Biphasic Analysis of Cartilage Stresses in the Patellofemoral Joint

Abstract

The objective of this study was to examine the state of stress within the solid matrix of articular cartilage in the patellofemoral joint, using anatomically faithful biphasic models of the articular layers, with the joint subjected to physiologic muscle force magnitudes. Finite element models of five joints were created from human cadaver knees. Biphasic sliding contact analyses were performed using FEBio software to analyze the response of the joint from 30 to 60 degrees of knee flexion. Results demonstrated that the collagen matrix always sustains tensile stresses, despite the fact that the articular layers are loaded in compression. The principal direction of maximum solid stresses was consistent with the known orientation of collagen fibrils in cartilage. The magnitudes of these tensile stresses under muscle forces representative of activities of daily living were well below tensile failure stresses reported in the prior literature. Results also hinted that solid matrix stresses were higher in the patellar versus femoral superficial zone. These anatomically correct finite element models predicted outcomes consistent with our understanding of structure-function relationships in articular cartilage, while also producing solid matrix stress estimates not observable from experiments alone, yet highly relevant to our understanding of tissue degeneration.

Keywords

cartilage mechanics - fibrous tissue - finite element analysis - biphasic contact

• References

• 1 Grelsamer RP, Dejour D, Gould J. The pathophysiology of patellofemoral arthritis. Orthop Clin North Am 2008; 39 (3) 269-274 , v
• 2 Buckwalter JA, Mankin HJ, Grodzinsky AJ. Articular cartilage and osteoarthritis. Instr Course Lect 2005; 54: 465-480
• 3 Ahmed AM, Burke DL, Yu A. In-vitro measurement of static pressure distribution in synovial joints—Part II: retropatellar surface. J Biomech Eng 1983; 105 (3) 226-236
• 4 Huberti HH, Hayes WC. Patellofemoral contact pressures. The influence of q-angle and tendofemoral contact. J Bone Joint Surg Am 1984; 66 (5) 715-724
• 5 Huberti HH, Hayes WC. Contact pressures in chondromalacia patellae and the effects of capsular reconstructive procedures. J Orthop Res 1988; 6 (4) 499-508
• 6 Haut RC. Contact pressures in the patellofemoral joint during impact loading on the human flexed knee. J Orthop Res 1989; 7 (2) 272-280
• 7 Elias JJ, Cosgarea AJ. Computational modeling: an alternative approach for investigating patellofemoral mechanics. Sports Med Arthrosc Rev 2007; 15 (2) 89-94
• 8 van Eijden TM, Kouwenhoven E, Weijs WA. Mechanics of the patellar articulation. Effects of patellar ligament length studied with a mathematical model. Acta Orthop Scand 1987; 58 (5) 560-566
• 9 Hirokawa S. Three-dimensional mathematical model analysis of the patellofemoral joint. J Biomech 1991; 24 (8) 659-671
• 10 Shah KS, Saranathan A, Koya B, Elias JJ. Finite element analysis to characterize how varying patellar loading influences pressure applied to cartilage: model evaluation. Comput Methods Biomech Biomed Engin 2015; 18 (14) 1509-1515
• 11 Dhaher YY, Kahn LE. The effect of vastus medialis forces on patello-femoral contact: a model-based study. J Biomech Eng 2002; 124 (6) 758-767
• 12 van Eijden TM, Kouwenhoven E, Weijs WA. The influence of anterior displacement of the tibial tuberosity on patellofemoral biomechanics. Int Orthop 1987; 11 (3) 215-221
• 13 Benvenuti JF, Rakotomanana L, Leyvraz PF, Pioletti DP, Heegaard JH, Genton MG. Displacements of the tibial tuberosity. Effects of the surgical parameters. Clin Orthop Relat Res 1997; (343) 224-234
• 14 Cohen ZA, Henry JH, McCarthy DM, Mow VC, Ateshian GA. Computer simulations of patellofemoral joint surgery. Patient-specific models for tuberosity transfer. Am J Sports Med 2003; 31 (1) 87-98
• 15 Cohen ZA, Roglic H, Grelsamer RP , et al. Patellofemoral stresses during open and closed kinetic chain exercises. An analysis using computer simulation. Am J Sports Med 2001; 29 (4) 480-487
• 16 Elias JJ, Saranathan A. Discrete element analysis for characterizing the patellofemoral pressure distribution: model evaluation. J Biomech Eng 2013; 135 (8) 81011
• 17 Heegaard J, Leyvraz PF, Curnier A, Rakotomanana L, Huiskes R. The biomechanics of the human patella during passive knee flexion. J Biomech 1995; 28 (11) 1265-1279
• 18 Besier TF, Gold GE, Beaupré GS, Delp SL. A modeling framework to estimate patellofemoral joint cartilage stress in vivo. Med Sci Sports Exerc 2005; 37 (11) 1924-1930
