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 Table of Contents  
Year : 2019  |  Volume : 4  |  Issue : 3  |  Page : 39-45

Principles and clinical applications of computational fluid dynamics in aneurysms of the abdominal aorta

Department of Vascular Surgery, Peking Union Medical College Hospital, Peking Union Medical College and Chinese Academy of Medical Sciences, Dongcheng District, Beijing, China

Date of Submission08-Jul-2020
Date of Acceptance16-Jul-2020
Date of Web Publication25-Aug-2020

Correspondence Address:
Dr. Yuehong Zheng
Department of Vascular Surgery, Peking Union Medical College Hospital, No 1. Shuaifuyuan, Dongcheng District,Beijing
Dr. Yuexin Chen
Department of Vascular Surgery, Peking Union Medical College Hospital, No 1. Shuaifuyuan, Dongcheng District, Beijing
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/ts.ts_7_20

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Computational fluid dynamics (CFD) is a branch of fluid mechanics, referring to the numerical analysis of flow fields. CFD is widely applied in blood flow analysis of abdominal aortic aneurysms (AAAs) and thoracoabdominal aortic aneurysms (TAAAs), providing precision information of the blood flow field and wall stresses of the cardiovascular system. It has the advantages of individualization and noninvasiveness. It is used to predict the risk of growth and rupture of AAA and to evaluate the outcomes after endovascular aortic repair. Focused on AAA and TAAA, this review introduces the principles and clinical research progresses of CFD and looks forward to the future research directions.

Keywords: Abdominal aortic aneurysm, computational fluid dynamics, endovascular aneurysm repair, finite element analysis, stent

How to cite this article:
Kan H, Sun X, Chen Y, Zheng Y. Principles and clinical applications of computational fluid dynamics in aneurysms of the abdominal aorta. Transl Surg 2019;4:39-45

How to cite this URL:
Kan H, Sun X, Chen Y, Zheng Y. Principles and clinical applications of computational fluid dynamics in aneurysms of the abdominal aorta. Transl Surg [serial online] 2019 [cited 2021 Dec 5];4:39-45. Available from: http://www.translsurg.com/text.asp?2019/4/3/39/293427

  Introduction Top

Computational fluid dynamics (CFD) is a distinct discipline of fluid mechanics that simulates the flow field using computer software. CFD, providing accurate information on the flow field, specifically applies to study the blood flow in the human circulatory system, especially in the aorta. CFD has great value in cardiovascular diseases' evaluation, diagnosis, treatment, and therapeutic device design.[1]

An aortic aneurysm is a localized dilatation of the aorta to greater than 1.5 times its original diameter. Thoracoabdominal aortic aneurysms (TAAAs) and abdominal aortic aneurysms (AAAs) refer to aneurysmal diseases of the abdominal aorta with or without thoracic aorta, respectively. TAAA is a rare disease with an incidence of 0.37/100,000 person-year.[2] Two-year survival rate of TAAA patients without surgical intervention was 24%, and more than half of the patients died of ruptured aneurysms.[3] The incidence of AAA is 13.2 per 100,000 person-year with a rupture rate of 2.2%. The mortality rate of AAA rupture in hospitalized patients is 45.7%.[4],[5],[6]

It is clinically important to evaluate the risk of aneurysm growth and rupture, to rationally design the AAA surgical treatment plan, and to monitor the long-term safety of the operation. CFD could assist clinicians to provide optimal management to patients on admission. This review aimed at elucidating the process of CFD analysis and introducing the CFD clinical applications in TAAA and AAA diseases in domestic and foreign literature.

  Principles of Computational Fluid Dynamics Top

Vascular model construction

The first step in CFD analysis is to establish a patient's individual blood vessel model. Both multidetector-row computed tomography (CT) and magnetic resonance imagining (MRI) allow the visualization of the thoracic and abdominal aorta, and the contrast between blood and aortic walls could be enhanced utilizing contrast agents. Combining electrocardiographic gating technology to trigger the image acquisition during specific phases in the cardiac cycle could reduce the effect caused by heart motion.[7]

Target blood vessels are selected and separated from the surrounding tissue according to the information such as the gray scale of the pixels or the shape. After segmenting and labeling the target blood vessel, the boundary contours are then connected layer by layer to reconstruct the three-dimensional (3D) blood vessel model.

