Truestress (MPa)

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Centre for Centre for Centre for

Centre for Health Health Health Health Engineering Engineering Engineering Engineering CNRS UMR 5146

StSt

StStééééphane Avril and coll.phane Avril and coll.phane Avril and coll.phane Avril and coll.

Full-field measurements and mechanical identification for biological soft tissues

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Imperial College - 2012/03/20 - Prof Stéphane AVRIL

Mines-Telecom National Institute

INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION

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The center for Health Engineering

Improving health through science and engineering.

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52 staff in Dec. 2011:

18 faculty + 5 tech , 27 PhD students, 3 Post Docs

Research activities

HEALTH ENGINEERING

FROM FUNDAMENTAL RESEARCH TO APPLICATIONS

Chemistry, kinetics, Thermodynamics Physics of solids Mechanics

Applied mathematics Operational research, Statistic

Image processing Computer science

Orthopedics

Oto-rhino –larygology Cardiovascular

Opthalmology Immunology

Regenerative medicine Nanomedicine

Logistics of health care structures

Biomechanics of soft tissues

Surface bioengineering in grafts and implants

Health-care engineering

Engineering of biomaterials and inhalated nanoparticles

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Research in biomechanics

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Today’s seminar

1. Leg compression biomechanics 2. Vascular wall biomechanics

Full-field measurements and mechanical identification for biological soft tissues

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Leg compression biomechanics

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Context

Veinous Veinous Veinous Veinous Veinous Veinous Veinous Veinous diseases diseasesdiseases diseases diseases diseasesdiseases diseases

Sportspeople Sportspeople Sportspeople Sportspeople Sportspeople Sportspeople Sportspeople Sportspeople

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State of the art

Without EC

Shear stress (MPa)

1. Venous blood flow

2. Applied pressure

3. Tissue deformation

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Patient-specific FE

modelling: the geometry

3D

reconstruction

1 2 3

4 5 6

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Patient-specific FE

modelling: the boundary conditions

Leg circ – Sock circ Sock circ

curvature

radius

Stiff

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Patient-specific FE

modelling: the boundary conditions

1 2 3

4 5 6

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Patient-specific FE model:

the material properties

INVERSE METHOD

Inner contour Outer contour model

target

R_model-R_target

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Results

Deep soft tissue Subcutaneous soft tissue

Averages:

8.2 ± 7 kPa 3.25 ± 0.9 kPa

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Results

1 2 3

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Results

Deep vein locations Pressure vs height

Hydrostatic Hydrostatic Hydrostatic

Hydrostatic pressure pressure pressure pressure

Pressure Pressure Pressure Pressure applied applied applied applied by by by by the

the the the socksocksocksock

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Results

1 2 3

Pressure Pressure Pressure

Pressure appliedappliedappliedapplied by the by the by the sockby the socksocksock

Hydrostatic Hydrostatic Hydrostatic Hydrostatic pressure pressure pressure pressure atatatat the

the the

the deepdeepdeepdeep veins veins veins veins

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Conclusions

The compression The compression The compression The compression treatmenttreatmenttreatment shouldtreatment shouldshouldshould bebebebe patientpatientpatient-patient--- specific

specific specific specific

TradeTradeTradeTrade----off off off off betweenbetweenbetweenbetween comfortcomfortcomfortcomfort issues and issues and issues and efficiencyissues and efficiencyefficiencyefficiency

S. Avril, P Badel, L Dubuis, J Debayle, S Couzan, JF Pouget, Patient specific modeling in venous deficiency, in “Patient-Specific Modeling in Tomorrow's Medicine”, edited by Amit Gefen, Springer-Verlag, in press, 2011.

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Future work

• Dynamic Dynamic Dynamic Dynamic responseresponseresponseresponse

• FluidFluidFluidFluid----structure interactionsstructure interactionsstructure interactionsstructure interactions

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Vascular wall biomechanics

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ascending aorta

arch of aorta ▶ a local dilation of the aorta

due to aortic wall weakening

Motivation: treating aortic aneurisms

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NumericalNumerical simulations NumericalNumerical simulations simulations aimedsimulations aimedaimedaimed atatatat supportingsupportingsupportingsupporting the the the the surgical

surgicalsurgical

surgical decisiondecisiondecisiondecision

Applicative research:

Towards predictive models?

