human aortic root dilatation

(1)

Institut Mines-Télé[email protected]

Finite-element predictions of human aortic root dilatation based on the homogenized constrained mixture model

Prof. Stéphane AVRIL

(2)

PARIS

AUVERGNE RHONE-ALPES

MINES SAINT-ETIENNE

First Grande Ecole

outside Paris

Founded in 1816

(3)

Institut Mines-Télé[email protected]@emse.fr

Aortic root dilatations and ascending thoracic aortic aneurysms (ATAA)

3 Stéphane Avril - 2018 July 23 - NYC WCCM

(4)

Risks: Aortic dissections

(5)

Surgical elective repair of ATAA

 Indications:

• Aortic insufficiency requiring surgical correction

• Size ⩾ 55 mm

• Size ⩾50 mm in patients with Marfan syndrome or bicuspid valves

• Growth rate ⩾1 cm/year

 More and more aneurysms are detected at an early stage (incidence >8% for males >65 years old).

 >90000 interventions per year in Europe and USA

(6)

Surgical techniques for ATAA repair

(7)

Context

 BUT:

• 25% ATAA < 5.5cm rupture : 15000 deaths ^** !

• 60% of ATAA > 5.5 cm never experience rupture!

• 9% mortality and morbidity after ATAA repair

 In summary: inappropriate decisions and misprogramed surgical interventions have major consequences!!

 Need insightful assistance from biomechanics 

** Pape et al, Aortic Diameter ≥5.5 cm Is Not a Good Predictor of Type A Aortic Dissection Observations From the International Registry of Acute Aortic Dissection (IRAD), Circulation, 2007

(8)

EXPERIMENTAL

WORK

(9)

Bulge inflation test

III) Inflation test device. Speckle pattern is made before starting the

inflation test Circumferential

A x ia l

Romo et al. Journal of Biomechanics - 2014

(10)

Davis et al. BMMB – 2015.

Davis et al. JMBBM – 2016

Zhao et al. Acta Biomaterialia - 2016

Identification of local material

properties

(11)

Institut Mines-Télé[email protected]@emse.fr 11

Rupture risk estimation

Physiological Stress

Stretch Stretch/Stress Curve

Rupture Stress

E

_in-vitro

= Tangent elastic modulus

Cauch y Stress (MP a)

1 1.1 1.2 1.3

Physiological Stretch

1.4 1.5 1.6 1.7

Rupture Stretch

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

Rupture stretch

Stéphane Avril - 2018 July 23 - NYC WCCM

(12)

Correlation between the stretch-based

rupture risk and the tangent elastic modulus

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

E _in-vitro (MPa)

Ru pture ris k

(13)

Institut Mines-Télé[email protected]

Olfa Trabelsi, Miguel A Gutierrez Cambron, Solmaz Farzaneh, Ambroise Duprey, Stéphane Avril.A non-invasive methodology for ATAA rupture risk estimation. Journal of Biomechanics 2017.

Relationship with aortic stiffness

The stretch based rupture risk criterion correlates to the aortic

stiffness measured by elastography techniques

(14)

RELATIONSHIP WITH HEMODYNAMICS

Preoperative dynamic imaging 4D MRI

CAD Mesh

Numerical resolution

Streamlines, velocity TAWSS

BCs

(15)

Relationship λ _rupture vs. TAWSSmax [Pa]

Spearman rho 0.867

P-value 0.001

(16)

Histological interpretation

 ATAA always manifests with damaged elastic fibers

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

Patient with

smallest γ _stretch Patient with

largest γ _stretch

elast coll

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

(17)

Summary

 2 ways of defining rupture:

 PWS – but unknown patient-specific strength

 γ _stretch correlated with in vivo circumferential stiffness

Higher stiffness  less risk because the aneurysm can more easily withstand

volume variation

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

(18)

THEORETICAL

WORK

(19)

Continuous process of proteolytic injury and tissue adaptation

19

PROTEOLYTIC INJURY

Strain HEALING

Stress

(20)

Constrained mixture theory

(21)

Layer-specific constitutive model

Strain-energy function based on the constrained mixture theory

Humphrey and Rajagopal, Math. Models Methods Appl. Sci., 2002 ; Bellini et al, ABME, 2014

