Method for approximating the ISB pelvic coordinate system on unilateral landmarks on a hemipelvis

When only having a hemipelvis, defining the International Society of Biomechanics (ISB) pelvic joint coordinate system (ISB coordinate system) is challenging but necessary for applying forces, describing movement patterns, and comparing literature. Thus, the aim of the study is to suggest a method to approximate the ISB coordinate system using a hemipelvis. A total of 66 human pelvic CT-scans were used to apply the ISB coordinate system based on landmarks on the full pelvis and a hemipelvic coordinate system (HP coordinate system) based solely on unilateral landmarks. The rotations between the orientation of these two frames were calculated for each case, and a generalized rotation for the whole cohort was derived, which can be used to approximate the ISB coordinate system on a hemipelvis. Applying the generalized rotation to an HP coordinate system leads to an approximated ISB coordinate system. The difference in orientation between the actual and approximated ISB coordinate systems in terms of axis angle representation was 5.49° ± 2.81°. Cross-validation with the Leave-one-out method showed an increase in error angles of 1.5 %. The proposed method makes it possible to approximate the ISB coordinate system on unilateral landmarks for known divergence values. This could be highly beneficial for biomechanical in vitro and in silico testing when only a hemipelvis is available.