Liliana Beldie, Brian Walker, Arup, Solihull, UK

Measurements and Characterisation of

Human Tissues and Structures, Greenwich

29th October 2009

The Importance of Test Data in Simulation

Contents

• Arup – General overview

• Case studies:• Eye modelling

• Muscle modelling

• Summary

Arup

Engineering consultancy: building,

civil, transport, power, oil & gas,

environmental, mechanical,

automotive, railway, aerospace,

product development, healthcare.

Formed in 1946, the firm now has over 9000 staff based in 70 offices in 32 countries

Arup - Example Major Projects

• City Hall, London

• Olympic Stadium, Beijing

• Channel Tunnel Rail Link, England

• Beijing National Aquatics Centre, The Water Cube

• Transforming pathology services

• Delivering mobile diagnostic services

• Bringing new service providers to

market

• Developing new ways to finance

property

• Introducing new ways of teaching

• Assisting leadership in clinical reform

• Developing therapeutic environments

• Improving the users experience

• Communicating the value of good

design

• Improving layout to transform performance

Arup HealthcareA range of services to the UK Healthcare business.

• Product development of new medical devices and materials

• Introducing new methods, enhancing performance, and improving safety.

Arup Healthcare

Arup – Advanced Technology

and Research

Arup AT+R

• Group within the Consultancy Division of Arup

• Provides technology solutions to External and

Internal Clients

• Areas of expertise include• Vehicle Engineering

• Crashworthiness

• Occupant Protection

• Nuclear Packaging

• Wind Engineering

• Seismic Engineering

• Software Development

• …….

Oasys LS-DYNA® Environment Software

Arup AT+R Biomedical

• Eye modelling for:• Impact

• IOP measurement

Eye Model for impact

• Impact with golf ball

• Material Models:

• Skin – Mooney-Rivlin material model;

• Globe and fat – Elastic

• Globe and fat – linear elastic material ok?

• Skin – Mooney-Rivlin material ok?

• What is the model used for?

Eye Model for IOP

• Glaucoma is the second leading cause of blindness in the world

• High Intra Ocular Pressure (IOP), i.e. >22mmHg, is one of the causes of glaucoma

• IOP is the only proven modifiable risk factor to reduce the rate of progression of glaucoma

• This implies constantly monitoring the IOP

• Direct measurement of IOP through cannulation

• Indirect measurement of IOP – Goldman Applanation Tonometry (GAT) which is the golden standard of IOP measurement

• IOPG = Applanating Force/ Contact area

• Small contact area – diameter 3.06mm – the applanation will elevate the IOP only slightly

• GAT is based on an average Central Cornea Thickness CCT = 0.520mm

Eye Model for IOP

• Corneal Central Thickness (CCT) range 0.427-0.620mm:

• African-Americans 0.521mm

• Japanese 0.531mm

• Caucasians 0.550mm

• Refractive surgery – thinning of cornea

• There is an association between reduced CCT and advanced glaucoma, which may be partly due to inaccuracies in correctly measuring IOP

• Doughty and Zaman showed that a 10% change in CCT could result in a 3.4mmHg difference in IOP; for example:

• A patient with a measured IOP of 20mmHg and a CCT of 0.450mm (approx. 20% below normal) could potentially have a true IOP of 27mmHg

• Conversely, a patient with the same measured IOP of 20mmHg but aCCT of 0.650mm could have a true IOP of 13mmHg

• Goldman Applanation Tonometry – applanation of cornea

• This will give the IOP – but includes the stiffness of the cornea

• Stiffness of cornea depends on:

• Thickness of cornea

• Geometry of cornea

• Material properties (due to for ex. age)

• Thickness of cornea can be measured in conjunction with IOP test and correction factor added

• What about geometry & material parameters?

• Detailed FE model would be useful

Eye Model for IOP

• Needed for detailed FE model of the eye:

1. Material data, i.e. Young’s modulus, stress/strain data, Poisson’s ratio, Bulk modulus, density &

2. Detailed MRI images of:

• Cornea

• Sclera

• Iris

• Lens

• Suspensoryligament of lens

• Aqueous & Vitreouschambers

Cornea

Sclera

Lens

Suspensoryligament of

lens

Iris

Aqueous anterior and

posterior body

Vitreous body

Eye Model for IOP

Eye Model for IOP

• Structure of cornea:

1. Epithelium

2. Bowman's Layer (0.008-0.014mm)

3. Corneal Stroma (0.500mm)

4. Descemet's Membrane (0.005-0.010mm)

5. Endothelium

• Previous studies showed that the layered nature of cornea is important for IOP simulation of measurements

1

2

3

45

Eye Model for IOP

• Cornea – example of data

• Diagram shows stress-strain relationship of porcine corneas 24h post mortem; control, 1% and 4% glutaraldehyde treatment to stiffen the cornea

• How to obtain material data for individual layers to build the ‘composite’ model of cornea?

