PowerPoint Presentation
The finite element muscle modelling cookbook
And the importance of fibresC. Antonio Snchez*Dept of Elec &
Comp EngUniversity of British ColumbiaVancouver, BC,
[email protected] E. LloydDept of Elec & Comp
EngUniversity of British ColumbiaVancouver, BC,
[email protected]
*presenting author
My name is Antonio, Im a PhD student at UBC, I work in the area
of volumetric muscle modelling
Today I am presenting our Finite Element Muscle Modelling
Cookbook; how we assemble these models of muscles from various data
sources.1Finite Element(FE) Muscle Models
Extensor Carpi Radialis LongusMasseterLike all good cookbooks,
we need to start with nice pictures (or in this case, videos) so we
know what were getting
Were focussing on skeletal muscles. They are made up of fibres,
and have this ability to contract, which then exerts forces on
bones, allowing us to move. These muscle can be quite simple, like
the Extensor Carpi Radialis Longus, or can have complex fibre
arrangements which allow a muscle to contract in different ways,
like this masseter.2FE Muscle Models
Volumetric MeshFibre Field(s)Constitutive Law(Blemker, 2005)Here
are the components of an FE muscle model - You have a volumetric
mesh that represents the muscle geometry and is able to deform It
is divided up into a bunch of building blocks, or elements. - Fibre
field that is associated with the muscle, affects the behaviour - A
mathematical description that binds the two together.
This law tells us how the tissue deforms according to various
stresses. Because of its fibrous structure, muscle tissue it is
anisotropic, depending on the fibre direction. So, this must be
included. It is also dependent on an activation level. When muscle
tissue is activated, this induces an internal stress which causes
it to contract along the direction of the fibres.
Note that this is a continuum approximation. We are not
simulating individual fibres. Instead of forces and lengths, we are
dealing with stresses and strains.
3Fibre Geometries
Fibre templates (Blemker & Delp, 2005)
Digitized Fibres (Ravichandiran et al., 2009)How do we assign a
fibre field to a particular muscle? Unfortunately, we cant
accurately measure fibres using conventional imaging techniques,
particularly for deep muscles.
The current standard practice is to register a field from a
minimal set of templates. Is this sufficient? How much of an impact
to small changes in this field make on simulations?
There is some great work coming out of UofT, where they are
digitizing fibres from cadavers through a dissection process. We
are currently investigating using these in our muscle models. That
way, we will have detailed muscle-specific templates.
Questions:How much detail do we need?
4Fibre Geometries
DigitizedTemplatePoint-to-Point (Axial)Heres an example of what
I mean. For the extensor carpi radialis muscle, a created three
different models. The first uses a fibre field based on the
digitized fibre set, the second uses a generic template, assuming
fibres run mostly parallel from end-to-end (which is true for this
particular muscle), and a simple point-to-point type of field,
assuming all fibres run in a single direction along the line of
action.
How much difference does it make?5Fibres matter!45
DigitizedTemplatePoint-to-Point (Axial)Well, let me jump to the
last slide, and say it can actually make quite a difference. If we
clamp the two ends and let this thing contract (isometric
contraction), you can see that we get different shapes. We can
measure the shape change using a Dice coefficient, which basically
measures the percentage overlap when you align these things.
The model using template fibres is off by about 20%, and the
simple point-to-point one is off by 10% compared to the model using
digitized fibres.
Alright, well maybe shape change isnt our primary concern. What
about forces generated6Fibres matter!
Axial has same force-length relationshipTemplate force is scaled
1.46xI measure the end-to-end forces produced during isometric
contraction, and create a force-length curve by gradually changing
the distance between end-points.
The axial has the same force-length profile as that for
digitized fibres, even though the shape was different. Okay but the
force-length relationship for the model using template fibres is
scaled by about 1.5 times, which is quite significant.7
Fibre-Rich FE MuscleTarget surface geometryTemplate volumetric
meshFibre geometry
IngredientsDirectionsCreate Volumetric MeshRegister template to
targetRecondition elements
Register Fibre FieldWrap fibres with surfaceRegister to
targetAssign element propertiesExtract directions from
fibresAlright, now lets jump back to the beginning and go through
how we put these models together.
- We assume you start with three things: a target surface
geometry, some kind of template volumetric mesh (Ill discuss why in
a second), and a fibre field. Step one:8Assign element
propertiesExtract directions from fibresRegister Fibre FieldWrap
fibres with surfaceRegister to target
Fibre-Rich FE MuscleTarget surface geometryTemplate volumetric
meshFibre geometry
IngredientsDirectionsCreate Volumetric MeshRegister template to
targetRecondition elements
Create the final volumetric mesh9Volumetric Meshes
Muscles are highly deformableStructured hexahedral meshes
preferredMost are hand-craftedInternational Union of Physiological
Sciences (IUPS) Physiome ProjectCollection of template meshes
Register template shapes to target geometryOne of the reasons
muscles are so hard to model using finite elements is that they are
highly deformable. In such cases, if you want accuracy and
robustness, you need structured hexahedral meshes. Unfortunately,
muscles can have quite complex shapes, and automatic generation of
well-conditioned structured hexahedral meshes is still an
open-problem.
These days, most meshes are hand-crafted, which takes a lot of
time and effort. This is really limiting the wide adoption of FE
models for muscles.
Luckily for us, thanks to Poul Nielson, who spoke earlier today,
we at least have a starting point: access to a set of volumetric
meshes that we can use as templates. These are part of the IUPS
Physiome Project.