[N. Demanget, S. Avril; P. Badel, L. Orgéas, C. Geindreau; J.-N. Albertini, J.-P. Favre, Computational comparison of the bending behaviour of aortic stent-grafts Journal of the Mechanical Behavior of

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Straight

Straight AAA withAAA with angulation of 60 angulation of 60°°

AAA withAAA with pronounced pronounced

Effect of angulation?

Stress analyses of Stress analyses of strentStress analyses of Stress analyses of strentstrentstrent graftsgraftsgrafts for grafts for for for differentdifferentdifferentdifferent aneurysm

aneurysmaneurysm

aneurysm angulations angulations angulations angulations

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Straight aneurysm

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Moderated angulation

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Severe angulation

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Objectives in Objectives in Objectives in Objectives in vascularvascularvascularvascular biomechanicsbiomechanicsbiomechanicsbiomechanics

1. 1. 1. 1. characterizationcharacterizationcharacterizationcharacterization of the of the of the mechanicalof the mechanicalmechanicalmechanical and the and the and the and the fracture

fracture fracture

fracture behaviourbehaviourbehaviourbehaviour of of of of bloodbloodbloodblood vesselsvesselsvesselsvessels in in in in physiologicalphysiologicalphysiologicalphysiological conditions

conditions conditions conditions

2. 2. 2. 2. establishestablishestablishestablish relationshipsrelationshipsrelationshipsrelationships betweenbetweenbetween the local between the local the local the local microstructure of

microstructure of microstructure of

microstructure of bloodbloodblood vesselsblood vesselsvesselsvessels and and and and theirtheirtheirtheir macroscopic

macroscopic macroscopic

macroscopic mechanicalmechanicalmechanicalmechanical and fracture and fracture and fracture behaviourand fracture behaviourbehaviourbehaviour

3. 3. 3. 3. predictpredictpredictpredict the changes of the changes of the changes of mechanicalthe changes of mechanicalmechanical propertiesmechanical propertiespropertiesproperties fromfromfromfrom the the

the the mechanobiologicalmechanobiologicalmechanobiologicalmechanobiological knowledgeknowledgeknowledgeknowledge

Fundamental research:

mechanics and mechanobiology of the vascular tissue

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Experimental considerations

UsualUsualUsualUsual protocolprotocolprotocolprotocol::::

Truestress (MPa)

True strain

diastole systole

Physiological modulus

Stress – Strain curve

[Duprey et. al., In-vitro characterisation of physiological and maximum elastic modulus of ascending thoracic aortic aneurysms using uniaxial

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longitudinal

circumferential

σ = F/S =1.7 MPa

Failure properties

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A multiA multiA multiA multi----layer layer layer layer materialmaterialmaterialmaterial

Passive Passive Passive Passive mechanicalmechanicalmechanical behaviormechanical behaviorbehaviorbehavior

Multi-layer

Matrix + different fibers

Arteries: a complex structure and behavior

Intima

Media

Smooth muscle cells Elastin

Elastin Elastin

Elastin fibersfibersfibersfibers Collagen Collagen Collagen

Collagen fibersfibersfibersfibers

Biologic sensor and filter

Adventitia CollagenCollagenCollagenCollagen fibersfibersfibersfibers

Anisotropy – Non linearities – Finite strains

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Anisotropic hyperelastic models for arteries

HyperelasticityHyperelasticityHyperelasticityHyperelasticity

Strain energy function:

2^nd Piola-Kirchhoff stress:

AnisotropicAnisotropicAnisotropicAnisotropic hyperelasticityhyperelasticityhyperelasticityhyperelasticity

( )

ψ = ψ E ^where ^E⁼¹₂

(

^{F F}^T^. ⁻^I

)

