Shear Elastic Modulus Estimation From Indentation and SDUV on Gelatin Phantoms
ABSTRACT Tissue mechanical properties such as elasticity are linked to tissue pathology state. Several groups have proposed shear wave propagation speed to quantify tissue mechanical properties. It is well known that biological tissues are viscoelastic materials; therefore, velocity dispersion resulting from material viscoelasticity is expected. A method called shearwave dispersion ultrasound vibrometry (SDUV) can be used to quantify tissue viscoelasticity by measuring dispersion of shear wave propagation speed. However, there is not a gold standard method for validation. In this study, we present an independent validation method of shear elastic modulus estimation by SDUV in three gelatin phantoms of differing stiffness. In addition, the indentation measurements are compared to estimates of elasticity derived from shear wave group velocities. The shear elastic moduli from indentation were 1.16, 3.40, and 5.6 kPa for a 7%, 10%, and 15% gelatin phantom, respectively. SDUV measurements were 1.61, 3.57, and 5.37 kPa for the gelatin phantoms, respectively. Shear elastic moduli derived from shear wave group velocities were 1.78, 5.2, and 7.18 kPa for the gelatin phantoms, respectively. The shear elastic modulus estimated from the SDUV, matched the elastic modulus measured by indentation. On the other hand, shear elastic modulus estimated by group velocity did not agree with indentation test estimations. These results suggest that shear elastic modulus estimation by group velocity will be bias when the medium being investigated is dispersive. Therefore, a rheological model should be used in order to estimate mechanical properties of viscoelastic materials.
- SourceAvailable from: lbum-crchum.com[show abstract] [hide abstract]
ABSTRACT: In the context of ultrasound dynamic elastography imaging and characterization of venous thrombosis, we propose a method to induce mechanical resonance of confined soft heterogeneities embedded in homogenous media. Resonances are produced by the interaction of horizontally polarized shear (SH) waves with the mechanical heterogeneity. Due to such resonance phenomenon, which amplifies displacements up to 10 times compared to non-resonant condition, displacement images of the underlying structures are greatly contrasted allowing direct segmentation of the heterogeneity and a more precise measurement of displacements since the signal-to-noise ratio is enhanced. Coupled to an analytical model of wave scattering, the feasibility of shear wave induced resonance (SWIR) elastography to characterize the viscoelasticity of a mimicked venous thrombosis is demonstrated (with a maximum variability of 3% and 11% for elasticity and viscosity, respectively). More generally, the proposed method has the potential to characterize the viscoelastic properties of a variety of soft biological and industrial materials.Journal of biomechanics 02/2010; 43(8):1488-93. · 2.66 Impact Factor
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ABSTRACT: Soft tissue characterization and modeling based on living tissues has been investigated in order to provide a more realistic behavior in a virtual reality based surgical simulation. In this paper, we characterize the nonlinear viscoelastic properties of intra-abdominal organs using the data from in vivo animal experiments and inverse FE parameter estimation algorithm. In the assumptions of quasi-linear-viscoelastic theory, we estimated the viscoelastic and hyerelastic material parameters to provide a physically based simulation of tissue deformations. To calibrate the parameters to the experimental results, we developed a three dimensional FE model to simulate the forces at the indenter and an optimization program that updates new parameters and runs the simulation iteratively. We can successfully reduce the time and computation resources by decoupling the viscoelastic part and nonlinear elastic part in a tissue model. The comparison between simulation and experimental behavior of pig intra abdominal soft tissue are presented to provide a validness of the tissue model using our approach.Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. 02/2005; 8(Pt 2):599-606.
