A mathematical model of the patellofemoral joint

van Eijden, T. M. G. J.; Kouwenhoven, E.; Verburg, J.; Weijs, W. A.

Affiliations

¹Department of Anatomy and Embryology, University of Amsterdam, Meibergdreef 15. 1105 AZ Amsterdam, The Netherlands

²Department of Medical Physics, University of Amsterdam, Meibergdreef 15. 1105 AZ Amsterdam, The Netherlands

Abstract

A mathematical model of the patellofemoral joint taking into account movements and forces in the sagittal plane is described. The system parameters of the model are the locations of the attachments of the quadriceps muscle and the patellar ligament, the length of the patellar ligament, the dimensions of the patella and the geometry of the articulating surfaces. They were obtained from ten autopsy knees. The model enables calculation of the relative position of the patella, patellar ligament and quadriceps tendon, the location of the patellofemoral contact point and the magnitude of the patellofemoral compression force and the force in the patellar ligament as a function of the location of the tibial tuberosity at different flexion-extension angles of the knee. The model is validated by comparing model data with experimentally determined data.

Links

DOI: 10.1016/0021-9290(86)90154-5

PubMed: 3700434

WoS: A1986A999100005

History

Received: 1985-03-23

Revised: 1985-10-1

Cited Works (5)

Year	Entry
1973	Smidt GL. Biomechanical analysis of knee flexion and extension. J Biomech. January 1973;6(1):79-92.
1984	Huberti HH, Hayes WC, Stone JL, Shybut GT. Force ratios in the quadriceps tendon and ligamentum patellae. J Orthop Res. 1984;2(1):49-54.
1976	Crowninshield R, Pope MH, Johnson RJ. An analytical model of the knee. J Biomech. 1976;9(6):397-405.
1984	Huberti HH, Hayes WC. Patellofemoral contact pressures: the influence of Q-angle and tendofemoral contact. J Bone Joint Surg. June 1984;66A(5):715-724.
1980	Wismans J, Veldpaus F, Janssen J, Huson A, Struben P. A three-dimensional mathematical model of the knee-joint. J Biomech. 1980;13(8):677-685.

Cited By (32)

