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Journal of Biomechanical Engineering | Volume 135 | Issue 4 | research-article
Research Papers

The Effect of the Variation in ACL Constitutive Model on Joint Kinematics and Biomechanics Under Different Loads: A Finite Element Study

[+] Author and Article Information
Zhixiu Hao

e-mail: haozx@tsinghua.edu.cn

Shizhu Wen

State Key Laboratory of Tribology,
Tsinghua University,
Beijing 100084, PRC

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received June 9, 2012; final manuscript received January 18, 2013; accepted manuscript posted February 19, 2013; published online April 2, 2013. Assoc. Editor: Richard E. Debski.

J Biomech Eng 135(4), 041002 (Apr 02, 2013) (9 pages) Paper No: BIO-12-1228; doi: 10.1115/1.4023696 History: Received June 09, 2012; Revised January 18, 2013; Accepted February 19, 2013
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The biomechanics and function of the anterior cruciate ligament (ACL) have been widely studied using both experimental and simulation methods. It is known that a constitutive model of joint tissue is a critical factor in the numerical simulation. Some different ligament constitutive models have been presented to describe the ACL material behavior. However, the effect of the variation in the ligament constitutive model on joint kinematics and biomechanics has still not been studied. In this paper, a three-dimensional finite element model of an intact tibiofemoral joint was reconstructed. Three ACL constitutive models were compared under different joint loads (such as anterior tibial force, varus tibial torque, and valgus tibial torque) to investigate the effect of the change of the ACL constitutive model. The three constitutive models corresponded to an isotropic hyperelasticity model, a transversely isotropic hyperelasticity model with neo-Hookean ground substance description, and a transversely isotropic hyperelastic model with nonlinear ground substance description. Although the material properties of these constitutive equations were fitted on the same uniaxial tension stress-strain curve, the change of the ACL material constitutive model was found to induce altered joint kinematics and biomechanics. The effect of different ACL constitutive equations on joint kinematics depended on both deformation direction and load type. The variation in the ACL constitutive models would influence the joint kinematic results greatly in both the anterior and internal directions under anterior tibial force as well as some other deformations such as the anterior and medial tibial translations under valgus tibial torque, and the medial tibial translation and internal rotation under varus torque. It was revealed that the transversely isotropic hyperelastic model with nonlinear ground substance description (FE model III) was the best representation of the realistic ACL property by a linear regression between the simulated and the experiment deformation results. But the comparison of the predicted and experiment force of ligaments showed that all the three ACL constitutive models represented similar force results. The stress value and distribution of ACL were also altered by the change in the constitutive equation. In brief, although different ACL constitutive models have been fitted using the same uniaxial tension curve and have the similar longitudinal material property, the ACL constitutive equation should still be carefully chosen to investigate joint kinematics and biomechanics due to the different transverse material behavior.
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Figures

Grahic Jump Location
Fig. 1

The finite element model of an intact tibiofemoral joint

+The finite element model of an intact tibiofemoral joint
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The finite element model of an intact tibiofemoral joint
Grahic Jump Location
Fig. 2

The comparison of the ACL stress-strain curve under three different constitutive models: (a) the uniaxial material behavior; (b) the transverse material behavior. The difference between the uniaxial material behaviors of model II and model III was so slight that difficult to show clearly in the figure. However, the transverse material behaviors simulated by the strain energy functions were greatly different.

+The comparison of the ACL stress-strain curve under three different constitutive models: (a) the uniaxial material behavior; (b) the transverse material behavior. The difference between the uniaxial material behaviors of model II and model III was so slight that difficult to show clearly in the figure. However, the transverse material behaviors simulated by the strain energy functions were greatly different.
View Large  |  Save Figure  |  Download Slide (.ppt)
The comparison of the ACL stress-strain curve under three different constitutive models: (a) the uniaxial material behavior; (b) the transverse material behavior. The difference between the uniaxial material behaviors of model II and model III was so slight that difficult to show clearly in the figure. However, the transverse material behaviors simulated by the strain energy functions were greatly different.
Grahic Jump Location
Fig. 5

The comparison of linear regression analyses between the FE simulated and experimental kinematic results. The x- and y-axis (Y1, Y2, and Y3) corresponded to the experimental and FE simulated kinematic results in model I, model II, and model III, respectively. The regression equations showed that the FE analysis results in model III had the strongest correlated relationship with the experimental results (Y3 = 0.8781X + 0.175, R2 = 0.8016).