= ∂ψ S ∂

E

f₁

Multiphoton-second harmonic generation (MP-SHG) microscope 600x

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Anisotropic hyperelastic models for arteries

FungFungFungFung’’’’s s s s phenomenologicalphenomenologicalphenomenologicalphenomenological modelmodelmodelmodel

MultilayeredMultilayeredMultilayeredMultilayered HolzapfelHolzapfelHolzapfelHolzapfel’’’’ssss histologyhistologyhistologyhistology----basedbasedbased modelbased modelmodelmodel

ez

eθ

( )

¹ ¹

(

²⁽ ⁱ ⁾²

)

2

k λ - 1 i = fibre1,

fibre2

k ψ = c I -3 +

2

∑

2k e - 1

(

¹

)

2

Q 2 2

11 θθ 22 zz 12 θθ zz

ψ = c

e − ^with Q = a E + a E + 2a E E

[Fung, Biorheology of soft tissues, Biorheology, 1973]

[Gasser, Holzapfel, Ogden, A new constitutive framework for arterial wall mechanics

isotropic anisotropic matrix fiber families

f1

f2

α

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Deformation gradient Lagrange strain

Aneurismal

aortic tissue Inflation test Optical Full-field measurement ( Full-field displacement)

Inverse procedure

Application of the special Identification of

material parameters Constitutive model

Methodology

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inflation device cylinder

pressure gage

in vivo loading environments

(biaxial stress state due to internal pressure) can be generated

Inflation test

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an excised cylindrical aneurismal aortic tissue

a square specimen removing loose connective tissue

finding an appropriate location to separate cut

adventitia media

media

adventitia

x y

diameter: 30mm

Materials

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camera

Instron machine protector

Undeformed Deformed

x y

tracks the gray value pattern Digital image

stereocorrelation

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Theory of finite deformation

Deformation gradient F

right Cauchy-Green tensor C = F^TF

Ux Uy Uz

from the undeformed and deformed

coordinates of each measurement data point Measured displacement

fields

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Identification of hyperelastic properties by Virtual Field Method

PrinciplePrinciplePrinciplePrinciple of identificationof identificationof identificationof identification

Iterative approach until reconstructed stresses minimize cost function J:

( )

^ij

( )

^*^ij ⁱ ^*ⁱ ²

virtual fields pressure states V V

J A = - σ , A :ε dV + T u dS

∂

 

 

 

∑ ∑ ∫

^E

∫

Internal Virtual Work

( IVW )

External Virtual Work

( EVW )

S. Avril, P. Badel, A Duprey. Anisotropic and hyperelastic identification of in vitro human arteries from full-field measurements. Journal of Biomechanics -2010, vol 43, N°15, pp 2978-2985.

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Results: material properties

0 100 200 300 400 500 600

1 2 3 4 5 6 7

k1 (kPa)

media adventitia

0 2000 4000 6000 8000 10000 12000

1 2 3 4 5 6 7

k2

media adventitia

0 10 20 30 40 50 60 70

1 2 3 4 5 6 7

angle (°)

media adventitia 0

0.2 0.4 0.6 0.8 1 1.2 1.4

1 2 3 4 5 6 7

thickness (mm)

media adventitia

Gasser et al.

average average average average

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Results: ultimate stress

Ultimate stress (MPa)

0.0000 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000

A A A A A A M M M M M M M M M

R = Curvature radius

λ_x and λ_y = measured stretches h = h /(λ λ ) = current thickness

σ σσ

σ = = = pR= pRpRpR/2h/2h/2h/2h

Average adventitia

Average media

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0 0.2 0.4 0.6 0.8 1 1.2

0 0.1 0.2 0.3 0.4

strain

stress (MPa)

0 0.2 0.4 0.6 0.8 1 1.2

0 0.1 0.2 0.3 0.4

strain

stress (MPa)

I

II

0 0.2 0.4 0.6 0.8 1 1.2

0 0.1 0.2 0.3 0.4

stress (MPa)

