Computational Framework for Studying Cardiovascular Biomechanics in Pathologies

Kexin Lin, Han Li, Igor Inga, Danial ShahmirzadiDepartment of Mechanical Engineering

Results Traumatic aortic rupture:

Strain results showed the maximum at the distal

end (smaller end of the plaque) and propagates

toward the neck of the stenosis.

Acoustic radiation:

The results show oscillating strain and stress

fields given the oscillatory nature of the ARFI

radiation force. The maximum strain and stress

values were found to take place at the smaller

end of the plaque (i.e. the distal end) and

propagating proximally back to the plaque over

time. It was also observed that the average

magnitude of stress and strain was higher initially

and decreased over time.

Thoracic Endovascular Aortic Repair

Wave propagation is obtained

on the aortic wall showing the

disruption of the wave

arriving at the stent

Aortic focal softening

Pulse wave propagation along soft inclusion models (3D waterfall plot and 2D spatial temporal plots.

IntroductionObtaining a quantitative understanding of the aortic biomechanicsduring health and disease provides significant information that canbe used to advance the disease assessment, monitoring andprevention methods. Owned to the advancements in computational power,numerical modeling of the aortic biomechanics has becoming power andeffective tools toward quantifying the aortic biomechanics. In this poster, acomputational framework has been shown to model various cardiovasculardiseases such as blunt Traumatic Aortic Rupture (TAR), Atherosclerosis plaques,Endovascular Aortic Repair (TEVAR), and focal softening, precursor to diseasessuch as Thoracic Aortic Aneurysm (TAA).

Traumatic Aortic Rupture (TAR): Traumatic Aortic Rupture (TAR). TAR is the leadingcause of mortalities in car accidents, affecting more than 35,000 people in US in 2010,according to National Vital Statistics Report published in 2012. Examining the mech-anical properties of aortic tissues under damage allow us to gain a better underratingof the damage mechanisms and to improve the severity assessment and preventionschemes on patients with TAR.

Acoustic Radiation Force Impulse (ARFI) imaging of vulnerable plaques: The rupture of plaque,including a large lipid core and a thin fibrous cap, is the most common cause of complications such asstroke and coronary heart failure. Acoustic Radiation Force Impulse (ARFI) imaging could show promisefor imaging these features noninvasively. Clinically, this could be used to distinguish vulnerable plaques,for which surgical intervention may be required, from those less prone to rupture.

Thoracic Endovascular Aortic Repair (TEVAR): TEVAR is a common clinical therapeutic practice forThoracic Aortic Aneurysm (TAA) and Thoracic Aortic Dissection (TAD), by which an endograft is secured to the interior of the aortic wall in order to help strengthening the weakened areas at the lesion and ensuring the opening of the lumen.

Modeling ParametersTraumatic aortic rupture:

• A three-layer model is constructed: The thicknesses of thethree layers are 2.61 mm, respectively, while the internal diameterwas 21 mm for the proximal descending part and 15.87 mm forthe distal aorta, and the length of the tube 200 mm.• Material properties is defined: The stress-strain behavior ofthe material is hype-elastic, nonlinear and isotropic. the strain-stress curves in circumferential direction are assumed as thestrain-stress curve of the three layers of the aorta, respectively.In this work, a third order polynomial form of the Ogden modelis used to express the principle stress andstrain.

• Boundary conditions: the proximal and distal aortaare fixed, blood is assumed to be standing. The forceapplied including two parts: impulse impact force4,500 N That lasts for 10 ms and a body force of chestacceleration which equals to 593,505 N.

ARFI on Atherosclerosis Plaque:• One model with 3 layers and plaque: The three layeris consisted of adventitia, media and intima and the thickness of them are 0.96mm, 1.32mm, 0.33mm. The plaque is consisted of lipid and cap, whose thickness are 2mm and 0.5mm. The hole length of descending part is 200mm. The length of plaque is 20mm which begins from 3/10 of the whole part near the heart along the descending.• Material properties: The Ogdenmodel is used in this model tosimulate the material of threelayers and plaque.• Boundary conditions: Onesection of the descending part isselected to be added with a forceimpulse. All parts stand body forcewith none flip condition betweeneach part.

