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Medical Engineering and Physics 39 (2017) 66–72

Contents lists available at ScienceDirect

Medical Engineering and Physics

journal homepage: www.elsevier.com/locate/medengphy

Model-dependent and model-independent approaches for evaluating

hepatic ﬁbrosis in rat liver using shearwave dispersion ultrasound

vibrometry

Haoming Lin

, Xinyu Zhang

a , b , c

, Yuanyuan Shen

a , b , c , ∗

, Yi Zheng

, Yanrong Guo

, Ying Zhu

Xianfen Diao

a , b , c

, Tianfu Wang

a , b , c

, Siping Chen

a , b , c

, Xin Chen

a , b , c , ∗

School of Biomedical Engineering, Shenzhen University, Shenzhen, China

National-Regional Key Technology Engineering Laboratory for Medical Ultrasound, Shenzhen, China

Guangdong Key Laboratory for Biomedical Measurements and Ultrasound Imaging, Shenzhen, China

Department of Electrical and Computer Engineering, St. Cloud State University, St. Cloud, MN 56301, USA

a r t i c l e i n f o

Article history:

Received 18 December 2015

Revised 18 October 2016

Accepted 23 October 2016

Keywords:

Liver ﬁbrosis

Shear wave velocity

Dispersion

Elastography

Model-dependent and model-independent

approaches

a b s t r a c t

This study assesses gradations of hepatic ﬁbrosis in rat livers using both model-dependent and model-

independent approaches. Liver ﬁbrosis was induced in 37 rats using carbon tetrachloride (CCl

); 6 rats

served as the controls. Shear wave velocity as a function of frequency, referred to as velocity dispersion,

was measured in vitro by an ultrasound elastography method called shearwave dispersion ultrasound vi-

brometry (SDUV). For the model-dependent approach, the velocity dispersion data were ﬁt to the Voigt

model to solve the viscoelastic modulus. For the model-independent approach, the pattern of the ve-

locity dispersion data was analyzed by linear regression to extract the slope and intercept features. The

parameters obtained by both approaches were evaluated separately using a receiver operating character-

istic (ROC) curve analysis. The results show that, of all the parameters for differentiating between grade

F0–F1 and grade F2–F4 ﬁbrosis, the intercept had the greatest value for the area under the ROC curve.

This ﬁnding suggests that the model-independent approach may provide an alternative method to the

model-dependent approach for staging liver ﬁbrosis.

1. Introduction

Liver ﬁbrosis results from chronic damage to the liver in

conjunction with excessive accumulation of extracellular matrix

protein. The main causes of liver ﬁbrosis include many types of

chronic liver diseases, such as hepatitis virus infection and alco-

holic and non-alcoholic fatty liver disease [1] . The gold standard

for assessing the degree of ﬁbrosis is biopsy. However, liver biopsy

is an invasive procedure with potential complications such as

bleeding and pain [2] . In addition, sampling errors may occur

because an extremely small portion of the liver is sampled and

liver ﬁbrosis is heterogeneously distributed [3] . Therefore, reliable,

simple and non-invasive methods for assessing liver ﬁbrosis are

needed [4,5] .

Recently, a number of ultrasound-based elastography tech-

niques, including strain elastography [6] , transient elastography

(TE) [7,8] , acoustic radiation force impulse (ARFI) imaging [9] ,

∗

Corresponding authors at: School of Biomedical Engineering, Shenzhen Univer-

sity, Shenzhen, China.

E-mail addresses: yyshen@szu.edu.cn (Y. Shen), chenxin@szu.edu.cn (X. Chen).

supersonic shear imaging (SSI) [10] , and shearwave dispersion

ultrasound vibrometry (SDUV) [11] , have been applied to non-

invasively measure the biomechanical properties of the liver for

evaluating ﬁbrosis. These techniques usually apply an external

force or acoustic radiation force to induce a deformation or dis-

placement in the soft tissue and detect the dynamic response

of the soft tissue to these forces, which relates qualitatively or

quantitatively to the mechanical properties of the soft tissue.

Some recent review papers have summarized various current

commercially available elastographic techniques and discussed

their characteristics, limitations and suitability for speciﬁc clinical

applications [12–14] . Of these methods, TE and ARFI have been

widely used in clinical practice for the evaluation of liver ﬁbrosis

and have been validated in large cohorts of patients with chronic

hepatitis B and C, and non-alcoholic fatty liver disease (NAFLD)

[15–22] . For the patients with viral hepatitis, the detection of

signiﬁcant ﬁbrosis (METAVIR score ≥ F2) is clinically important

because it indicates that patients should receive antiviral treat-

ment [23] . It is regarded that both TE and ARFI can provide

reliable measurements of liver stiffness for assessing signiﬁcant

ﬁbrosis and can help to reduce the use of liver biopsies [24] .

http://dx.doi.org/10.1016/j.medengphy.2016.10.007

H. Lin et al. / Medical Engineering and Physics 39 (2017) 66–72 67

Table 1

Model-dependent and model-independent parameters at different ﬁbrosis stages. Num-

bers in parentheses are normalized standard deviations (SD/mean).

