The finite element muscle modelling cookbook AND THE

The finite element muscle modelling cookbook AND THE IMPORTANCE OF FIBRES C. Antonio Sánchez* 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

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

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

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

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

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

Fibres matter! Axial has same force-length relationship Template force is scaled 1. 46 x

Fibre-Rich FE Muscle Ingredients q Target surface geometry q Template volumetric mesh q Fibre geometry 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

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

Volumetric Meshes Deformable Registration Element Conditioning Poor Good

Fibre-Rich FE Muscle Ingredients q Target surface geometry q Template volumetric mesh q Fibre geometry 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

Fibre Registration (Lee et al. , 2012)

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

Fibre-Rich FE Muscle Ingredients q Target surface geometry q Template volumetric mesh q Fibre geometry 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

Extracting Orientations • Evaluated at integration points • Find fibres in neighbourhood

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

… AND THE IMPORTANCE OF FIBRES ?

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

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

Extensor Carpi Radialis

Flexor Digitorum Superficialis

Flexor Digitorum Superficialis Axial force scaled 1. 12 x Template force is scaled 1. 26 x

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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