Deposition stretch (Λ ^𝑗 _s ) of each constituent

𝐅 _tot ^𝑗 = 𝐅𝚲 ^𝑗 _s

Collagen Elastin

SMC Load

(22)

Layer-specific constitutive model

Volumetric contributions of strain-energy function

Damage

Active contribution of smooth muscle cells

(23)

Homogenized G&R

constrained mixture model

Stéphane Avril - 2018 July 23 - NYC WCCM 23

𝐅 _tot ^𝑗 = 𝐅 _e ^𝑗 𝐅 _gr ^𝑗 𝐅 _gr ^𝑗 = 𝐅 _r ^𝑗 𝐅 _g ^𝑗

𝐅 _r ^𝑗 and 𝐅 _g ^𝑗 should be calculated if the artery is not in the homeostatic state

Elastic and inelastic decomposition of deformation gradient

Strain-energy function based on the constrained mixture theory

(24)

Homogenized G&R

constrained mixture model

Collagen mass production

ሶϱ ^𝑗 (t) = ϱ ^𝑗 (t)𝑘 _σ ^𝑗 𝜎 ^𝑗 𝑡 − 𝜎 _h ^𝑗

𝜎 _h ^𝑗 + ሶ𝜉 ^𝑗 (𝑡)

Inelastic deformation due to remodeling

ሶϱ ^𝑗 (t)

ϱ ^𝑗 (t) + 1

𝑇 ^𝑗 𝐒 ^𝑗 − 𝐒 _pre ^𝑗 = 𝜕𝐒 ^𝑗

𝜕𝐂 _e ^𝑗 : (𝐂 _e ^𝑗 𝐋 ^𝑗 _r ) 𝐋 ^𝑗 _r = ሶ𝐅 _r ^𝑗 𝐅 _r ^𝑗−1

Cyron et al, Biomech Model Mechanobiol (2016) 15:1389–1403, Braeu et al, Biomech Model Mechanobiol (2017)

16(3):889-906

(25)

Homogenized G&R

constrained mixture model

Inelastic deformation due to growth

ሶ𝐅 _g = ሶ𝐅 _g ^𝑗 = ෍

𝑗=1 𝑛

ሶ 𝐆 ^𝑗

ሶ 𝐆 ^𝑗 = ሶϱ ^𝑗 (t)

ϱ ^𝑗 (t) 𝐅 _g ^𝑗−𝑇 : 𝐁 ^𝑗

𝐁 ^𝑗

𝐁 ^𝑗 = 𝑎 _𝑔 ⊗ 𝑎 _𝑔 𝐁 ^𝑗 = ^𝟏

3 𝐈 Anisotropic

growth Isotropic

growth

(26)

COMPUTATIONAL

WORK

(27)

Finite-element implementation

 FE software ABAQUS coupled with UMAT

 Reference configuration is the in vivo configuration

Bellini et al, ABME, 2014 Mousavi et al, BMMB, 2017

(28)

Modeling of a bulge inflation test including pre-test deformation

Model parameters are calibrated against pressure/deflection curves

(29)

Hoop stress in patient specific ATAA

Zero pressure

Systolic pressure Geometry at

diastole

(30)

Prediction of mechanical damage in bulge inflation tests

Damage during bulge inflation test (luminal side in)

(31)

Damage during bulge inflation test (luminal side out)

Prediction of mechanical damage

in bulge inflation tests

(32)

Gradient-enhanced G&R healing model

k=0

k=5.0 k=0.5

k=1.0

(33)

Growth and remodeling with continuous medial proteolytic injury

Stéphane Avril - 2018 July 23 - NYC WCCM 33

Effects of rate of collagen mass production and of loss of SMC

contractility

(34)

Effects of curvature Adventitia Media

Growth and remodeling with continuous

medial proteolytic injury

(35)

human aortic root dilatation

Finite-element predictions of human aortic root dilatation based on the homogenized constrained mixture model

Prof. Stéphane AVRIL

PARIS

AUVERGNE RHONE-ALPES

MINES SAINT-ETIENNE

First Grande Ecole

outside Paris

Founded in 1816

Aortic root dilatations and ascending thoracic aortic aneurysms (ATAA)

Risks: Aortic dissections

Surgical elective repair of ATAA

 Indications:

• Aortic insufficiency requiring surgical correction

• Size ⩾ 55 mm

• Size ⩾50 mm in patients with Marfan syndrome or bicuspid valves

• Growth rate ⩾1 cm/year

 More and more aneurysms are detected at an early stage (incidence >8% for males >65 years old).

