1. Prof. Anthony Petrella Musculoskeletal Modeling & Inverse Dynamics MEGN 536 – Computational Biomechanics

2. MSM for Medical Device Design  Musculoskeletal Modeling (MSM) may be applied to activities of daily living (ADL) to find…  Kinematics – potential joint motions of interest  Kinetics – loading in joints or regions of skeleton  Muscle forces acting on skeleton  These data may be used directly in design or applied to lower scale models (FE) to focus on tissue level and implant performance in situ

3. MSM Governing Equations  MSM generally rigid body dynamics  Newton-Euler equations most common, other methods (e.g., Lagrange’s equations)  General 3D form of Newton-Euler:  For the 2D case (x-z plane) we can simplify to:

4. Inverse vs. Forward Dynamics  You will often here ref. to forward and inverse dynamics in context of MSM simulation  Figure summarizes core difference  OpenSim commonly known for forward dynamics  AnyBody commonly known for inverse dynamics (Otten, 2003)

5. Inverse vs. Forward Dynamics  FD: start with forces  accel’s  Integrate explicitly in time to get velocities and positions  Stability is not guaranteed  ID: start with positions  Differentiate wrt time to get velocities and accel’s  forces  Small position errors amplified by numerical differentiation (Hoffman, Numerical Methods for Scientists and Engineers, McGraw Hill, 1992)

6. MSM Inputs & Outputs (inverse)  Inputs to a MSM simulation usually are…  Anthropometric measures (body mass, segment props)  Marker coordinates from experimental mocap system  Ground reaction force (GRF) measurements  Electromyography (EMG) traces for important muscles  Outputs include…  All kinematics for segments and joints  Joint reaction forces at all joints  Muscle forces throughout skeleton  Interface forces between body and objects in environment  Forces expressed as F = a * Strength, where a is activation level in range [0,1]

7. Practical Difference: Forward vs. Inverse  ID generally solves for forces in each increment of motion independently  FD may consider entire motion cycle and include muscle activation / deactivation dynamics  Not necessary for accurate simulation of many activities (Anderson and Pandy, 2001)

8. Inverse Dynamics  Essential Skill  ID common, some FD methods even begin with ID  Number of parameters grows quickly  software such as AnyBody necessary for practical problems  You will do an ID problem by hand for a simple, 2-segment arm model  General steps…  Kinematics (given)  Inverse Dynamics  Muscle Force Calculation shoulder hand elbow