Simulation Analysis: Estimating Joint Loads OpenSim Workshop

Investigating a Simulation: Moments Accelerations Velocities. Angles EMGs Forces Musculotendon Dynamics Musculoskeletal Geometry Multibody Dynamics ∫∫ Controls Simulated Movement OpenSim Model Analysis Analysis Analysis Analysis An analysis probes and reports data from the model during a simulation. Fiber/Tendon Lengths Moment Arms Body Kinematics Joint Reactions

The Analyze Tool: Analyze Tool Model Analysis Analysis Analysis Controls Analyze Tool Results Simulation States Model Analysis Analysis Analysis Analysis An analysis probes and reports data from the model during a simulation.

Example: Quantifying Joint Loads Design Biomedical Devices Predict Tissue Stress Study degradation Orient to patella picture Argenson et al, J. Biomech 2005 Besier et al, MED. SCI. SP & EXERCISE, 2006 USC2000, 2009, http://www.flickr.com/photos/usc2000/3189533413/

Joint Reaction Analysis Calculate reaction forces and moments in joints Choose the joint load representation Available from the Analyze Tool

Joint Reaction Analysis Two Part discussion Conceptual Overview: Estimating joint forces and moments during gait. Demonstration: Static Optimization and a Joint Reaction Analyses.

           

What loads are transferred across the joint interface? Cut apart the joint What loads are transferred across the joint interface? Joint loads constrain the tibia to move on the ellipse.     Joint reaction loads prevent the tibia from penetrating the ellipse, but allow the tibia to rotate and translate around the ellipse.  

Estimating Joint Loads Know Model Joint Kinematics External Loads Muscle Forces Fit to measurements Estimate Visual cue for static optimization similarities Calculate Joint Reaction Forces and Moments

Static Optimization Complete dynamic description Input Output Model Joint Kinematics External Loads Output Muscle Forces Muscle Activations Complete dynamic description  

Joint Reaction analysis calculates joint loads in a post processing step. This step traverses all joints in the musculoskeletal model. Sn-2 Sn-1   Sn  

Joint Reaction analysis calculates joint loads in a post processing step. This step traverses all joints in the musculoskeletal model.   Sn-1  

Joint Reaction analysis calculates joint loads in a post processing step. This step traverses all joints in the musculoskeletal model. Sn-2  

Si-1 Si Remove? Si+1  

         

        Add reformated equations where LHS is reaction force  

Joint Reaction Analysis: Setting It Up Inputs from Static Optimization Model Kinematics External Loads data Residual Actuators Inputs specific to JointReaction Muscle force data Joints of interest Bodies of interest Coordinate reference frames Go conceptual Output *_JointReaction_ReactionLoads.sto

Induced acceleration analysis OpenSim Workshop

Induced Acceleration Analysis Equations of motion M: Mass matrix Q: Generalized coordinates G: Gravity V; Coriolis and centrifugal effects S: Generalized force due to contact elements S: Muscle force F: Generalized force (muscle force) R: Force transformation materix (moment arms) M is the mass matrix, q are the generalized coordinates, G is the generalized force due gravity, V is the force due to Coriolis and centrifugal effects, S is the resulting generalized force due to contact elements, and f is a muscle force or any other applied force transformed to a generalized force via a force transmission matrix, R (which, for a muscle, contains its moment arms).

Induced Acceleration Analysis Perturbation Induced Acceleration Perturb muscle force (1N) and study effect on COM acceleration Forward integration over 0.03s Computationally expensive (days) Sensitive to contact stiffness Sensitive to time interval OpenSim 2.4 Liu, 2006 There are several issues with this approach, including the need to use very stiff contact springs in order for the contact force sensitivity to remain linear over a small integration interval, which makes forward integration of the system dynamics slow. Second, results are sensitive to the selection of the contact stiffness and the time interval over which the change in contact force is evaluated. Applying stiff 3-dimensional linear and torsional springs approximates rigid constraints imposed by a weld constraint, effectively eliminating the 6 degrees of freedom at the point of contact. Stiff 3D linear and torsional springs approximate a weld constraint