 >90000 interventions per year in Europe and USA

Surgical techniques for ATAA repair

Context

 BUT:

• 25% ATAA < 5.5cm rupture : 15000 deaths ** !

• 60% of ATAA > 5.5 cm never experience rupture!

• 9% mortality and morbidity after ATAA repair

 In summary: inappropriate decisions and misprogramed surgical interventions have major consequences!!

 Need insightful assistance from biomechanics 

EXPERIMENTAL

WORK

Bulge inflation test

III) Inflation test device. Speckle pattern is made before starting the

inflation test Circumferential

A x ia l

Romo et al. Journal of Biomechanics - 2014

Davis et al. BMMB – 2015.

Davis et al. JMBBM – 2016

Zhao et al. Acta Biomaterialia - 2016

Identification of local material

properties

Rupture risk estimation

Physiological Stress

Stretch Stretch/Stress Curve

Rupture Stress

E

= Tangent elastic modulus

Cauch y Stress (MP a)

Physiological Stretch

Rupture Stretch

γ stress = Physiological stress Rupture stress γ stretch = Physiological stretch

Rupture stretch

Correlation between the stretch-based

rupture risk and the tangent elastic modulus

E in-vitro (MPa)

Ru pture ris k

Relationship with aortic stiffness

The stretch based rupture risk criterion correlates to the aortic

stiffness measured by elastography techniques

RELATIONSHIP WITH HEMODYNAMICS

Preoperative dynamic imaging 4D MRI

CAD Mesh

Numerical resolution

Streamlines, velocity TAWSS

BCs

Relationship λ rupture vs. TAWSSmax [Pa]

Spearman rho 0.867

P-value 0.001

Histological interpretation

 ATAA always manifests with damaged elastic fibers

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

Patient with

smallest γ stretch Patient with

largest γ stretch

elast coll

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

Summary

 2 ways of defining rupture:

 PWS – but unknown patient-specific strength

 γ stretch correlated with in vivo circumferential stiffness

Higher stiffness  less risk because the aneurysm can more easily withstand

volume variation

• 25% ATAA < 5.5cm rupture : 15000 deaths ^** !

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

E _in-vitro (MPa)

Relationship λ _rupture vs. TAWSSmax [Pa]

smallest γ _stretch Patient with

largest γ _stretch

 γ _stretch correlated with in vivo circumferential stiffness

Deposition stretch (Λ ^𝑗 _s ) of each constituent

𝐅 _tot ^𝑗 = 𝐅𝚲 ^𝑗 _s

𝐅 _tot ^𝑗 = 𝐅 _e ^𝑗 𝐅 _gr ^𝑗 𝐅 _gr ^𝑗 = 𝐅 _r ^𝑗 𝐅 _g ^𝑗

𝐅 _r ^𝑗 and 𝐅 _g ^𝑗 should be calculated if the artery is not in the homeostatic state

ሶϱ ^𝑗 (t) = ϱ ^𝑗 (t)𝑘 _σ ^𝑗 𝜎 ^𝑗 𝑡 − 𝜎 _h ^𝑗

𝜎 _h ^𝑗 + ሶ𝜉 ^𝑗 (𝑡)

ሶϱ ^𝑗 (t)

ϱ ^𝑗 (t) + 1

𝑇 ^𝑗 𝐒 ^𝑗 − 𝐒 _pre ^𝑗 = 𝜕𝐒 ^𝑗

𝜕𝐂 _e ^𝑗 : (𝐂 _e ^𝑗 𝐋 ^𝑗 _r ) 𝐋 ^𝑗 _r = ሶ𝐅 _r ^𝑗 𝐅 _r ^𝑗−1

ሶ𝐅 _g = ሶ𝐅 _g ^𝑗 = ෍

ሶ 𝐆 ^𝑗

ሶ 𝐆 ^𝑗 = ሶϱ ^𝑗 (t)

ϱ ^𝑗 (t) 𝐅 _g ^𝑗−𝑇 : 𝐁 ^𝑗

𝐁 ^𝑗

𝐁 ^𝑗 = 𝑎 _𝑔 ⊗ 𝑎 _𝑔 𝐁 ^𝑗 = ^𝟏