Skip to main content
Log in

A rigorous method for evaluation of the 6D compliance of external fixators

  • Original paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Gardner TN, Weemaes M (1999) A mathematical stiffness matrix for characterising mechanical performance of the orthofix daf. Med Eng Phys 21(2):65–71

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Gruber C (1988) Mécanique générale. Presses Polytechniques et Universitaires Romandes, Lausanne

    MATH  Google Scholar 

  • 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

    Google Scholar 

  • Huiskes R, Chao EY (1986) Guidelines for external fixation frame rigidity and stresses. J Orthop Res 4(1):68–75

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

  • Przemieniecki JS (1968) Theory of matrix structural analysis. McGraw-Hill, New York

    MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • Sladicka SJ, Duffin SR, Erpelding JM (1998) A biomechanical strength comparison of external fixators. J Trauma 44(6):965–969

    Article  Google Scholar 

  • Vidal J (1983) External fixation. yesterday, today, and tomorrow. Clin Orthop Relat Res 180:7–14

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Philippe K. Zysset.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-006-0052-z

Keywords

Navigation