Year	Entry
1990	Yamaguchi GT. Performing whole-body simulations of gait with 3-D, dynamic musculoskeletal models. In: Winters JM, Woo SL-Y, eds. Multiple Muscle Systems: Biomechanics and Movement Organization. New York, NY: Springer-Verlag; 1990:663-679.
2020	Shu L, Li S, Sugita N. Systematic review of computational modelling for biomechanics analysis of total knee replacement. Biosurf Biotribol. March 2020;6(1):3-11.
2001	Weiss JA, Gardiner JC. Computational modeling of ligament mechanics. Crit Rev Biomed Eng. 2001;29(3):303-371.
1989	Yamaguchi GT, Zajac FE. A planar model of the knee joint to characterize the knee extensor mechanism. J Biomech. 1989;22(1):1-10.
1989	Essinger JR, Leyvraz PF, Heegard JH, Robertson DD. A mathematical model for the evaluation of the behaviour during flexion of condylar-type knee prostheses. J Biomech. 1989;22(11-12):1229-1241.
1991	Hirokawa S. Three-dimensional mathematical model analysis of the patellofemoral joint. J Biomech. 1991;24(8):659-671.
1992	Lafortune MA, Cavanagh PR, Sommer HJ III, Kalenak A. Three-dimensional kinematics of the human knee during walking. J Biomech. April 1992;25(4):347-357.
1995	Heegaard J, Leyvraz PF, Curnier A, Rakotomanana L, Huiskes R. The biomechanics of the human patella during passive knee flexion. J Biomech. November 1995;28(11):1265-1279.
2015	Hicks JL, Uchida TK, Seth A, Rajagopal A, Delp SL. Is my model good enough? best practices for verification and validation of musculoskeletal models and simulations of movement. J Biomech Eng. February 2015;137(2):020905.
1995	Bendjaballah MZ, Shirazi-Adl A, Zukor DJ. Biomechanics of the human knee joint in compression: reconstruction, mesh generation and finite element analysis. Knee. June 1995;2(2):69-79.
2014	Adams MJ. Multi-Scale Modeling and Analysis Via Surrogate Modeling Techniques for in Vivo Knee Loading Predictions [Master's thesis]. Colorado School of Mines; 2014.
1998	Piazza SJ. Simulation-Based Design of Total Knee Replacements [PhD thesis]. Evanston, IL: Northwestern University; December 1998.
1996	Bendjaballah MZ. Modélisation et analyse par éléments finis d'un genou humain [PhD thesis]. École polytechnique de Montréal; October 1996.
2002	Moglo KE. Analyse non linéaire par éléments finis du genou humain sous charges complexes en flexion [PhD thesis]. École polytechnique de Montréal; October 2002.
2012	Marouane H. Effet de la force de compression sur la réponse passive de l'articulation du genou: Une étude numérique non-linéaire [Master's thesis]. École polytechnique de Montréal; November 2012.
2014	Adouni M. Analyse biomécanique de l'articulation de genou durant la bipédie humaine [PhD thesis]. École polytechnique de Montréal; July 2014.
2021	Wheatley MGA. Why Do We Have Patellae? An Investigation of Patellofemoral Function and Dysfunction [PhD thesis]. Queen's University; November 2021.
1989	Yamaguchi GT. Feasibility and Conceptual Design of Functional Neuromuscular Stimulation Systems for the Restoration of Natural Gait to Paraplegics Based on Dynamic Musculoskeletal Models [PhD thesis]. Stanford University; August 1989.
1997	Sheehan FT. A Non-Invasive, in Vivo Study of the Patella Using Cine Phase Contrast Magnetic Resonance Imaging: 3D Kinematics and Tendon Strain [PhD thesis]. Stanford University; August 1997.
2006	Shin CS. The Development, Validation, and Applications of a Three-Dimensional Dynamic Specimen-Specific Knee Model to Study Acl Strain [PhD thesis]. Stanford University; September 2006.
2010	McWalter EJ. In Vivo Assessments of Patellofemoral Kinematics and Contact Areas With Applications to Osteoarthritis [PhD thesis]. Vancouver, BC: University of British Columbia; September 2010.
1996	Hasler EM. In-Vivo Knee Loading Before and After ACL Transection in an Animal Model [PhD thesis]. Calgary, AB: University of Calgary; September 1996.
1996	Stergiou P. Biomechanical Factors Associated With Patellofemoral Pain Syndrome in Runners [Master's thesis]. Calgary, AB: University of Calgary; January 1996.
2000	Kralovic BJ. The Effects of Patellofemoral Kinematics on Joint Congruence and Cartilage Stresses [Master's thesis]. Calgary, AB: University of Calgary; January 2000.
2002	Baker SN. In-Vivo Quantification of Patellofemoral Joint Contact Force Using a Mathematical Model [Master's thesis]. Calgary, AB: University of Calgary; January 2002.
1995	Hsieh Y-F. Tibiofemoral and Patellofemoral Mechanics in the Anterior Cruciate Ligament Reconstructed Knee [PhD thesis]. University of Illinois at Chicago; 1995.
1988	Son K. Biomechanical Analyses of Weight-Moving Tasks in the Seated Position [PhD thesis]. University of Michigan; 1988.
2013	Deneweth JM. Mapping the Biomechanical Properties of Human Knee Cartilage [PhD thesis]. University of Michigan; 2013.
1996	Powers CM. The Role of the Vasti in Patellar Kinematics and Patellofemoral Pain [PhD thesis]. University of Southern California (USC); May 1996.
2003	Ward SR. The Influence of Patella Alta on Knee Extensor Mechanics and Patellofemoral Joint Stress [PhD thesis]. University of Southern California (USC); December 2003.
1994	Ziegler JM. A Dynamic Computational Model of the Human Knee Joint With Implementation in Two Optimal Control Models [PhD thesis]. University of Texas at Austin; August 1994.
1997	Shelburne KB. Modeling the Mechanics of the Normal and Reconstructed Knee Joint [PhD thesis]. University of Texas at Austin; May 1997.