A Regression Approach to Assess Bone Mineral Density of Patients undergoing Total Hip Arthroplasty through Gait Analysis

Total Hip Arthroplasty (THA) is the gold standard for hip replacement surgery. It can be performed with two different kinds of prostheses: cemented and uncemented. The surgeons have always decided on the type of prosthesis based on the age, sex of the patient and bone stock on x rays. In this paper 42 subjects underwent THA and performed both gait analysis and bone mineral density (BMD) evaluation through CT scans; spatial and temporal gait parameters were used to predict BMD of the distal and proximal parts of the femur before and one year after surgery using machine learning regression analysis. A simple linear regression (LR) and k-nearest neighbor (KNN) were implemented coding with Python Scikit-Learn libraries and some evaluation metrics were computed: the coefficient of determination (R2), mean absolute error, mean squared error and root mean squared error. Both the algorithms had a R2 greater than 75% in predicting both proximal and distal; particularly, LR obtained the highest score of 88.4% in predicting the BMD before the THA and of 81.3% after the THA. All the R2 of KNN ranged from 75% and 77%. All the calculated errors were always below 0.001. In conclusion, this research shows the feasibility of gait parameters for assessing the follow-up after 52 weeks of patients undergoing THA by predicting the BMD. Moreover, the results give insights about the relationship between the patterns of gait and BMD.