Model/non-model Parameter Fibrosis stage

F0 F1 F2 F3 F4

Voigt μ (kPa) 0.81 1.42 1.91 2.35 3.53

(0.14) (0.13) (0.18) (0.17) (0.14)

η (Pa s) 1.07 1.22 1.61 1.6 4 1.61

(0.12) (0.25) (0.17) (0.11) (0.21)

Slope (mm) 3.60 3.00 3.26 3.19 2.23

(0.15) (0.26) (0.19) (0.20) (0.13)

Intercept (kPa) 0.51 1.02 1.48 1. 61 2.86

(0.24) (0.14) (0.21) (0.24) (0.15)

Table 2

The AUROC, sensitivity, and speciﬁcity values of elas-

ticity, viscosity, intercept and slope for staging signif-

icant ﬁbrosis (METAVIR score ≥ F2).

Parameter AUROC Sensitivity Speciﬁcity

Elasticity 0.98 0.90 1.0 0

Viscosity 0.89 1.0 0 0.64

Intercept 0.99 0.90 1.00

Slope 0.42 0.10 0.93

Most of the ultrasound-based elastography techniques use the

group velocity of the shear wave to characterize the stiffness of

liver. The underlying assumption is that the liver is purely elastic

and the dispersion caused by viscosity is neglected. However,

many recent studies have observed that dispersion of the shear

wave occurs in the liver [25,26] , which indicates that a viscoelastic

description may be beneﬁcial. Hence, a viscoelastic description of

the mechanical behavior is more nearly accurate and physically

correct than a purely elastic one. Furthermore, the viscosity as well

as the elasticity of the tissue can provide useful information about

the pathological state of the tissue [27] . Recently, some studies

have examined frequency-dependent shear wave velocity, referred

to as velocity dispersion then applied the dispersion to charac-

terize the tissue in a model-dependent or a model-independent

manner [28–32] . The model-dependent approach assumes that the

behavior of the tissue under investigation accords with a certain

physical model and ﬁts the dispersive properties to the model to

solve the model parameters [33] . Most of the studies that adopted

this approach used the Voigt model to obtain the viscoelasticity

of liver. Alternatively, the model-independent approach directly

obtains features from the dispersive properties without any rhe-

ological model assumptions. Barry et al. used a linear function

to ﬁt the dispersion curve of the shear velocity and obtained the

slope and intercept of the dispersion for assessing liver viscoelastic

properties [30] . They hypothesize that increasing amounts of fat in

the normal liver will increase the slope of shear wave dispersion,

while slightly reducing the speed of sound [30] . This hypothesis

was supported by some studies in phantoms and mouse livers

[30,31] . In a recent paper, Parker reviewed the empirical ﬁndings

across a number of studies and summarized the dispersion (or

slope) range in lean and steatotic livers [34] .

To date, the model-independent approach has only been used

for steatosis. Although Barry et al. suggested increasing collagen

content (more elastic) would increase the dispersion intercept

[30] , they did not conﬁrm the model-independent approach in

liver ﬁbrosis. Information about the change of the dispersion

pattern during ﬁbrosis development is very limited. Our previous

study measured the in vitro viscoelasticity of rat liver with hepatic

ﬁbrosis using shear waves induced by an acoustic radiation force

[35] . The curve of the velocity dispersion was ﬁtted using the

Voigt model to derive the elasticity and viscosity. The objective

of the previous study was to evaluate the diagnostic performance

of viscoelasticity, as obtained by the model-dependent approach,

for staging liver ﬁbrosis. However, we observed several limitations

of the model-dependent approach in that study and expected to

investigate the feasibility of model-independent approach in the

future study. This study is an extension of that previous work.

The goal of this current study was to estimate liver ﬁbrosis using

both model-dependent and model-independent approaches and to

systematically compare the performances of both approaches from

a variety of perspectives.

2. Materials and methods

2.1. Animal model

Liver ﬁbrosis was induced in male Sprague-Dawley (SD) rats

weighing 200 −220 g (Guangdong Medical Laboratory Animal

Center, Guangdong, China). Thirty seven rats were given carbon

tetrachloride (CCl

) for different numbers of days to induce dif-

ferent stages of liver ﬁbrosis (F1–F4) and six healthy rats were

used as a control group (F0). 50% CCl

in olive oil was injected

subcutaneously twice per week. The dose was 0.6 mL/100 g rat

weight the ﬁrst time and 0.3 mL/100 g the remaining times. Three,

ﬁve, eight and ten weeks after the ﬁrst injection, some rats (14,

5, 9, and 9, respectively) were sacriﬁced and the left lateral lobes

of the rat livers were harvested for ultrasound measurements. The

other lobes of the rat livers were ﬁxed in 10% buffered formalin

for histological assessment. The ﬁbrosis stage was ultimately

determined by the histological result, not by the length of time

that the rats had been exposed to CCl

. All of the procedures were

approved by the Animal Care Committee guidelines of Shenzhen

University and the Guangdong Medical Laboratory Animal Center.

2.2. Histological assessment

The excised liver tissues were ﬁxed in 10% formalin solution for

at least 24 h. After washing and dehydrating, they were embedded

in paraﬃn and sliced to a thickness of 7 μm. The paraﬃn slices

were stained with Masson’s trichrome by histopathology tech-

nicians. Two slices from each rat were used for the histological

assessment. The slices were analyzed using an Olympus BX41

microscope by pathologists who were blind to the results of the

ultrasound measurements. The stage of ﬁbrosis was evaluated

according to the METAVIR scoring system [36] .

2.3. Ultrasound measurements

The rat liver samples were measured in vitro by a custom-

made ultrasound system, which can produce a radiation force

and track the shear wave propagation using the SDUV technique.

The excitation sequence for the radiation force consisted of 10

tone bursts, with each tone burst having a central frequency of

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