UNCORRECTED PROOF
H. Lin et al. / Viscoelastic properties of normal rat liver measured by ultrasound elastography 3
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in a common frequency range between 25.0 and 62.5 Hz and validates MRE as a method for investi-
gating the rheology of liver tissue. Bernal et al. [30] used SSI (20–400 Hz) to measure the viscoelastic
properties of blood clots and carried out classical rheometry experiments (0.25–25 Hz) on the same
blood samples taken within the first few seconds of coagulation. A similar work was conducted earlier
by Schmitt et al. to characterize blood clot viscoelasticity by dynamic ultrasound elastography [31].
The studies mentioned above showed that elasticity measured by elastography was in good agreement
with that measured by rheological tests. However, few studies have tried to validate the viscosity ob-
tained by elastography. Specifically, elastography and rheological tests usually use different frequency
bands that typically range from 100 to 600 Hz for elastography and 0 to 50 Hz for rheometry. This raises
the question of the effect of frequency on the viscoelastic results as measured by the two methods. More
importantly, with complementary frequency ranges, would the two methods provide mutual information
about the rheological behavior of the tissue, and better characterize its elastic and viscous components,
compared with a single method? Addressing these questions could considerably advance the develop-
ment and application of ultrasound elastography and, consequently, contribute to better understanding
of the rheological behavior of the tissue.
The present study used an ultrasound elastography method called shearwave dispersion ultrasound
vibrometry (SDUV) and classic rheometry test to measure the shear viscoelastic modulus of rat liver.
Because the frequency ranges of the two methods were different, we could not directly compare the
results of the two methods. Instead, the dispersive data from the two methods were combined to assess
the viscoelastic properties of liver in a reasonable way. The goal was twofold. First, we aimed to demon-
strate the validity of SDUV for quantitatively measuring liver viscoelasticity by correlating it with the
conventional rheometric techniques. Second, we combined the dispersive data from both methods to
explore the rheological behavior of liver over a broader frequency range.
2. Methods
2.1. Theory
Rheological tests measure the dynamic mechanical behavior of biological tissues. A sinusoidal shear
strain ε(t) = ε
0
e
iωt
is imposed on the tissue to induce a sinusoidal shear stress σ(t) = σ
0
e
i(ωt+δ)
.The
ratio of stress to strain is represented as the complex shear modulus [32]:
G(ω) =
σ
0
e
i(ωt+δ)
ε
0
e
iωt
=
σ
0
ε
0
(cos δ + i sin δ) = G
(ω) + iG
(ω), (1)
where ε
0
is the shear strain amplitude, σ
0
is the shear stress amplitude, ω is the angular frequency, δ is
the phased-shifted angle, and G
and G
are the storage modulus and loss modulus, respectively. The
complex modulus can be related to elasticity and viscosity by different rheological models. In this study,
we used the following rheological models (Fig. 1), which consist of different combinations of a spring
and a dashpot.
The relationship between the complex modulus and the viscoelastic parameters are as follows [33]:
G(ω) = G
+ iG
=
⎧
⎪
⎪
⎨
⎪
⎪
⎩
μη
2
ω
2
μ
2
+ω
2
η
2
+ i
μ
2
ηω
μ
2
+ω
2
η
2
Maxwell,
μ + iηω Vo i g t ,
μ
1
μ
2
2
+ω
2
η
2
(μ
1
+μ
2
)
μ
2
2
+ω
2
η
2
+ i
μ
2
2
ηω
μ
2
2
+ω
2
η
2
Zener,
(2)
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