Efficacy and efficiency of multivariate linear regression for rapid prediction of femoral strain fields during activity. (January 2019) - Ziaeipoor, Hamed; Martelli, Saulo; Pandy, Marcus; Taylor, Mark
Highlights: Full femoral strain was calculated using a multi-linear regression (MLR) model. A similar behaviour observed between different activities. The peak difference with corresponding finite-element (FE) calculations was 8.6% of the maximum computed micro-strain. The MLR-based surrogate model was faster than the finite-element analysis for solving 209 frames or more. The MLR's solution time for 1000 frames of motion was approximately 21% of the time required for the corresponding FE model. Abstract: Multivariate Linear Regression-based (MLR) surrogate models were explored to reduce the computational cost of predicting femoral strains during normal activity in comparison with finite element analysis. The musculoskeletal model of one individual, the finite-element model of the right femur, and experimental force and motion data for normal walking, fast walking, stair ascent, stair descent, and rising from a chair were obtained from a previous study. Equivalent Von Mises strain was calculated for 1000 frames uniformly distributed across activities. MLR surrogate models were generated using training sets of 50, 100, 200 and 300 samples. The finite-element and MLR analyses were compared using linear regression. The Root Mean Square Error (RMSE) and the 95th percentile of the strain error distribution were used as indicators of average and peak error. The MLR model trained using 200 samples (RMSE < 108 µε; peak error < 228 µε) was used as a reference. The finite-element method required 66 s per frame on a standard desktop computer. The MLR model required 0.1 s per frame plus 1848 s of training time. RMSE ranged from 1.2% to 1.3% while peak error ranged from 2.2% to 3.6% of the maximum micro-strain (5020 µε). Performance within an activity was lower during early and late stance, with RMSE of 4.1% and peak error of 8.6% of the maximum computed micro-strain. These results show that MLR surrogate models may be used to rapidly and accurately estimate strain fields in long bones during daily physical activity.