A numeric symbolic tool in total hip arthroplasty

Monitoring the result of a surgical operation of total hip arthroplasty is of the utmost importance, both for evaluating the condition of the prosthesis itself, its successful stability, or to promptly diagnose the necessity for a correction. To meet this need, at the Rizzoli Orthopaedic Institutes a software system is under development; in particular, the accurate detection of the acetabular cup, through its radiographic evaluation, is under study and constitutes the motivation for this work. We exploit the symbolic resources and the graphical capabilities of a system such as Mathematica, to simulate problem and model and validate numerical results obtained on real data. The problem naturally leads to an ill conditioned, overdetermined system, in which both the matrix and the known term entries are affected by measurement errors. A C implementation of a least squares fitting method is then provided; results are reported, related to a set of real data problems.