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The influence of geometry on the stress distribution in joints — a finite element analysis

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Abstract

The incongruity of human joints is a phenomenon which has long been recognized, and recent CT-osteoabsorptiometric findings suggest that this incongruity influences the distribution of stress in joints during their normal physiological use. The finite element method (FEM) was therefore applied to five different geometric configurations consistent with the anatomy of articular surfaces, and a program with variable contact areas (Marc) was used to calculate the stress distribution for loads of 100 to 6 900 N. The assumption of congruity between head and socket results in a “bell-shaped” distribution of stress with a maximum value of 61.5 N/mm2 in the depths of the socket, decreasing towards zero at its edges. In the model with a flatter socket the von Mises stresses are higher (max. 101.3 N/mm2); with a deeper socket, lower (max. 53.0 N/mm2). If the diameter of the head is greater, the stresses build up from the periphery of the socket and move towards its depths as the load increases. The combination of an oversized head and a deeper socket results in the most satisfactory stress distribution (max. 43.2 N/mm2). These results extend previous photoelastic findings with incongruous joint surfaces. The calculated mechanical conditions show a relationship to the location of osteoarthritic changes, and are reflected by the distribution pattern of subchondral bone density. A more satisfactory stress distribution is found with functionally advantageous, incongruous joint surfaces (oversized head and deepened socket) than in the congruous joint, and a better nutritive situation for the articular cartilage seems likely. The geometry of the joint is therefore a physiologically important and quantifiable factor contributing to an optimized transmission of forces in joints.

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References

  • Afoke NYW, Byers PD, Hutton WC (1980) The incongruous hip joint: a casting study. J Bone Joint Surg 62 B:511–514

    Google Scholar 

  • Bünck S (1990) Krümmungs- und Kontaktflächenverhältnisse der Articulatio humeroradialis. Anat Anz 171:45–53

    Google Scholar 

  • Bullough PG (1981) The geometry of diarthrodial joints, its physiological maintenance, and the possible significance of age-related changes in geometry-to-load distribution and the developement of osteoarthritis. Clin Orthop 156:61–66

    Google Scholar 

  • Bullough PG, Jagannath A (1983) The morphology of the calcification front in articular cartilage. J Bone Joint Surg 65 B:72–78

    Google Scholar 

  • Bullough P, Goodfellow J, Greenwald AS, O'Connor S (1968) Incongruent surfaces in the human hip joint. Nature 217:1290

    Google Scholar 

  • Bullough P, Goodfellow J, O'Connor J (1973) The relationship between degenerative changes and load bearing in the human hip. J Bone Joint Surg 55 B:746–758

    Google Scholar 

  • Brown TD, Vrahas MS (1984) The apparent elastic modulus of the juxtarticular subchondral bone of the femoral head. J Orthop Res 2: 32–38

    Google Scholar 

  • Carter DR (1984) Mechanical loading histories and cortical bone remodeling. Calcif Tissue Int 36:519–524

    Google Scholar 

  • Carter DR, Hayes WC (1977) The compressive behaviour of bone as a two-phased porous structure. J Bone Joint Surg 59 A:954–962

    Google Scholar 

  • Carter DR, Rapperport DJ, Fyhrie DP, Schurmann DJ (1987a) Relation of coxarthrosis to stresses and morphogenesis — a finite element analysis. Acta Orthop Scand 58:611–619

    Google Scholar 

  • Carter DR, Orr TE, Fyhrie DP (1987b) Relationship between loading history and femoral cancellous bone architecture. J Biomech 22: 231–244

    Google Scholar 

  • Carter DR, Wong M, Orr TE (1991) Musculoskeletal ontogeny, phylogeny, and functional adaptation. J Biomech 24:3–16

    Google Scholar 

  • Day WH, Swanson SAV, Fremann MAR (1975) Contact pressures in the loaded human cadaver hip. J Bone Joint Surg 57B:302–313

    Google Scholar 

  • Eckstein F, Müller-Gerbl M, Putz R (1992) Distribution of subchondral bone density and cartilage thickness in the human patella. J Anat 180:425–433

    Google Scholar 

  • Eckstein F, Steinlechner M, Müller-Gerbl M, Putz R (1993a) Mechanische Beanspruchung und subchondrale Mineralisierung des menschlichen Ellbogengelenks — eine CT-osteoabsorptiometrische Studie. Unfallchirurg 96:99–104

    Google Scholar 

  • Eckstein F, Löhe F, Steinlechner M, Müller-Gerbl M, Putz R (1993b) Kontaktflächen des menschlichen Humeroulnargelenks in Abhängigkeit von der Anpreßkraft — ihr Zusammenhang mit subchondraler Mineralisierung und Gelenkflächenmorphologie der Incisura trochlearis. Ann Anat 175:545–552

    Google Scholar 

  • Eckstein F, Löhe F, Schulte E, Müller-Gerbl M, Milz S, Putz R (1993c) Physiological incongruity of the humero-ulnar joint: — a functional principle of optimized stress distribution acting upon articulating surfaces. Anat Embryol 188:449–455