Commonly used image segmentation software include Mimics (Materialise, Belgium) and open source software such as 3D slicer,[8] ITK Snap,[9] and SimVascular.[10] Most of these software integrate a variety of image segmentation algorithms, while allowing researchers to manually modify the selected area. In addition, the deep learning neural network models also have great potential in image segmentation.[11]

Boundary conditions

Boundary condition refers to the definition of parameters, such as flow, pressure, and resistance at the inlet and outlet of the model and the properties of the vessel wall. By setting appropriate boundary conditions, the effect of the rest of the cardiovascular system on the vessel model can be simulated. Blood flow rate and velocity, prescribed at the inlet, can be measured by phase contrast MRI (PC-MRI) or ultrasound and can also refer to ideal conditions in the literature.[12] PC-MRI is an MRI technique used to measure the blood flow field. 2D PC-MRI can be used to measure the average and peak flow velocity at a certain vessel cross-section in a cardiac cycle, while 4D Flow MRI is capable of acquiring the flow field data in the whole blood vessel.[13] Compared with ultrasound, PC-MRI can obtain more comprehensive flow field information. However, peak flow velocity may be underestimated by 2D PC-MRI due to partial volume effect, while long scanning time had limited the clinical acceptance of 4D Flow MRI.[14] Doppler ultrasound has the advantages of high popularity and low cost but requires an operator to accurately align the blood vessel axis when measuring the flow velocity.[13]

Zero and/or constant pressure were used as boundary conditions at outlets in early researches, which could not obtain the pressure field.[15],[16] An alternative approach is to utilize reduced-order models which use parameters such as resistance or impedance. Such reduced-order models include 1D network model[17],[18] and lumped-parameter model,[19],[20],[21] among which the three-element Windkessel model is an effective model for simulating the character of downstream vascular network.[22]

In earlier blood flow simulations, the blood vessel walls are often treated as being rigid without deformation.[16] Although the rigid wall hypothesis helps reduce the workload of the calculation, the hypothesis will affect the accuracy of the simulation to a certain extent. Rigid wall hypothesis cannot be used to evaluate the changes of the interaction between blood vessel and stent grafts caused by the deformation of the blood vessel, neither the stress within the vessel wall.[23] In the elastic wall model, parameters such as the elastic modulus of the blood vessel wall can be defined, and a reasonable blood pressure level can be restored by adjusting the boundary conditions at the inlet and outlet to simulate the deformation of the blood vessel wall.[24] Rational selection of the models based on the availability of clinical data can help obtain more realistic simulation results and reduce the computational load.[25]

Numerical simulation

The continuity equation (1) describes the continuity of the fluid, and the momentum equation (2) describes the conservation of the momentum of the fluid. These two equations, together constitute the Navier–Stokes (N–S) equations, form a linear system of equations describing the fluid velocity, pressure, and shear stress, represented by U, P, and τ, respectively, in the equations.

Finite element analysis (FEA) is a common method, integrated in computer software packages, for the numerical solution of N–S equations. The basic idea is discretization, by means of which the flow field is divided into tens of thousands of grids using Euler or Lagrangian scheme. Each grid is controlled by the N–S equation, and the blood flow field can be obtained by solving the equations of all of the grids at each time step. Blood can be assumed to be a Newtonian fluid with a constant viscosity, but the actual viscosity increases where shear force is low. Therefore, a non-Newtonian fluid model could restore a more realistic blood flow state and could more accurately calculate blood flow rate and wall shear stress (WSS).[26] Biological behaviors of cellular components in the blood, such as platelet activation and aggregation, can also be further analyzed using particle tracking and material transportation algorithms.[27],[28]

For the elastic wall model, corresponding algorithms are needed to be applied for fluid–structure interaction (FSI) analysis to integrate the motion of the blood vessel wall and the internal blood flow field changes to simulate the interaction between the blood flow and the blood vessel wall. The elastic wall model can provide more information than the rigid wall in many aspects, including the wall stress and the blood flow velocity transmission, but the calculation load is significantly higher.[29],[30]

Mechanobiology and vascular remodeling

Wall stress is the internal stress generated by the vessel wall deformation and distributed along the circumferential direction. Wall stress and WSS are important factors in the microenvironment of the endothelial cells and vascular smooth muscle cells (VSMCs), which participate in the vascular homeostasis and remodeling. Abnormal stress could change the biological behavior of the endothelial cells and VSMCs and remodel of the blood vessel wall in a long time period.[31] The remodeling of the blood vessel together with the abnormal state of blood flow promotes the growth and rupture of the abdominal aortic aneurysms.

