A novel training-free method for real-time prediction of femoral strain

Surrogate methods for rapid calculation of femoral strain are limited by the scope of the training data. We compared a newly developed training-free method based on the superposition principle (Superposition Principle Method, SPM) and popular surrogate methods for calculating femoral strain during activity. Finite-element calculations of femoral strain, muscle, and joint forces for five different activity types were obtained previously. Multi-linear regression, multivariate adaptive regression splines, and Gaussian process were trained for 50, 100, 200, and 300 random samples generated using Latin Hypercube (LH) and Design of Experiment (DOE) sampling. The SPM method used weighted linear combinations of 173 activity-independent finite-element analyses accounting for each muscle and hip contact force. Across the surrogate methods, we found that 200 DOE samples consistently provided low error (RMSE < 100 µε), with model construction time ranging from 3.8 to 63.3 h and prediction time ranging from 6 to 1236 s per activity. The SPM method provided the lowest error (RMSE = 40 µε), the fastest model construction time (3.2 h) and the second fastest prediction time per activity (36 s) after Multi-linear Regression (6 s). The SPM method will enable large numerical studies of femoral strain and will narrow the gap between bone strain prediction and real-time clinical applications.