Wear patterns of, and wear volume formulae for, hemispherical acetabular cup liners

This study analyzed wear patterns of, and wear volume formulae for, hemispherical acetabular cup liners used in total hip replacement. The geometric patterns of the wear surface were first classified, then wear volume formulae were derived by integral calculus. Based on the theoretical maximal and minimal wear volumes, three-dimensional wear models constructed using SolidWorks® software or published formulae were used to verify the accuracy of the formulae proposed in this study. Analytical results showed that, with the exception of the pattern of a wear angle of 90°, hemispherical liner wear can be divided into two patterns. Once the wear pattern is determined from the wear angle and depth, a wear formula is applied to calculate the wear volume. The formulae and wear patterns described herein are crucial for more accurate performance evaluation of existing hip components implanted in patients, as well as for designing new hip components.