Instead of hand-crafting a mesh from scratch for each subject,
we register one of the same muscle (or similar) from this set of
templates, speeding up the mesh-generation process.10Volumetric
Meshes
PoorGoodElement ConditioningDeformable Registration
For muscles with simple shapes, we can get away with using
simple templates. For this masseter, I use a rectangular grid as a
template. All we need to do is apply a deformable registration
technique to morph the template to the new geometry. This is a
finite-element based registration.
Unfortunately, this process can sometimes leave us with poorly
conditioned elements ones that have highly irregular shapes. The
less regular, the less robust your model will be. So, to combat
this, were working on a method to push some of those internal nodes
around to improve the conditioning.11Assign element
propertiesExtract directions from fibres
Create Volumetric MeshRegister template to targetRecondition
elements
Register Fibre FieldWrap fibres with surfaceRegister to
target
Fibre-Rich FE MuscleTarget surface geometryTemplate volumetric
meshFibre geometry
IngredientsDirections
Step 2, register the fibre field12Fibre Registration
(Lee et al., 2012)As an initial step, we convert the set of
fibres into a volume by wrapping them with a surface. Thank-you to
Dongwoon Lee from UofT for helping us with this. Basically,
elliptic cylinders are fit around each fibre, minimizing gaps
between them. The cylinders are then smoothed together with an
interpolation function. To get a volume, a dense grid is sampled,
detecting whether each point falls within the collection of
cylinders.
The result is a surface geometry that entirely surrounds the
fibre field.13Fibre Registration
Video courtesy of Benjamin Gilles, INRIA Grenoble(Gilles et al.,
2007)Once we have this wrap surface, we use it to morph the whole
thing to our target geometry. Here, we see a frame-based
registration method it is somewhat similar to the FEM method we saw
earlier, but doesnt require the use of a volumetric mesh...
instead, the behaviour of governed by a bunch of 6DOF points inside
the volume.14
Register Fibre FieldWrap fibres with surfaceRegister to
target
Create Volumetric MeshRegister template to targetRecondition
elements
Target surface geometryTemplate volumetric meshFibre
geometry
Ingredients
Assign element propertiesExtract directions from fibres
Fibre-Rich FE MuscleDirectionsNow that we have a mesh and fibre
field registered with our target geometry, we need to put them
together so we can simulate it.15
Extracting Orientations
Evaluated at integration pointsFind fibres in neighbourhoodWe
cant use all the fibres we get, because we are limited by the
resolution of the mesh. Each element has a set number of
integration points, which is where the muscle behaviour is
evaluated. To make sure we use as much of the fibre field as
possible, we average fibre orientations within a neighbourhood
about each integration point. The radius of these neighbourhoods
should be chosen to maximize coverage of the fibre field, while
minimizing overlap which would cause smoothing. Here, we show the
neighbourhood spheres, coloured by the type of fibres found
inside.16
Extracting Orientations
Evaluated at integration pointsFind fibres in neighbourhoodIf we
zoom in on one of these spheres, you can see the fibre segments
inside, and we compute the principal orientation of these segments
using an SVD17Finite Element(FE) Muscle ModelsExtensor Carpi
Radialis LongusMasseter
And with that, we are done with the construction. Now its just a
matter of assigning values to various material parameters, which we
either look up in the literature, or rely on the clinicians to
measure.18 AND THE IMPORTANCE OF FIBRES ?19Preliminary
simulationsWhat level of detail is important?Axially along
muscleMinimal set of templatesFibres typically run between tendon
sheetsAre there important intricacies?
Simulation:Isometric contractionGeneric muscle propertiesIgnored
tendon componentIt remains to determine what level of detail is
required. Given a particular mesh resolution, we can only use so
much were going to be doing some smoothing anyway. Can we get away
with simple axial assumptions, or a minimal set of templates. We do
know that fibres generally run between attachment sites on tendon
sheets, is this enough, or are there important intricacies?
In this preliminary work, I simulate isometric contractions by
clamping the ends, and use generic muscle properties from the
literature. For now, I ignore the tendon components.20Fibre
Geometries
DigitizedTemplatePoint-to-Point (Axial)21Extensor Carpi
Radialis
22Flexor Digitorum Superficialis
I repeated the litmus test with a second muscle, the flexor
digitorum superficialis
Again, you can see noticeable shape difference under
contraction23Flexor Digitorum Superficialis
Axial force scaled 1.12xTemplate force is scaled 1.26xAgain the
three cases produced different results, this time plotted vs muscle
activation. 24Implications and Future WorkImplications:Might not be
sufficient to use simple templatesGeometric deformation is
sensitive to fibre orientations
Questions to answer:How much detail is enough?Can fibres be
registered between subjects?Future Work:Include tendon
structuresAccurate attachment sitesMesh-Free ImplementationIn
conclusion, maybe the detailed fibre information is important, and
its not enough to use simple templates depending on what youre
interested in. Also, deformation was found to be particularly
sensitive to small changes in fibre orientation, which might make
that a difficult metric to validate against. Although, that might
change when the muscle is connected to other tissues.
We still need to answer: how much detail is enough? We are
partly limited by FE mesh resolution, but maybe theres a point
before that where more fibre measurements do not significantly
affect simulation.
Also, we are working on the assumption that we can take a fibre
field from one subject and use it for another. Maybe the fibre
architecture varies significantly between subjects and if
simulations are sensitive to this variation, that suggests were not
justified in doing this.
Our next steps are to start considering tendon components, both
in fibre registration stage and simulation stage. We also need to
worry more about attachment sites.
25EXTRA SLIDES26