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ABSTRACT: Delay estimation is used in ultrasonic imaging to estimate blood or soft tissue motion, to measure echo arrival time differences for phase aberration correction, and to estimate displacement for tissue elasticity measurements. In each of these applications delay estimation is performed using speckle signals which are at least partially decorrelated relative to one another. Delay estimates which utilize such data are subject to large errors known as false peaks and smaller magnitude errors known as jitter. While false peaks can sometimes be removed through nonlinear processing, jitter errors place a fundamental limit on the performance of delay estimation techniques. The authors apply the Cramer-Rao Lower Bound to derive an analytical expression which predicts the magnitude of jitter errors incurred when estimating delays using radio frequency (RF) data from speckle targets. The analytical expression presented includes the effects of signal decorrelation due to physical processes, corruption by electronic noise, and a number of other factors. Simulation results are presented which show that the performance of the normalized cross correlation algorithm closely matches theoretical predictions. These results indicate that for poor signal to noise ratios (0 dB) a small improvement in signal to noise ratio can dramatically reduce jitter magnitude. At high signal to noise ratios (30 dB) small amounts of signal decorrelation can significantly increase the magnitude of jitter errors.< >IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 04/1995; · 1.82 Impact Factor
1706 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 58, NO. 6, JUNE 2011
Shear Elastic Modulus Estimation From Indentation
and SDUV on Gelatin Phantoms
Carolina Amador*, Student Member, IEEE, Matthew W. Urban, Member, IEEE, Shigao Chen, Member, IEEE,
Qingshan Chen, Kai-Nan An, and James F. Greenleaf, Life Fellow, IEEE
Abstract—Tissue mechanical properties such as elasticity are
wave propagation speed to quantify tissue mechanical properties.
It is well known that biological tissues are viscoelastic materials;
therefore, velocity dispersion resulting from material viscoelastic-
ity is expected. A method called shearwave dispersion ultrasound
measuring dispersion of shear wave propagation speed. However,
there is not a gold standard method for validation. In this study,
we present an independent validation method of shear elastic mod-
ulus estimation by SDUV in three gelatin phantoms of differing
stiffness. In addition, the indentation measurements are compared
to estimates of elasticity derived from shear wave group velocities.
The shear elastic moduli from indentation were 1.16, 3.40, and
5.6 kPa for a 7%, 10%, and 15% gelatin phantom, respectively.
SDUV measurements were 1.61, 3.57, and 5.37 kPa for the gelatin
phantoms, respectively. Shear elastic moduli derived from shear
wave group velocities were 1.78, 5.2, and 7.18 kPa for the gelatin
phantoms, respectively. The shear elastic modulus estimated from
the SDUV, matched the elastic modulus measured by indentation.
On the other hand, shear elastic modulus estimated by group ve-
locity did not agree with indentation test estimations. These results
suggest that shear elastic modulus estimation by group velocity
will be bias when the medium being investigated is dispersive.
Therefore, a rheological model should be used in order to estimate
mechanical properties of viscoelastic materials.
Index Terms—Elasticity, indentation, shearwave dispersion ul-
trasound vibrometry (SDUV).
ing methods introduce mechanical excitation to tissue and then
ONINVASIVE measurement of tissue mechanical prop-
erties as an estimator for tissue pathology is an emerging
Manuscript received April 27, 2010; revised August 16, 2010 and December
of current version May 18, 2011. This work was supported in part by National
Institutes of Health under Grant DK082408. Asterisk indicates corresponding
*C. Amador is with the Ultrasound Research Laboratory, Department of
Physiology and Biomedical Engineering, Mayo Clinic College of Medicine,
Rochester, MN 55905 USA (e-mail: firstname.lastname@example.org).
M. W. Urban, S. Chen, and J. F. Greenleaf are with the Ultrasound Re-
search Laboratory, Department of Physiology and Biomedical Engineering,
Mayo Clinic College of Medicine, Rochester, MN 55905 USA (e-mail: urban.
email@example.com; firstname.lastname@example.org; email@example.com).
Q. Chen and K.-N. An are with the Biomechanics Laboratory, Division of
Orthopedic Research, Mayo Clinic College of Medicine, Rochester, MN 55905
USA (e-mail: firstname.lastname@example.org; email@example.com).
Digital Object Identifier 10.1109/TBME.2011.2111419
The first proposed elasticity imaging methods either excite tis-
sue externally, as in ultrasound elastography , or use focused
ultrasound to produce acoustic radiation force to push tissue as
in acoustic radiation force impulse (ARFI) imaging . While
elastography and ARFI are useful approaches, they do not pro-
vide a quantitative measure of tissue stiffness; both methods
typically form a 2-D image providing a relative map of tissue
stiffness. Shear wave propagation speed methods, such as mag-
netic resonance elastography (MRE) , shear wave elasticity
imaging , transient elastography (TE) , and supersonic
shear imaging (SSI) , have been proposed to quantify tissue
mechanical properties. Most of these methods consider a pure
elastic medium to describe the tissue mechanical properties,
therefore only tissue elasticity is quantified.
