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MEGN 536 – Computational Biomechanics

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

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MEGN 536 – Computational Biomechanics

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

  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 • 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

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