Achievement of Targeted Posterior Slope in the Medial Opening Wedge High Tibial Osteotomy: a Mathematical Approach

High tibial osteotomy (HTO) for medial compartment knee osteoarthritis is preferred in the activity patient since it allows patients to return to sports and recreational activities similar to the preoperative level. The purpose of this study was to mathematically formulate medial and anteromedial opening gaps in the medial opening wedge HTO to achieve a targeted tibial posterior slope. The change of posterior slope angle was mathematically derived in terms of the medial and anteromedial opening gaps, and the medial opening angles. The derived equations were validated by comparing them with those directly measured by performing simulated HTOs. In the triangular geometries of osteotomy planes, measured from three-dimensional osteotomy models of 30 knee patients, the mean anteromedial, medial, and lateral included angles were 92.4 degrees, 53.9 degrees, and 33.7 degrees, respectively, and the mean lateral-medial edge length was 53.3 mm. The ratio of the anteromedial opening gap to the posterior opening gap should be "sin(the medial included angle)xcos(the lateral included angle)/sin(the anteromedial included angle)" to maintain an intact posterior tibial slope angle. With the derived equations, surgeons can estimate the opening gaps and opening angles to get a targeted posterior tibial slope with a medial opening angle.