Meeting, Sept 11Muscle Fibers and Volumetric Models

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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) 2

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

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3D Models• Johansson 00:• FEM including active component in constitutive, toy examples with single fiber

direction

• Lemos 01:• FEM, multi-pennate toy example, for volumetric deformation

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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

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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

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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 7

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

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Frame-based Approach• Francois Faure et 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

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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

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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

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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 heads12