Finite element analysis of strain-stiffening behaviors of tendons:Compared with shear wave elasticity imaging
Date Issued
2014
Date
2014
Author(s)
Chu, Tang-Ting
Abstract
The function of tendon is to transmit the energy generated by muscles to the bone to help body movement. Tendons play a key role to regulate the force output by releasing or storing the energy in order to present from avoid taking damages. These functionalities depends on its proper tensile stiffness, i.e., the Young''s modulus E of the tendon along the stretching direction of the tendon. Tendon injuries areoften result from an over-use disease, which and isare closely related to the mechanical loading imposed on the tendon during physical activity. Therefore, to study the changes of tendons stiffness with respect to various external loads will help us distinguish between normal and pathological state of tendon and track the effectiveness of treatment. In recent years, the ultrasound-based shear wave elasticity imaging has been widely used to quantify tissue elasticity. Especially in the isotropic, homogeneous and linearly elastic medium, the Young’s modulus can be approximately derived from shear modulus. In our previous ex vivo experiments of SWEI and tensile test, we clearly demonstrated both the shear wave velocities and tensile moduli of the normal/injured tendons increased as the pre-stretches increased. When the tendons were preloaded from 0 to 3N, the tensile moduli of the samples increased from 2.69 to 13.78 MPa, while the mean velocities of shear waves propagating along the longitudinal axis of the tendons increased from 7.29 to 21.40 m/s, Likewise, the tensile moduli in the injured tendons increased from 1.43 to 8.5 MPa as the preloads increased, while the mean velocities of shear waves propagating increased from 6.01 to 17.74 m/s. However, the Young’s modulus derived from shear wave velocities (i.e. E=3ρ(v_s)^2) cannot’t be coincided with the Young’s modulus measured by uniaxial tensile test. In other words, there are few quantitative models available to interpret the SWEI results measured in tendons due to their complex architecture and nonlinear mechanical behaviors. In addition, if we use the transverse isotropic model to characterize the mechanical properties of tendon, we need to measure five elastic constants, C_11, C_13, C_33,C_44 and C_66. These constants can be obtained by measuring the longitudinal and shear wave velocities propagating through tendons. However, in practical use, it is difficult to measure these constants. In order to assist us in building elasticity imaging of tendon, in this study, we used the transverse isotropic model and hyperelastic model to describe the fiber orientation and strain-stiffening behaviors of tendons. A transverse isotropic hyperelastic model using ABAQUS was employed and shear wave propagation was simulated in the modeled tendons when they were pre-stretched by loads varying from 0 to 3 N. Our preliminary results successfully recapitulated the trend of changes of shear wave velocities with respect to different pre-stretches observed in SWEI. The simulated velocity of shear waves propagating along the longitudinal axis of the control tendons increased from 15.9 to 23.61 m/s. On the other hand, the simulated velocity of shear waves propagating along the longitudinal axis of the injured tendons increased from 14.26 to 16.43 m/s. In short, the simulated velocities with respect to various loads in this model agreed well with that measured in ex vivo experiments, especially in the higher stressed level. These results show that merging transverse isotropic model and hyperelastic model appropriately can be used to interpret the changes of elasticity when tendons subjected to loads. Our work provides a quantitative basis to explain the strain-stiffening behaviors of tendons measured by SWEI and highlights the potential of applying SWEI to quantitatively assess mechanical dysfunction of injured tendons.
Subjects
彈性影像
肌腱
剪切波
ABAQUS
數值模擬
Type
thesis
File(s)![Thumbnail Image]()
Loading...
Name
ntu-103-R01945029-1.pdf
Size
23.32 KB
Format
Adobe PDF
Checksum
(MD5):f7499e73bb0dd96e6aaef559b42a09c2