Institut Mines-Télécomavril@emse.fr
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
Institut Mines-Télécomavril@emse.fravril@emse.fr
Aortic root dilatations and ascending thoracic aortic aneurysms (ATAA)
3 Stéphane Avril - 2018 July 23 - NYC WCCM
Risks: Aortic dissections
Institut Mines-Télécomavril@emse.fravril@emse.fr
Surgical elective repair of ATAA
5 Stéphane Avril - 2018 July 23 - NYC WCCM
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
Institut Mines-Télécomavril@emse.fravril@emse.fr
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
7 Stéphane Avril - 2018 July 23 - NYC WCCM
EXPERIMENTAL
WORK
Institut Mines-Télécomavril@emse.fravril@emse.fr
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
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Davis et al. BMMB – 2015.
Davis et al. JMBBM – 2016
Zhao et al. Acta Biomaterialia - 2016
Identification of local material
properties
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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
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
Institut Mines-Télécomavril@emse.fr
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
RELATIONSHIP WITH HEMODYNAMICS
Preoperative dynamic imaging 4D MRI
CAD Mesh
Numerical resolution
Streamlines, velocity TAWSS
BCs
Institut Mines-Télécomavril@emse.fravril@emse.fr 15
Relationship λ rupture vs. TAWSSmax [Pa]
Spearman rho 0.867
P-value 0.001
Stéphane Avril - 2018 July 23 - NYC WCCM
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
Institut Mines-Télécomavril@emse.fravril@emse.fr 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
Stéphane Avril - 2018 July 23 - NYC WCCM
THEORETICAL
WORK
Institut Mines-Télécomavril@emse.fravril@emse.fr
Continuous process of proteolytic injury and tissue adaptation
19
PROTEOLYTIC INJURY
Strain HEALING
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Stress
Stress
Constrained mixture theory
Institut Mines-Télécomavril@emse.fravril@emse.fr 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
Stéphane Avril - 2018 July 23 - NYC WCCM
Deposition stretch (Λ 𝑗 s ) of each constituent
𝐅 tot 𝑗 = 𝐅𝚲 𝑗 s
Collagen Elastin
SMC Load
Layer-specific constitutive model
Volumetric contributions of strain-energy function
Damage
Active contribution of smooth muscle cells
Institut Mines-Télécomavril@emse.fravril@emse.fr
Homogenized G&R
constrained mixture model
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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
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
Institut Mines-Télécomavril@emse.fravril@emse.fr 25
Homogenized G&R
constrained mixture model
Stéphane Avril - 2018 July 23 - NYC WCCM
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
COMPUTATIONAL
WORK
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Finite-element implementation
FE software ABAQUS coupled with UMAT
Reference configuration is the in vivo configuration
Stéphane Avril - 2018 July 23 - NYC WCCM
Bellini et al, ABME, 2014 Mousavi et al, BMMB, 2017
Modeling of a bulge inflation test including pre-test deformation
Model parameters are calibrated against pressure/deflection curves
Institut Mines-Télécomavril@emse.fravril@emse.fr
Hoop stress in patient specific ATAA
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Zero pressure
Systolic pressure Geometry at
diastole
Prediction of mechanical damage in bulge inflation tests
Damage during bulge inflation test (luminal side in)
Institut Mines-Télécomavril@emse.fravril@emse.fr 31
Damage during bulge inflation test (luminal side out)
Stéphane Avril - 2018 July 23 - NYC WCCM
Prediction of mechanical damage
in bulge inflation tests
Gradient-enhanced G&R healing model
k=0
k=5.0 k=0.5
k=1.0
Institut Mines-Télécomavril@emse.fravril@emse.fr
Growth and remodeling with continuous medial proteolytic injury
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Effects of rate of collagen mass production and of loss of SMC
contractility
Effects of curvature Adventitia Media
Growth and remodeling with continuous
medial proteolytic injury
Institut Mines-Télécomavril@emse.fravril@emse.fr
SUMMARY
Novel numerical model based on the constrained mixture theory including damage and G&R ;
Layer specific model which can capture the response of each layer of arterial wall if any growth and remodeling occurs;
Need to improve computational and experimental sides.
35 Stéphane Avril - 2018 July 23 - NYC WCCM
Computational mechanics in the OR for vascular surgery?
www.predisurge.com
Institut Mines-Télécomavril@emse.fravril@emse.fr
Acknowledgements
Funding:
ERC-2014-CoG BIOLOCHANICS
Joan Laubrie
Jamal Mousavi
Di Zuo
Yiqian He
Olfa Trabelsi
Aaron Romo
Jin Kim
Pierre Badel
Frances Davis
Victor Acosta
Solmaz Farzeneh
Francesca Condemi
Cristina Cavinato
Jérôme Molimard
Baptiste Pierrat
Claudie Petit
Ambroise Duprey
Jean-Pierre Favre
Jean-Noël Albertini
Salvatore Campisi
Magalie Viallon
Pierre Croisille
Chiara Bellini
Matthew Bersi
Jay Humphrey
Christian Cyron
Fabian Braeu
Nele Famaey
37 Stéphane Avril - 2018 July 23 - NYC WCCM