Effects of K-wire diameter and insertion angle on femoral bone medial closing-wedge osteotomies: a finite element study

Abstract

Medial closing-wedge surgery for distal femoral osteotomy is employed to correct genu valgum by correcting coronal plane malalignment. This procedure involves pre-surgery planning, creating a wedge incision, performing the osteotomy, and stabilizing with plates and screws. However, hinge fractures during wedge closure present significant challenges, often necessitating revisions. Contemporary solutions have explored the use of k-wires, and this study investigates their biomechanical implications. The interplay between k-wire insertion angle and diameter, often overlooked in existing literature, is a critical determinant of their efficacy in achieving successful osteotomies, highlighting gaps in our understanding of these key parameters. We hypothesize that k-wire mechanics vary with insertion angle and diameter. This study examines the introduction of k-wires at different angles (30°, 45°, and 60°) and diameters (1.6, 1.8, and 2 mm) using computed tomography-based finite element models to assess structural integrity during femoral medial closing-wedge osteotomy. Results reveal angle-dependent stress variations, with 60° configurations exhibiting favorable patterns that reduce tensile and compressive loads and plastic deformation-crucial in preventing hinge fractures. Diameter variations show no significant differences in stresses or system stiffness. It was also found that while angle significantly affects stresses, lower diameters appear optimal only in combination with higher angles. Comparative analysis of k-wire systems with a naïve model demonstrates that k-wires at a 60° angle reduce tensile and compressive loadings and plastically deformed volume fractions, thus lowering fracture risk. This study underscores the importance of optimizing k-wire placement and configuration, particularly highlighting the significance of the insertion angle. Future research should expand the range of angles and diameters tested and examine different femoral geometries and osteotomy angles to provide a more comprehensive understanding and enhanced clinical application.

Keywords: Biomechanics; Digital twin; Hinge fracture prevention; In silico; K-wire; Orthopedics; Stress and strain analysis; Structural stability; Surgical optimization.

Fig. 1

Planning and intraoperative imaging. Knee with a valgus alignment and planning for the surgery indicating the wedge for an exemplary patient (a). Intraoperatively, wedge location is planned (b). Closing of the wedge may in some cases lead to a fracture at the hinge (c), which may be prevented by insertion of a Kirschner wire (k-wire) to protect the hinge.

Fig. 2

Overview of the workflow used in this study. The segmentation of bone geometry from CT data and introduction of an exemplary surgical wedge (first row), placement of k-wire in different configurations and meshing the system instances (second row) including both without k-wire and with k-wire, assigning subject-specific material properties and running the finite element analysis (third row).

Fig. 3

Output measures versus angle variation (left) and diameter variation (right) of a defined trajectory at the hinge bone. Differences were detected for variation in the angle of insertion of the k-wire for maximum tensile principal stresses, with 30° exhibiting the highest and 60° the lowest stresses (a). No differences were measured for compressive stress (b). The volume fraction of plastically deformed elements was lowest at a 60° insertion angle, with a stepwise increase as the angle decreased (c) while no difference in stiffness was measured for the assembly (d). For variations in diameter, no significant differences were measured for all parameters (e–h).

Fig. 4

Heatmaps indicating the output measure combinations for angle and diameter variations: Angle-diameter heatmap for tensile maximum principal stresses (a), compressive maximum principal stresses (b), volume fraction (c), and stiffness (d).

Fig. 5

Longitudinal normal stress induced on the superior surface of distal femur in contact with the proximal part for different angles (left) and diameters of the k-wire (right). Positive values indicate tensile and negative values indicate compressive stresses. The path on which the values have been read is highlighted using the white arrows, running on the superior osteotomy surface from the lateral cortico-osteotomy junction traversing medially toward the medial hinge apex, aligned with the expected line of stress transfer during wedge closure.