- Email: [email protected]
Optimal inverse dynamic simulation of human gait
S42
Abstracts / Gait & Posture 39S (2014) S1–S141
Table 1 Summary kinematics data describing how GCSH mean differs from combined mean. Difference from combined mean
Pelvic tilt Hip flex Knee flex Ankle Pelvic obl. Hip abd Pelvic rot Hip rot Foot progr
RMS
Mean
SD
Max. abs
0.13◦ 1.06◦ 1.59◦ 1.30◦ 0.40◦ 0.57◦ 0.72◦ 2.87◦ 2.13◦
−0.08◦ 0.28◦ 0.00◦ −0.63◦ 0.02◦ 0.08◦ 0.04◦ −2.74◦ 1.88◦
0.10◦ 1.03◦ 1.61◦ 1.15◦ 0.40◦ 0.57◦ 0.72◦ 0.87◦ 1.02◦
0.23◦ 1.74◦ 3.19◦ 3.51◦ 0.75◦ 0.94◦ 1.25◦ 3.97◦ 4.13◦
Diff. from mean SD
−0.07◦ −0.27◦ −0.06◦ 0.74◦ −0.06◦ −0.20◦ 0.00◦ 1.33◦ 0.13◦
RMS2 = mean2 + SD2 ). The maximum difference was also calculated. Data for GCSH is provided in Table 1. For two centers data for RCH will be identical for RMS and maximum absolute differences but opposite for signed values. This will not be the case if more than two centers are compared in this way. The standard deviation represents the variability of measurement. This is combined of physiological variability and measurement error. It tends to be relatively constant over the gait cycle and the average value is thus taken as representative measure for each variable. The smaller this value, the more consistent a specific protocol has been applied. Results: The data is remarkably consistent throughout the graphs and this is confirmed by the tabulated data. Small changes in shape are consistent with the RCH sample (black lines) walking a little faster than the GSCH sample. The RCH data also suggest more internal hip rotation and more external foot progression than the GSCH data. Discussion and conclusions: Both centers use the conventional gait model as represented by PlugInGait (VICON, Oxford, UK) but there are differences in the detail of how this is applied. McGinley et al. suggested that differences of 2◦ or less can be considered acceptable and the data shows that most variables, with the exception of hip rotation are below or only little more than this threshold. http://dx.doi.org/10.1016/j.gaitpost.2014.04.059 055 Optimal inverse dynamic simulation of human gait R. Fluit 1,∗ , M.S. Andersen 2 , N. Verdonschot 1,3 , H.F.J.M. Koopman 1 1 Laboratory of Biomechanical Engineering, University of Twente, Enschede, The Netherlands 2 Department of Mechanical Engineering, Aalborg University, Aalborg, Denmark 3 Orthopaedic Research Lab, Radboud University Medical Centre, Nijmegen, The Netherlands
E-mail address: r.fl[email protected] (R. Fluit). Introduction and aim: Using musculo-skeletal models to predict the functional outcome of severe orthopaedic interventions represents a major challenge in the biomechanics community. Combining an optimal inverse model [1] and a ground reaction force (GRF) predictive model [2] is a promising tool in predicting whether and how patients may walk, postoperatively. In an optimal inverse model, both the inverse dynamic input (i.e. the joint angles and the GRFs) and the problem of unknown muscle forces
URL: http://www.TLEMsafe.eu (R. Fluit).
