Abstract
External fixators are standard devices to stabilize bone fractures and their compliance aims at producing an interfragmentary motion that promotes rapid and successful healing. While evaluation of their axial compliance is a routine test, the quantification and interpretation of their full 6 × 6 compliance matrix is an extensive and delicate task. In this context, the objective of this study was to develop, validate and demonstrate the potential of a rigorous method to quantify their 6 × 6 compliance matrix. An experimental system was developed to apply six independent static forces and moments to an external fixator in the field of view of two infrared cameras quantifying the induced motion. The system was then tested with a calibration structure which compliance could be calculated analytically and numerically. Finally, the system was applied to compare three configurations of a commercial external wrist fixator. The results of the method proved to be reproducible and highly consistent with the linear elasticity theory in the physiological range of small deformations. A rigorous method for evaluation of the 6D compliance becomes therefore available for research in mechanobiology of fracture healing by external fixation.
Similar content being viewed by others
References
Beaupre GS, Hayes WC, Jofe MH, White AA (1983) Monitoring fracture site properties with external fixation. J Biomech Eng 105(2):120–126
Bishop NE, Schneider E, Ito K (2003) An experimental two degrees-of-freedom actuated external fixator for in vivo investigation of fracture healing. Med Eng Phys 25(4):335–340
Caja V, Kim W, Larsson S, YCE (1995) Comparison of the mechanical performance of three types of external fixators: linear, circular and hybrid. Clin Biomech 10(8):401–406
Carter DR, Blenman PR, Beaupre GS (1988) Correlations between mechanical stress history and tissue differentiation in initial fracture healing. J Orthop Res 6:736–748
Chang D, Kummer FJ, Egol K, Tejwani N, Wolinsky P, Koval KJ (2002) Biomechanical comparison of five external wrist fixators. Bull Hosp Jt Dis 61(1–2):40–44
Chao EY, Kasman RA, An KN (1982) Rigidity and stress analyses of external fracture fixation devices—a theoretical approach. J Biomech 15(12):971–983
Chao EYS, Aro HT (1997) Biomechanics of fracture fixation. In: Mow VC, Hayes WC (eds) Basic orthopaedic biomechanics. Lippincott-Raven Publishers, Philadelphia, pp 317–351
Claes LE, Heigele CA (1999) Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing. J Biomech 32(3):255–266
Draper ER, Wallace AL, Strachan RK, Hughes SP, Nicol AC, Paul JP (1995) The design and performance of an experimental external fixation device with load transducers. Med Eng Phys 17(8):618–624
Draper ER, Strachan RK, Hughes SP, Nicol AC, Paul JP (1997) The design and performance of an experimental external fixator with variable axial stiffness and a compressive force transducer. Med Eng Phys 19(8):690–695
Drijber FL, Finlay JB, Dempsey AJ (1992) Evaluation of linear finite-element analysis models’ assumptions for external fixation devices. J Biomech 25(8):849–855
Duda GN, Kirchner H, Wilke HJ, Claes L (1998) A method to determine the 3-d stiffness of fracture fixation devices and its application to predict inter-fragmentary movement. J Biomech 31(3):247–252
Finlay JB, Moroz TK, Rorabeck CH, Davey JR, Bourne RB (1987) Stability of ten configurations of the Hoffmann external-fixation frame. J Bone Joint Surg Am 69(5):734–744
Frykman GK, Tooma GS, Boyko K, Henderson R (1989) Comparison of eleven external fixators for treatment of unstable wrist fractures. J Hand Surg (Am) 14(2 Pt 1):247–254
Frykman GK, Peckham RH, Willard K, Saha S (1993) External fixators for treatment of unstable wrist fractures. a biomechanical, design feature, and cost comparison. Hand Clin 9(4):555–565
Gardner TN, Weemaes M (1999) A mathematical stiffness matrix for characterising mechanical performance of the orthofix daf. Med Eng Phys 21(2):65–71
