Residual Reduction Chand T. John

Subject-Specific Simulation Preprocess Marker Position Data Force Plate Data Hospitals Scale Model to Subject Simulation Inverse Kinematics Analysis

NMBL Simulation Problem qexp(t1), …, qexp(tN) Fleft(t1), …, Fleft(tN) Fright(t1), …, Fright(tN) Tleft(t1), …, Tleft(tN) Tright(t1), …, Tright(tN) COPleft(t1), …, COPleft(tN) COPright(t1), …, COPright(tN) Pad, filter, spline-fit IK qexp(t) Fleft(t), Tleft(t), COPleft(t) Fright(t), Tright(t), COPright(t) “Inverse Dynamics” via Forward Dynamic Simulation u(t1’), …, u(tM’) Forces(t1’), …, Forces(tM’) Tracking q(t1’), …, q(tM’)

Simulation Challenges Maintain efficiency without losing accuracy Dynamic optimization is accurate but slow1,2 Maintain consistency between3: experimental kinematics (from marker data) experimental kinetics (from force plate data) 1 F. C. Anderson, M. G. Pandy. Dynamic Optimization of Human Walking. Journal of Biomechanical Engineering 123: 381-390, 2001. 2 F. C. Anderson, M. G. Pandy. Static and Dynamic Optimization Solutions for Gait Are Practically Equivalent. Journal of Biomechanics 34: 153-161, 2001. 3 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press.

Existing Simulation Algorithms Dynamic Optimization1 Optimal Tracking2 Computed Muscle Control3 Speed Slow (weeks) (days) 10 minutes Predict Novel Movement Emergent Behavior Tracking (but not all DOFs) Performance Criteria Any Global Static Only at each time step  (Exp – Model)2 VarExp 1 F. C. Anderson, M. G. Pandy. Dynamic Optimization of Human Walking. Journal of Biomechanical Engineering 123: 381-390, 2001. 2 R. R. Neptune. Optimization Algorithm Performance in Determining Optimal Controls in Human Movement Analyses. Journal of Biomechanical Engineering 121(2): 249-252, 1999. 3 D. G. Thelen, F. C. Anderson, S. L. Delp. Generating Dynamic Simulations of Movement using Computed Muscle Control. Journal of Biomechanics 36: 321-328, 2003.

The Model Generalized Coordinates (DOF) Pelvis z position Pelvis x position Pelvis y position Pelvis tilt angle Pelvis list angle Pelvis rotation angle Right hip flexion angle Right hip adduction angle Right hip rotation angle Right knee flexion angle Right ankle angle Right subtalar angle Left hip flexion angle Left hip adduction angle Left hip rotation angle Left knee flexion angle Left ankle angle Left subtalar angle Lumbar extension angle Lumbar bending angle Lumbar rotation angle We ignore metatarsophalangeal (MTP) angles, so our numbering is a bit different from that in the images above. 1 F. C. Anderson, M. G. Pandy. Dynamic Optimization of Human Walking. Journal of Biomechanical Engineering 123: 381-390, 2001. 2 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press.

CMC Simulation Pipeline Preprocess Marker Position Data Force Plate Data Hospitals Scale Model to Patient Simulation Computed Muscle Control Inverse Kinematics Analysis 1 D. G. Thelen, F. C. Anderson, S. L. Delp. Generating Dynamic Simulations of Movement using Computed Muscle Control. Journal of Biomechanics 36: 321-328, 2003.

Unconstrained CMC Simulation Model: 8 segments, 21 DOF, 92 Hill-type muscle-tendon units Input: experimental kinematic data, kinetic ground reaction data Output: muscle excitations, forces, torques; resulting kinematics 1 D. G. Thelen, F. C. Anderson, S. L. Delp. Generating Dynamic Simulations of Movement using Computed Muscle Control. Journal of Biomechanics 36: 321-328, 2003. 2 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press.

Unconstrained CMC Problems Dynamic inconsistency between: Whole-body motion (kinematics) Foot-floor interaction (kinetics) Due to: Measurement errors Modeling assumptions So fictitious “residual” forces are needed to keep model from falling over 1 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press. 2 M. van de Panne, A. Lamouret. Guided Optimization for Balanced Locomotion. Computer Animation and Simulation ‘95, 165-177, Springer-Verlag/Wien. 1995.

REA-CMC Simulation Pipeline Preprocess Marker Position Data Force Plate Data Hospitals Scale Model to Patient REA CMC Simulation Inverse Kinematics Analysis 1 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press.

REA-CMC Simulation qx(t0) qb(t0) qx’’(ti) qb’’(ti) Nonlinear optimization Initial states Accelerations qx(t0) qb(t0) Solve for accelerations using equations of motion (i = 0, 1, …, N) qx’’(ti) qb’’(ti) qx(ti + 1), qx’(ti + 1) qb(ti + 1), qb’(ti + 1) Integrate forward in time (i = 0, 1, …, N – 1) Combine with other experimental kinematics (i = 0, 1, …, N) CMC qexp(t) Fit with seventh-order splines qexp(ti) 1 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press.

REA-CMC Problems Same data, different time intervals lead to different solutions Code chops time interval in half automatically Back angles changed unrealistically when simulating longer than half-gait cycle Large changes to lumbar extension for small reductions in error Exaggerated lumbar rotation (transverse trunk rotation) Model of head, arms, torso may be too simplistic Residuals are not mass-normalized Different walking speeds lead to different results Speed filtering may be altering accelerations 1 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press.

