A new geometric model to quantify the area of glenoid bone defect and medialisation of the native joint line in glenohumeral arthritis

Purpose To propose a geometric model to quantify the bone defect and the glenoid medialisation (in millimetres) compared to the native joint line. We also evaluated the reliability of this geometric model. Methods Using two-dimensional CT imaging, we built a hypothetical triangle on the axial scan consisting of the following: side A, length (millimetres) of the glenoid bone; side B, average length (millimetres) of the glenoid in a healthy population; side C, the missing side; and angle α , the retroversion angle calculated using the Friedman method. The resulting triangle represents the bone defect, and its height represents the medialisation of the native joint line. To estimate inter-operator reliability, two physicians (operator 1 and operator 2) took the following measurements: angle α , side A, side C, semi-perimeter, area defect and height. Results Forty participants (mean age ± SD 45 ± 10 years, range 26–43 years)—22 women and 18 men—participated in the study. We applied the cosine theorem (Carnot theorem) to calculate side C. After obtaining the three sides, the area of the triangle can be determined. Once the area is known, it is possible to extrapolate the height of the triangle, which corresponds to the loss of vault depth due to the bone defect. With respect to inter-operator reliability, the ICCs for all measurements were > 0.99, exhibiting a very high correlation. Conclusions The proposed geometric model can be used to quantify the glenoid bone deficit and the glenoid medialisation compared to the native joint line, which can be used to improve surgical treatment.