Relevance of the hyperelastic behavior of cruciate ligaments in the modeling of the human knee joint in sagittal plane
DOI:
https://doi.org/10.17533/udea.redin.n76a15Keywords:
preoperative planning, mechanisms, Davies’ method, hyperelastic behavior, knee modelingAbstract
The rupture of the anterior cruciate ligament (ACL) is the most common injury of the human knee. When surgery is required, it is helpful for orthopedic surgeons to scientifi cally defi ne the best position for the graft, which approximates the functionality of an intact ACL. To accomplish that, it is crucial to estimate the force acting on the ligament (or graft) in response to an external load applied to the knee. This force is called the in-situ force. The objective of this research is to evidence the relevance of the hyperelastic behavior of cruciate ligaments in the two-dimensional modeling of the knee. To achieve this, a sequential method of modeling is proposed based on the theory of mechanisms and Davies’ method. In a fi rst approach the cruciate ligaments are treated as rigid bodies, and in a second approach, as hyperelastic bodies. These two approaches are then compared. The model provides information to assist the preoperative planning, by simulation of the ACL positions and in- situ forces. The proposed methodology consists of four steps and an experimental procedure performed by a robotic manipulator to obtain the in-situ forces. Experimental in-situ forces are used to validate the proposed model. Besides helping the preoperative planning, the model allows verifying two relevant biomechanical hypotheses: 1. During the simulation of the ACL in-situ force, the modeling of the cruciate ligaments as rigid links shows similar results to the modeling, which considers the hyperelastic behavior (more complex). 2. The ACL in-situ force can be well approximated when the knee is modeled as a two-dimensional four bar mechanism. Based on the results it can be concluded that the forces obtained by simulations that consider the hyperelastic behavior of the cruciate ligaments are close to the forces obtained by simulations that consider the cruciate ligaments as rigid bodies. It can also be noted that the simulated results are quite similar to the experimental results, which is important considering that the proposed model is simplified.
Downloads
References
S. Woo, C. Wu, O. Dede, F. Vercillo, S. Noorani. “Biomechanics and anterior cruciate ligament reconstruction”. Journal of Orthopaedic Surgery and Research. Vol. 1. 2006. pp. 1-9.
K. Olanlokun, D. Wills. “A spatial model of the knee for the preoperative planning of knee surgery”. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine. Vol. 216. 2002. pp. 63-75.
N. Sancisi, V. Parenti. “A 1 dof parallel spherical wrist for the modelling of the knee passive motion”. Mechanism and Machine Theory. Vol. 45. 2010. pp. 658- 665.
A. Ottoboni, V. Parenti, A. Leardini. On the limits of the articular surface approximation of the human knee passive motion models. Proceedings of the 17th AIMeTA Congress of Theoretical and Applied Mechanics. Firenze, Italy. 2005. pp. 1-11.
N. Sancisi, D. Zannoli, V. Parenti, C. Belvedere, A. Leardini. “A one-degree-of-freedom spherical mechanism for human knee joint modelling”. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine. Vol. 225. 2011. pp. 725-735.
S. Woo, S. Abramowitch, R. Kilger, R. Liang. “Biomechanics of knee ligaments: injury, healing, and repair”. Journal of biomechanics. Vol. 39. 2006. pp. 1-20.
S. Woo, R. Fox, M. Sakane, G. Livesay, T. Rudy, F. Fu. “Biomechanics of the ACL: Measurements of in-situ force in the ACL and knee kinematics”. The Knee. Vol. 5. 1998. pp. 267-288.
T. Davies. “Freedom and constraint in coupling networks”. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. Vol. 220. 2006. pp. 989-1010.
T. Davies. “Circuit actions attributable to active couplings”. Mechanism and Machine Theory. Vol. 30. 1995. pp. 1001-1012.
L. Laus, H. Simas, D. Cruz, D. Martins. “Efficiency of gear trains determined using graph and screw theories”. Mechanism and Machine Theory. Vol. 1. 2012. pp. 296-325.
D. Ponce, C. Roesler, D. Martins. “A human knee joint model based on screw theory and its relevance for preoperative planning”. Mecánica Computacional. Vol. 31. 2013. pp. 3847-3871.
D. Ponce, D. Martins, C. Roesler, F. Rosa, A. Ocampo. Modeling of human knee joint in sagittal plane considering elastic behavior of cruciate ligaments. Proceedings of the 22nd International Congress of Mechanical Engineering (COBEM). São Paulo, Brazil. 2013. pp. 5853-5864.
D. Pioletti, L. Rakotomanana, P. Leyvraz. “Strain rate effect on the mechanical behavior of the anterior cruciate ligament–bone complex”. Medical Engineering & Physics. Vol. 21. 1999. pp. 95-100.
J. O’Connor, T. Shercliff, E. Biden, J. Goodfellow. “The geometry of the knee in the sagittal plane”. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine. Vol. 203. 1989. pp. 223-233.
J. O’Connor, A. Zavatsky. “ACL function in the normal knee”. Biomecánica. Vol. 3. 1995. pp. 121-132.
P. Williams, G. Peura, A. Hoffman. A model of knee motion in the sagittal plane. Proceedings of the IEEE Seventeenth Annual Northeast, Bioengineering Conference. Worcester, USA. 1991. pp. 273-274.
J. Bradley, D. Fitzpatrick, D. Daniel, T. Shercliff, J. O’Connor. “Orientation of the cruciate ligament in the sagittal plane”. Journal of Bone and Joint Surgery. Vol. 70. 1988. pp. 94-99.
B. Clement, G. Drouin, G. Shorrock, P. Gely. “Statistical analysis of knee ligament lengths”. Journal of Biomechanics. Vol. 22. 1989. pp. 767-774.
R. Crowninshield, M. Pope, R. Johnson. “An analytical model of the knee”. Journal of Biomechanics. Vol. 9. 1976. pp. 397-405.
C. Wang, P. Walker, B. Wolf. “The effects of flexion and rotation on the length patterns of the ligaments of the knee”. Journal of Biomechanics. Vol. 6. 1973. pp. 587- 592.
F. Freudenstein. “Approximate synthesis of four-bar linkages”. Resonance. Vol. 15. 2010. pp. 740-767.
J. Selig. “Rigid Transformations”. Introductory Robotics. 1st ed. Ed. Prentice Hall. London, UK. 1992. pp. 7-18.
L. Tsai. “Basic Concepts of Graph Theory”. Mechanism Design: Enumeration of Kinematic Structures According to Function. 1st ed. Ed. CRC Press LLC. New York, USA. 2001. pp. 33-58.
T. Davies. “Mechanical networks—iii wrenches on circuit screws”. Mechanism and Machine Theory. Vol. 18. 1983. pp. 107-112.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Revista Facultad de Ingeniería Universidad de Antioquia
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Revista Facultad de Ingeniería, Universidad de Antioquia is licensed under the Creative Commons Attribution BY-NC-SA 4.0 license. https://creativecommons.org/licenses/by-nc-sa/4.0/deed.en
You are free to:
Share — copy and redistribute the material in any medium or format
Adapt — remix, transform, and build upon the material
Under the following terms:
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
NonCommercial — You may not use the material for commercial purposes.
ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
The material published in the journal can be distributed, copied and exhibited by third parties if the respective credits are given to the journal. No commercial benefit can be obtained and derivative works must be under the same license terms as the original work.
