PowerPoint Presentation

The finite element muscle modelling cookbook

And the importance of fibresC. Antonio Snchez*Dept of Elec & Comp EngUniversity of British ColumbiaVancouver, BC, Canadaantonios@ece.ubc.caJohn E. LloydDept of Elec & Comp EngUniversity of British ColumbiaVancouver, BC, Canadalloyd@cs.ubc.ca

*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