Rupture risk estimation in thoracic aortic aneurysms

(1)

Institut Mines-Télécom

Rupture risk estimation in thoracic aortic aneurysms

Prof Stéphane AVRIL (avril@emse.fr)

Eugenie Lamothe Colloquium Series

(2)

Where do I come from?

PARIS

RHONE-ALPS AREA

LYON-SAINT-ETIENNE

Historical site Founded in 1816

Demanget et al., Perrin et al.

(3)

Rupture risk estimation in ATAAs using distensibility measurements

Dr Olfa TRABELSI, Dr Ambroise DUPREY,

Prof Stéphane AVRIL (avril@emse.fr)

(4)

What is an ATAA and why is serious?

dissection

(5)

Epidemiology statistics

5

Incidence : 10.4 per 100 000 persons

Elevated mortality without treatment for acute aortic dissection:

50% in 48 hours / 90% in 3 months BAV patients: ½ develops an ATAA

Stéphane Avril - McGill - Oct 20, 2016

(6)

Risk management

 The International Registry of Acute Aortic Dissection (IRAD):

among 591 type A aortic dissection, 59% had a diameter <5.5 cm (Pape, 2007)

5.5 cm

Possible complication Possible

stability

Decision of surgical repair based on a measure if the Maximal Diameter

(7)

Institut Mines-Télécom 7

Recent developments in computational modeling and challenges

Index of Rupture?

Peak Wall Stress

Strength

Finite-element modeling

O. Trabelsi, et al, Patient specific stress and rupture analysis of ascending thoracic aneurysms, J. Biomech. (2015).

G. Martufi, et al, Is There a Role for Biomechanical Engineering in Helping to Elucidate the Risk Profile of the Thoracic Aorta?, Ann. Thorac. Surg. 101 (2016) 390–398.

S. Pasta et al., Constitutive modeling of ascending thoracic aortic aneurysms using microstructural parameters, Med. Eng. Phys. 38 (2016) 121–130.

(8)

SAINT-ETIENNE PROTOCOL

31 Patients with ATAA

Preoperative dynamic

imaging

Dynamic CT Scanner

4D MRI

Collection of intraoperative aortic segment

Mechanical inflation tests

Histological Analysis

2014

2016

(9)

Institut Mines-Télécom Stéphane Avril - McGill - Oct 20, 2016 9

Inverse membrane analysis + digital image correlation  stress

& strain reconstruction.

biaxial failure properties

Trabelsi, O., Davis, F.M., Rodriguez-Matas, J.F., Duprey, A., Avril, S. Patient specific stress and rupture analysis of ascending thoracic aneurysms.

Journal of Biomechanics, 2015.

Bulge inflation tests

Blood flow

(10)

Bulge inflation tests

(11)

Stress strain analysis in the bulge test

σ

_rup

: Rupture stress, λ

_rup

: Rupture stretch,

Physiological Stress

Stretch Stretch/Stress Curve

Rupture Stress

Physiological elastic modulus

Ca uchy Stre ss (MPa)

1 1.1 1.2 1.3

Physiological Stretch

1.4 1.5 1.6 1.7

Rupture Stretch

(12)

Results

 Rupture properties in function of:

• Age

• Type of test: inflation, axial and circumferential tensile tests

• Physiological circumferential modulus E _physio

• Aortic valve: 8 BAV / 23 TAV

 31 patients :

• Mean age 65 (24-80)

• 84% male

• Mean in vivo diameter 54 mm (49-65)

 Rupture mode:

• Only Intima/media in 55% of cases, similar to dissection

 σ _rup and λ _rup not correlated with the diameter or the type of

aortic valve

(13)

Rupture profiles

50% of aortas r uptured wi th an ang le θ equ al to 9 0 °

Bl oo d flow

(14)

(p<0,01)

σ _rup

λ _rup

Age dependence of rupture properties

Corr elation with age

(15)

Comparison of mechanical tests

Duprey A, et al. Biaxial rupture properties of ascending thoracic aortic aneurysms. Acta Biomaterialia 2016.

(16)

Comparison with other studies

0 1 2 3 4 5 6

0 10 20 30 40 50 60 70 80 90 100

σ _rup

Age

R.J. Okamoto et al,, Ann. Biomed. Eng. 30 (2002) 624–635.

D.A. Vorp et al,, Ann. Thorac. Surg. 75 (2003) 1210–1214.

C.M. García-Herrera et al., Med. Biol. Eng. Comput. 50 (2012) 559–566.