are solved simultaneously by formulating a minimization function [3]. Using Newton’s Second Law, the GRF-predictive model estimates the GRFs that corresponds with the optimized motion, thereby guaranteeing dynamic consistency. Patients/materials and methods: Gait lab measurements of 10 healthy subjects were performed at the Radboud University Medical Centre. Three gait trials at comfortable speed of each subject, 30 in total, were analysed with a full body model using a musculoskeletal modelling system (AnyBody 4.2.1, AnyBody Technology A/S). Following Schwartz and Rozumalski (2008) [4], for each gait trial, all joint angles and pelvis position (33 degrees of freedom in total) were arranged in a single gait vector g. Then, 30 gait features fk were obtained by computing the singular value decomposition of the matrix G containing all concatenated gait vectors g. The gait features fk form an optimal orthonormal basis to describe the variability present in the measured gait patterns. An mth order approximation of any gait pattern can be found by multiplying the first m gait features with the feature components ck . Using a genetic algorithm (Optimization Toolbox of Matlab), new gait patterns were predicted by optimizing only m feature components ck , based on a multi-objective performance criterion: metabolic energy consumption and 100-Gait Deviation Index (GDI). The latter criterion favours gait patterns that are close to normal gait. An additional constraint ensured that the muscle activity stayed below 100 percent activation. Using the optimization algorithm, a pareto front was estimated containing all optimal gait patterns of a single healthy subject with respect to the chosen performance criteria. A virtual patient was created in which the right Rectus Femoris and right Vastus Lateralis were removed. Again, a pareto front was estimated containing all optimal gait patterns of the virtual patient. Results: The first gait feature described the average gait pattern, the following gait features described the variability present in the measured gait patterns. By optimizing only the first 5 or 10 gait features, already 79.5 and 90.3 percent of the variability was explained, respectively. The optimal solutions of the virtual patient were similar to the healthy subject, but shifted along the axis of metabolic energy consumption. Because two muscles were removed in the virtual patient, the model can recruit the muscles less optimal, increasing the metabolic energy consumption. Discussion and conclusions: Combining optimal inverse dynamics and a GRF predictive model is an important step towards predicting whether and how patients may walk after a severe orthopaedic surgery. Future work will focus on further validation of the predictive model using pre- and post-op gait lab measurements of hip dysplasia and tumor patients. Within the TLEMsafe project, software is developed to quickly generate subject-specific musculo-skeletal models. Combining this software with the predictive gait model represents an important step towards predicting the outcomes of orthopaedic surgeries. Acknowledgement The authors acknowledge the financial support provided by the European Commission through the FP7 Project.
Reference [1] Fluit R, et al.4th Dutch BioMedical Engineering Conference. 2013. [2] Andersen MS, et al.24th Congress of International Society of Biomechanics. 2013. [3] Rasmussen J, et al. 12th Conference of the European Society of Biomechanics 2000. [4] Schwartz MH, Rozumalski A. Gait Posture 2008;29:351–7.
http://dx.doi.org/10.1016/j.gaitpost.2014.04.060
Abstracts / Gait & Posture 39S (2014) S1–S141
Table 1 Summary kinematics data describing how GCSH mean differs from combined mean. Difference from combined mean
Pelvic tilt Hip flex Knee flex Ankle Pelvic obl. Hip abd Pelvic rot Hip rot Foot progr
RMS
Mean
SD
Max. abs
0.13◦ 1.06◦ 1.59◦ 1.30◦ 0.40◦ 0.57◦ 0.72◦ 2.87◦ 2.13◦
−0.08◦ 0.28◦ 0.00◦ −0.63◦ 0.02◦ 0.08◦ 0.04◦ −2.74◦ 1.88◦
0.10◦ 1.03◦ 1.61◦ 1.15◦ 0.40◦ 0.57◦ 0.72◦ 0.87◦ 1.02◦
0.23◦ 1.74◦ 3.19◦ 3.51◦ 0.75◦ 0.94◦ 1.25◦ 3.97◦ 4.13◦
Diff. from mean SD
−0.07◦ −0.27◦ −0.06◦ 0.74◦ −0.06◦ −0.20◦ 0.00◦ 1.33◦ 0.13◦
RMS2 = mean2 + SD2 ). The maximum difference was also calculated. Data for GCSH is provided in Table 1. For two centers data for RCH will be identical for RMS and maximum absolute differences but opposite for signed values. This will not be the case if more than two centers are compared in this way. The standard deviation represents the variability of measurement. This is combined of physiological variability and measurement error. It tends to be relatively constant over the gait cycle and the average value is thus taken as representative measure for each variable. The smaller this value, the more consistent a specific protocol has been applied. Results: The data is remarkably consistent throughout the graphs and this is confirmed by the tabulated data. Small changes in shape are consistent with the RCH sample (black lines) walking a little faster than the GSCH sample. The RCH data also suggest more internal hip rotation and more external foot progression than the GSCH data. Discussion and conclusions: Both centers use the conventional gait model as represented by PlugInGait (VICON, Oxford, UK) but there are differences in the detail of how this is applied. McGinley et al. suggested that differences of 2◦ or less can be considered acceptable and the data shows that most variables, with the exception of hip rotation are below or only little more than this threshold. http://dx.doi.org/10.1016/j.gaitpost.2014.04.059 055 Optimal inverse dynamic simulation of human gait R. Fluit 1,∗ , M.S. Andersen 2 , N. Verdonschot 1,3 , H.F.J.M. Koopman 1 1 Laboratory of Biomechanical Engineering, University of Twente, Enschede, The Netherlands 2 Department of Mechanical Engineering, Aalborg University, Aalborg, Denmark 3 Orthopaedic Research Lab, Radboud University Medical Centre, Nijmegen, The Netherlands
E-mail address: r.fl[email protected] (R. Fluit). Introduction and aim: Using musculo-skeletal models to predict the functional outcome of severe orthopaedic interventions represents a major challenge in the biomechanics community. Combining an optimal inverse model [1] and a ground reaction force (GRF) predictive model [2] is a promising tool in predicting whether and how patients may walk, postoperatively. In an optimal inverse model, both the inverse dynamic input (i.e. the joint angles and the GRFs) and the problem of unknown muscle forces
URL: http://www.TLEMsafe.eu (R. Fluit).