Molecular mechanisms

Dynamic balance exists in healthy blood vessel wall tissues between the production and catabolism of collagen fibers. However, elastin is basically synthesized in the early stages of human growth and development and maintained at a stable level. With a half-life up to several decades, the content of elastin gradually decreases when growing older.[32]

Endothelial cells and smooth muscle cells detect changes in wall stress and WSS through surface proteins and transmit signals to the nucleus through second messengers or cytoskeleton to regulate the transcription of different genes.[31] The diameter of the vessel can be tuned in different ways, by modulating a diverse set of cellular activities. VSMCs synthesize collagen when the wall stress increases and secretes matrix metalloproteinases when the wall stress decreases, promoting collagen and elastin to decompose and VSMC to proliferate.[33] When WSS decreases, endothelial cells inhibit the secretion of endothelial NO synthetase[34] and secrete endothelin-1 to reduce the vessel diameter and promote collagen synthesis by VSMCs.[35] Local segment remodeling is achieved through the proliferation and secretion of inflammatory cells and activated smooth muscle cells, as well as the degradation of matrix by various proteases.

Growth and remodeling models

Aortic growth and remodeling models, constructed based on the observations of the biomechanical mechanisms in the above paragraph, could simulate the process of gradual expansion and remodeling of the arterial wall that has lost part of its elastin.[36],[37] Humphrey et al.[38] put forward the constrained mixture model (CMM) model, where the constituents of the arterial wall are the mixture of elastin, collagen, VSMCs, and extracellular matrix. Arterial wall tissue undergoes elastin degradation and collagen turnover due to the induction of low WSS and wall stress, and the weak points gradually become bulge. Collagen fibers are continuously metabolized and renewed, remodeling the vascular morphology to an expanded state.[39]

Figueroa et al.[40] proposed the fluid–solid growth (FSG) model integrating the FSI simulation with the CMM model. On the one hand, the FSI simulation provides average WSS and cavity wall stress parameters, which are the basis for the CMM vascular remodeling process simulation. On the other hand, updated vascular morphology and distribution of wall compliance serve for the FSI analysis to estimate the cavity wall stress parameters. FSG model provides a more accurate and personalized predictive analysis for chronic vascular remodeling diseases such as aneurysms.

The G&R models realize computer simulation of aneurysm expansion and remodeling, with the simulation results consistent with the wall tissue pathology observations.[41] The shape of the model after expansion and remodeling resembles the clinically observed aneurysms. Although imaging techniques can obtain individualized blood vessel morphology, this technology is still a certain distance away from predicting the risk of aneurysm or rupture in healthy people, due to the lack of the individualized distribution information of the blood vessel wall components. Still, it deepens our understanding of the formation process of AAA and produces new approaches to simulate pathological processes, including vascular stenosis and neointimal hyperplasia.[42],[43]

  Growth and Rupture of Aortic Aneurysms Top

Abdominal aortic aneurysm growth rate

The researches on the relationship between the wall stress and the growth rate of AAA are controversial. Although AAAs with fast growth rate or rupture AAAs in most studies are associated with higher peak wall stress (PWS), there are also studies that show no correlations between AAA growth rate and wall stress.[44],[45] This controversy suggests that the perspective of hemodynamics may not be comprehensive in explaining the growth of AAA.

Pathological studies revealed that both the oxygen content and the tissue strength of AAA wall tissue covered by thrombus decrease indicate that thrombus may promote the progress of AAA.[46] Prospective studies utilizing CFD simulation have found that thrombus is prone to form at the site of low WSS and is consistent with the site of expansion in the long term.[47]

The cavity of AAA can be divided into stagnation regions and flow regions using the material transport algorithm. Platelets are exposed to a large shear rate at the junction of the flow zone and the stagnation zone, causing the platelet activation. The low shear rate in the stagnation zone, especially near the vascular wall, is conducive to platelet adhesion.[48] CFD researches provide theoretical support for the relationship between WSS and aneurysm progression and have application value in predicting AAA growth rate.

