Transcript Problems in modeling orbital mechanics with the finite

Master Thesis presentation
BioMechanical Engineering
By:
Supervisors:
Joris Moerkerken
Prof. dr. ir. Fred van Keulen
Prof. dr. Huib Simonsz
Dr. ir. Matthijs Langelaar
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By Joris Moerkerken
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Organization
• Background
• Problem statement
• Methods
– A three dimensional model
– A two dimensional model approach
• Results
• Critical areas
• Conclusions
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Background
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Background
Sliding and friction between the eye and Tenon’s capsule
Eye- lid muscle
Tenon’s
capsule
Orbital wall
Eye-lid
Optic nerve
Rectus muscles
Eye-ball
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Background
Why model these structures?
• Insight in functionality of anatomical
structures.
• Mechanical properties of these structures
could help in surgical interventions.
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Background
• Mechanical models of the human eye were
created in the past.
• This was always done in systems with 3
degrees of freedom.
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Background
• In reality eye rotation is not about a single
point.
• The eye can translate and rotate on the fat, this
gives the eye 6 degrees of freedom.
• Modeling such a complex mechanical structure
can be done with the finite element (FE)
method.
• FE is used to predict deformation and stresses
in complex structures in many fields.
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Background
• How to built an FE model in 5 steps:
– 1: Obtain structure surface
– 2: Subdivide surface into cubes or elements
The whole system of elements is called: mesh
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Background
– 3: Each element needs material properties
– 4: The whole system of elements needs
boundary conditions (BC’s).
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Background
– 5: Apply conditions for a simulation
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Background
• This was first done in 2001 by van den Bedem and
Schutte.
– limited rotation (15°) real eye can go up to 50°.
• Later attempts were done to improve the model:
– Beerepoot et al. 2006, muscle model.
– Goudsmit et al. 2009, detailed anatomical structures.
• No improvement on rotation performance, still
maximum 15°. It was not clear what caused this limited
rotation.
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Summary so far
• Eye is suspended on the orbital fat.
• Modeling the mechanics of the eye in the orbit
shows functionality of anatomical structures.
• A mechanical model of the orbit was made in
2001 with the FE method.
• This model and later models did allow for
maximum 15° rotation of the eye.
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Problem statement
The goal of this study is to identify and
analyze the problems in the finite element
model of orbital mechanics in order to be able
to simulate full eye rotations.
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Methods
• Find causes of the limited rotation in the 3D
model.
• How to do this in a 3D model?
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Problem: what is happening?
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Problem: what is happening?
• What stops the simulation?
– In FE a simulation conists of several calculation
steps.
A solution is approximated, no exact solution exists
– If a simulation step convergece, the simulation can
proceed with the next step.
– If a step does not converge, the simulation is
stopped.
– In this model the simulation stopped because
convergence could not be reached.
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A new modeling approach
• Three dimensional analysis is extremely
time consuming
• A lack of insight and overview of the model
leads to an uncontrollable situation
• A controllable situation is needed to solve
the problems
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Methods
• One way to simplify the situation is to go
back to 2D.
• Faster simulations
• One plane to analyse instead of 3D
environment
• A more insightful situation is formed.
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How to built a 2D model
The 5 steps:
• 1: Obtain structure surface
– MRI slice
– Overlay curves on the surfaces
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How to built a 2D model
2: Create mesh
3: Assign material properties
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How to built a 2D model
• 4: Apply boundary conditions
– Orbital wall, muscle back ends and the optic
nerve back end are fixed.
– Important determinant in model: contact
between structures.
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How to built a 2D model
Sliding between structures
• Fat and eye
• Fat and orbital wall
• Fat and muscles
• Fat and optic nerve
• Muscles and eye
• Muscles and orbital wall
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How to built a 2D model
• 5: simulate eye rotation
– Contract one muscle
– Relax the antagonist muscle
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Recap
• The 3D FE model was unsuited to identify
problems
• A 2D FE approach was thought to create a
controllable base to find problems
• A 2D FE model was built
• A rotation can now be simulated
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2D simulations
• Rule out causes of problems:
– First rotate the eye about a fixed point excluding
the fat
– Add structures to see where problems start to
occur
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2D model: Muscle contraction
• Simulate eye rotation about a fixed point.
• No problems were found in this simulation.
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2D model: eye rotation with two muscles
• Simulate eye rotation about a fixed point.
• No problems here either.
