SIMULATION OF AGONIST AND ANTAGONIST MUSCLE ACTIVATION PATTERNS IN BIDIRECTIONAL POSTURAL PERTURBATION IN CATS A Thesis Presented to The Academic Faculty by Alexander Koenig In Partial Fulfillment of the Requirements for the Degree Master of Science in the School of Electrical and Computer Engineering Georgia Institute of Technology August 2006 COPYRIGHT © 2006 ALEXANDER KOENIG SIMULATION OF AGONIST AND ANTAGONIST MUSCLE ACTIVATION PATTERNS IN BIDIRECTIONAL POSTURAL PERTURBATION IN CATS Approved by: Dr. Lena H. Ting, Advisor School of Biomedical Engineering Georgia Institute of Technology Dr. Robert Lee School of Biomedical Engineering Georgia Institute of Technology Dr. Magnus Egerstedt School of Electrical Engineering Georgia Institute of Technology Date Approved: 7th July 2006 Für meine Eltern – Danke für Wurzeln und Flügel! ACKNOWLEDGEMENTS The final version of this thesis turned out to be very different from what I intended it to be in the beginning. I thank my advisor Dr. Lena Ting for introducing me to the world of science and trusting in me during the changes my work underwent. I have the highest respect for her professional skills and want to thank her for pushing me in the right direction at the right time. Thanks to my reading committee, Dr. Robert Lee and Dr. Magnus Egerstedt for investing their time and commitment. I also want to thank to my colleagues: Dr. Anindo Roy, who mentored me until he left the Neurolab, Lucas McKay for great help with Matlab, Torrence Welch and Kartik Sundar for all their suggestions and improvements, Keith van Antwerp for explaining me the world of muscle contraction and my colleagues Jevin Scrivens, Nate Bunderson and Gelsy Torres-Oviedo for their tips and for proof reading - literal German translations sometimes just don’t do it.. Thanks to my roommates for allowing me to mess up their party schedule by asking for quiet on the weekends. Finally, I want to thank Danie Meyer for all her commitment to me, to my work and for her patience with me. iv TABLE OF CONTENTS ACKNOWLEDGEMENTS...........................................................................iv LIST OF TABLES.......................................................................................viii LIST OF FIGURES.......................................................................................ix SUMMARY.................................................................................................xiii INTRODUCTION..........................................................................................1 1.1 Motivation...................................................................................................1 1.2 Research Question......................................................................................3 BACKGROUND............................................................................................5 2.1 Overview.....................................................................................................5 2.2 Introduction to perturbation experiments and models................................5 2.3 Review of previous research on postural control modeling........................6 2.3.1 Postural control models of body dynamics, time delays and muscle models.................................................................................6 2.3.2 Postural control models of the CNS................................................9 2.3.3 Modeling critiques and our extension...........................................10 2.4 Dependency between platform kinematics and EMG shape....................11 2.4.1 EMG scales with platform velocity and acceleration...................11 2.4.2 Our perturbation extensions..........................................................13 2.5 Introduction to muscle models..................................................................14 2.5.1 Muscle contraction........................................................................14 2.5.2 Mechanical properties of a muscle...............................................15 v 2.5.3 Muscle models..............................................................................16 2.6 Somatosensory loss...................................................................................17 METHODS...................................................................................................20 3.1 Overview...................................................................................................20 3.2 Experimental Approach............................................................................21 3.3 Simulated data...........................................................................................25 3.4 Antagonistic muscle behavior through bidirectional perturbations..........25 3.5 Increasing model complexity with two muscles.......................................26 3.6 Predicting two EMGs with one PID controller.........................................27 3.7 Moment arms and negative EMGs...........................................................31 3.8 Predicting two EMGs with two PID controllers.......................................31 3.9 Matlab procedures.....................................................................................33 3.9.1 Optimization.................................................................................33 3.9.2 Normalization...............................................................................34 RESULTS.....................................................................................................35 4.1 Overview...................................................................................................35 4.2 Simultaneous prediction of antagonistic EMGs.......................................35 4.2.1 Two PID controllers predict EMG better than one.......................35 4.2.2 First order muscle models predict EMG better than second order models..................................................................................39 4.2.3 Muscular excitation dynamics appear to be lumped in neural time delay......................................................................................40 4.2.4 Representative optimized prediction for uni and bidirectional perturbations.................................................................................41 4.2.5 Further evidence for the correctness of our model.......................47 4.3 Shortening of a muscle prior to its contraction will not alter weighing of CoM kinematics....................................................................................49 vi 4.3.1 Overview.......................................................................................49 4.3.2 Gain variations of agonist Kp and Kv are results of the optimization..................................................................................49 4.3.3 Large gain variations in antagonist acceleration feedback are a result of CoM position and velocity kinematics...........................54 4.3.4 None optimized predictions with unidirectional feedback gains..55 4.3.5 Gains remain constant for changes in displacement magnitude...58 4.4 Results of the investigations of effects of somatosensory loss.................60 4.4.1 Representative predictions for uni and bidirectional perturbations for somatosensory loss cats...........................................................60 4.4.2 Comparison of intact vs. B6 