D.P. Sokolis et al, Med. Biol. Eng. Comput. 50 (2012) 1227–1237 C. Forsell et al, Ann. Thorac. Surg. 98 (2014) 65–71

S. Sugita. Card Eng Tech. 3:1 (2011) 41-51.

J.E. Pichamuthu et al., Ann. Thorac. Surg. 96 (2013) 2147–2154 A. Duprey at al. Acta Biomater 2016)

(17)

Comparison with other studies

Stéphane Avril - McGill - Oct 20, 2016 17

1 1,2 1,4 1,6 1,8 2 2,2

0 10 20 30 40 50 60 70 80 90 100

λ _rup

Age

R.J. Okamoto et al,, Ann. Biomed. Eng. 30 (2002) 624–635.

D.A. Vorp et al,, Ann. Thorac. Surg. 75 (2003) 1210–1214.

C.M. García-Herrera et al., Med. Biol. Eng. Comput. 50 (2012) 559–566..

D.P. Sokolis et al, Med. Biol. Eng. Comput. 50 (2012) 1227–1237 C. Forsell et al, Ann. Thorac. Surg. 98 (2014) 65–71

S. Sugita. Card Eng Tech. 3:1 (2011) 41-51.

J.E. Pichamuthu et al., Ann. Thorac. Surg. 96 (2013) 2147–2154 A. Duprey at al. Acta Biomater 2016)

(18)

Rupture risk estimation

Physiological Stress

Stretch Stretch/Stress Curve

Rupture Stress

E

_physio

= Physiological elastic modulus

Ca uchy Stre ss (MPa)

1 1.1 1.2 1.3

Physiological

1.4 1.5 1.6 1.7

Rupture Stretch

γ _stress = Physiological stress Rupture stress γ _stretch = Physiological stretch

Rupture stretch

(19)

Age dependence of rupture risks

γ _stress γ _stretch

(20)

E _physio is correlated to the risk of rupture

MPa MPa MPa MPa

(21)

Correlation between γ _stretch and E _physio

(22)

31 Patient with ATAA

Preoperative dynamic

imaging

Dynamic CT Scanner

4D MRI

Collection of intraoperative aortic segment

Mechanical inflation tests

Histological Analysis

2014

2016

SAINT-ETIENNE PROTOCOL

(23)

Histological interpretation

 ATAA enlargement is a consequence of elastin damage

 More and more collagen tends to be recruited in the physiological range

Patient with smallest γ _stretch

Patient with largest γ _stretch

elast col

M.R. Hill et al,, J. Biomech. 45 (2012) 762–771

(24)

31 Patient with ATAA

Preoperative dynamic

imaging

Dynamic CT Scanner

4D MRI

Collection of intraoperative aortic segment

Mechanical inflation tests

Histological Analysis

2014

2016

SAINT-ETIENNE PROTOCOL

(25)

Distensibility measurements using the dynamic CT scan

 D = (A _max -A _min )/A _min /(P _max -P _min )

 E _physio = 2R/Dh

(26)

Correlation between γ _stretch and E _physio

R² = 0,7709 R² = 0,6959

0,8 0,82 0,84 0,86 0,88 0,9 0,92 0,94 0,96 0,98 1

in vivo in vitro

Linéaire (in vivo) Linéaire (in vitro)

g ^stretch

E ^physio (MPa)

(27)

Summary

 2 ways of defining rupture:

 PWS – but unknown patient-specific strength

 γ _stretch correlated with in vivo distensibility

Higher distensibility  less risk because the aneurysm can more easily withstand volume variation

C. Martin et al., Acta Biomater. 9 (2013) 9392–9400

(28)

Future work

 Extend the analysis to other patients

 Define a threshold for the new risk of rupture

 Predict the long-term evolution of this

criterion for small aneurysms using

mechanobiological models

(29)

Acknowledgements

Funding:

ERC-2014-CoG BIOLOCHANICS

 Olfa Trabelsi

 Ambroise Duprey

 Aaron Romo

 Pierre Badel

 Frances Davis

 Jean-Pierre Favre

 Victor Acosta

 Jamal Mousavi

 Solmaz Farzeneh

 Francesca Condemi

 Miguel Angel Gutierrez

 Oscar Alberto Mendoza

(30)

Inverse characterization of regional, nonlinear and anisotropic properties of arteries

MR Bersi, C Bellini, P Di Achille, K Genovese, JD Humphrey, S Avril

(31)

INTRODUCTION AND RATIONALE:

EXAMPLE OF ATAA PHYSIOPATHOLOGY

Disturbed

hemodynamics

Laminar flow

(32)

POINT OF VIEW OF MECHANOBIOLOGY

Altered mechanics induce biological responses, including gene

expression, protein activation and cell phenotype

(33)

POINT OF VIEW OF BIOMECHANICS

Macroscopic manifestations ultimately dictate the mechanical functionality and structural integrity of the aortic wall

Martufi et al. Biomech. Model.