Shear wave speed csin a pure elastic medium is related to the
shear modulus G, and density ρ by
The wave speed in a given medium can be defined by the ve-
locity of a single frequency component (phase velocity) or the
velocity of the wave packet (group velocity). In a nondispersive
medium, phase velocity is the same as group velocity. In such
circumstance, the wave velocity is independent of frequency. In
contrast, in a dispersive medium, the wave speed is dependent
on frequency; therefore, phase velocity is not the same as group
velocity in a dispersive medium. Dispersion can be caused by
both tissue geometry and material properties.
It has been established that soft biological tissues exhibit
a combination of elastic and viscous behavior . A mate-
rial subject to periodic oscillations exhibits a complex modulus
M(ω) described by 
M(ω) = M1(ω) + jM2(ω)
where the real part M1(ω) is the elastic or storage modulus, and
the imaginary part M2(ω) is the loss or viscous modulus. The
model. The Voigt model has been shown to be appropriate for
describing viscoelastic properties of tissue in the low frequency
range (50–500 Hz) –. The complex shear modulus for
the Voigt model is given by M1(ω) = μ1and M2(ω) = ωμ2,
where μ1is shear elastic modulus and μ2is viscosity .
A few elasticity imaging methods take advantage of the dis-
persive nature of soft tissue and can quantitatively solve for
both tissue elasticity and viscosity , –. Even though
sonoelastography  and SSI  can provide maps of shear
0018-9294/$26.00 © 2011 IEEE
AMADOR et al.: SHEAR ELASTIC MODULUS ESTIMATION FROM INDENTATION AND SDUV ON GELATIN PHANTOMS1707
modulus and viscosity, specialized hardware is necessary to im-
plement both methods.
A method called shearwave dispersion ultrasound vibrome-
try (SDUV) can be used to quantify both tissue shear elasticity
and viscosity by evaluating dispersion of shear wave propaga-
tion speed over a certain bandwidth , . It is desirable to
have an inexpensive, reproducible tool to validate SDUV mea-
surements. Mechanical testing is usually regarded as the gold
standard method, but mechanical testing devices are usually
Chen etal. have reported a quantitative model for asphere vi-
brated by two ultrasound beams in a homogeneous viscoelastic
medium . In this study, a Doppler laser vibrometer was
used to measure the mechanical frequency response of the
sphere. Although this method can estimate material proper-
ties in an independent manner, its main disadvantage is that
the medium around the target must be optically clear. To over-
come this problem, a single element ultrasound transducer can
be used to measure the sphere time-domain response , ,
which was then fit using a model to obtain estimates of the
shear elasticity and viscosity. However, these methods are not
suitable for tissue mechanical properties characterization since
a sphere must be embedded within a homogeneous tissue.
Therefore, a more comprehensive study is needed to validate
as stress-relaxation, quasi-static, and dynamic test have been
used on biological tissues . Mechanical tests had been used
to evaluate the accuracy of elasticity methods such as MRE,
ARFI, and TE. MRE measurements have been compared to
compression tests and dynamic tests on tissue like gelatin phan-
toms of varying elasticity , . An integrated indentation
and ARFI imaging has been used to characterize soft tissue
stiffness . TE measurements have been compared to ten-
sile tests and dynamic test on a tissue like polymers , .
Cross-validation between MRE and ultrasound-based transient
elastography had been made in homogeneous tissue mimick-
ing phantoms , . Dynamic tests allow estimation of
the change in tissue property parameters versus frequency,
but the material needs to be characterized one frequency at
a time. Quasi-static methods include compression tests, ten-
sile tests, and indentation tests. Compared to the others, in-
dentation tests have been widely used to assess the mechan-
ical properties of tissues. Their main advantage is that they
can be applied both ex vivo and in vivo , –. The
indentation test is considered a gold standard test to assess
elastic mechanical properties. Furthermore, it is attractive be-
cause of its widespread use and ease of implementation, with
its only requirement is to have a surface for indenter contact
The purpose of this study is to validate linearity and
phase velocity assumptions of SDUV estimations of shear
elastic modulus with quasi-static indentation measurements
of elastic modulus on gelatin phantoms of differing stiff-
ness. In addition, the indentation measurements are com-
pared to estimates of elasticity derived from shear wave group
tion depth, a is the indenter radius, and h is the material thickness.
Experimental setup, where F is the indentation force, δ is the indenta-
A. Indentation Test
in this study. Fig. 1 illustrates a lateral infinite isotropic elastic
material with a finite thickness resting on a rigid half space.