Goodship AE, Watkins PE, Rigby HS, Kenwright J (1993) The role of fixator frame stiffness in the control of fracture healing. an experimental study. J Biomech 26(9):1027–1035
Gruber C (1988) Mécanique générale. Presses Polytechniques et Universitaires Romandes, Lausanne
Hoffmann R, McKellop HA, Sarmiento A, Lu B, Ebramzadeh E (1991) Three-dimensional measurement of fracture gap motion. biomechanical study of experimental tibial fractures with anterior clasp fixator and ring fixator. Unfallchirurg 94(8):395–400
Huiskes R, Chao EY (1986) Guidelines for external fixation frame rigidity and stresses. J Orthop Res 4(1):68–75
Juan JA, Prat J, Vera P, Hoyos JV, Sanchez-Lacuesta J, Peris JL, Dejoz R, Alepuz R (1992) Biomechanical consequences of callus development in Hoffmann, Wagner, Orthofix and Ilizarov external fixators. J Biomech 25(9):995–1006
Kassi JP, Hoffmann JE, Heller M, Raschke M, Duda GN (2001) Evaluating the stability of fracture fixation systems: mechanical device for evaluation of 3-d stiffness in vitro. Biomed Tech 46(9):247–252
Klein P, Schell H, Streitparth F, Heller M, Kassi JP, Kandziora F, Bragulla H, Haas NP, Duda GN (2003) The initial phase of fracture healing is specifically sensitive to mechanical conditions. J Orthop Res 21(4):662–669
Kowalski M, Schemitsch EH, Harrington RM, Chapman JR, Swiontkowski MF (1996) Comparative biomechanical evaluation of different external fixation sidebars: stainless-steel tubes versus carbon fiber rods. J Orthop Trauma 10(7):470–475
Lacroix D, Prendergast PJ (2002) A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading. J Biomech 35(9):1163–1171
Merloz P, Maurel N, Marchard D, Lavaste F, Barnole J, Faure C, Butel J (1991) Three-dimensional rigidity of the ilizarov external fixator (original and modified) implanted at the femur. experimental study and clinical deductions. Rev Chir Orthop Reparatrice Appar Mot 77(2):65–76
Nakata RY, Chand Y, Matiko JD, Frykman GK, Wood VE (1985) External fixators for wrist fractures: a biomechanical and clinical study. J Hand Surg (Am) 10(6 Pt 1):845–851
Park SH, O’Connor K, McKellop H, Sarmiento A (1998) The influence of active shear or compressive motion on fracture-healing. J Bone Joint Surg Am 80(6):868–878
Patterson RM, Nicodemus CL, Viegas SF, Elder KW, Rosenblatt J (1997) Normal wrist kinematics and the analysis of the effect of various dynamic external fixators for treatment of distal radius fractures. Hand Clin 13(1):129–141
Pauwels F (1980) Biomechanics of the locomotor apparatus. Springer, Berlin Heidelberg New York
Przemieniecki JS (1968) Theory of matrix structural analysis. McGraw-Hill, New York
Simpson NS, Wilkinson R, Barbenel JC, Kinninmonth AW (1994) External fixation of the distal radius. a biomechanical study. J Hand Surg (Br) 19(2):188–192
Sladicka SJ, Duffin SR, Erpelding JM (1998) A biomechanical strength comparison of external fixators. J Trauma 44(6):965–969
Vidal J (1983) External fixation. yesterday, today, and tomorrow. Clin Orthop Relat Res 180:7–14
Wilke HJ, Ostertag G, Claes L (1994) A three-dimensional goniometer linkage system for the analysis of movement with six degrees of freedom. Biomed Tech 39(6):149–155
Winemaker MJ, Chinchalkar S, Richards RS, Johnson JA, Chess DG, King GJ (1998) Load relaxation and forces with activity in hoffman external fixators: a clinical study in patients with colles’ fractures. J Hand Surg (Am) 23(5):926–932
Wolfe SW, Swigart CR, Grauer J, Slade JF, Panjabi MM (1998) Augmented external fixation of distal radius fractures: a biomechanical analysis. J Hand Surg (Am) 23(1):127–134
Wolfe SW, Lorenze MD, Austin G, Swigart CR, Panjabi MM (1999) Load-displacement behavior in a distal radial fracture model. the effect of simulated healing on motion. J Bone Joint Surg Am 81(1):53–59
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Meleddu, A., Barrault, S. & Zysset, P.K. A rigorous method for evaluation of the 6D compliance of external fixators. Biomech Model Mechanobiol 6, 253–264 (2007). https://doi.org/10.1007/s10237-006-0052-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10237-006-0052-z