Report

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 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 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: 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) 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) 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] 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 100 Excitation Level Activation Level 90 80 Control Signal (%) 70 60 50 40 30 20 (Anderson and Pandy, 2001) 10 0 0 10 20 30 40 50 60 Time (ms) 70 80 90 100 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… shoulder Kinematics (given) Inverse Dynamics Muscle Force Calculation hand elbow