The material deforms under the action of a rigid axisymmetric
indenter pressed normal to the surface by an axial force F.
Shear tractions between indenter and material are assumed
rigid surface. For a flat-end cylindrical indenter, the effective
shear elastic modulus G is
(1 − ν)
where ν is the Poisson ratio, F is the indentation force, δ is
the indentation depth, a is the indenter radius, h is the material
thickness, and κ is a geometry factor. Values of κ for a range of
a/h and ν have been estimated by Hayes et al. .
B. Principles of SDUV
SDUV applies a focused ultrasound beam to generate har-
monic shear waves or impulse shear waves that propagate out-
ward from the vibration center , . Chen et al. originally
reported using modulated ultrasound to create harmonic shear
toms using shear wave dispersion , . A limitation of this
method was that the modulation frequency had to be changed
width. This method was advanced to make faster measurements
by transmitting repeated tonebursts of ultrasound . A single
toneburst could be used to generate shear wave dispersion but
the SNR at high frequencies may be poor. Although repeated
tonebursts require more acquisition time compared to a single
toneburst, the advantage of using repeated tonebursts is that
shear waves are created that have motion amplitudes with high
SNR at harmonics of the repetition frequency , .
For an isotropic, viscoelastic, homogenous material modeled
using the Voigt model the shear wave propagation speed cs
1708 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 58, NO. 6, JUNE 2011
depends on the frequency of shear wave ωs
where ρ, μ1, and μ2are the density, shear elastic modulus, and
viscosity of the medium, respectively.
The shear wave speed is estimated from its phase measured
at least at two locations separated by Δr along its traveling path
where Δφs= φ1− φ2 is the phase change over the traveled
The shear wave speed is then estimated with (5). Dispersion
measurements at fundamental frequency of 50 Hz and its har-
monics of 100, 150, 200 Hz, etc., are fit by (4) to solve for shear
elastic modulus and viscosity.
A. Gelatin Phantom Characterization
Three sets of gelatin phantoms were made to compare shear
phantoms were made using 300 Bloom gelatin (Sigma-Aldrich,
St. Louis, MO) and glycerol (Sigma-Aldrich, St. Louis, MO)
different values of the shear elastic modulus. A preservative of
potassium sorbate (Sigma-Aldrich, St. Louis, MO) was added
particles (Sigma-Aldrich, St. Louis, MO) with size 20 μm were
also added with a concentration of 0.5% by volume to provide
adequate ultrasonic scattering.
To evaluate the suitability of Hayes’ model, two different
samples (cylindrical shape) thicknesses were used. Similarly,
the impact of sample diameter was evaluated by using three
different sample diameters (four samples of each type) and two
flat-end cylindrical indenter sizes, a 3-mm indenter diameter
and a 2-mm indenter diameter. Table I summarizes the sample
Additionally, a block of gelatin (15 cm × 15 cm × 4 cm) was
made from the same batch of each gelatin solution preparation
for use in SDUV experiments.
B. Indentation Test
Quasi-static unconfined uniaxial indentation experiments
ElectroForce 3200). A 50 g load cell was used to record load as
The sampling frequency was 20 kHz. The noise floor of the
system was about 0.15 mN. The linear region of the force–
displacement curve was defined as described by Zhai et al. .
The absolute difference from the raw data and the fit was cal-
culated. A threshold is equal to three times the system’s floor
noise was set. A data window of approximately 20 samples (5%
SAMPLE CHARACTERIZATION FOR MECHANICAL TEST (FOUR SAMPLES OF
EACH TYPE WERE MADE)
of indenter diameter) was linearly fit. The data window was in-
creased until the absolute difference or error was just below the
threshold. Each sample was compressed four times.
Fig. 2 illustrates the experimental setup. The “Push Trans-
ducer” (custom made with piezo crystals from Boston Piezo-
Optics, Inc., Bellingham, MA) has a diameter of 44 mm, a
center frequency of 3 MHz and a focal length of 70 mm. Shear
waves generated at the transducer focal point propagate through
gelatin phantom and vibration was detected by a single element
diameter of 12.7 mm, a center frequency of 5 MHz and a 50 mm
focus length (Detect Transducer). The “Push Transducer” and
“Detect Transducer” were aligned confocally with a pulse echo
technique using a small sphere as a point target. The force was
localized 5 mm deep into the gelatin phantom surface.