cats..................................................67 DISCUSSION...............................................................................................69 5.1 Limitations and further annotations..........................................................71 5.2 Future work...............................................................................................71 APPENDIX A - UNIDIRECTIONAL GAINS OF ALL CATS..................73 APPENDIX B - EMG PREDICTIONS WITH CONSTANT GAINS........75 REFERENCES .............................................................................................98 vii LIST OF TABLES Table 1: Available recorded muscle EMGs for all cats....................................................24 Table 2: Available number of intact and B6 datasets for each cat....................................25 Table 3: Comparison of prediction quality for first vs. second order muscle model........40 Table 4: Cat Bear, dataset 10: Controller gain values and time delays............................45 Table 5: Correlation coefficients between recorded and predicted EMG.........................48 Table 6: Cat Bear: dataset 10. r2 values for BFMA and SRTA........................................58 Table 7: All controller gains and time delays for the optimized B6 trials........................65 Table 8: Cat Bear, unidirectional gains of perturbation eight for muscles SRTA and unidirectional gains of perturbation 16 for muscle MGAS..............................................73 Table 9: Cat Bear, unidirectional gains of perturbation eight for muscles STEN and unidirectional gains of perturbation 16 for muscle FDL..................................................73 Table 10: Cat Bear, unidirectional gains of perturbation eight for muscles SRTA and unidirectional gains of perturbation 16 for muscle BFMA...............................................73 Table 11: Cat Sooty, unidirectional gains of perturbation eight for muscles SRTA and unidirectional gains of perturbation 16 for muscle BFMA...............................................74 Table 12: Cat Squrl, unidirectional gains of perturbation eight for muscles SRTA and unidirectional gains of perturbation 16 for muscle BFMA...............................................74 Table 13: Cat Knobi, unidirectional gains of perturbation eight for muscles ILPS and unidirectional gains of perturbation 16 for muscle GLUT...............................................74 viii LIST OF FIGURES Figure 1: Stick figure models for perturbation experiment................................................7 Figure 2: EMG composition via weighed sum of CoM kinematics...................................9 Figure 3: Dependency of EMG on the platform kinematics.............................................12 Figure 4: Comparison between human and cat EMG.......................................................13 Figure 5: Perturbations......................................................................................................14 Figure 6: Force length and force velocity relationship.....................................................16 Figure 7: Nonlinear model of a muscle.............................................................................17 Figure 8: Experimental setup............................................................................................22 Figure 9: all 16 available perturbations............................................................................23 Figure 10: EMG activity of SRTA and BFMA for a bidirectional perturbation..............26 Figure 11: One link inverted pendulum models for simulation of postural control experiments. ....................................................................................................................27 Figure 12: Block diagram of the simulation system of a postural control experiment with one controller.............................................................................................................28 Figure 13: Block diagram of the simulation system of a postural control experiment with two controllers...........................................................................................................32 Figure 14: EMG prediction with one PID controller, cat Bear, dataset 10.......................36 Figure 15: Linear regression analysis of EMG correlation coefficients for varying acceleration and velocity gain...........................................................................................37 Figure 16: EMG Prediction with two independent PID controllers.................................38 Figure 17: Box plot for delta r2 values for SRTA and BFMA of cat Bear.......................39 Figure 18: EMG prediction with first and second order muscle model............................41 Figure 19: Predicted antagonistic EMGs for bidirectional perturbation...........................43 ix Figure 20: Predicted antagonistic EMGs for unidirectional perturbation.........................44 Figure 21: Cat Bear, dataset 10 - optimized EMG predictions for SRTA and BFMA ....46 Figure 22: Correlation between recorded CoM acceleration and recorded EMG............47 Figure 23: All gains for all datasets of cat Bear................................................................51 Figure 24: Box plots for all intact gains of cat Bear.........................................................52 Figure 25: EMG composition via CoM kinematics..........................................................53 Figure 26: Unidirectional controller gains for bidirectional perturbation simulation.......55 Figure 27: Cat Bear, dataset 10, all trials, not optimized..................................................57 Figure 28: Predicted antagonistic EMGs for bidirectional perturbation...........................61 Figure 29: Predicted antagonistic EMGs for unirectional perturbation............................62 Figure 30: Cat Bear, dataset 86, B6, all optimized EMGs................................................63 Figure 31: All gains cat bear, datasets 80 and 86.............................................................64 Figure 32: Box plots for all intact gains of cat Bear.........................................................65 Figure 33: Cat Bear, dataset 86 (B6), all trials simulated with the gains of the unidirectional perturbation gains......................................................................................66 Figure 34: Comparison intact vs. B6 EMG prediction.....................................................67 Figure 35: Cat Bear, dataset 10, muscles SRTA vs. BFMA without further optimization: simulated with the gains of the unidirectional perturbations of trial eight and 16...........76 Figure 36: Cat Bear, dataset 10, muscles STEN vs. FDL without further optimization: simulated with the gains of the unidirectional perturbations of trial eight and 16...........77 Figure 37: Cat Bear, dataset 10, muscles SRTA vs. MGAS without further optimization: simulated with the gains of the unidirectional perturbations of trial eight and 16...........78 Figure 38: Cat Bear, dataset 11, muscles SRTA vs. BFMA without further optimization: simulated with the gains of the unidirectional perturbations of trial eight and 16...........79 Figure 39: Cat Bear, dataset 11, muscles STEN vs. FDL without further optimization: simulated with the gains of the unidirectional perturbations of trial eight and 16...........80 x