Meeting, Sept 11 Muscle Fibers and Volumetric Models 1

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 3

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 4

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 5

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 6

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 8

Frame-based Approach Francois Faure et al 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 9

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 10

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 11

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 12