The pulse repetition frequency of the push tonebursts was
50 Hz and the toneburst length was 300 μs. The propagation
of the shear wave was tracked by the single element transducer
in pulse-echo mode over a lateral range of 10 mm. The pulse
repetition frequency of the “Detect Transducer” was 1.6 kHz
for the 7% and 10%. Because the 15% gelatin phantom was
of the “Detect Transducer” for the 15% gelatin phantom was
The ultrasound echoes were digitized at 100 MHz and pro-
cessed by thecross-spectrum analysis previously described 
to estimate the shear phase gradient. The shear wave propaga-
tion speed was calculated by (5) and dispersion measurements
from 50 to 400 Hz were fit by (4) to solve for shear elastic
modulus and viscosity. The group velocity for each phantom
was calculated by evaluating the time shifts in the shear waves
versus position and using
where cgisthe group velocity, and Δt is the time shiftmeasured
over a distance Δr.
AMADOR et al.: SHEAR ELASTIC MODULUS ESTIMATION FROM INDENTATION AND SDUV ON GELATIN PHANTOMS1709
generated by (1) “Push Transducer” coupled to the phantom, transmitting re-
peated tonebursts of ultrasound. A separated transducer acts as the detector (2)
Illustration of the experimental setup. SDUV applies a localized force
During each experiment, the single element transducer was
moved by 1-mm intervals 11 times on y-axis (see Fig. 2). This
of interest. Additionally, SDUV measurements were repeated at
four different regions.
A. Indentation Test
1, see Table I) of 7%, 10%, and 15% gel phantom with a 2-mm
indenter diameter is shown in Fig. 3.
All three phantom samples showed a linear response up to
linear region was 9, 40, and 63 mN for 7%, 10%, and 15%
Table II shows the influence of sample thickness and sample
and 17 times the indenter radii. Similarly, the sample diameter
was approximately 9.2, 13.8, 23.3, and 35 times the indenter
radii. Because the geometry factor κ is not very sensitive to
Poisson’s ratio ν from 0.45 to 0.5 for a/h ratio range from 0.05
to 0.20, the Poisson’s ratio ν was set to 0.475.
The displacement amplitude estimates over 50 ms for 7%
gelatin phantom are shown in Fig. 4 and as calculated by the
cross-spectrum method . The peak displacement amplitude
was approximately 18, 16, and 12 μm at 4, 6, and 8 mm away
from the vibration center.
and 15% gelatin phantoms over 200 ms are shown in Fig. 5.
The frequency at which the amplitude is highest, or the center
frequency of broadband signal, is denoted as ωp. The center
frequencies of the SDUV response, from 0 to 200 ms, were 100
Hz for 7% phantom, 350 Hz for 10% phantom and 100 Hz for
the 15% phantom. The group velocity, is described by Morse
and Ingard as the“velocity of progress of the“center of gravity”
ple type 1, see Table I). The three symbols represent the linear region for the
three gelatin phantoms. The three line types represent the raw data for the three
SHEAR ELASTIC MODULUS (kPa) FOR DIFFERENT SAMPLE DIAMETER d,
INDENTER DIAMETER 2a, AND SAMPLE THICKNESS
The three symbols represent three sets of the measured amplitude for 4, 6, and
8 mm away from the vibration center.
1710 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 58, NO. 6, JUNE 2011
symbols represent 7%, 10%, and 15% gelatin phantoms.
Magnitude spectra of the velocity signals over 200 ms. The three
the vibration center. The three symbols represent 7%, 10%, and 15% gelatin
phantoms. The solid line represents linear regression.
Time shift estimates for the gelatin phantoms over 3–8 mm away from
of a group of waves that differ somewhat in frequency .”
The center of gravity was calculated by 
?ω · |V (ω)|2
of the velocity signal for each gelatin phantom was 200, 350,
and 250 Hz for the 7%, 10%, and 15% gelatin phantoms.
Fig. 6 shows the distance from the vibration center versus
time shift for 7%, 10%, and 15% gel phantoms over 5 mm. The
time shifts were calculated by cross-correlation method .
The solids lines are linear regression for the time shifts. The
group velocity was calculated from (6).
The group velocity (slope of solid lines in Fig. 6) for each
gelatin phantom was 1.33, 2.35, and 3.15 m/s for 7%, 10%,
and 15%, respectively. By assuming a nondispersive medium,
in other words, by setting μ2 = 0 in (4), and also assuming
the vibration center. The four symbols represent four sets of estimated phase
The solid line represents linear regression.
