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The finite element muscle modelling cookbook AND THE IMPORTANCE OF FIBRES C. Antonio Snchez* Dept of Elec & Comp Eng University of British Columbia Vancouver, BC, Canada antonios@ece.ubc.ca John E. Lloyd Dept of Elec & Comp Eng University of British Columbia Vancouver, BC, Canada lloyd@cs.ubc.ca *presenting author

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Finite Element(FE) Muscle Models Extensor Carpi Radialis Longus Masseter

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FE Muscle Models Term Stress tensor Strain tensor Strain-energy density Fibre direction/activation Volumetric Mesh Fibre Field(s) Constitutive Law (Blemker, 2005)

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Fibre Geometries Fibre templates (Blemker & Delp, 2005)Digitized Fibres (Ravichandiran et al., 2009)

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Fibre Geometries Digitized Template Point-to-Point (Axial)

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Fibres matter! 45 Digitized Template Point-to-Point (Axial)

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Fibres matter! Axial has same force-length relationship Template force is scaled 1.46x

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Fibre-Rich FE Muscle Target surface geometry Template volumetric mesh Fibre geometry Ingredients Directions 1.Create Volumetric Mesh Register template to target Recondition elements 2.Register Fibre Field Wrap fibres with surface Register to target 3.Assign element properties Extract directions from fibres

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3.Assign element properties Extract directions from fibres 2.Register Fibre Field Wrap fibres with surface Register to target Fibre-Rich FE Muscle Target surface geometry Template volumetric mesh Fibre geometry Ingredients Directions 1.Create Volumetric Mesh Register template to target Recondition elements

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Volumetric Meshes Muscles are highly deformable Structured hexahedral meshes preferred Most are hand-crafted International Union of Physiological Sciences (IUPS) Physiome Project Collection of template meshes Register template shapes to target geometry

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Volumetric Meshes PoorGood Element ConditioningDeformable Registration

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3.Assign element properties Extract directions from fibres 1.Create Volumetric Mesh Register template to target Recondition elements 2.Register Fibre Field Wrap fibres with surface Register to target Fibre-Rich FE Muscle Target surface geometry Template volumetric mesh Fibre geometry Ingredients Directions

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Fibre Registration (Lee et al., 2012)

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Fibre Registration Video courtesy of Benjamin Gilles, INRIA Grenoble (Gilles et al., 2007)

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2.Register Fibre Field Wrap fibres with surface Register to target 1.Create Volumetric Mesh Register template to target Recondition elements Target surface geometry Template volumetric mesh Fibre geometry Ingredients 3.Assign element properties Extract directions from fibres Fibre-Rich FE Muscle Directions

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Extracting Orientations Evaluated at integration points Find fibres in neighbourhood

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Extracting Orientations Evaluated at integration points Find fibres in neighbourhood

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Finite Element(FE) Muscle Models Extensor Carpi Radialis Longus Masseter

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AND THE IMPORTANCE OF FIBRES ?

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Preliminary simulations What level of detail is important? Axially along muscle Minimal set of templates Fibres typically run between tendon sheets Are there important intricacies? Simulation: Isometric contraction Generic muscle properties Ignored tendon component

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Fibre Geometries Digitized Template Point-to-Point (Axial)

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Extensor Carpi Radialis

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Flexor Digitorum Superficialis

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Axial force scaled 1.12x Template force is scaled 1.26x

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Implications and Future Work Implications: Might not be sufficient to use simple templates Geometric deformation is sensitive to fibre orientations Questions to answer: How much detail is enough? Can fibres be registered between subjects? Future Work: Include tendon structures Accurate attachment sites Mesh-Free Implementation

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EXTRA SLIDES