0 0.2 0.4 0.6 0.8 1 1.2

0 0.1 0.2 0.3 0.4

stress (MPa)

I

II

0 0.2 0.4 0.6 0.8 1 1.2

0 0.1 0.2 0.3 0.4

stress (MPa)

0 0.2 0.4 0.6 0.8 1 1.2

0 0.1 0.2 0.3 0.4

stress (MPa)

0 0.2 0.4 0.6 0.8 1 1.2

0 0.1 0.2 0.3 0.4

stress (MPa)

0 0.2 0.4 0.6 0.8 1 1.2

0 0.1 0.2 0.3 0.4

stress (MPa)

I II

III IV

0 0.2 0.4 0.6 0.8 1 1.2

0 0.1 0.2 0.3 0.4

strain

stress (MPa)

0 0.2 0.4 0.6 0.8 1 1.2

0 0.1 0.2 0.3 0.4

strain

stress (MPa)

0 0.2 0.4 0.6 0.8 1 1.2

0 0.1 0.2 0.3 0.4

strain

stress (MPa)

0 0.2 0.4 0.6 0.8 1 1.2

0 0.1 0.2 0.3 0.4

strain

stress (MPa)

I II

III IV

media adventitia

Results: stress strain curves

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the failure of aneurismal aortic tissue is oriented along preferred directions!

x y

Rupture is characterized by oblique tears in the circumferential direction

Characterization of rupture

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Rupture angle (°)

10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00

Average adventitia

Average media

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p = 0.02 MPa 0.029 MPa 0.038 MPa 0.047 MPa

Rupture mode

A B

ε

x

ε

xy

ε

y

Modes of rupture

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▶ the failure stress in the axial direction is much higher

in the adventitia layer (about three times) compared to that in the media layer

▶ the failure in the aneurismal aortic tissue may initiate in the media layer

▶ means that the adventitia layer plays a very important role in preventing the artery from rupture

Modes of rupture

Delamination of the layer may occur before the rupture

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Age effect: Tissue degeneration?

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Future Future Future Future workworkworkwork

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From microscopic

constitution to macroscopic behaviour

Multiphoton-second harmonic generation (MP-SHG) microscope 600x

Mechanobiology

Modelling

Strength and mechanics

Diseases WhatWhatWhatWhat are the are the are the are the factorsfactorsfactors thatfactors thatthatthat regulateregulateregulateregulate ??

the the the

the mechanicalmechanicalmechanicalmechanical propertiespropertiespropertiesproperties and and and and strength

strength strength

strength of of of of arteriesarteriesarteriesarteries????

Tissue

environment

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In vivo imaging

MRI MRI MRI MRI measurementsmeasurementsmeasurementsmeasurements

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StudentsStudentsStudentsStudents: : : Ambroise Duprey, Jin Kim, Alexandre Franquet, Nicolas : Demanget, Aaron Romo, Tristan Belzacq

ColleaguesColleaguesColleaguesColleagues::::

Dr Pierre Badel (Ecole des Mines Saint-Etienne) Dr Katia Genovese (Univ. Basilicata)

Prof Jean-Pierre Favre (Univ Hospital Saint-Etienne) Dr Alexandre Delache (Saint-Etienne University) Prof Emmanuel Leriche (Lille University)

Prof Valérie Deplano (Marseille University) Institutions and Institutions and Institutions and Institutions and fundingfundingfundingfunding partnerspartnerspartners::::partners

Acknowledgements

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Invitation

Truestress (MPa)

Centre for Centre for Centre for

Centre for Health Health Health Health Engineering Engineering Engineering Engineering CNRS UMR 5146

52 staff in Dec. 2011:

18 faculty + 5 tech , 27 PhD students, 3 Post Docs

( )

(

)

( )

(

)

∑

(

)

Theory of finite deformation

( )

( )

∑ ∑ ∫

∫

Ultimate stress (MPa)

Rupture is characterized by oblique tears in the circumferential direction

Rupture angle (°)

ε

ε

ε

http://euromech534.emse.fr