    Google Scholar 

  • Goodfellow JW, Bullough PG (1967) The pattern of aging of the articular cartilage of the elbow joint. J Bone Joint Surg 49 B:174–181

    Google Scholar 

  • Goodfellow JW, Mitsou A (1977) Joint surface incongruity and its maintenance. J Bone Joint Surg 59B:446–451

    Google Scholar 

  • Gray ML, Pizzanelli AM, Grodzinsky AJ, Lee RC (1988) Mechanical and physicochemical determinants of the chondrocyte biosynthetic response. J Orthop Res 6:777–792

    Google Scholar 

  • Greenwald AS (1991) Biomechanics of the hip. In: Steinberg ME (ed) The hip and its disorders. Saunders, Philadelphia, pp 47–56

    Google Scholar 

  • Greenwald AS, O'Connor JJ (1971) The transmission of load through the human hip joint. J Biomech 4:507–528

    Google Scholar 

  • Hackenbroch M (1943) Die Arthrosis deformans der Hüfte. Thieme, Leipzig

    Google Scholar 

  • Hayes WC, Snyder B, Levine BM, Ramaswamy S (1982) Stress — morphology relationships in trabecular bone of the patella. In: Gallgher RH, Simon BR, Johnson PC, Gross JF (eds) Finite elements in biomechics. Wiley, Chichester

    Google Scholar 

  • Huiskes R, Chao EYS (1983) A survey of finite element analysis in orthopedic biomechanics: the first decade. J Biomech 16:385–409

    Google Scholar 

  • Ingelmark BE, Ekholm R (1948) A study on variations in the thickness of articular cartilage in association with rest and periodical load. Acta Soc Med Upsalien 53:61–74

    Google Scholar 

  • Jones IL, Klamfeldt DDS, Sandstrom T (1982) The effect of continuous mechanical pressure upon the turnover of articular cartilage proteoglycans in vitro. Clin Orthop 165:283–289

    Google Scholar 

  • Kempson GE, Spivey CJ, Swanson SAV, Freeman AR (1971) Patterns of cartilage stiffness on normal and degenerate human femoral heads. J Biomech 4:597–609

    Google Scholar 

  • Knauss P (1981) Materialkennwerte und Festigkeitsverhalten des spongiösen Knochengewebes am coxalen Human-Femur. Biomed Tech (Berlin) 26:200–210

    Google Scholar 

  • Kummer B (1968) Die Beanspruchung des menschlichen Hüftgelenks. 1. Allgemeine Problematik. Z Anat Entwicklungsgesch 127:277–285

    Google Scholar 

  • Kummer B, Breul R, Stauss M, Lohscheidt K (1987) Spannungsverteilung über Kugelgelenkflächen. Verh Anat Ges 81:445–446

    Google Scholar 

  • Lewis PR, McCutchen CW (1959) Experimental evidence for weeping lubrication in mammalian joints. Nature 184:1285

    Google Scholar 

  • Löhe F, Eckstein F, Putz R (1993) Dehnung des Lig. transversum acetabuli. Unfallchirurg (in press)

  • Merz BR (1993) Finite Elemente-Analyse von exzidierten Femora basierend auf der quantitativen Computer Tomographie. Dissertation, ETH Zürich

    Google Scholar 

  • Miyanaga Y, Fukubayashi T, Kurosawa H (1984) Contact study of the hip joint. Arch Orthop Trauma Surg 103:13–17

    Google Scholar 

  • Mockenhaupt J (1990) Pressure distribution in partly contacting joints — a computerized simulation model. Anat Anz 171:313–321

    Google Scholar 

  • Müller-Gerbl M, Putz R (1993) Zur Morphologie und Mechanik der Gelenke in Abhängigkeit vom Lebensalter. In: Pesch HJ, Stöß H, Kummer B (eds) Osteologie aktuell VII. Springer Berlin Heidelberg New York, pp 38–41

    Google Scholar 

  • Müller-Gerbl M, Putz R, Kenn R (1992) Demonstration of subchondral bone density patterns by three dimensional CT osteoabsorptiometry as a noninvasive method for in vivo assessment of individual longterm stresses in joints. J Bone Miner Res 7 [Suppl 2]:411–418

    Google Scholar 

  • Müller-Gerbl M, Putz R, Kenn R, Kierse R (1993) People in different age groups show different hip joint morphology. Clin Biomech 8: 66–72

    Google Scholar 

  • Oberländer W, Breul R, Kurrat HJ (1984) Die Querfurche des Ellbogengelenkes. Eine biomechanische Deutung ihrer Entstehung. Z Orthop 122:623–742

    Google Scholar 

  • O'Driscoll SW, Keeley FW, Salter RB (1988) Durability of regenerated articular cartilage produced by free autogenous periostal grafts in major full thickness defects in joint surfaces under the influence of continuous passive motion: a follow up at one year. J Bone Joint Surg 70A:595–606

