The superior accuracy of a novel method in total hip wear calculations following radiographic measurement

BACKGROUND: Polyethylene wear is one of the major concerns of orthopedic surgeons. However, there is no standardized calculation method for the wear rate following radiographic measurement. The purpose of this study was to propose a novel method of wear calculation and to compare its accuracy with a representative conventional method. METHODS: Relative position of the center of the femoral head to that of the cup progresses in one direction following arthroplasty surgery because of bedding-in and wear. We predetermined the amount of bedding-in, wear rate, and random error in measuring the head center position in a 2-dimensional plane. We calculated the wear rate using the head center coordinates over a certain number of measurement periods using a representative conventional method and our novel method. The conventional method consisted of transforming vector data into scalars and conducting a least-squares method. The least-squares method was directly applied to each component of the vector in the novel method. We evaluated the accuracy of these methods by comparing the expected value for the wear rate with their predetermined true values. RESULTS: If the error were limited to being random, the novel method could provide the predetermined wear rate as the calculation result. However, the conventional method could not. CONCLUSION: We recommend using the novel method for the wear calculation rather than the conventional method because of its mathematical accuracy. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12891-021-04964-5.