Musculoskeletal Modeling and Simulation of Human Movement Workshop (WS5)

Transcription

1 Musculoskeletal Modeling and Simulation of Human Movement Workshop (WS5) Massimo Sartori Department of Neurorehabilitation Engineering University Medical Center Göttingen, Germany Monica Reggiani Department of Management and Engineering University of Padova, Italy September 15-18, 2014 Summer School on Neurorehabilitation Baiona, Spain

2 Our Research neuro- musculoskeletal modeling real-time

3 EMG-driven Modeling EMGs neuro- musculoskeletal model joint rotation forces joint compressive force joint compliance real-time modeling patient-machine interaction

4 EMG-driven Modeling how do people modulate bone-to-bone forces? joint rotation forces joint compressive force joint compliance real-time modeling patient-machine interaction

5 Patient-Prosthesis Interaction trans-femoral amputees different motor-tasks different prostheses contra-lateral leg behavior 5

6 Towards Neurorehabilitation Technologies muscle excitation multi-joint configuration Fleischer et al. IEEE T-RO 2008 EMG-driven musculoskeletal model EMG-based proportional control 6

7 Your Turn!

8 Purpose of the Workshop CREATE musculoskeletal models ground up INVESTIGATE musculoskeletal movement ACCESS low-level OpenSim through MATLAB OpenSim MATLAB 8

9 MOtoNMS Two Hands-on Examples batch process IK and ID THE INVERSE PROBLEM MATLAB scripting Dynamic Simulation THE FORWARD PROBLEM 9

10 What is Now OpenSim? OpenSim is an application 10

11 Visualize complex movement patterns Probe forces that are difficult to measure Perform what if studies Identify cause-effect relationships

12 MOtoNMS Hands-on Exercise 1 batch process IK and ID Forces Musculoskeletal Geometry Moments Accelerations Velocities. Multibody d dt d dt Angles Position Data Force Data Video Cameras Reflec7ve Markers The inverse problem 12

13 MOtoNMS Hands-on Exercise 1 batch process IK and ID Forces Musculoskeletal Geometry Moments Accelerations Velocities. Multibody d dt d dt Angles Position Data Force Data Video Cameras Reflec7ve Markers 13

14 MOtoNMS Hands-on Exercise 1 batch process IK and ID Forces Musculoskeletal Geometry Moments Accelerations Velocities. Multibody d dt d dt Angles Position Data Force Data Inverse Kinematics Identify research question for the inverse problem Determine what should be measured and modeled Compute joint kinematics Filter and differentiate joint kinematics 14

15 MOtoNMS Hands-on Exercise 1 batch process IK and ID Computing Joint Kinematics 15

16 MOtoNMS Hands-on Exercise 1 batch process IK and ID Differentiation Amplifies High-Frequency Noise x xʹ ( t) xʹ ʹ ( t) x ʹ 1 Hz signal ( t) = 20 sin( 2π t) + sin( 20π t) t ( t) = 40 π cos( 2π t) + 20π cos( 20π t) t x ʹ ʹ x 10 Hz noise SNR = 20 SNR = 2 ( t) = 80π sin( 2π t) 400π sin( 20π t) SNR =

17 MOtoNMS Hands-on Exercise 1 batch process IK and ID Forces Musculoskeletal Geometry Moments Accelerations Velocities. Multibody d dt d dt Angles Position Data Inverse Force Data Inverse Kinematics mg T m! y I! θ m, I m! x Fy Fx θ r x, x!,! x y, y!,! y θ,! θ,! θ ΣF x = mx! ΣF y = my! ΣT = I! θ Derive equations of motion defining the model Solve equations of motion for joint moments 17

18 MOtoNMS Hands-on Exercise 1 batch process IK and ID Forces Musculoskeletal Geometry Moments Accelerations Velocities. Multibody d dt d dt Angles Position Data Static Optimization Inverse Force Data Inverse Kinematics Major extensors Major flexors g Gastrocnemius Tibialis anterior ta s Soleus Extensor digitorum ed tp Tibialis posterior Net ankle moment M a Use musculoskeletal geometry and assumptions about force distribution to estimate individual muscle forces 18

19 MOtoNMS Hands-on Exercise 1 batch process IK and ID Static Optimization Determines the best set of muscle forces that Produce net joint moments at a discrete time Do not violate muscle force limits Optimize a performance criterion Performance criterion attempts to capture the goal of the neural control system Minimize muscle force? Minimize muscle stress? Major flexors Tibialis anterior ta Extensor digitorum g Net ankle moment Major extensors s ed tp Gastrocnemius Soleus Tibialis posterior M a 19

20 MOtoNMS Hands-on Exercise 1 batch process IK and ID Static Optimization minimize subject to f M ( ) F m Function of muscle forces [ ] ( t) = [ F ( t) r ( t) + F ( t) r ( t) ] F ( t) r ( t) + F ( t) r ( t) F ( t) r ( t) a ta ta ed ed g g s s + tp tp F ta ( t) 900N Fed( ( t) 800 Fg( t) Fs t) 2500 ( t) Ftp N 1500N N 1500N Major flexors Tibialis anterior ta Extensor digitorum g Major extensors s ed tp Gastrocnemius Soleus Tibialis posterior Net ankle moment M a 20

