An analytical model of lateral condylar plate working length

Abstract

Background: The locking plate is a common device to treat distal femur fractures. Healing is affected by construct stiffness, thus many surgeon-controlled variables such as working length have been examined for their effects on strain at the fracture. No convenient analytical model which aids surgeons in determining working length has yet been described. We propose an analytical model and compare it to finite element analysis and cadaveric biomechanical testing.

Methods: First, an analytical model based on a cantilever beam equation was derived. Next, a finite element model was developed based on a CT scan of a "fresh-frozen" cadaveric femur. Third, biomechanical testing in single-leg stance loading was performed on the cadaver. In all methods, strain at the fracture was recorded. An ANCOVA test was conducted to compare the strains.

Findings: In all models, as the working length increased so did strain. For strain at the fracture, the shortest working length (35 mm) had a strain of 8% in the analytical model, 9% in the finite element model, and 7% for the cadaver. The longest working length (140 mm) demonstrated strain of 15% in the analytical model, and the finite element and biomechanical tests both demonstrated strain of 14%.

Interpretation: The strain predicted by the analytical model was consistent with the strain observed in both the finite element and biomechanical models. As demonstrated in existing literature, increasing the working length increases strain at the fracture site. Additional work is required to refine and establish validity and reliability of the analytical model.

Keywords: Analytical model; Distal femur fracture; Dynamic condylar screw; Finite element analysis; Lateral condylar plate.

Fig. 1.

Four working lengths defined for use across the three methodologies. Red circles represent non-locking screws in the diaphyseal portion of the lateral condylar plate. Yellow circles represent solid locking screws in the distal block.

Fig. 2.

Analytical model describing the forces in the femur, modeling the femur as (a) cantilever beam with body weight being applied across the most distal screw on the femoral diaphysis with (b) the corresponding forces and movements exerted on the femur. Displacement in this model was considered the deflection of the beam.

Fig. 3.

Boundary conditions and loading for finite element model which was repeated for biomechanical testing.

Fig. 4.

Strains for each working length across the three methodologies using (a) body weight load and (b) twice body weight load.

Fig. 5.

(a) Heat map for stresses on the lateral condylar plate at the fracture site with bone and (b) without bone for the 140 mm working length with body weight loading. Von Mises Stresses are given in MPa.

Fig. 6.

Maximum von Mises stress in the implant across the four working lengths in the finite element model for body weight and twice body weight loads.

Fig. 7.

Load vs displacement curves for all working lengths. Indicators show initial stiffness (IS) and end stiffness (ES) portions of the curve in the biomechanical model.