Induced Acceleration Analysis Perturbation Induced Acceleration Perturb muscle force (1N) and study effect on COM acceleration Forward integration over 0.03s Instantaneous effect Computationally expensive (days) Computationally efficient (minutes) Sensitive to contact stiffness Sensitive to time interval OpenSim 2.4 OpenSim 3.0 onwards Liu, 2006 . replaces the contribution of contact with an appropriate kinematic constraint. Kinematic constraint reaction forces are resolved simultaneously with the constrained equations of motion: [M]q¨+[C]Tλ[C]q¨=G(q)+V(q,q˙)+[R]f=B(t,q,q˙) where the constraint matrix, C, maps from components of constraint reaction forces λ , to a system generalized force (replacing the applied external force or compliant contact model, S). The kinematic constraints on positions and velocities are differentiated so that they are expressed in terms of conditions on the coordinate accelerations. The left-hand side contains the accelerations and the right-hand side defines the conditions on accelerations described as a function, B, of time, system position, and/or system velocity. Replaces the contribution of contact with an appropriate kinematic constraint. Kinematic constraint reaction forces are resolved simultaneously with the constrained equations of motion

Induced Acceleration Analysis Model Contact (Allows relative rotation) Pure rolling OpenSim provides several constraint types that are supported with an Induced Acceleration Analysis, including Point, Weld, and RollingOnSurface constraints, as summarized in the figure below. A Point constraint forces two points on separate bodies to remain coincident, but allows free relative rotation about that point, similar to a ball-and-socket joint. A Weld is similar, but also constrains the orientation of the two bodies to remain fixed to one another. A RollingOnSurface describes a constraint on a rolling body that is in contact with a plane defined on another body (Hamner et al., 2010). Translations of the point of contact normal to the plane are constrained only if the point of contact penetrates into the surface of the plane; otherwise, the point is free to lift off. When the point is in contact with the plane, its velocity relative to the plane is constrained to be zero in the plane. Finally, when in contact with the plane, the rolling body is constrained not to rotate about the normal of the surface (i.e., no twisting) at the point of contact. These four individual constraints define the kinematic behavior known as pure rolling. The point at which the constraint is applied is obtained from the point of application of a corresponding external force being applied during a forward simulation. In the case of the Weld, the orientations of the bodies are set according to current values of the generalized coordinates. constraint on a rolling body in contact with a plane defined on another body (Hamner et al., 2010)

Induced Acceleration Analysis Verify superposition Contribution to com acceleration (Liu, 2006) Kinematic or Bodykinematic Analysis When analyzing the results of an induced acceleration analysis, it is important to test whether the sum of the accelerations induced by each muscle and by gravity is equal to the total acceleration. Since the induced acceleration analysis determines the acceleration of each actuator to the total acceleration, summing the induced acceleration of all the actuators should give the total acceleration. For example, you may want to compute the sum of the contributions of each muscle force and other forces to mass center acceleration and compare that to the net acceleration of the mass center (see Liu et al., 2006 and Hamner et al., 2010). The output file for each coordinate or body acceleration contains the "total" or summed induced accelerations from all of the actuators. This total acceleration can be compared to the original accelerations of joints or the mass center which can be obtained by running the "Kinematics" analysis or "Body Kinematics" analysis in OpenSim. OpenSim also can report constraint reaction forces, such that the induced reaction forces can be summed and compared to the total simulated and/or measured reaction forces to test the accuracy of the constraint in representing the contact conditions.   Next: How to Use IAA

Induced Acceleration Analysis How to use IA: COM vs angular kinematics Requires Muscle force distribution (e.g. SO) Does not work in case of missing contact forces (e.g. unilateral forces during double stance)

Example of IAA Gait2393 model Run: Scale IK (RRA) SO Analysis