Thoracic Endovascular Aortic Repair• Placing an endograft inside the lumen of the aorta to alleviatepressure against the aortic wall. Understanding a simplified modelof wall local softening (soft inclusion).• The objective is to characterize the pulse wave propagationalong endografted aorta to study deformation along aortic walland to Characterize the pulse wave propagation along softinclusion models to study deformation along weaker portionsof aortic wall.

ConclusionFeasibility of using finite element methods to establish a numerical platform for describing cardiovascular dynamic fluid-solid interaction models.

Applications of the numerical platform to examine various cardiovascular diseases such as bluntTraumatic Aortic Rupture (TAR), Atherosclerosis plaques, Endovascular Aortic Repair (TEVAR), andfocal softening, precursor to diseases such as Thoracic Aortic Aneurysm (TAA).

It was found that numerical model has been effective in providing insights into the phenomena and theresults can be used to better interpret the experimental and clinical findings

Ongoing studies are being conducted to improve the numerical model by incorporating morephysiologically-relevant modeling parameters

Stevens Innovation ExpoApril 30, 2014

www.stevens.edu/expo

Blunt traumatic aortic rupture(trauma.org 9:4 2004)Lipid and aortic plaque (Allen D et

al 2014)

FEM of reconstructionof real accident (Belwadi 2012)

Eli Atar, Alexander Belenky, Menashe Hadad, Ehud Ranany, Shlomo Baytner and Gil N. Bachar et al 2006

The CT scan of human aorta, D part is the descending aorta (Adapted from Sang-Hyun Lee et al, 2007)

Three-layer aorta model in Abaqus

Intima0.33mm

Media1.32mm

Adventitia0.96mm

27mm 21m

m

Cross section Close up

Schematic models of impact and deccelartion forces on traumatic aortic rupture model

50mm

Impact force

Acceleration force

Stent Model in aortaThree-layer aorta stent model in abaqus

Intima0.33mm

Media1.32mm

Adventitia0.96mm

27mm 21m

m

Cross section Close up

75mm Stent

Strain-stress curves of three layers and plaque

Str

es

s (

kPa

)

ARFI acoustic radiation

Cap0.5mm

Lipid2mm

Eulerian Domain

Focused Ultrasound System

Schematic representation of ARFI applications on plaque imaging

Simplified model of aortic focal softening

Cross section of the focal softening model

Flow Direction

Peak wave

Computational Framework• Software: Abaqus 6.11, Solidworks 2013, Matlab R2013a

• Dell Precision, Intel Core i7-3840QM, 32Gb Ram

• Inclusion model

• total number of Lagrangian elements: 591,796

• total number of Eulerian elements: 95,750

• time increment 6e-5 s

• simulation time = 15 ms, actual run time ~ 10 h

• Stent model

• total number of Lagrangian elements: 252,296

• total number of Eulerian elements: 266,537

• time increment 1e-7 s

• simulation time = 50 ms, actual run time ~ 70 h

• Atherosclerosis plaques model

• total number of Lagrangian elements: 687,546

• total number of Eulerian elements: 2,184,372

• time increment 7e-8 s

• simulation time = 0.5 ms, actual run time ~ 12 h

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Model with one small soft inclusion (Young’s Modulus E=2.56 Mpa

Long- and short-axis cross section views of Strain (a & c), and Stress (b & d), fields on the aortic wall and plaque

Adventitia

Media

Intima

Stent

Fluid flow

Stent model cross section close up

Wall displacement on the endografted aorta showing the wave propagationsRight befor the stent

Flow

Wave propagation

Stent

Impact force

Strain map of the aortic wall and plaque under impact ladong at the distal end and center of the stenosis