Efficacy and Efficiency of Multivariate Linear Regression for Rapid Prediction of Femoral Strain Fields during Activity

© 2018 IPEM. Published by Elsevier Ltd. This manuscript version is made available under the CC-BY-NC-ND 4.0 license: http://creativecommons.org/licenses/by-nc-nd/4.0/ This author accepted manuscript is made available following 12 month embargo from date of publication (December 2018) in accordance with the publisher’s archiving policy.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

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

© 2019 Elsevier Ltd. This manuscript version is made available under the CC-BY-NC-ND 4.0 license: http://creativecommons.org/licenses/by-nc-nd/4.0/ This author accepted manuscript is made available following 12 month embargo from date of publication (February 2019) in accordance with the publisher’s archiving policySurrogate 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

Population-based bone strain during physical activity: A novel method demonstrated for the human femur

Statistical methods are increasingly used in biomechanics for studying bone geometry, bone density distribution and function in the population. However, relating population-based bone variation to strain during activity is computationally challenging. Here, we describe a new method for calculating strain in a population, using the Superposition Principle Method Squared (SPM2), and we demonstrate the method for calculating strain in human femurs. Computed-tomography images and motion capture while walking in 21 healthy adult women were obtained earlier. Variation of femur geometry and bone distribution were modelled using active shape and appearance modelling (ASAM). Femoral strain was modelled as the weighted sum of strain generated by each force in the model plus a strain variation assumed a quadratic function of the ASAM scores. The quadratic coefficients were fitted to 35 instances drawn from the ASAM model by varying each eigenmode by ± 2 SD. The equivalent strain in matched finite-element and SPM2 calculations was obtained for 40 frames of walking for three independent cases and 50 ASAM instances. Finite-element and SPM2 solutions for walking were obtained in 44 and 3 min respectively. The SPM2 model accurately predicted strain for the three independent instances (R-squared 0.83–0.94) and the 50 ASAM instances (R-squared 0.95–1.00). The method developed enables fast and accurate calculation of population-based femoral strain.</p

An efficient computational model for predicting the strain distribution during common physical activities:Surrogate modelling VS FE simulations

The ability to calculate femoral strain during a broad range of physical activities is essential to study the risk of fracture for the elderly population. Strain prediction using the current Finite Element-Musculoskeletal (FE-MS) models is computationally expensive [1]. Surrogate Modelling (SM) offers a unique alternative for predicting the strain field over the femur in a fraction of the time needed by FE-MS models. The objectives of this research were (i) to develop a surrogate model than can accurately and efficiently predict the strain distribution for five different activities, and (ii) to assess the effect of increasing the number of samples on the accuracy of the results

Medicine and the virtual physiological human

The Virtual Physiological Human (VPH) is a European initiative that focuses on a methodological and technological framework that enables collaborative investigation of the human body as a single complex system. This collective framework will make possible to share resources and observations formed by institutions and organizations, creating disparate but integrated computer models of the mechanical, physical, and biochemical functions of a living human body. The VPH initiative has constituted the base for integrating heterogeneous data sources into mechanistic computer models of most anatomical systems. This chapter focuses on VPH-related models of the human musculoskeletal system in orthopedics with a view toward personalized, predictive, and preventative medicine. We present the integration of technologies combining heterogeneous data sources, experimental, and numerical methods focusing on the anabolic effect of physical activity as a means for reducing the risk of hip fracture and for determining anatomical, physiological, and surgery factors in short- and long-term stability of total hip replacements.</p