21 MOtoNMS Hands-on Exercise 1 batch process IK and ID Static Optimization f f f nm ( ) = F m F m m= 1 nm ( Fm ) = m= 1 3 F m PCSAm F m k PCSAm ( F ) = ( a ) m nm m= 1 Possible validations 2 m= 1 Muscle force Use output to drive a forward dynamic simulation Compare qualitatively to experimental EMG Compare to measured forces (instrumented hip implant, buckle transducer in tendon) nm m 2 Difficult to define and validate a good criterion (Muscle stress) 3 ~ Metabolic energy (Muscle activation) 2 Major flexors Tibialis anterior ta Extensor digitorum g Net ankle moment Major extensors s ed tp Gastrocnemius Soleus Tibialis posterior M a 21

22 Hands-on Exercise 2 Inverse Forces Moments Accelerations Velocities. Angles Neural Command Muscle Physiology Musculoskeletal Geometry Multibody d dt d dt Observed Movement Forward Neural Command EMGs Musculotendon Forces Musculoskeletal Geometry Moments Multibody Velocities. Accelerations Angles Observed Movement MATLAB scripting Dynamic Simulation THE FORWARD PROBLEM 22

23 Hands-on Exercise 2 Neural Command EMGs Musculotendon Forces Musculoskeletal Geometry Moments Multibody Velocities. Accelerations Angles Observed Movement CONTROLS muscle excitation SOURCES EMG Static optimization Controller INITIAL STATES joint angles joint velocities muscle activations fiber lengths STATES joint angles fiber lengths ANALYSES Point Kinematics Actuator Power MATLAB scripting Dynamic Simulation THE FORWARD PROBLEM 23

24 Hands-on Exercise 2 Neural Command EMGs Musculotendon Forces Musculoskeletal Geometry Moments Multibody Velocities. Accelerations Angles Observed Movement x(t) a(t) muscle activation, a fiber length, l! MATLAB scripting Dynamic Simulation THE FORWARD PROBLEM 24

25 Hands-on Exercise 2 Neural Command EMGs Forces Moments Musculotendon Musculoskeletal Geometry Multibody Velocities. Accelerations Angles Observed Movement muscle lines of action moment arms MATLAB scripting Dynamic Simulation THE FORWARD PROBLEM 25

26 Hands-on Exercise 2 Neural Command EMGs Musculotendon Forces Musculoskeletal Geometry Moments Multibody Velocities. Accelerations Angles Observed Movement m 3, I 3 joint angles, q joint velocities, u! q 2 q 3 m 2, I 2 m 1, I 1 y MATLAB scripting q 1 z x Dynamic Simulation THE FORWARD PROBLEM 26

27 Hands-on Exercise 2 Neural Command EMGs Musculotendon Forces Musculoskeletal Geometry Moments Accelerations Velocities. Angles Multibody Observed Movement MATLAB scripting Integration of system equations: a! l! [ ] 1 M( q) { τ( a, l, l! ) C( q,q! ) + ( q) } q! = G = Α( a, x) = Λ( a, l, q) Numerical Integration: 5 th order Runge-Kutta-Feldberg Variable Step Integrator Dynamic Simulation THE FORWARD PROBLEM 27

28 OpenSim Achitecture: Interface Layers Application main() OpenSim (GUI) Application Object interfaces define the tool library plug-in Analysis Solver Manager Analysis Modeling Model ModelComponent SimTK API SimTK::System Common, Math, Simbody

29 OpenSim Achitecture: Interface Layers MATLAB scripting Application main() tool OpenSim (GUI) Application library plug-in Solver Manager Analysis Model ModelComponent SimTK API SimTK::System Common, Math, Simbody Create and Simulate Models

30 OpenSim Model Class Structure Model Body Joint Constraint Force Controller

31 Tree Topology of Multibody Models Each body is connected by ONE joint to create a chain or open tree structure. Body Torso FreeJoint Body Ground Body Left Hand PinJoint Body WeldConstraint Weight WeldJoint Body Weight WeldJoint PinJoint Body Right Hand Constraint is required to form a closed loop

32 Joint Reference Frames parent body P P Joint B child body B B o P o B specified by joint location and orientation P specified by joint locationinparent and orientationinparent Joint coordinates specify the kinematics of B relative to P

33 Organization vs Computation An OpenSim model and its components encapsulate properties of the physical system (mass, inertia, strength, etc ) and know how to add themselves to the underlying computational system (equations) to be solved. Model Body Joint Constraint State compute something SimTK::System (MultibodySystem) Force Controller

34 Force::Muscles Force::Contact Force::Spring Force::Actuator Controller::Ac:va:on Controller::Coordinate WeldJoint Body Ground Body PlaAorm FreeJoint Body Trunk PinJoint Body Arm Body Sphere WeldJoint Contact::Geometry 5 bodies 4 joints 2 contact geometries 9 forces 2 controllers