Elastography: general field of elasticity
imaging.
• Sonoelastography: the use of ultrasound for
imaging of tissue elastic parameters.
• The above terms can be combined with
strain, stress, velocity, amplitude, phase,
vibration,…etc.
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Direct Measurement
PC
step-motor
object
RS-232
balance
•Hooke’s law: stress=elastic modulus*strain (=Ce).
•Strain is displacement/original length.
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Typical Results
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Static Approach
PC
Trigger
ADC
step-motor
transducer
P/R
phantom
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Compression Strain Sonoelastography
• Static deformation.
• Displacement is estimated by crosscorrelating the signals pre- and postcompression.
• Strain is the spatial derivative of
displacement.
• Assume uniform or simple stress
distribution.
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Strain Estimation
 u1
 x1
O
Strain
 u2
x2
Pressure
 u1
 u 2 -  u1
e 

 x1
x2
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Baseband Displacement Estimation
 Cross correlation based baseband speckle tracking
B1(t) = A(t- 1)exp(-j 1)
B2(t) = A(t- 2)exp(-j 2)
C(t) = - B1(t+)  B2*()d
1 - 2 = C(0)  
u = V  (1-2)  2
e = u  x
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Complications
• Stress distribution may be complicated.
• Speckle decorrelation due to scatterer redistribution:
– Decorrelation reduces the accuracy of
displacement estimation.
– Temporal stretching may be applied.
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Temporal Stretching
• Pre-compressed signal r1(t)=s(t)*p(t)+n1(t),
where
– s1(t) is the scattering distribution function.
– p(t) is the system’s impulse response.
– n1(t) is measurement noise.
• Post-compressed signal r2(t)=s(t/a-t0)*p(t)+n2(t).
• After stretching r3(t)= r2(at) =s(t-t0)*p(at)+n2(at).
• The scaling factor a=1-e.
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Temporal Stretching
• Accuracy of the correlation based time
delay estimation can be improved,
particularly at large strain.
• Such a model ignores scatterer motion in
lateral and elevational directions.
• Correlation coefficient may be used to
directly estimate strain.
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Multiple step compression strain
sonoelastography
• A static approach.
• Multiple steps of small strains are accumulated for
lower speckle decorrelation.
• Neighboring vertical pixels, instead of pixels from
consecutive frames, are used to avoid aliasing of
the baseband approach (i.e., displacement is less
than quarter wavelength).
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Forward Problem
• Given the distribution of Young’s modulus,
applied force and boundary condition,
predict the strain fields.
• “Plain strain state” is usually created to
reduce the 3D problem to 2D.
• Assuming isotropy, Young’s modulus is
simply three times the shear modulus.
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Inverse Problem
• Given 2D strain distribution, boundary
conditions and applied force, find the
Young’s modulus distribution.
• Both incompressible and compressible
media are treated.
• Reconstruction is based on solving partial
differential equations.
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Tissue Incompressibility
• Soft tissue is often assumed incompressible, i.e.,
total volume is unchanged with applied force.
• Divergence of the displacement vector is zero.
• Incompressibility can be applied to measure lateral
displacement. Note that conventional phase
sensitive techniques are only sensitive to axial
motion. This is the same problem encountered in
Doppler imaging.
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Vibration Amplitude
Sonoelastography.
• Low frequency vibration (20-1000Hz) is
applied externally.
• Tissue under inspection vibrates internally.
• Elasticity is assessed based on amplitude of
the vibration.
• Doppler imaging is used to measure the
vibration.
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Vibration Amplitude
Sonoelastography
Original Signal s (t )  A cos( 0t )
Vibrating velocity v(t )  vm cos( L t )
Inst. frequency of received signal  0   m cos( L t )
 m  2vm 0 cos / c



 m
s (t )  A cos  0t 
sin(  L t )  A  J n (  ) cos( 0t  n L t )
L
n  -


 m 2vm 0


L
 Lc
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Vibration Amplitude
Sonoelastography
• By using Doppler techniques to detect the
vibrating target, and select proper threshold,
softer target (large vibration amplitude) will
be present and stiffer target (small vibration
amplitude) will be absent.
• Bistable images.
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Shear Wave Remote Palpation
• Tissue elasticity is done based on the spatial
and temporal characteristics of the induced
shear wave.
• Shear waves are induced by radiation force
produced by a focused ultrasound beam.
• Shear strain is localized due to high
attenuation.
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