Aneurysm rupture

The undesirable consequence of the continued growth of AAA is rupture, which may lead to death.[6] The main basis for the clinical assessment of the risk of aneurysm rupture is the maximum diameter of the aneurysm and its growth rate. FEA can provide more information through point-by-point force analysis of aneurysms to help predict the risk of rupture. In a prospective study,[50] the baseline PWS value of AAAs which ruptured afterward was significantly different from those undergone elective surgical operation. The locations of rupture were consistent with the sites where PWS located, suggesting that high PWS value could be used as an indicator of intervention. Other studies have also found that PWS values in clinically symptomatic or ruptured AAAs are significantly higher than asymptomatic AAAs.[51] In addition, AAA rupture site is associated with slow blood flow and small WSS. The possible explanation is that AAA rupture is related to the weakening of the blood vessel wall caused by low WSS-induced growth remodeling.[52]

Spatial differences and individual differences of the tissue strength exist in the AAA wall. The average strength of AAA tissues can be measured byin vitro tissue stretching experiments. The tissue strength is affected by the factors such as gender, mural thrombus, tissue oxygen content, and calcification. Adjusting the strength parameters of the blood vessel wall tissue based on the presence of thrombosis or calcification in the patient's aneurysm could help establish a more individual blood vessel model.[53],[54] When using FEA to assess the risk of AAA rupture, the use of a vascular model of patient-specific thickness and tissue strength could improve the accuracy of the simulation.[55]

  Surgical Complications Assessment Top

Stent graft migration

With a dragging effect of blood flow imposed on the stent graft, it is at risk of displacement. The drag force and radial pressure of the blood flow on the stent could be calculated by CFD. The friction coefficient between the vessel wall and the stent material under different conditions is measured by in vitro experiments so that the researchers can predict the risk of stent displacement.[56]

The deformation of the stent and the friction between the stent graft and the vessel wall can be simulated in silico[57] to discover possible risk factors for stent displacement. The short-neck AAAs with insufficient length of the proximal anchoring area have a risk of stent displacement greater than that of the AAAs with sufficient length of the proximal anchoring area. Such simulation result is consistent with the clinical observation that the AAAs with short proximal tumor neck have higher probabilities of complications after endovascular therapy.[58]

AAAs with distorted aneurysmal neck have a higher risk of proximal type I endoleak and stent displacement after operation,[59] and this phenomenon has also been verified in the computational model.[57] It might be beneficial to evaluate the stability of the stent graft when designing the surgical plan, to select stents of appropriate size and compliance according to different aneurysm morphologies, to use the CFD method to simulate the interaction of the stent and the blood vessel, and to evaluate the risk of stent displacement before surgery.


Endoleak after endovascular aortic repair (EVAR) may cause pressure increase in the aneurysmal sac, promoting the sac to further expand or even rupture.[60] Type I endoleak refers to the situation where blood leaks into the aneurysmal sac from the proximal or distal end of the junction between the stent graft and the vessel wall. The stent graft may not attach tightly to the vessel wall where the aortic wall retracts more slowly and temporarily separates from the stent graft when blood pressure drops.[61] The elastic wall model and FSI simulation are utilized to calculate the stress, blood flow velocity, and elastic retraction time of the blood vessel wall, therefore useful in type I endoleak assessment.[62]

Type II endoleak occurs when one or more branch blood vessels supply to the aneurysmal sac.In vitro experiments suggested that the intralumenal pressure of type II endoleak is related to the pressure of the supplying artery.[63] Li et al.[64] established an idealized type II endoleak model where the aneurysmal sac is connected to the inferior mesenteric artery; the higher blood pressure can be transmitted to the supply artery via communicating arteries, causing high sac pressure and increased risk.[65] Supplying artery pressure in the type II endoleak is difficult to measure, which is a direction of further research.

Displacement of the stent module could cause type III endoleak at the junction of the modules. The friction between the stent modules keeps the connection between the stents stable, while the pressure and shear stress of the blood flow imposed on the stent module may cause the distal module to detach from the proximal module. If the length of the stent overlap area is insufficient and the friction is less than the blood flow shear force, separation might occur between the stent modules and the risk of type III endoleak could increase.[57]

Imaging techniques including CT angiography, angiography, and contrast-enhanced ultrasound are used to detect endoleak after endovascular operations.[66] CFD is of great benefit in predicting the risk of different types of endoleak in the long term through assessing whether type II endoleak increases the risk of aneurysm rupture or the long-term stability of complex stent grafts, and CFD helps determine the frequency of follow-up for patients with high risk of type I or type III endoleak.