Mechanobio. pp. 917–928, 2014.

(34)

CHALLENGES AND OBJECTIVES

Fundamentally understand local structure–function relationships in aortic aneurysms.

This requires an approach permitting:

1. To reconstruct the regional distribution of mechanical properties of the aorta during aneurysm growth.

2. To investigate their correlation with the underlying

microstructure and its evolutions.

(35)

APPROACH

1. Experiments

2. Material model

3. Inverse method

(36)

APPROACH

1. Experiments

2. Material model

3. Inverse method

(37)

TENSION – INFLATION OF MICE AORTAS

Gleason, et al. J. Biomech. Eng.

126(6), p. 787, 2004.

Humphrey , Cardiovascular Solid Mechanics, 2002

(38)

MEASUREMENT OF THE RESPONSE USING DIGITAL IMAGE CORRELATION

classical panoramic

(39)

PANORAMIC DIGITAL IMAGE CORRELATION - pDIC

Genovese et al, CMBBE, 14, p. 213- 237, 2011.

(40)

Full-field strain measurement across the outer surface of the artery

Posterior Posterior Anterior

ANT

POST

Circumferential Green Strain

(41)

APPROACH

1. Experiments

2. Material model

3. Inverse method

(42)

CONSTITUTIVE MODEL

Bellini, et al., Ann. Biomed. Eng., 42(3), pp. 488–502, 2014

(43)

CONSTITUTIVE MODEL

FE implementation

Bellini, et al., Ann. Biomed. Eng., 42(3), pp. 488–502, 2014

(44)

PARAMETERS TO BE IDENTIFIED

(45)

APPROACH

1. Experiments

2. Material model

3. Inverse method

(46)

Inverse approach – traditional approach

Set of materials properties

Resolution of forward problem

Deviation between predictions and measurements minimization

initialization

Identification of

material properties

(47)

Inverse approach – traditional approach

Set of materials properties

Resolution of forward problem

Deviation between predictions and

measurements minimization

initialization

Identification of material properties 1. Write the weak form of the problem:

𝑅 𝑢, 𝑤, µ = 0 ∀𝑤

2. Discretize and represent as a linear

combination of piecewise bilinear functions 𝑢 ^ℎ = 𝑈 _𝑖 𝜑 _𝑖 (x)

𝑤 ^ℎ = 𝑊 _𝑖 𝜑 _𝑖 (x) µ ^ℎ = µ _𝑖 𝜑 _𝑖 (x)

3. Implement a finite-element implicit

resolution using the BFGS algorithm

(48)

Inverse approach – traditional approach

Set of materials properties

Resolution of forward problem

Deviation between predictions and measurements minimization

initialization

Identification of material properties

J(µ)= 𝑇 𝑢 − 𝑇(𝑢 ^𝑒𝑥𝑝 ) ² + ^𝛼 ₂ 𝐵(µ)

Oberai et al., Inverse problems, 19, pp. 297-313, 2003

(49)

Set of materials properties

Resolution of forward problem

Deviation between predictions and measurements minimization

initialization

Identification of material properties

1. Use a gradient based method (steepest descent or BFGS)

2. Need to derive the gradient of J with respect to µ at each iteration. With the adjoint method, this requires the resolution of 2 forward problems

3. Very unstable with hyperelastic models: many risks that the forward problems have a poor convergence

Inverse approach – traditional

approach

(50)

Alternative inverse approach:

the virtual fields method

Set of materials properties

3D estimation of

stresses

Deviation to the principle

of virtual power minimization

initialization

Identification of material properties

Bersi et al., J Biomech Eng, 2016

(51)

A FE model of each artery is built

Each artery is meshed with 5x40x25 hexahedrons

A quasi incompressible Neo-Hookean material is set

The measured displacements are assigned on the nodes of the outer surface as BCs

The Dirichlet problem is solved

3D estimation of

stresses

3D estimation of

strains

Alternative inverse approach:

the virtual fields method

(52)

Set of materials properties

3D estimation of

stresses

Deviation to the principle

of virtual power minimization

initialization

Identification of

material properties Simple application of

the constitutive model for each element

Alternative inverse approach:

the virtual fields method

(53)

We are looking for the material properties at a position x ₀ . 2 virtual fields are considered.

