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Meeting, Sept 11

Meeting, Sept 11. Muscle Fibers and Volumetric Models. Muscle Fibers. Muscle fiber orientation (pennation) has direct impact on skeletal forces Not all fibers are activated at once, they are excited by groups of motor neurons

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Meeting, Sept 11

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  1. Meeting, Sept 11 Muscle Fibers and Volumetric Models

  2. Muscle Fibers • Muscle fiber orientation (pennation) has direct impact on skeletal forces • Not all fibers are activated at once, they are excited by groups of motor neurons • Point-to-point models incorporate a single pennation angle along action line (Zajac 89, Delp 90)

  3. 3D Models • Allow for contact, volume preservation and non-penetration constraints • Scheepers 97 / Wilhelms 97 / Kahler 02 • Implicit surface techniques • Potential field defined by blending ellipsoid primitives • Chen 92 / Zhu 98: • Simplified linear FEM model, muscle surface embedded in an FEM lattice • No internal muscle architecture • Hirota 01: • Isotropic FEM with contact forces, but no force generation

  4. 3D Models • Johansson 00: • FEM including active component in constitutive, toy examples with single fiber direction • Lemos01: • FEM, multi-pennate toy example, for volumetric deformation

  5. 3D Models • Teran 05: • Finite Volume Method, applied to tetrahedral elements • Body-Centered Cubic (BCC)Tetrahedral lattice • 10x speed-up, compared to FEM, but results not validated • Blemker 05: • FEM with active component/fiber directions in constitutive model • Use hand-crafted template fiber arrangement • Geometric/moment-arm validation for hip flexion • Currently used in ArtiSynth

  6. Pseudo-3D Models • “Graphical” 3D models • Dynamics driven by p2p model along line of action • Volumetric deformation based on length of action line • B-Spline solid (Ng-Thow-Hing 00), radial forces (Porcher-Nedel 98, Aubel 02), medial representation (Gilles 07) • A type of “skinning”, contact forces can be transmitted back to medial lines

  7. Key Points • Fiber pennation is important, should be captured in model • Most muscle simulations still use point-to-point representations • 3D methods generally lack validation, and include only a basic description of fiber patterns • FEM meshes are either hand-crafted or tetrahedral • Tetrahedral meshes exhibit locking artifacts, hex meshes are preferred • Automatic hex mesh generation is still an open problem • Much of current 3D research focuses on graphics applications, sacrificing fidelity for speed

  8. Mesh-Free Methods • Relatively new field, mostly developed in last 20 years • Eliminate much of the hassle involved in mesh generation • Traditional FEM methods will require you to re-mesh an entire volume to change scale, which is a non-trivial problem • Rely on the “Weakened weak formulation” (W2) • Can be point-based, edge-based, or cell-based • Smoothed Point-Interpolation Methods (S-PIM) • Can produce upper-bound solutions with no volumetric locking (FEM methods typically produce lower-bound solutions) • Offers possibility of "soft" models that work well with tetrahedra • Smoothed Finite Element Method (S-FEM), linear version of S-PIM • S-PIM and S-FEM are currently used in solid mechanics and computational fluid dynamics problems

  9. Frame-based Approach • Francois Faureet al. 2011 • A type of “mesh-free” method • Introduce material properties directly into the shape functions, as opposed to simple radial-basis functions used in S-PIM • Allow very coarse discretization for non-uniform stiffness • Currently only linear, isotropic material • Focused on applications in graphics

  10. Questions to be answered: • For what situations is a point-to-point muscle not sufficient (if any) • For kinematic studies? • For dynamic studies? • What level of detail is required to show significant differences? • Resolution of FEM mesh • Resolution of muscle fiber description • Can we develop a mesh-free method that incorporates the non-linear/anisotropic behaviour of skeletal muscle tissue? • Evaluation of models • Compare to state-of-the-art point-to-point • Various resolutions of FEM

  11. Next Steps • Construct bone-joint model of forearm/wrist/hand • Implement point-to-point muscle/tendon model • Align all arm fibers to FEM muscle meshes (or muscle meshes to fibers) • Implement FEM muscle model • Note: still significant work to create valid meshes, attachment areas, tendons • Investigate existing mesh-free methods, with the goal of creating one to handle muscle actuation

  12. Issues with current model • Fiber alignment: • If geometries very different, alters pennation angle significantly • Take a look at Mayo. Rav.’s thesis, attempted to compensate • Incomplete muscles / missing tendon components • Use tendons from fiber scans • May need to go back to visible human data • Un-natural shapes • Bicep/Tricep too large, tricep has wrong number of heads

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