• GAT simulation

Eye Model for IOP

107 No initial pressure

Measured IOP: 2.6mmHg

106 with initial pressure 16.5mmHg (2.2e-3MPa)

Measured IOP: 18.2mmHg

Muscle modelling

Brian Walker, Liliana Beldie, Arup, Solihull, UKStephen Richmond, Yongtao Lu, Cardiff University, Cardiff, UK

Muscle modelling

• Maxillofacial surgery – a specialist surgical procedure involving the correction or rebuilding of the face following trauma or disease

• Bimaxillary Osteotomy:• Le Fort I Osteotomy of the Maxilla

• Sagittal Split Osteotomy of the Mandible

• The computer simulation of the surgery would provide:

• Tool for preoperative planning –various scenarios can be tested

• Realistic prediction of the resulting facial appearance

• The FE facial model can also be used for facial expressions and speech simulation

Muscle modelling

Temporalis

Orbicularis

Oculi

Masseter

Buccinator

Depressor

Anguli Oris

Levator Labii

Superioris Alaeque

Nasi (LLSAN)

Levator Labii

Superioris

Zygomaticus

major and minor

Orbicularis

Oris

Depressor Labii

Inferioris

Mentalis

The FE model with the muscles listed – page 1:

Risorius

Geniohyoid

Mylohyoid

Stylohyoid

Posterior

DigastricAnterior

Digastric

Hyoid bone

The FE model with the muscles listed (20) – page 2:

Medial Pterygoid

Lateral

Pterygoid

FE simulations using LS-DYNA

• Two types of analyses:

• Maxillofacial osteotomy – the maxilla and mandible are severed and repositioned; the muscles are non active during this simulation

• Facial expressions – user defined material to capture the muscle contraction

• Muscle – active, non-linear, anisotropic and viscoelastic

• Hill’s three-element model proposed in 1938 still used today, based on frog sartorius muscle:

CE

PE

SEE

FMFM

fv(λ˙f)ft(t)

L

PE = Parallell (passive) element

SE = Serial element

CE = Contractile (active) element

ft(t) = Activation function

fλ(λf) = Force-stretch

function

fv(λ˙f) = Force-velocity function

fλ(λf)

Constitutive muscle model

PE

CESE

Isometric Contraction(constant muscle length):

- CE shortens- SE lengthens and - PE is constant

Concentric contraction(muscle shortening):

- CE, SE and PE shorten

CESE

PE

Constitutive muscle model

Constitutive muscle model

• The mechanical property of an incompressible transversally isotropic soft tissue is uniquely determined by its strain energy density, from which the stress-strain relationship can be calculated

• Strain energy proposed for active quasi-compressible fibre-enforced and

hyperelastic muscle (J.A.C.Martins et al. 1998):

)()()( 1 JUUIUU Jff

C

I ++= λ

Where: (isotropic matrix)

(muscle fibre)

(volume change)

( ) ( )[ ]{ }13expC

1

C

1 −−= IbcIU I

( ) ( )21

1−= J

DJU J

),()(),,( sfSEfPEsaff UUU λλλλαλ +=∆

Withwhere stretch ratio in PE

in un-deformed config.

where is stretch ratio in SE

−

= ∫,0

,)1(4)( 1

2

0

f

dU f

m

fPE

λ

λλσλ

otherwise

1for >fλ

λβλλλ λα

deUf

s

sfSE ∫ −= −

1

)1(]1[),(

fλ

sλ

fλ

Constitutive muscle model (Meier & Blickhan 2000)

passiveσ lengthvelocityactivationactive σσσσ ++=

• The FE model of skeletal muscle can be created as the sum of the passive

and the active contribution

• The passive muscle is a hyperelastic rubber-like material when extended

• The stress in the active muscle can be formulated as a sum:

changevolumeisometricactivepassivetotal _σσσσσ +++=

• User Defined muscle material model for LS-DYNA

• The FE constitutive model of the muscle is active, quasi-incompressible, fibre-enforced and hyperelastic

Constitutive muscle model

Passive elongation Activated elongation

• A couple of validation results shown below

• Comparison to test results from Davis et al (2002) and Myers et al (1998) for rabbit Tibialis Anterior muscle

Constitutive muscle modelE

ngin

ee

rin

g S

tre

ss (

Pa

)

En

gin

ee

rin

g S

tre

ss (

Pa

)

Engineering Strain (%)Engineering Strain (%)

Disgust

Pre-surgery Post-surgery

Pre-surgery Post-surgery

Smile

Maxillofacial osteotomy – FE simulation

• Maxilla 5.0mm Forward & 4.0mm Up

• Mandible 8mm Rearward & 4.0mm Up

Maxillofacial osteotomy – FE simulation

• Maxilla 5.0mm Forward & 4.0mm Up

• Mandible 8mm Rearward & 4.0mm Up

Maxillofacial osteotomy – Comparison FE simulation vs. Patient

images 6 month Post-surgery using Geomagic Qualify 10

Summary

• The area of computer simulations in biomechanics is increasing rapidly with the advances in:

• Computational power

• Imaging techniques

• Limiting factor is the quality of reliable biological material data

• Limited in-vivo data available

• More constitutive material models needed

• Limited human data available

• Material data is patient specific and changes with:

• Age

• Gender

• Race

• Medical condition

Summary

• However, these limitations should not prevent us moving the technology forward; useful results are being obtained using data derived from other sources:

• Animal data

• Extrapolation of existing data

• Sensitivity studies using a range of parametric variations on the values used

• More accurate data will be obtained as the technology progresses

Thank you