1. A local virtual radial “bulge”: u(x) = [f(x-x ₀ ) /r ² ] e _r

2. Local virtual axial extension: v(x) = f(x-x ₀ ) (z e _z –x/2 e _x –y/2 e _y ) Where f(x-x ₀ ) = exp(-||x-x ₀ || ² /d²)

Deviation to the principle

of virtual power

Alternative inverse approach:

the virtual fields method

Avril et al. J. Biomech. 43 (15), p 2978-2985, 2010 www.camfit.fr

(54)

J =

c

₃¹

,c

₃^2,3

min ,c

₃⁴

,𝛼,𝛽 min

c

^𝑒

,c

₂¹

,c

₂^2,3

,c

₂⁴

J u

𝐴 + J v 𝐵

minimization

2 p 

Linear least-squares Resolution:

Alternative inverse approach:

the virtual fields method

(55)

Summary of the inverse approach

Set of materials properties

3D estimation of

stresses

Deviation to the principle

of virtual power minimization

initialization

Identification of material properties

(56)

RESULTS

1. Validation on control arteries 2. Application to ATAAs

3. Future work on dissected aneurysms

Con tro l

ctio n A T A A

(57)

RESULTS

1. Validation on control arteries 2. Application to ATAAs

3. Future work on dissected aneurysms

Con tro l

Di sse ctio n A T A A

(58)

Local estimation of the quality of the minimization

(59)

Examples of identified material parameters

Bersi et al., J Biomech Eg, 2016

(60)

Reconstruction of local strain energies

(61)

Reconstruction of local linearized stiffnesses

(62)

Validation against traditional stress strain analysis

(63)

RESULTS

1. Validation on control arteries 2. Application to ATAAs

3. Future work on dissected aneurysms

Con tro l

Di sse ctio n A T A A

(64)

Study Design

Fibrillin 1 mgR/mgR Fibulin 4 SMC KO

Control

(65)

pDIC measurements

Fibrillin 1 mgR/mgR Fibulin 4 SMC KO

dorsal

ventral inflation

6852 6913 CS79 CS38

dorsal ventral

𝜆

_𝑧^𝑖𝑣

= 1.31 𝑂𝐷

_𝑚𝑎𝑥

= 3.62 mm

𝜆

_𝑧^𝑖𝑣

= 1.20 𝑂𝐷

_𝑚𝑎𝑥

= 3.15 mm

𝜆

_𝑧^𝑖𝑣

= 1.43 𝑂𝐷

_𝑚𝑎𝑥

= 2.93 mm

𝜆

_𝑧^𝑖𝑣

= 1.41

𝑂𝐷

_𝑚𝑎𝑥

= 3.02 mm

inflation

(66)

Fibrillin 1 mgR/mgR Fibulin 4 SMC KO

Full-Field Thickness Estimation using OCT

(67)

Fibrillin 1 mgR/mgR Fibulin 4 SMC KO

Full-Field Thickness Estimation using OCT

(68)

• Stored Energy (@ 𝜆 _𝑧 ^𝑖𝑣 and 80 mmHg)

Fibrillin 1 mgR/mgR Fibulin 4 SMC KO

Full-Field Material Parameter Estimation

(69)

• Circumferential linearized stiffness (@ 𝜆 _𝑧 ^𝑖𝑣 and 100 mmHg)

Fibrillin 1 mgR/mgR Fibulin 4 SMC KO

Full-Field Material Parameter Estimation

(70)

• Axial linearized stiffness (@ 𝜆 _𝑧 ^𝑖𝑣 and 100 mmHg)

Fibrillin 1 mgR/mgR Fibulin 4 SMC KO

Full-Field Material Parameter Estimation

(71)

Fibrillin 1 mgR/mgR

Lower energy on the outer curvature for mgR

The location of ulceration for mouse CS38

Heterogeneity of the strain energy

(72)

RESULTS

1. Validation on control arteries 2. Application to ATAAs

3. Future work on dissected aneurysms

Con tro l

ctio n A T A A

(73)

Angiotensin-II Infusion Model of AAD

• Male ApoE ^-/- mice at 16-20 weeks of age surgically implanted with subcutaneous osmotic pump lateral to dorsal midline at mid-scapular region

• Maintained constant infusion of ANG-II at a rate of 1000 ng/kg/min

Anterior Posterior

Aortic Dissection

Dissecting Aortic Aneurysm

Suprarenal Descending Thoracic

Posterior Anterior

Intact Aorta

(74)

Experimental Approach

 Angiotensin-II Infusion Model of AAD

 Timeline

 Peak in macrophage activity at day 4 with dissection occurring between days 1 and 4 followed by associated remodeling from days 4 to 10.