Thrombosis and stent graft occlusion

Thrombus formation in the stent graft is another important complication after EVAR. The detachment of the embolus could cause distal embolism and re-intervention is needed if the thrombus causes occlusion in the stent graft. The probability of thrombosis is related to platelet aggregation and coagulation factor concentration. Platelets are activated under high shear stress, while newly generated activated coagulation factors cannot be effectively removed under the low shear rate associated with blood stasis.[67] Once the flow field information including blood flow velocity and shear rate at various positions is obtained, it could be used to calculate the shear force experienced by the platelets throughout the movement path.[68] By calculating the extent of platelet activation and its distribution in the flow field, it is possible to simulate the long-term thrombus formation pattern and to evaluate the long-term stability and patency of the stent graft.[69] After platelets are activated at high shear stress site, they aggregate in low shear rate sites to form thrombi. Such sites could by located by CFD simulation by calculating shear stress and residence time that are conducive to platelet deposition.[70]

Branch stents and chimney technology are used to treat aneurysms involving the renal artery and superior mesenteric artery. The chimney technology refers to extending the stent from the branch artery into the main stent graft of the aorta in a parallel manner, and the part in the aorta is located between the artery wall and the aortic stent. When the chimney stent enters the branch artery, it bends and forms an angle. Due to the compression of the aortic stent, the shape of the stent may change and affect the blood flow state within, resulting in thrombosis and occlusion.[71],[72] CFD simulations could exhibit the flow field in the branch stent, providing information concerning the performance and failure mechanisms of intravascular devices, and predict the risk and guide the use of anticoagulant drugs.

Avenues for future research

Follow-up cohort of CFD simulation should be further developed in the future to promote the application of CFD in the assessment and treatment of aneurysm diseases. Cohort studies are suitable for exploring and testing etiology hypotheses. For instance, the verification of the relationship between low WSS and high PWS and AAA growth and rupture.[73] The cohort of CFD simulation in patients undergone EVAR will provide valuable insights in exploring the causes of complications, including stent displacement, endoleak, and thrombosis. The establishment of CFD follow-up cohorts will help explore the predictive value of hemodynamic parameters for clinical prognosis and promote the development of related basic research and the establishment of a theoretical system for prognostic prediction.

CFD has a broad prospect to be applied in the design of vascular surgery plans. Based on the simulation of blood flow using the individualized blood vessel model and boundary conditions, different surgery plan and outcomes can be simulated before the patient's operation through artificial modification of the blood vessel model (such as adding bypass blood vessels[74] and changing the local blood vessel morphology). The expected improvement of blood pressure and blood flow perfusion after the corresponding surgical plan could be obtained, which can be used as a prediction and reference for evaluating short-term postoperative efficacy. Combining the relevant indicators obtained from the simulation and the information provided by the aforementioned CFD follow-up cohort can further evaluate and predict the long-term efficacy of the surgical plan. The simulated prognosis of different surgical plans can assist clinicians in formulating the best surgical plan before surgery.

To meet the needs of surgical simulation, it is necessary to establish a more personalized FSI calculation model, to improve the individualized blood vessel model of patients with spatial distribution heterogeneity, and to restore the true arterial wall thickness, tissue strength, and elastic modulus.[53],[54] Detailed mechanical properties of artificial blood vessels, stents, and other medical devices[75] are required to simulate the interaction between the blood flow, blood vessels, and intravascular devices and long-term stability of stent grafts. New algorithms for the simulation of self-expansion process of the stent are needed to predict the shape and angle of the stent after expanding to achieve more accurate surgical simulation.[76]

As a numerical simulation method, CFD has been widely used in the prediction of the growth and rupture risk of aneurysms of the descending and abdominal aorta and the designation of endovascular operation plans and prognostic analysis, and CFD has proved its value in assisting assessment and treatment of aneurysm diseases.

Although evidence of multicenter clinical trials of CFD simulation in aneurysm diseases treatment is still lacking, the popularity of CFD could be expected with the advancement of high-resolution imaging and computing performance and the development of commercial software packages. Continuing to develop the aneurysm diseases assessment and treatment cohort assisted by CFD simulation and improving the CFD calculation model are the future directions, which will further improve the understanding and the level of clinical treatment of aneurysm diseases.

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Conflicts of interest

There are no conflicts of interest.

