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Finite Element-Derived Surrogate Models of Locked Plate Fracture Fixation Biomechanics

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Abstract

Internal fixation of bone fractures using plates and screws involves many choices—implant type, material, sizes, and geometric configuration—made by the surgeon. These decisions can be important for providing adequate stability to promote healing and prevent implant mechanical failure. The purpose of this study was to develop mathematical models of the relationships between fracture fixation construct parameters and resulting 3D biomechanics, based on parametric computer simulations. Finite element models of hundreds of different locked plate fixation constructs for midshaft diaphyseal fractures were systematically assembled using custom algorithms, and axial, torsional, and bending loadings were simulated. Multivariate regression was used to fit response surface polynomial equations relating fixation design parameters to outputs including maximum implant stresses, axial and shear strain at the fracture site, and construct stiffness. Surrogate models with as little as three regressors showed good fitting (R 2 = 0.62–0.97). Inner working length was the strongest predictor of maximum plate and screw stresses, and a variety of quadratic and interaction terms influenced resulting biomechanics. The framework presented in this study can be applied to additional types of bone fractures to provide clinicians and implant designers with clinical insight, surgical optimization, and a comprehensive mathematical description of biomechanics.

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Abbreviations

L plate :

Length of plate

d gap :

Fracture gap size

N screws :

Number of screws

L inner :

Working length between inner screws

L outer :

Working length between outer screws

E implant :

Implant material elastic modulus

σ plate_max :

Max von Mises stress of plate

σ screw_max :

Max von Mises stress of screw

k axial :

Axial stiffness of the fracture fixation construct

k torsion :

Torsional stiffness of the fracture fixation construct

k bending :

Bending stiffness of the fracture fixation construct

ε axial :

Interfragmentary axial strain

ε shear :

Interfragmentary shear strain

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Acknowledgments

This project is funded, in part, under a grant with the Pennsylvania Department of Health using Tobacco CURE Funds. Project no. S-15-196L was supported by AO Foundation, Switzerland. Additional support was received from the National Center for Advancing Translational Sciences, Grant KL2 TR000126. Fracture fixation plates and screws were donated by Depuy Synthes. Disclosure: H.W. and V.M.C. have no conflicts of interest to disclose. G.S.L. has received implants and CAD files for research as PI from Depuy-Synthes. J.S.R. is a speaker for product related instructional courses for Smith and Nephew, and is a consultant for Depuy-Synthes.

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Authors and Affiliations

  1. Department of Orthopaedics and Rehabilitation, Penn State College of Medicine, 500 University Drive, Mail Code H089, Hershey, PA, 17033, USA

    Hwabok Wee, J. Spence Reid & Gregory S. Lewis

  2. Department of Public Health Sciences, Penn State College of Medicine, Hershey, PA, USA

    Vernon M. Chinchilli

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  1. Hwabok Wee
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Correspondence to Gregory S. Lewis.

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Associate Editor Peter E. McHugh oversaw the review of this article.

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Wee, H., Reid, J.S., Chinchilli, V.M. et al. Finite Element-Derived Surrogate Models of Locked Plate Fracture Fixation Biomechanics. Ann Biomed Eng 45, 668–680 (2017). https://doi.org/10.1007/s10439-016-1714-3

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  • DOI: https://doi.org/10.1007/s10439-016-1714-3

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