Day 0 4 6 8 10 12 14 21 28

ANG-II Infusion

IHC showing medial infiltration of macrophages after 48 hours

of treatment

(75)

Material discretization

O

^W_AD

O

_AD^L

Wall Lumen

Thrombus

L

_AD

L

_FL

H

_AD

O

_AD^L

B A

Contours of model through planes A and B:

Segmented 3D model: Clipping planes:

Along A: Along B:

(76)

Optical Coherence Tomography (OCT) data are available from the experiments

Requires further developments of the inverse approach to be employed

Future work

0 °

+90 °

180 ° -90 °

OC T Laser

Merged Cross-Section

x y

(2D)

Male ApoE -/- 21d ANG-II

(77)

Rupture risk estimation in thoracic aortic aneurysms

Rupture risk estimation in thoracic aortic aneurysms

Prof Stéphane AVRIL (avril@emse.fr)

Eugenie Lamothe Colloquium Series

Where do I come from?

PARIS

RHONE-ALPS AREA

LYON-SAINT-ETIENNE

Historical site Founded in 1816

Demanget et al., Perrin et al.

Rupture risk estimation in ATAAs using distensibility measurements

Dr Olfa TRABELSI, Dr Ambroise DUPREY,

Prof Stéphane AVRIL (avril@emse.fr)

What is an ATAA and why is serious?

dissection

Epidemiology statistics

Incidence : 10.4 per 100 000 persons

Elevated mortality without treatment for acute aortic dissection:

50% in 48 hours / 90% in 3 months BAV patients: ½ develops an ATAA

Risk management

 The International Registry of Acute Aortic Dissection (IRAD):

among 591 type A aortic dissection, 59% had a diameter <5.5 cm (Pape, 2007)

5.5 cm

Possible complication Possible

stability

Decision of surgical repair based on a measure if the Maximal Diameter

Recent developments in computational modeling and challenges

Index of Rupture?

Peak Wall Stress

Strength

Finite-element modeling

SAINT-ETIENNE PROTOCOL

31 Patients with ATAA

Preoperative dynamic

imaging

Dynamic CT Scanner

4D MRI

Collection of intraoperative aortic segment

Mechanical inflation tests

Histological Analysis

2014

2016

Inverse membrane analysis + digital image correlation  stress

& strain reconstruction.

biaxial failure properties

Bulge inflation tests

Blood flow

Bulge inflation tests

Stress strain analysis in the bulge test

σ

: Rupture stress, λ

: Rupture stretch,

Physiological Stress

Stretch Stretch/Stress Curve

Rupture Stress

Physiological elastic modulus

Ca uchy Stre ss (MPa)

Physiological Stretch

Rupture Stretch

Results

 Rupture properties in function of:

• Age

• Type of test: inflation, axial and circumferential tensile tests

• Physiological circumferential modulus E physio

• Aortic valve: 8 BAV / 23 TAV

 31 patients :

• Mean age 65 (24-80)

• 84% male

• Mean in vivo diameter 54 mm (49-65)

 Rupture mode:

• Only Intima/media in 55% of cases, similar to dissection

 σ rup and λ rup not correlated with the diameter or the type of

aortic valve

Rupture profiles

50% of aortas r uptured wi th an ang le θ equ al to 9 0 °

Bl oo d flow

(p<0,01)

(p<0,01)

σ rup

λ rup

• Physiological circumferential modulus E _physio

 σ _rup and λ _rup not correlated with the diameter or the type of

σ _rup

λ _rup

σ _rup

λ _rup

γ _stress = Physiological stress Rupture stress γ _stretch = Physiological stretch

γ _stress γ _stretch

E _physio is correlated to the risk of rupture

Correlation between γ _stretch and E _physio

Patient with smallest γ _stretch

Patient with largest γ _stretch

 D = (A _max -A _min )/A _min /(P _max -P _min )

 E _physio = 2R/Dh

Correlation between γ _stretch and E _physio

g ^stretch

E ^physio (MPa)

 γ _stretch correlated with in vivo distensibility