Effect of the sagittal osteotomy inclination angle on the posterior tibial slope change in high tibial osteotomy: three-dimensional simulation study

Abstract

In performing medial open-wedge high tibial osteotomy, it is recommended not to alter the posterior tibial slope. However, it remains unclear whether the osteotomy inclination angle affects the posterior tibial slope in the sagittal plane. This study aimed to verify how anterior or posterior osteotomy inclination angle affects the tendency of change in the posterior tibial slope and to conduct quantitative analysis of the extent to which the posterior tibial slope changes according to the degree of the osteotomy inclination angle change in MOWHTO. Computed tomography images of 30 patients who underwent MOWHTO were collected. Three-dimensional models of preoperative original tibia were reconstructed, and virtual osteotomies were performed. The sagittal osteotomy inclination angles formed by the osteotomy line and the medial tibial plateau line were classified as positive in case of anteriorly inclined osteotomy and negative in case of posteriorly inclined osteotomy. Thirteen osteotomies were performed for each tibial model at intervals of 5° from - 30° to 30°. The posterior tibial slope was assessed, and the proportional relationship between the sagittal osteotomy inclination angle and the posterior tibial slope change was analyzed. The posterior tibial slope changed significantly after osteotomy (p < 0.001), except for the cases where the sagittal osteotomy inclination angles were 5°, 0°, and - 5°. Anteriorly and posteriorly inclined osteotomy caused increase and decrease in the posterior tibial slope, respectively. As the inclination angle increased by 1°, the posterior tibial slope increased by 0.079° in anterior inclination osteotomy, while in posterior inclination osteotomy, as the inclination angle decreased by 1°, the posterior tibial slope decreased by 0.067°. The osteotomy inclination angle in the sagittal plane significantly affected the posterior tibial slope. When there was an inclination angle occurred between the osteotomy line and the medial tibial plateau line in the sagittal plane, the posterior tibial slope changed after MOWHTO. The posterior tibial slope tended to increase in anteriorly inclined osteotomy and decrease in posteriorly inclined osteotomy. The change in the posterior tibial slope was proportionally related to the absolute value of the osteotomy inclination angle.

Figure 1

Steps to create a three-dimensional (3D) model of a pre-osteotomy original tibia. (A) reconstructed 3D model of tibia without soft tissue. (B) Virtual elimination of plate and screws from the 3D model (C) Rotation axis setting with the position about 1.0 cm before the lateral cortex and 1.5 cm below the articular surface as the hinge for restoration to pre-osteotomy original tibia. (D) Restoration to preoperative status of tibia by rotating the proximal segment around the rotation axis and eliminating the osteotomy gap. These figures were created using the Mimics software (version 17; Materialise, Leuven, Belgium).

Figure 2

Positioning of point 1 (P1), point 2 (P2), and point 3 (P3) on the three-dimensional (3D) images of tibia. A. Determination of the joint plane and the coordinate system of proximal tibia by defining the x-, y-, and z-axes in the 3D model. The joint plane was defined by the 3 points (the most medial point of the medial tibial plateau, the most posterior point of the medial tibial plateau, and the most lateral point on the lateral tibial plateau). The x-axis was defined by the line connecting the centers of the best-fit circles of the medial and lateral plateau on the joint plane. The y- and z-axes were defined by cross-product of the x-axis B. Initially, P1, the starting point of osteotomy, was placed on the anteromedial cortex of proximal tibia, 3.5 cm below the medial end of the tibial plateau. P2, which was used as a hinge, was located 1.0 cm medially from the lateral cortex of tibia on the x-axis and 1.5 cm below the articular surface on the z-axis. C. In the axial plane, P2 was positioned at the midpoint of the entire length of anteroposterior articular surface. D. In the sagittal plane, P3 was placed at the posteromedial cortex of tibia. The angle between the line formed by P1 and P3 and the line of the medial tibial plateau was defined as the osteotomy inclination angle in the sagittal plane. These figures were created using the Mimics software (version 17; Materialise, Leuven, Belgium).

Figure 3

In the sagittal plane, the angle between the dotted line formed by P1 and P3 and the solid line parallel to the medial tibial plateau line was defined as the osteotomy inclination angle. (A) Parallel osteotomy line (0°). (B) Anteriorly inclined osteotomy line (10°). (C) Posteriorly inclined osteotomy line (− 10°). These figures were created using the Mimics software (version 17; Materialise, Leuven, Belgium).

Figure 4

Simulation of osteotomy was performed. Thirteen osteotomy inclination angles in the sagittal plane were applied to the three-dimensional tibial model. The osteotomy inclination angle was changed from − 30° to 30° at intervals of 5° by changing the position of P3. The anterior-to-posterior osteotomy opening gap ratio was maintained at 67%. (A) Anteriorly inclined osteotomy (0°, 10°, 20°, 30°). (B) Posteriorly inclined osteotomy (0°, − 10°, − 20°, − 30°). These figures were created using the Mimics software (version 17; Materialise, Leuven, Belgium).

Figure 5

Measurement of the posterior tibial slope. In a true lateral position, the image of the 3D tibial model was captured and the posterior tibial slope was measured. The medial tibial plateau line and the line perpendicular to the line bisecting the tibial shaft were drawn. Posterior tibial slope was defined by the angle formed by these two lines. (A) Posterior tibial slope of the preoperative original tibia. (B) Posterior tibial slope of the virtually osteotomized tibia. PTS = posterior tibial slope. These figures were created using the Mimics software (version 17; Materialise, Leuven, Belgium).

Figure 6

Scatter plots of the posterior tibial slopes according to the change of the sagittal osteotomy inclination angle. (A) Anteriorly inclined osteotomy. (B) Posteriorly inclined osteotomy. These figures were created using the R statistical software (version 3.6.2; R Foundation for Statistical Computing, Vienna, Austria).