a biomechanical contribution

(1)

Centre for Biomedical and Healthcare Engineering CNRS UMR 5307

Stéphane Avril and coll.

Prevention of aneurism rupture in the ascending thoracic aorta:

a biomechanical contribution

(2)

Frankfurt - 2013/02/28 - Stéphane AVRIL

MY INSTITUTE

(3)

3

Mines-Saint-Etienne

• Created by Royal Decree in 1816

• 1500 graduate & post-graduate students

• Academic staff: 100

• Ranking: top 10 French "Grandes Ecoles"

• Missions:

– Educate future managers in science and technology

– Develop applied research meeting the needs of industry

Saint-Etienne Paris

Marseille

Lyon

(4)

Center for Biomedical and Healthcare engineering

17 professors, 30 PhD students and postdocs

Soft tissue

biomechanics

Surface and Healthcare

engineering

Biomaterials and

inhaled

(5)

5

Prevention of aneurism rupture

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

inflation device

(6)

Patient specific and predictive finite

element modeling of endografts

(7)

7

Patient specific and predictive finite

element modeling of endografts

(8)

Towards patient specific and

predictive modeling of aortic valves

(9)

9

PREVENTION OF ANEURISM

RUPTURE FROM A

BIOMECHANICAL

POINT OF VIEW

(10)

Patient specific modeling

[McGloughlin T. Biomechanics and mechanobiology of aneurysms. 2012, Springer

(11)

11

MAIN ISSUE WITH THE NUMERICAL APPROACH

What are the patient-specific material properties of the

tissue?

(12)

 A multi-layer material

 Passive mechanical behavior

 Multi-layer

 Matrix + different fibers

Arteries: a complex structure and behavior

Intima Media

Smooth muscle cells Elastin fibers

Collagen fibers

Biologic sensor and filter

Adventitia Collagen fibers

(13)

13

Arteries: a complex structure and

behavior

(14)

Anisotropic hyperelastic models for arteries

 Hyperelasticity

Strain energy function:

2 ^nd Piola-Kirchhoff stress:

 Anisotropic hyperelasticity

 

ψ = ψ E ^where ^E ⁼ ¹ ₂  ^{F F I} ^T ^. ^ 

=  ψ S 

E

f

₁

(15)

15

Anisotropic hyperelastic models for arteries

 Fung’s phenomenological model

 Multilayered Holzapfel’s histology-based model

e

z

e

θ



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 and a comparative study of material models.

Journal of Elasticity

, 2000]

isotropic anisotropic matrix fiber families

f

₁

f

₂

α

(16)

Patient specific modeling

(17)

17

MAIN ISSUE WITH THE NUMERICAL APPROACH

What is the patient-specific strength of the tissue?

(18)

Quantify the risk of rupture for each patient…

(19)

19

SUMMARY:

2 BIG QUESTIONS

What are the patient-specific material properties of the

tissue?

What is the patient-specific strength of the tissue?

(20)

 1. Analyze in vitro the local stress fields leading to rupture in the aneurismal tissue

 2. Establish relationships between the elastic properties of the tissue and the rupture

 3. Relate microstructural damage to macroscopic elastic and fracture properties

 4. Predict the strength directly from in vivo biomechanical response

IDEA/ BIOMECHANICAL

EXPERIMENTAL APPROACH

(21)

21

INTRODUCTION ABOUT

BIOMECHANICAL EXPERIMENTAL

APPROACHES

(22)

Experimental considerations

 Usual protocol:

0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40 1,60 1,80 2,00

0,00 0,20 0,40 0,60 0,80 1,00

Stress (Mpa)

Strain

Stress-Strain curve

Maximum Elastic Modulus

Tru e st ress (MP a)

True strain

diastole systole

Physiological modulus

Stress – Strain curve

(23)

23

Biomechanical comparison of aneurismal and healthy tissue

Vorp DA, Schiro BJ, Ehrlich MP, Juvonen TS, Ergin MA, Griffith BP. Effect of aneurysm on the tensile strength and biomechanical behaviour of the ascending thoracic aorta. Ann Thorac Surg 2003; 75(4):1210-4.

(24)

Tensile rupture mode

(25)

25

Need of biaxial tension

Sacks MS. Biaxial mechanical evaluation of planar biological materials. J. Elast. 61:199–246, 2000

(26)

W < 10 mJ/cm ²

Delamination properties

(27)

27

SUMMARY:

LOTS OF AVERAGE VALUES BUT…

Lack of local analyses

Where does the rupture initiates?

(28)

MATERIALS AND

METHODS

(29)

29

Deformation gradient Lagrange strain

Aneurismal

aortic tissue Inflation test Optical Full-field measurement

( Full-field displacement)

Inverse procedure

Full-field

Stress reconstruction

Constitutive model

Calculation of stress at rupture

Methodology

(30)

Deformation gradient Lagrange strain

Aneurismal

aortic tissue Inflation test Optical Full-field measurement

( Full-field displacement)

Inverse procedure

Full-field

Stress reconstruction

Constitutive model

Methodology

(31)

31

an excised cylindrical aneurismal aortic tissue

a square specimen removing loose connective tissue

finding an appropriate location to separate

specimen is mounted on the inflation test device

making a speckle pattern separated layers two layers are pulled each other to separate cut

adventitia media

media

adventitia

x

y

diameter: 30mm

Materials

(32)