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2D model: eye rotation on fat
• Simulate eye rotation on the fat.
• To rule out problems with the fat.
• A finer mesh was chosen, adequate for this problem?
• Rotation on the fat seems problematic.
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2D model: eye rotation on fat including
the optic nerve
• Problems were observed.
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Problems in modeling the fat
• Fat is almost incompressible
• Fat is highly inhomogeneous
• Mechanical behavior is different in each
region
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Problems in modeling the fat
Incompressible material:
• No change in volume (isovolumetric) when
compressed
• Results in overly stiff response of the
element
• Results in too small displacement
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Results: four main problems
• Distorted mesh
• Contact between structures is not simulated
correctly
– Penetration of elements
– Loss of contact
• How to choose a correct mesh size
• Incompressible behavior of elements
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Results 2D model
• These problems cannot be solved one at the
time, they relate to each other.
• This 2D model shows problems, the causes
of these problems are still not found.
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Results 2D model
Now it is time to look at the areas where the
problems occur in order to find causes and
possible solutions.
• Three critical areas
• Simulate focussed subtasks
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Critical areas
• 1: Muscle attachment on the eye
• 2: Optic nerve attachment on the eye
• 3: Fat directly behind the eye
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Critical area (2) Optic nerve attachment
on the eye
What happens in this area?
Fat flows around the optic nerve as the eye
rotates (Schaafsma 2010).
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Critical area (2) Optic nerve attachment
on the eye
Is this flow behavior observed in the model?
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Critical area (2) Optic nerve attachment
on the eye
Flow behavior not observed in the
simulation.
We do observe:
•
•
•
•
1: Highly distorted mesh: large deformations.
2: Penetration of elements occurs.
3: Bad incompressible behavior.
4: A gap is formed: lack of pressure gradients.
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Critical area (2) Optic nerve attachment
on the eye
1: Highly distorted mesh, what happens here?
Aspect ratio is negative, the simulation does
not converge
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Critical area (2) Optic nerve attachment
on the eye
1: Highly distorted mesh
How to prevent bad aspect ratios?
– Remesh algorithm is employed:
• Creates a new mesh in the calculation step where a
distorted mesh is formed.
– Remesh criteria:
• Based upon distorted mesh
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Critical area (2) Optic nerve attachment
on the eye
2: Penetration problems, what happens here?
• Contact algorithm
– Searches for contact in an area around the
elements.
– Creates ties between nodes.
– Looses contact if the seperation treshold is
exceeded (e.g. positive reaction force)
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Critical area (2) Optic nerve attachment
on the eye
2: Penetration problems
Sensible for stepsize!
• Nodes are searched at a certain distance of the
element side.
• This distance is smaller than 5% of the
smallest element side.
• If an element has a larger displacement in one
step compared to this distance, no contact is
detected: penetration occurs.
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Results 2D model
3: Bad incompressible behavior:
It was found that a specialized group of
elements called “Herrmann elements” can
cope with incompressible material behavior.
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Results 2D model
• 4: A gap is formed
– No adequate solution was found.
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Critical area (2) Optic nerve attachment
on the eye
Proposed solutions:
• Contact problem:
– Adaptive stepsize: link stepsize to deformation
fields, this prevents penetration
• Distorted mesh problem:
• Remesh the original mesh when the mesh gets distorted, this
prevents distortion
• Herrmann elements for incompressible
behavior
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Critical area (2) Optic nerve attachment
on the eye
Performance improved.
• No mesh distortion
• No penetration
• Still a gap...
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Back to our original 2D model
• Incorperate solutions that were found in the
analyses of the critical areas shows:
– Improved simulation:
• No distorted mesh
• No penetration
• Allow for rotations up to 30°
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Conclusions
• 3D model unsuited to identify problems
• Problems could be found in the 2D model
• Split up this complex modeling task in more
focused subtasks shows causes of problems
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Conclusions
Better performance of the model is expected if
• Adaptive stepping procedure is used
• Remeshing of distorted mesh is used
• Herrmann elements for incompressible
behavior are used
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Conclusions
There is however still the problem of lack of
pressure gradient. The problem of gaps
could not be solved adequately.
FE simulations are specially created to
model solid structures. Fat seems to behave
more like a fluid.
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Conclusions
The elements representing the orbital fat
impeed the large deformations occuring in
the orbit and leave gaps in the mesh:
This raises the question whether the orbital
fat could be modeled properly with FE.
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