Phase estimates for the 7% gelatin phantom over 3–8 mm away from
a linear elastic material, where group velocity is same as the
phase velocity for all frequencies, the shear elastic modulus by
(1) for the 7%, 10%, and 15% gelatin phantom was 1.77, 5.52,
and 9.92 kPa, respectively.
The phase of shear waves at frequencies 50–400 Hz was es-
timated by Kalman filter . Fig. 7 illustrates the phase of
shear wave at frequencies 100–400 Hz for the 7% gel phan-
tom. There is a linear relation between shear wave phase and
propagation distance. The solid lines are linear regressions for
the phase estimates. The coefficients of determination R2of the
linear regressions were greater than 0.95, 0.97, and 0.96 for the
that the linear assumption of (5) is appropriate.
Fig. 8 shows shear wave propagation speed as a function of
The symbols represent the mean shear wave speed of four
repetitions for each gelatin phantom. Error bars represent the
standard deviation of the measured shear wave speed at each
particular frequency four times. The solid lines are the least
mean square fits from (4) that give a shear elastic modulus of
μ1 = 1.61, 3.30, and 5.37 kPa and viscosity of μ2 = 0.85,
1.43, and 2.14 Pa·s for 7%, 10%, and 15% gelatin phantoms,
respectively. The median absolute error, that is, the median of
the absolute difference between the Voigt model fit and exper-
imental data, was 0.09, 0.14, and 0.23 m/s for 7%, 10%, and
15% gelatin phantom, respectively.
The use of Hayes’ model is suitable for describing small de-
formation indentation on lateral infinite isotropic elastic media.
it is important to satisfy its assumed boundary conditions. Shear
elastic modulus was slightly underestimated when the sample
is caused by the violation of the assumption of lateral infinite
AMADOR et al.: SHEAR ELASTIC MODULUS ESTIMATION FROM INDENTATION AND SDUV ON GELATIN PHANTOMS1711
represent 7, 10 and 15% gelatin phantoms. The solid lines are fits from the
Voigt dispersion model, which gives estimates of shear elastic modulus (μ1)
and viscosity (μ2) shown at the bottom of this figure.
Shear wave speed measured from 50 Hz to 400 Hz. The three symbols
geometry. Not surprisingly, there was not a significant varia-
tion of shear elastic moduli for different sample thickness (see
Table II) for the 7% and 10% gelatin phantom. However, shear
elastic modulus was slightly different for the 15% gelatin phan-
tom for different sample thickness. These observations agree
with finite element method simulations described by Zhai et al.
, suggesting that a sample with 5 kPa of Young’s modulus
is large enough when its thickness and diameter are over 15
times of the indenter radii. Therefore, the shear elastic modulus
for the 7%, 10%, and 15% gelatin phantoms were 1.16, 3.40,
and 5.60 kPa, respectively (see Table II). However, a more suit-
able model should include both sample thickness and sample
diameter in consideration.
The peak displacement amplitude estimated by SDUV was
and therefore within a linear region of a force–displacement
curve. Tissue response to a harmonic excitation using different
voltage amplitudes on the “Push Transducer” has shown a fairly
independent relationship between shear wave speed and excita-
force and displacement . Similarly, the force–displacement
curve from the indentation experiments was linear for up to
were nonlinear for large displacements (larger than 1 mm), in-
dentation can be used to assess elastic components of mechani-
The phase estimates at high frequencies showed more varia-
tent in all three phantoms. Because the displacement amplitude
is decreased at high frequencies, the error of the phase estimates
is expected to increase at high frequencies . However, the
coefficients of determination R2of the linear regressions were
high in all three phantoms.
Table III shows a comparison between group velocity cg,
phase velocity evaluated at center of gravity cs(ωc) and phase
GROUP VELOCITY, PHASE VELOCITY EVALUATED AT CENTER OF GRAVITY AND
PHASE VELOCITY EVALUATED AT CENTER FREQUENCY
ities calculations were close to group velocities for the 7% and
10% gelatin phantom. The magnitude spectrum of the velocity
signal for the 15% phantom (see Fig. 5) was broader compared
to the other phantoms. This could be a reason why the group
velocity for the 15% gelatin phantom was rather different than
the phase velocities. In theory, the group velocity should be
identical or close to the phase velocity csevaluated at ωc.