RRA-CMC Simulation Pipeline Preprocess Marker Position Data Force Plate Data Hospitals Scale Model to Subject Simulation Inverse Kinematics Analysis CMC RRA

REA vs. RRA vs. Unconstrained Kinematics Kinetics Constrained Constrained RRA + CMC REA + CMC Unconstrained CMC RRA will aim to keep the error that must be allowed due to modeling errors (like lack of arm motion) while throwing out excessive error. We expect zero DC offset for periodic motion. Unconstrained Unconstrained Whole-Body Motion Residuals

RRA-CMC Simulation  CMC CMC Residual Curves DC Offsets CMC Change in Kinematics Choose clamping values for each residual curve Alter torso center of mass and back angles to remove DC offsets  CMC

Sensitivity Analysis CMC Alterations One subject Torso center of mass x-coordinate ±0.01, ±0.03, ±0.05, ±0.095 y-coordinate ±0.01, ±0.03, ±0.05, ±0.1 z-coordinate ±0.01, ±0.03, ±0.05, ±0.1 Back angles Lumbar extension ±0.3, ±1.0, ±3.0, ±5.0, ±7.0, ±10.0 Lumbar bending ±0.3, ±1.0, ±3.0, ±5.0, ±7.0, ±10.0 Lumbar rotation ±0.3, ±1.0, ±2.0, ±5.0, ±7.0, ±10.0 One subject S26, child with CP Residual Curves DC Offsets CMC

Torso COM Sensitivity tx – 0.095 -4.47796 tx – 0.05 -3.93798 tx – 0.03 -3.69801 tx – 0.01 -3.45806 Default -3.33809 tx + 0.01 -3.21812 tx + 0.03 -2.97820 tx + 0.05 -2.73828 tx + 0.095 -2.19852

Lumbar Rotation Insensitivity lr – 10.0 -3.48397 lr – 7.0 -3.43946 lr – 5.0 -3.41011 lr – 2.0 -3.36664 lr – 1.0 -3.35232 lr – 0.3 -3.34235 Default -3.33809 lr + 0.3 -3.33384 lr + 1.0 -3.32395 lr + 2.0 -3.30992 lr + 5.0 -3.26845 lr + 7.0 -3.24138 lr + 10.0 -3.20173

Sensitivity Analysis Changing the lumbar rotation angle does not seem to affect the residual forces or moments significantly The families of residual curves appear to be smooth functions of the perturbation amount applied to the torso center of mass or back angles Only small perturbations are needed to make the DC offsets in RRA reasonably small RRA-CMC running time: 17 hours 60 simulations 60 minutes 1 hour × = 17 minutes/simulation

Original Residual Curve Limits   FX FY FZ MX MY MZ Max 4.877432 41.56897 11.79984 2.031777 1.99916 12.76662 Min -22.8771 -40.4885 -2.32523 -13.8106 -2.89894 -20.3816

RRA’s Improvements over REA Should run for longer time intervals with high accuracy RRA can run on any model Residuals applied anywhere on model Can distribute corrections across parameters using clamping, instead of restricting to back angles and pelvis position

REA vs RRA vs BSP Estimation REA-CMC1 RRA-CMC BSP Estimation2 Alterable Parameters Initial back, pelvis All input parameters Inertial parameters “Required” Data Full model kinematics All tracked kinematics Arm and leg kinematics Error Minimized Back, pelvis kinematics Overall kinematics GRFs and torques 1 D. G. Thelen, F. C. Anderson. Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking from Experimental Data. Journal of Biomechanics, in press. 2 B. J. Fregly, J. A. Reinbolt. Estimation of Body Segment Parameters from Three-Dimensional Gait Data Using Optimization. International Symposium on 3D Analysis of Human Movement, 13-16, 2004.

Effects of Arm Motion Arm motion and vertical free moments balance trunk torques caused by lower extremity Arm motion less important at slower walking speeds Arm fixation alters vertical free moments and transverse forces more in males than in females 1 Y. Li, W. Wang, R. H. Crompton, M. M. Gunther. Free Vertical Moments and Transverse Forces in Human Walking and Their Role in Relation to Arm-Swing. J Exp Bio 204: 47-58, 2001.

Resolving Redundancy http://pages.cpsc.ucalgary.ca/~parker/501/boha3d.gif

Resolving Redundancy Danger of optimization: falling into local minima that are not global minima; more local minima for longer time intervals cause problem for REA Monte Carlo simulation Simulated annealing1,2 better but slower Surgery for surgery 1 R. R. Neptune. Optimization Algorithm Performance in Determining Optimal Controls in Human Movement Analyses. Journal of Biomechanical Engineering 121(2): 249-252, 1999. 2 J. S. Higginson, R. R. Neptune, F. C. Anderson. Simulated Parallel Annealing within a Neighborhood for Optimization of Biomechanical Systems. Journal of Biomechanics 38: 1938-1942, 2005.

Next Steps Optimization weights on 100-10-1 scale Automatic correction suggestions Command-line repeatable RRA-CMC Automatic generation of result reports Software dissemination (February) Clamping sensitivity analysis Automatic clamping, suggestions, 