March 6th, 2009

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The Mechanical Behavior of Orbital Fat in a Finite Element Model of Orbital Mechanics

by Frans-Willem Goudsmit

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Human eye movement

• To view objects when the head is moving

• Gaze towards new object of interest that pop up

• Maintaining gaze on interesting objects

• Follow objects as they move

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• The human eye• Previous mechanical models• Need for a new model• Finite element principle• Construction of the model• Results• Conclusions

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Koornneef L. Architecture of the musculo-fibrous apparatus in the human orbit. Acta Morpol Neerl-Scan 1977;15:35-64.

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Tissue interaction

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What is the relation between the material properties of the orbital fat and the mechanical behavior of the eye and eye muscles?

What are the interactions between the moving parts and the orbital fat, in the orbit?

Research questions

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Clinical relevance

• Orbital traumas, e.g. blow-out fracture

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Clinical relevance

• Orbital traumas, e.g. blow-out fracture

• Orbital tumors

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Clinical relevance

• Orbital traumas, e.g. blow-out fracture

• Orbital tumors

• Graves disease

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Clinical relevance

• Orbital traumas, e.g. blow-out fracture

• Orbital tumors

• Graves disease

• Surgery

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Clinical relevance

• Orbital traumas, e.g. blow-out fracture

• Orbital tumors

• Graves disease

• Surgery

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Previous models

• Complex tissue interactions are simplified with one single force vector• Rotating sphere around a fixed point • Exclusion or merger of tissue• Simplified geometries

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Need for a new model

• A lumped model does not give insight in the complex interactions between the several tissues in the orbit.

• For full evaluation of the mechanics of the orbital fat a model with six degrees of freedom is needed.

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Finite element models

Schutte S, van den Bedem SPW, van Keulen F, van der Heim FCT, Simonsz HJ. A finite-element analysis model of orbital biomechanics. Vision Research 2006;46:1724-1731.

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Finite Element Principle

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Finite Elements in a muscle

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Construction of a Finite Element Model of Orbital Mechanics

Geometries

Material Properties

Tissue interaction

Load cases

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Construction of a Finite Element Model of Orbital Mechanics

Geometries

Marien van DittenGerard DunningSieuwerd LaddéKlaas de Vries

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MRI-images

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Obtained surfaces

Fifth order NURBS surfaces

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Finite Element Model

4-node tetrahedron mesh

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Construction of a Finite Element Model of Orbital Mechanics

Geometries

Material Properties

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Material properties

•Homogenous and isotropic•Eye•Optic nerve•Fat

•Properties of fat were measured in the past

Schoemaker et al., Elasticity, viscosity and deformation of retrobulbar fat in eye rotation. Invest Ophthalmol Vis Sci., 2006 Nov;47(11):4819-26.

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Material properties

• Eye muscles are modeled as homogenous orthotropic

• Muscle contracts along fibers

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Muscle

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Muscles

• Muscle contracts along fibers• Direction dependent material properties

No available software to model muscle tissue!

We need a proper muscle model.

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Fiber orientation

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Contraction

• Contraction with constant volume

• Muscle contraction is simulated using a thermal expansion coefficient

• Negative in fiber direction• Positive in other two directions

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Construction of a Finite Element Model of Orbital Mechanics

Material Properties

Tissue interaction

Geometries

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Tissue interaction

Fixed or sliding?

• Fat and orbital wall

• Muscles and eye• Fat and optic nerve• Fat and muscles

• Fat and eye

• Muscles and orbital wall

• Superior oblique and superior rectus muscle• Inferior oblique and inferior rectus muscle

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Tissue interaction

Are the interactions between the moving parts and the orbital fat based on sliding or on attachment?

• Two mechanical models• Sliding• Tissue attachment

• Results of horizontal rotation are compared with MRI

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First finite element model of the human orbit including sliding!!

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Construction of a finite element model of Orbital Mechanics

Material Properties

Tissue interaction

Load cases

Geometries

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Load case

Series of loads and displacements to simulate a situation.

• Initial displacements in the model• The outer boundary of the fat• Back-end of eye muscles, fat and optic nerve

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Model vs in-vivo measurements

• Interpretation of results

• Validation of the model

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Load case 1

• Pretension of the straight muscles

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Load case 2

• Contraction of a rectus muscle and relaxation of the antagonist resulting in rotation

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Load case 3 & 4

• Two forced duction tests• Horizontal forced duction• Torsional forced duction

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Results

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Muscle paths

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Resultsy

x

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Tissue interaction

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Results

• Horizontal forced duction creates a displacement towards the direction of the nose

• Very soft orbital fat facilitates easy eye rotation

• Very soft fat gives enough support to the eye to rotate around a virtual point of rotation

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Conclusions

• The mechanical behavior of fat and eye muscles can be well described with the finite element model based on the known properties of the orbital fat. As confirmed by comparisons with in-vivo measurements.

• The predictions of the model can not be entirely validated with the use of a homogenous isotropic material.

• The eye can not rotate without sliding between the tissues inside the human orbit. Frictionless sliding between interacting tissues facilitates eye movements.