The shear wave speed versus frequency results in Fig. 8 fits
well with the Voigt model, particularly for the softer phantom.
Stiffer phantoms seem to have peaks at certain frequencies that
deviate from the ideal Voigt model, however the absolute error
between the Voigt model fit and experimental data were not
significantly large. Shear wave estimation may be affected by
tissue geometry depending on the type of wave that is being
excited. For instance, mathematical models for shear wave dis-
persion of antisymmetric Lamb and Rayleigh suggest that shear
quencies when the material thickness is larger than one to two
wavelengths of the wave . Although the largest wavelength,
about 42 mm for the 15% gelatin phantom at 50 Hz, was ap-
proximately equal to the phantom thickness, substantial errors
for measurement of the shear wave speed related to phantom
thickness are not expected. SDUV generates pure shear waves,
that is, a shear wave propagating in an infinite medium; there-
fore, SDUV assumes there are no reflections from boundaries.
In addition, the phase gradient in (5) assumes that there is only
one wave traveling one direction. Therefore, reflections from
the surface may cause variations in the phase and cause errors
in the speed measurements.
ing a complex shear elastic modulus. The compression rate for
the indentation test was 0.1 mm/s and each gelatin showed a lin-
ear response up to 1 mm compression; therefore, the excitation
frequency for indentation test was approximately 0.1 Hz. Be-
cause the excitation frequency from the indentation test is close
to zero, the shear elastic modulus estimation by indentation test
should be the same or close to the real component of the shear
complex modulus on the Voigt model.
Fig. 9 provides a summary of the shear elastic modulus esti-
ror bars represent the standard deviation of the measured shear
elastic modulus for each particular phantom at four different
The shear elastic modulus estimated from group velocity
measurements can definitively differentiate the three phantoms.
1712 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 58, NO. 6, JUNE 2011
test, and group velocity. Mean ± SD, n = 4.
Shear elastic moduluscomparison between phase velocity,indentation
(diamonds and dashed line) and SDUV phase velocity (squares and dotted line).
The continuous line represents an ideal correlation.
Linear correlation comparing indentation test with group velocity
However, these values do not agree well with both the inden-
tation experiment results and phase velocity results, especially
when the phantom is stiffer. This disagreement could be at-
tributed to the fact that gelatin phantoms are dispersive ,
, ; therefore, the wave speed is dependent on frequency.
Shear elastic modulus estimation from the indentation test and
phase velocity for the 7% phantom were slightly different. This
could be due to inhomogeneities on gelatin samples. The cellu-
lose component, introduced for ultrasound scattering, did tend
to settle down in the sample molds while the gelatin was liquid.
Because the 7% gelatin is less viscous, the cellulose distribution
was probably different compared to the other phantoms.
dentation test with group velocity and SDUV phase velocity is
shown in Fig. 10. The correlation coefficients were 0.98 for the
group velocity and 0.99 for the SDUV phase velocity method.
Although the correlation coefficients are similar and large, most
likely because the number of gelatin phantoms is small, the
shear elastic modulus correlation between SDUV phase veloc-
ity method and indentation test is closer to the ideal correlation
(continues line on Fig. 10). On the other hand, the shear elas-
tic modulus correlation between group velocity and indentation
test seem considerably different from the ideal correlation, sug-
gesting that shear elastic modulus estimation by group velocity
will be bias when the medium being investigated is dispersive.
Therefore, a rheological model should be used in order to esti-
mate mechanical properties of viscoelastic materials. Because
tissues are more viscous than these phantoms , , ,
this would be the case for tissues as well. This study shows
acceptable agreement of shear elastic moduli estimates from
SDUV phase velocity method and indentation test on gelatin
Inthispaper, we present an independent validation method of
elastic modulus estimation by SDUV in gelatin phantoms. The
shear elastic modulus, estimated from the SDUV phase velocity
method, matched the elastic modulus measured by the inden-
tation method. The shear elastic modulus estimated by group
velocity did not agree with indentation test estimations. These
results suggest that a rheological model for linear viscoelastic
material must be used to estimate elastic modulus on gelatin
phantoms and soft tissue.
 R. Muthupillai, D. J. Lamos, P. J. Rossman, J. F. Greenleaf, A. Manduca,
and R. L. Ehman, “Magnetic resonance elastography by direct visual-
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New York: McGraw-Hill,
Carolina Amador (S’09) was born in Medellin,
Colombia, on April 14, 1984. She received the B.S.
genieria de Antioquia, Medellin, Colombia, in 2006.
