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Technical Briefs

Modeling Bicortical Screws Under a Cantilever Bending Load

[+] Author and Article Information
Thomas P. James

Department of Mechanical Engineering,
Department of Orthopedics,
Tufts University,
Boston, MA 02111
e-mail: thomas.james@tufts.edu

Brendan A. Andrade

Department of Mechanical and
Aerospace Engineering,
Princeton University,
Princeton, NJ 08544

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received February 20, 2013; final manuscript received September 8, 2013; accepted manuscript posted October 8, 2013; published online October 24, 2013. Editor: Beth Winkelstein.

J Biomech Eng 135(12), 124502 (Oct 24, 2013) (9 pages) Paper No: BIO-13-1089; doi: 10.1115/1.4025651 History: Received February 20, 2013; Revised September 08, 2013; Accepted October 08, 2013

Cyclic loading of surgical plating constructs can precipitate bone screw failure. As the frictional contact between the plate and the bone is lost, cantilever bending loads are transferred from the plate to the head of the screw, which over time causes fatigue fracture from cyclic bending. In this research, analytical models using beam mechanics theory were developed to describe the elastic deflection of a bicortical screw under a statically applied load. Four analytical models were developed to simulate the various restraint conditions applicable to bicortical support of the screw. In three of the models, the cortical bone near the tip of the screw was simulated by classical beam constraints (1) simply supported, (2) cantilever, and (3) split distributed load. In the final analytical model, the cortices were treated as an elastic foundation, whereby the response of the constraint was proportional to screw deflection. To test the predictive ability of the new analytical models, 3.5 mm cortical bone screws were tested in a synthetic bone substitute. A novel instrument was developed to measure the bending deflection of screws under radial loads (225 N, 445 N, and 670 N) applied by a surrogate surgical plate at the head of the screw. Of the four cases considered, the analytical model utilizing an elastic foundation most accurately predicted deflection at the screw head, with an average difference of 19% between the measured and predicted results. Determination of the bending moments from the elastic foundation model revealed that a maximum moment of 2.3 N m occurred near the middle of the cortical wall closest to the plate. The location of the maximum bending moment along the screw axis was consistent with the fracture location commonly observed in clinical practice.

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Figures

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Fig. 1

Geometry, nomenclature, and local coordinate system used to model a bicortical screw used in conventional plating (nonlocking)

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Fig. 2

Beam mechanics model representing the distal cortex as simply supported, RO

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Fig. 3

Beam mechanics model representing the distal cortex by distributed reaction forces, R1 and R2

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Fig. 4

Beam mechanics model of a bicortical screw with the cortices represented as an elastic foundation with a linear spring constant, kb

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Fig. 5

(a) Significant features of the test apparatus used to apply a cantilever bending load to a bicortical screw and (b) backside of the test apparatus showing a dial indicator measuring gauge pin movement as the body of the screw deflects

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Fig. 6

Conceptual model of the measurement system used to determine deflection of a bicortical screw under a cantilever bending load

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Fig. 7

Deflection of screw axis predicted by the various models as compared to the experimental measurement for applied loads of 225 N, 445 N, and 670 N. The abscissa markers (X) indicate the boundaries of the cortical walls.

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Fig. 8

(a) Bending moment within the screw (670 N applied force). The maximum moment occurs within the proximal cortex for each model. (b) The location of screw fracture observed in clinical practice is often within the proximal cortex [24].

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