Deformation gradient Lagrange strain

Aneurismal

aortic tissue Inflation test Optical Full-field measurement

( Full-field displacement)

Inverse procedure

Full-field

Stress reconstruction

Constitutive model

Methodology

(33)

33

inflation device cylinder

pressure gage

in vivo loading environments

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

Inflation test

(34)

Deformation gradient Lagrange strain

Aneurismal

aortic tissue Inflation test Optical Full-field measurement

( Full-field displacement)

Inverse procedure

Full-field

Stress reconstruction

Constitutive model

Methodology

(35)

35

camera

Instron machine protector

Undeformed Deformed

x y

tracks the gray value pattern

in each subset during deformation

Digital image stereocorrelation

(36)

Deformation gradient Lagrange strain

Aneurismal

aortic tissue Inflation test Optical Full-field measurement

( Full-field displacement)

Inverse procedure

Full-field

Stress reconstruction

Constitutive model

Methodology

(37)

37

Theory of finite deformation

Deformation gradient F

Green-Lagrange strain tensor E = 1/2(C - I) right Cauchy-Green tensor C = F ^T F

Ux Uy Uz

from the undeformed and deformed

coordinates of each measurement data point

Assumption: plane stress

homogeneous initial thickness incompressibility

Measured displacement fields

(38)

p = 0.02 MPa 0.029 MPa 0.038 MPa 0.047 MPa

A B

 x



 y

Field differentiation

(39)

39

ℎ = ℎ ₀

2𝐸 ₁₁ − 1 2𝐸 ₂₂ − 1

Thickness evolution

(40)

Deformation gradient Lagrange strain

Aneurismal

aortic tissue Inflation test Optical Full-field measurement

( Full-field displacement)

Inverse procedure

Full-field

Stress reconstruction

Constitutive model

Methodology

(41)

41

Stress reconstruction

 Membrane elastostaticsy

σ

₁₁

σ

₂₂

σ

₁₂

(42)

Deformation gradient Lagrange strain

Aneurismal

aortic tissue Inflation test Optical Full-field measurement

( Full-field displacement)

Inverse procedure

Full-field

Stress reconstruction

Constitutive model

Methodology

(43)

43

MATERIALS AND

METHODS

(44)

Experimental method

 Alternative testing system

1

(45)

45

(46)

RESULTS

(47)

47

Results

(48)

Rupture modes

(49)

49

Ultimate stresses

inflation device

(50)

DISCUSSION

(51)

51

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

(52)

Thickness evolution

The tissue thinning starts to localize very early before the rupture

-> presence of aneslatic response in very local areas

(53)

53

▶ 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

(54)

Conclusion and

Future work

(55)

55

Conclusions

 The strength of the tissue is heterogeneous

 Existence of weaker zones in the tissue

 Damage develops in the weaker zones

 Damage leads to rupture when the pressure increases.

 What is the microstructural specificity of the weaker zone?

 Does it affect the elastic response in the

physiological domain?

(56)

a biomechanical contribution

Centre for Biomedical and Healthcare Engineering CNRS UMR 5307

Stéphane Avril and coll.

Prevention of aneurism rupture in the ascending thoracic aorta:

a biomechanical contribution

MY INSTITUTE

Mines-Saint-Etienne

• Created by Royal Decree in 1816

• 1500 graduate & post-graduate students

• Academic staff: 100

• Ranking: top 10 French "Grandes Ecoles"

• Missions:

– Educate future managers in science and technology

– Develop applied research meeting the needs of industry

Saint-Etienne Paris

Marseille

Lyon

Center for Biomedical and Healthcare engineering

17 professors, 30 PhD students and postdocs

Soft tissue

biomechanics

Surface and Healthcare

engineering

Biomaterials and

inhaled

Prevention of aneurism rupture

inflation device

Patient specific and predictive finite

element modeling of endografts

Patient specific and predictive finite

element modeling of endografts

Towards patient specific and

predictive modeling of aortic valves

PREVENTION OF ANEURISM

RUPTURE FROM A

BIOMECHANICAL

POINT OF VIEW

Patient specific modeling

MAIN ISSUE WITH THE NUMERICAL APPROACH

What are the patient-specific material properties of the

tissue?

 A multi-layer material

 Passive mechanical behavior

 Multi-layer

 Matrix + different fibers

Arteries: a complex structure and behavior

Intima Media

Smooth muscle cells Elastin fibers

Collagen fibers

Biologic sensor and filter

Adventitia Collagen fibers

Arteries: a complex structure and

behavior

Anisotropic hyperelastic models for arteries

 Hyperelasticity

Strain energy function:

2 nd Piola-Kirchhoff stress:

 Anisotropic hyperelasticity

 

ψ = ψ E where E = 1 2  F F I T .  

=  ψ S 

E

f

Anisotropic hyperelastic models for arteries

 Fung’s phenomenological model

 Multilayered Holzapfel’s histology-based model

e

e













k λ - 1 i = fibre1,

fibre2

k ψ = c I -3 +

2  2k e - 1

 1 

2

2 ^nd Piola-Kirchhoff stress:

ψ = ψ E ^where ^E ⁼ ¹ ₂  ^{F F I} ^T ^. ^ 

^

^

 ¹ 

W < 10 mJ/cm ²