She is currently working toward the Ph.D. degree in
biomedical engineering at the Mayo Clinic College
of Medicine in Rochester, MN.
She has been a visiting undergraduate student at
the Biomedical Imaging Resource at Mayo Clinic,
Rochester, MN. Her research interest includes non-
invasive evaluation of mechanical properties of soft
1714 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 58, NO. 6, JUNE 2011
Matthew W. Urban (S’02–M’07) was born in Sioux
Falls, SD, on February 25, 1980. He received the
B.S. degree in electrical engineering at South Dakota
biomedical engineering at the Mayo Clinic College
of Medicine, Rochester, MN, in 2007.
He is currently an Assistant Professor in the De-
partment of Biomedical Engineering, Mayo Clinic
College of Medicine. He has been a Summer Un-
dergraduate Fellow at the Mayo Clinic Biomechan-
ics Laboratory. His current research interests include
ultrasonic signal and image processing, vibro-acoustography, and vibrometry
Dr. Urban is a member of the Eta Kappa Nu, the Tau Beta Pi, and the Acous-
tical Society of America.
Shigao Chen (M’02) received the B.S. and M.S. de-
grees in biomedical engineering from Tsinghua Uni-
Ph.D. degree in biomedical imaging from the Mayo
Graduate School, Rochester, MN, in 2002.
He is currently an Assistant Professor at Mayo
Graduate School, and an Associate Consultant in De-
partment of Biomedical Engineering, Mayo Clinic
College of Medicine. His research interest includes
noninvasive quantification of viscoelastic properties
of soft tissue using ultrasound.
ical engineering from the University of Memphis,
Memphis, TN, in 2001.
He is a currently a Research Engineer at the Or-
thopedic Biomechanics Laboratory, Mayo Clinic in
Rochester, MN, and an Assistant Professor of Bio-
of more than 50 scientific articles and book chapters,
most being in peer-reviewed journals.
biomaterials, orthopedics, and magnetic resonance
Mr. Chen has received several awards from various societies.
Kai-Nan An received the Ph.D. degree in mechani-
cal engineering and applied mechanics in 1975 from
Lehigh University in Bethlehem, Bethlehem, PA.
Since 1993, he has been the Director of the Or-
thopedic Biomechanics Laboratory, Mayo Clinic in
Rochester, MN, and a Professor of Bioengineering,
Mayo Medical School. He was named the John and
Posy Krehbiel Professor of Orthopedics, Mayo Med-
ical School, in 1993. He is a co-author of more than
700 scientific articles and book chapters, most being
in peer-reviewed journals.
His research interests include biomechanics, biomaterials, orthopedics, and
as a Fellow of the ASME in 2007. He is a founding member of the American
Institute for Medical and Biological Engineering, and serves as advisor to grad-
uate students and research fellows, as well as various medical and engineering
James F. Greenleaf (M’73–SM’84–F’88) was born
in Salt Lake City, UT, on February 10, 1942. He re-
ceived the B.S. degree in electrical engineering from
the University of Utah, Salt Lake City, in 1964, the
engineering science from the Mayo Graduate School
of Medicine, Rochester, MN, and Purdue University,
West Lafayette, IN, in 1970.
He is currently a Professor of Biomedical En-
gineering and an Associate Professor of Medicine,
Mayo Medical School, and a Consultant in Department of Physiology, Bio-
physics, and Cardiovascular Disease and Medicine, Mayo Foundation. He has
12 patents. His special field of interest is ultrasonic biomedical science, and he
has published more than 237 peer-reviewed articles and edited or authored five
books in the field.
Dr. Greenleaf is a recipient of the 1986 J. Holmes Pioneer Award and the
1998 William J. Fry Memorial Lecture Award from the American Institute of
Ultrasound inMedicine,and isaFellow oftheAmerican Institute ofUltrasound
From 1990 to 1991, he was the Distinguished Lecturer for IEEE Ultrasonics,
nical Committee for the Ultrasonics Symposium for seven years. He served on
the IEEE Ultrasonics, Ferroelectrics, and Frequency Control Society (UFFC-S)
Subcommittee on Ultrasonics in Medicine/IEEE Measurement Guide Editors,
and on the IEEE Medical Ultrasound Committee. He was the President of the
UFFC-S in 1991 and the Vice President for Ultrasonics from 1992 to 2003.