Transcript C. Antonio Sánchez

The finite element muscle
modelling cookbook
AND THE IMPORTANCE OF FIBRES
C. Antonio Sánchez*
John E. Lloyd
Dept of Elec & Comp Eng
University of British Columbia
Vancouver, BC, Canada
[email protected]
Dept of Elec & Comp Eng
University of British Columbia
Vancouver, BC, Canada
[email protected]
*presenting author
Finite Element(FE) Muscle Models
Extensor Carpi Radialis Longus
Masseter
FE Muscle Models
Fibre Field(s)
Volumetric Mesh
Constitutive Law
𝜕𝑊(𝒗, 𝒂)
𝑺=
𝜕𝑬
(Blemker, 2005)
Term
𝑺
𝑬
𝑊
𝒗, 𝒂
Stress tensor
Strain 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
≈ 81% overlap
Point-to-Point (Axial)
≈ 88% overlap
45
Fibres matter!
Axial has same force-length relationship
Template force is scaled 1.46x
Fibre-Rich FE Muscle
Ingredients
 Target surface geometry
 Template volumetric mesh
 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-Rich FE Muscle
Ingredients
 Target surface geometry
 Template volumetric mesh
 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
 Target surface geometry
 Template volumetric mesh
 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
 Target surface geometry
 Template volumetric mesh
 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
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 1.12x
Template force is scaled 1.26x
Axial ≈ 84% overlap
Template ≈ 79% overlap
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
EXTRA SLIDES