+The comparison of linear regression analyses between the FE simulated and experimental kinematic results. The x- and y-axis (Y1, Y2, and Y3) corresponded to the experimental and FE simulated kinematic results in model I, model II, and model III, respectively. The regression equations showed that the FE analysis results in model III had the strongest correlated relationship with the experimental results (Y3 = 0.8781X + 0.175, R2 = 0.8016).
View Large  |  Save Figure  |  Download Slide (.ppt)
The comparison of linear regression analyses between the FE simulated and experimental kinematic results. The x- and y-axis (Y1, Y2, and Y3) corresponded to the experimental and FE simulated kinematic results in model I, model II, and model III, respectively. The regression equations showed that the FE analysis results in model III had the strongest correlated relationship with the experimental results (Y3 = 0.8781X + 0.175, R2 = 0.8016).
Grahic Jump Location
Fig. 4

The distributions of maximal principal stress on ACL with different constitutive models: (a) under 134 N anterior tibial force; (b) under 10 Nm valgus tibial torque; (c) under 10 Nm varus tibial torque. Note: Pro.- Proximal; Dis.- Distal; Ant.- Anterior; Pos.- Posterior.

+The distributions of maximal principal stress on ACL with different constitutive models: (a) under 134 N anterior tibial force; (b) under 10 Nm valgus tibial torque; (c) under 10 Nm varus tibial torque. Note: Pro.- Proximal; Dis.- Distal; Ant.- Anterior; Pos.- Posterior.
View Large  |  Save Figure  |  Download Slide (.ppt)
The distributions of maximal principal stress on ACL with different constitutive models: (a) under 134 N anterior tibial force; (b) under 10 Nm valgus tibial torque; (c) under 10 Nm varus tibial torque. Note: Pro.- Proximal; Dis.- Distal; Ant.- Anterior; Pos.- Posterior.
Grahic Jump Location
Fig. 3

The comparisons of the kinematic result of the tibia in the three models: (a) under 134 N anterior tibial force; (b) under 10 Nm varus tibial torque; (c) under 10 Nm valgus tibial torque. The unit of all the translations was millimeter (mm) and the unit of all the rotation was degree (deg).

+The comparisons of the kinematic result of the tibia in the three models: (a) under 134 N anterior tibial force; (b) under 10 Nm varus tibial torque; (c) under 10 Nm valgus tibial torque. The unit of all the translations was millimeter (mm) and the unit of all the rotation was degree (deg).
View Large  |  Save Figure  |  Download Slide (.ppt)
The comparisons of the kinematic result of the tibia in the three models: (a) under 134 N anterior tibial force; (b) under 10 Nm varus tibial torque; (c) under 10 Nm valgus tibial torque. The unit of all the translations was millimeter (mm) and the unit of all the rotation was degree (deg).
Grahic Jump Location
Fig. 6

The comparison of linear regression analyses between the FE simulated and experimental force results in ligaments. The x- and y-axis (Y1, Y2, and Y3) corresponded to the experimental and FE simulated force results in model I, model II, and model III, respectively. The regression equations and correlation coefficients showed that the force results simulated by the three FE models were similar.

+The comparison of linear regression analyses between the FE simulated and experimental force results in ligaments. The x- and y-axis (Y1, Y2, and Y3) corresponded to the experimental and FE simulated force results in model I, model II, and model III, respectively. The regression equations and correlation coefficients showed that the force results simulated by the three FE models were similar.
View Large  |  Save Figure  |  Download Slide (.ppt)
The comparison of linear regression analyses between the FE simulated and experimental force results in ligaments. The x- and y-axis (Y1, Y2, and Y3) corresponded to the experimental and FE simulated force results in model I, model II, and model III, respectively. The regression equations and correlation coefficients showed that the force results simulated by the three FE models were similar.

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