  References Top

Taylor CA, Figueroa CA. Patient-specific modeling of cardiovascular mechanics. Annu Rev Biomed Eng 2009;11 (1):109-34.  Back to cited text no. 1
Panneton JM, Hollier LH. Nondissecting thoracoabdominal aortic aneurysms: Part I. Ann Vasc Surg 1995;9 (5):503-14.  Back to cited text no. 2
Crawford ES, DeNatale RW. Thoracoabdominal aortic aneurysm: Observations regarding the natural course of the disease. J Vasc Surg 1986;3 (4):578-82.  Back to cited text no. 3
Kühnl A, Erk A, Trenner M, Salvermoser M, Schmid V, Eckstein HH. Incidence, treatment and mortality in patients with abdominal aortic aneurysms. Dtsch Arztebl Int 2017;114 (22-23):391-8.  Back to cited text no. 4
Brown LC, Powell JT. Risk factors for aneurysm rupture in patients kept under ultrasound surveillance. UK small aneurysm trial participants. Ann Surg 1999;230 (3):289-96.  Back to cited text no. 5
Abdulameer H, Al Taii H, Al-Kindi SG, Milner R. Epidemiology of fatal ruptured aortic aneurysms in the United States (1999-2016). J Vasc Surg 2019;69 (2):378-84.e2.  Back to cited text no. 6
Kachelriess M, Ulzheimer S, Kalender WA. ECG-correlated imaging of the heart with subsecond multislice spiral CT. IEEE Trans Med Imaging 2000;19 (9):888-901.  Back to cited text no. 7
Fedorov A, Beichel R, Kalpathy-Cramer J, Finet J, Fillion-Robin JC, Pujol S, Bauer C, Jennings D, Fennessy F, Sonka M, Buatti J, Aylward S, Miller JV, Pieper S, Kikinis R. 3D Slicer as an image computing platform for the Quantitative Imaging Network. Magn Reson Imaging 2012;30 (9):1323-41.  Back to cited text no. 8
Yushkevich PA, Piven J, Hazlett HC, Smith RG, Ho S, Gee JC, Gerig G. User-guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability. Neuroimage 2006;31 (3):1116-28.  Back to cited text no. 9
Updegrove A, Wilson NM, Merkow J, Lan H, Marsden AL, Shadden SC. SimVascular: An open source pipeline for cardiovascular simulation. Ann Biomed Eng 2017;45 (3):525-41.  Back to cited text no. 10
Withey D, Koles Z. A review of medical image segmentation: Methods and available software. Int J Bioelectromagn 2008;10 (3):125-48.  Back to cited text no. 11
Morbiducci U, Ponzini R, Gallo D, Bignardi C, Rizzo G. Inflow boundary conditions for image-based computational hemodynamics: Impact of idealized versus measured velocity profiles in the human aorta. J Biomech 2013;46 (1):102-9.  Back to cited text no. 12
Stadlbauer A, van der Riet W, Globits S, Crelier G, Salomonowitz E. Accelerated phase-contrast MR imaging: Comparison of k-t BLAST with SENSE and Doppler ultrasound for velocity and flow measurements in the aorta. J Magn Reson Imaging 2009;29 (4):817-24.  Back to cited text no. 13
Vasanawala SS, Hanneman K, Alley MT, Hsiao A. Congenital heart disease assessment with 4D flow MRI. J Magn Reson Imaging 2015;42 (4):870-86.  Back to cited text no. 14
Stuhne GR, Steinman DA. Finite-element modeling of the hemodynamics of stented aneurysms. J Biomech Eng 2004;126 (3):382-7.  Back to cited text no. 15
Taylor CA, Hughes TJ, Zarins CK. Finite element modeling of three-dimensional pulsatile flow in the abdominal aorta: Relevance to atherosclerosis. Ann Biomed Eng 1998;26 (6):975-87.  Back to cited text no. 16
Formaggia L, Gerbeau JF, Nobile F, Quarteroni A. numerical treatment of defective boundary conditions for the Navier–Stokes Equations. SIAM J Numer Anal 2002;40 (1):376-401.  Back to cited text no. 17
Formaggia L, Gerbeau JF, Nobile F, Quarteroni A. On the coupling of 3D and 1D Navier–Stokes equations for flow problems in compliant vessels. Comput Methods Appl Mech Eng 2001;191 (6):561-82.  Back to cited text no. 18
Quarteroni A, Veneziani A. Analysis of a geometrical multiscale model based on the coupling of ODE and PDE for blood flow simulations. Multiscale Model Simul 2003;1(2):173-95.  Back to cited text no. 19