are solved simultaneously by formulating a minimization function [3]. Using Newton’s Second Law, the GRF-predictive model estimates the GRFs that corresponds with the optimized motion, thereby guaranteeing dynamic consistency. Patients/materials and methods: Gait lab measurements of 10 healthy subjects were performed at the Radboud University Medical Centre. Three gait trials at comfortable speed of each subject, 30 in total, were analysed with a full body model using a musculoskeletal modelling system (AnyBody 4.2.1, AnyBody Technology A/S). Following Schwartz and Rozumalski (2008) [4], for each gait trial, all joint angles and pelvis position (33 degrees of freedom in total) were arranged in a single gait vector g. Then, 30 gait features fk were obtained by computing the singular value decomposition of the matrix G containing all concatenated gait vectors g. The gait features fk form an optimal orthonormal basis to describe the variability present in the measured gait patterns. An mth order approximation of any gait pattern can be found by multiplying the first m gait features with the feature components ck . Using a genetic algorithm (Optimization Toolbox of Matlab), new gait patterns were predicted by optimizing only m feature components ck , based on a multi-objective performance criterion: metabolic energy consumption and 100-Gait Deviation Index (GDI). The latter criterion favours gait patterns that are close to normal gait. An additional constraint ensured that the muscle activity stayed below 100 percent activation. Using the optimization algorithm, a pareto front was estimated containing all optimal gait patterns of a single healthy subject with respect to the chosen performance criteria. A virtual patient was created in which the right Rectus Femoris and right Vastus Lateralis were removed. Again, a pareto front was estimated containing all optimal gait patterns of the virtual patient. Results: The first gait feature described the average gait pattern, the following gait features described the variability present in the measured gait patterns. By optimizing only the first 5 or 10 gait features, already 79.5 and 90.3 percent of the variability was explained, respectively. The optimal solutions of the virtual patient were similar to the healthy subject, but shifted along the axis of metabolic energy consumption. Because two muscles were removed in the virtual patient, the model can recruit the muscles less optimal, increasing the metabolic energy consumption. Discussion and conclusions: Combining optimal inverse dynamics and a GRF predictive model is an important step towards predicting whether and how patients may walk after a severe orthopaedic surgery. Future work will focus on further validation of the predictive model using pre- and post-op gait lab measurements of hip dysplasia and tumor patients. Within the TLEMsafe project, software is developed to quickly generate subject-specific musculo-skeletal models. Combining this software with the predictive gait model represents an important step towards predicting the outcomes of orthopaedic surgeries. Acknowledgement The authors acknowledge the financial support provided by the European Commission through the FP7 Project.
Reference [1] Fluit R, et al.4th Dutch BioMedical Engineering Conference. 2013. [2] Andersen MS, et al.24th Congress of International Society of Biomechanics. 2013. [3] Rasmussen J, et al. 12th Conference of the European Society of Biomechanics 2000. [4] Schwartz MH, Rozumalski A. Gait Posture 2008;29:351–7.
http://dx.doi.org/10.1016/j.gaitpost.2014.04.060