• 19 Islam K, Duke K, Mustafy T, Adeeb SM, Ronsky JL, El-Rich M. A geometric approach to study the contact mechanisms in the patellofemoral joint of normal versus patellofemoral pain syndrome subjects. Comput Methods Biomech Biomed Engin 2015; 18 (4) 391-400
• 20 Mow VC, Kuei SC, Lai WM, Armstrong CG. Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. J Biomech Eng 1980; 102 (1) 73-84
• 21 Armstrong CG, Mow VC. Variations in the intrinsic mechanical properties of human articular cartilage with age, degeneration, and water content. J Bone Joint Surg Am 1982; 64 (1) 88-94
• 22 Holmes MH, Lai WM, Mow VC. Singular perturbation analysis of the nonlinear, flow-dependent compressive stress relaxation behavior of articular cartilage. J Biomech Eng 1985; 107 (3) 206-218
• 23 Mow VC, Gibbs MC, Lai WM, Zhu WB, Athanasiou KA. Biphasic indentation of articular cartilage—II. A numerical algorithm and an experimental study. J Biomech 1989; 22 (8–9) 853-861
• 24 Park S, Krishnan R, Nicoll SB, Ateshian GA. Cartilage interstitial fluid load support in unconfined compression. J Biomech 2003; 36 (12) 1785-1796
• 25 Soltz MA, Ateshian GA. Experimental verification and theoretical prediction of cartilage interstitial fluid pressurization at an impermeable contact interface in confined compression. J Biomech 1998; 31 (10) 927-934
• 26 Krishnan R, Kopacz M, Ateshian GA. Experimental verification of the role of interstitial fluid pressurization in cartilage lubrication. J Orthop Res 2004; 22 (3) 565-570
• 27 Ateshian GA, Lai WM, Zhu WB, Mow VC. An asymptotic solution for the contact of two biphasic cartilage layers. J Biomech 1994; 27 (11) 1347-1360
• 28 Ateshian GA, Wang H. A theoretical solution for the frictionless rolling contact of cylindrical biphasic articular cartilage layers. J Biomech 1995; 28 (11) 1341-1355
• 29 Schinagl RM, Gurskis D, Chen AC, Sah RL. Depth-dependent confined compression modulus of full-thickness bovine articular cartilage. J Orthop Res 1997; 15 (4) 499-506
• 30 Krishnan R, Park S, Eckstein F, Ateshian GA. Inhomogeneous cartilage properties enhance superficial interstitial fluid support and frictional properties, but do not provide a homogeneous state of stress. J Biomech Eng 2003; 125 (5) 569-577
• 31 Kwak SD, Ahmad CS, Gardner TR , et al. Hamstrings and iliotibial band forces affect knee kinematics and contact pattern. J Orthop Res 2000; 18 (1) 101-108
• 32 Ateshian GA, Henak CR, Weiss JA. Toward patient-specific articular contact mechanics. J Biomech 2015; 48 (5) 779-786
• 33 Maas SA, Ellis BJ, Ateshian GA, Weiss JA. FEBio: finite elements for biomechanics. J Biomech Eng 2012; 134 (1) 011005
• 34 Kwak SD, Blankevoort L, Ateshian GA. A mathematical formulation for 3D quasi-static multibody models of diarthrodial joints. Comput Methods Biomech Biomed Engin 2000; 3 (1) 41-64
• 35 Ateshian GA, Maas S, Weiss JA. Finite element algorithm for frictionless contact of porous permeable media under finite deformation and sliding. J Biomech Eng 2010; 132 (6) 061006
• 36 Meyer SA, Brown TD, Pedersen DR, Albright JP. Retropatellar contact stress in simulated patella infera. Am J Knee Surg 1997; 10 (3) 129-138
• 37 Ateshian GA. The role of interstitial fluid pressurization in articular cartilage lubrication. J Biomech 2009; 42 (9) 1163-1176
• 38 Lai WM, Hou JS, Mow VC. A triphasic theory for the swelling and deformation behaviors of articular cartilage. J Biomech Eng 1991; 113 (3) 245-258
• 39 Maroudas AI. Balance between swelling pressure and collagen tension in normal and degenerate cartilage. Nature 1976; 260 (5554) 808-809
• 40 Meachim G, Denham D, Emery IH, Wilkinson PH. Collagen alignments and artificial splits at the surface of human articular cartilage. J Anat 1974; 118 (Pt 1) 101-118
• 41 Aspden RM, Hukins DW. Collagen organization in articular cartilage, determined by X-ray diffraction, and its relationship to tissue function. Proc R Soc Lond B Biol Sci 1981; 212 (1188) 299-304
• 42 Abernethy PJ, Townsend PR, Rose RM, Radin EL. Is chondromalacia patellae a separate clinical entity?. J Bone Joint Surg Br 1978; 60-B (2) 205-210
• 43 Ficat RP, Philippe J, Hungerford DS. Chondromalacia patellae: a system of classification. Clin Orthop Relat Res 1979; (144) 55-62
• 44 Repo RU, Finlay JB. Survival of articular cartilage after controlled impact. J Bone Joint Surg Am 1977; 59 (8) 1068-1076
• 45 Kempson GE. Relationship between the tensile properties of articular cartilage from the human knee and age. Ann Rheum Dis 1982; 41 (5) 508-511
• 46 Huang AH, Baker BM, Ateshian GA, Mauck RL. Sliding contact loading enhances the tensile properties of mesenchymal stem cell-seeded hydrogels. Eur Cell Mater 2012; 24: 29-45