    Google Scholar 

  • Orr JF (1992) Two and three dimensional photoelastic techniques. In: Miles AW, Tanner KE (eds) Strain measurement biomechanics. Chapmann, London

    Google Scholar 

  • Pauwels F (1963) Die Druckverteilung im Ellbogengelenk, nebst grundsätzlichen Bemerkungen über den Gelenkdruck. 11. Beitrag zur funktionellen Anatomie und kausalen Morphologie des Stützapparates. Z Anat Entwicklugnsgesch 123:643–667

    Google Scholar 

  • Pauwels F (1980) Biomechanics of the locomotor apparatus. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Putz R, Fischer H (1993) Altersunterschiede der Anordnung der kollagenen Fasern im Gelenkknorpel. In: Pesch HJ, Stöß H, Kummer B (eds) Osteologie aktuell 7. Springer, Berlin Heidelberg New York, pp 42–44

    Google Scholar 

  • Rapperport DJ, Carter DR, Schurmann DJ (1985) Contact finite element stress analysis of the hip joint. J Orthop Res 3:435–446

    Google Scholar 

  • Riede UN, Heitz P, Ruedi T (1971) Gelenkmechanische Untersuchungen zum Problem der posttraumatischen Arthrosen im oberen Sprunggelenk. 2. Einfluß der Talusform auf die Biomechanik des oberen Sprunggelenks. Langenbecks Arch Chir 330:174–184

    Google Scholar 

  • Rohlmann A, Mössner U, Bergmann G (1983) Finite-element-analysis and experimental investigation in a femur with hip endoprothesis. J Biomech 16:727–742

    Google Scholar 

  • Rushfeldt PD, Mann RW (1979) Influence of cartilage geometry on the pressure distribution in the human hip joint. Science 204: 413–415

    Google Scholar 

  • Sah RLY, Kim YJ, Doong JYH, Grodzinsky AJ, Plaas AHK, Sandy JD (1989) Biosynthetic response of cartilage expiants to dynamic compression. J Orthop Res 7:619–636

    Google Scholar 

  • Salter RB, Field P (1960) The effects of continuous compression on living articular cartilage. J Bone Joint Surg 42A: 31–49

    Google Scholar 

  • Salter RB, Simmonds DF, Malcolm BW, Rumble EJ, Mac-Michael D, Clements ND (1980) The biological effect of continuous passive motion on the healing of full-thickness defects in articular cartilage. J Bone Joint Surg 62 A:1232–1251

    Google Scholar 

  • Schröder DW, Gall H (1992) Zum biomechanischen Einfluß der Synovialflüssigkeit auf die Funktion der Gelenke. Zuckerschwerdt, München

    Google Scholar 

  • Soslowsky LJ, Flatow EL, Bigliani LU, Pawluk RJ, Ateshian GA, Mow VC (1992) Quantitation of in situ contact areas at the glenohumeral joint: a biomechanical study. J Orthop Res 10:524–534

    Google Scholar 

  • Tillmann B (1971) Die Beanspruchung des menschlichen Ellenbogengelenkes. 1. Funktionelle Morphologie der Gelenkflächen. Z Anat Entwicklungsesch 134:328–342

    Google Scholar 

  • Tillmann B (1973b) Zur Lokalisation von degenerativen Veränderungen am Femurkopf bei der Coxarthrose. Z Orthop 111:23–27

    Google Scholar 

  • Tillmann B (1978) A contribution to the functional morphology of articular surfaces. Thieme, Stuttgart

    Google Scholar 

  • Trias A (1961) Effect of persistent pressure on the articular cartilage. An experimental study. J Bone Joint Surg 43B: 376–386

    Google Scholar 

  • Walmsley T (1928) Articular mechanics of the diarthroses. J Bone Joint Surg 10 B:40–45

    Google Scholar 

  • Wynarsky GT, Greenwald AS (1983) Mathematical model of the human ankle joint. J Biomech 16:241–251

    Google Scholar 

  • Zienkiewicz OC, Taylor RL (1989) The finite element method, 4th edn, vol 1. Basic formulation and linear problems. McGraw Hill, London

    Google Scholar 

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Authors and Affiliations

  1. Anatomische Anstalt der Ludwig Maximilians Universität München, Pettenkoferstrasse 11, D-80336, München, Germany

    Felix Eckstein & Reinhard Putz

  2. Institut für Biomedizinische Technik und Medizinische Informatik der ETH Zürich, ETH Zentrum, CH-8092, Zürich, Swizzerland

    Beat Merz & Peter Schmid

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  1. Felix Eckstein
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  2. Beat Merz
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  4. Reinhard Putz
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Eckstein, F., Merz, B., Schmid, P. et al. The influence of geometry on the stress distribution in joints — a finite element analysis. Anat Embryol 189, 545–552 (1994). https://doi.org/10.1007/BF00186828

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