Laganà K, Balossino R, Migliavacca F, Pennati G, Bove EL, de Leval MR, Dubini G. Multiscale modeling of the cardiovascular system: Application to the study of pulmonary and coronary perfusions in the univentricular circulation. J Biomech 2005;38 (5):1129-41.  Back to cited text no. 20
Quarteroni A, Ragni S, Veneziani A. Coupling between lumped and distributed models for blood flow problems. Comput Vis Sci 2001;4 (2):111-24.  Back to cited text no. 21
Pirola S, Cheng Z, Jarral OA, O'Regan DP, Pepper JR, Athanasiou T, Xu XY. On the choice of outlet boundary conditions for patient-specific analysis of aortic flow using computational fluid dynamics. J Biomech 2017;60 (1):15-21.  Back to cited text no. 22
Taylor CA, Draney MT, Ku JP, Parker D, Steele BN, Wang K, Zarins CK. Predictive medicine: Computational techniques in therapeutic decision-making. Comput Aided Surg 1999;4 (5):231-47.  Back to cited text no. 23
Formaggia L, Moura A, Nobile F. On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations. ESAIM Math Model Numer Anal 2007;41 (4):743-69  Back to cited text no. 24
Morris PD, Narracott A, von Tengg-Kobligk H, Silva Soto DA, Hsiao S, Lungu A, Evans P, Bressloff NW, Lawford PV, Hose DR, Gunn JP. Computational fluid dynamics modelling in cardiovascular medicine. Heart 2016;102 (1):18-28.  Back to cited text no. 25
Abbasian M, Shams M, Valizadeh Z, Moshfegh A, Javadzadegan A, Cheng S. Effects of different non-Newtonian models on unsteady blood flow hemodynamics in patient-specific arterial models with in-vivo validation. Comput Methods Programs Biomed 2020;186:105185.  Back to cited text no. 26
Hansen KB, Arzani A, Shadden SC. Mechanical platelet activation potential in abdominal aortic aneurysms. J Biomech Eng 2015;137 (4):041005.  Back to cited text no. 27
Li ZY, Sadat U, U-King-Im J, Tang TY, Bowden DJ, Hayes PD, Gillard JH. Association between aneurysm shoulder stress and abdominal aortic aneurysm expansion: A longitudinal follow-up study. Circulation 2010;122 (18):1815-22.  Back to cited text no. 28
Figueroa C, Vignon-Clementel I, Jansen K, Hughes T, Taylor C. A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Comput Methods Appl Mech Eng 2006;195 (41–43):5685-706.  Back to cited text no. 29
Tallec P. Fluid structure interaction with large structural displacement. Comput Methods Appl Mech Eng 2001;190 (24-25):3039-67.  Back to cited text no. 30
Qi YX, Han Y, Jiang ZL. Mechanobiology and vascular remodeling: From Membrane to nucleus. Adv Exp Med Biol 2018;1097:69-82.  Back to cited text no. 31
Cocciolone AJ, Hawes JZ, Staiculescu MC, Johnson EO, Murshed M, Wagenseil JE. Elastin, arterial mechanics, and cardiovascular disease. Am J Physiol Heart Circ Physiol 2018;315 (2):H189-H205.  Back to cited text no. 32
Newby AC. Matrix metalloproteinases regulate migration, proliferation, and death of vascular smooth muscle cells by degrading matrix and non-matrix substrates. Cardiovasc Res 2006;69 (3):614-24.  Back to cited text no. 33
Koskinas KC, Chatzizisis YS, Antoniadis AP, Giannoglou GD. Role of endothelial shear stress in stent restenosis and thrombosis: Pathophysiologic mechanisms and implications for clinical translation. J Am Coll Cardiol 2012;59 (15):1337-49.  Back to cited text no. 34
Rizvi MA, Katwa L, Spadone DP, Myers PR. The effects of endothelin-1 on collagen type I and type III synthesis in cultured porcine coronary artery vascular smooth muscle cells. J Mol Cell Cardiol 1996;28 (2):243-52.  Back to cited text no. 35
Humphrey JD. Vascular adaptation and mechanical homeostasis at tissue, cellular, and sub-cellular levels. Cell Biochem Biophys 2008;50 (2):53-78.  Back to cited text no. 36
Wu J, Shadden SC. Coupled simulation of hemodynamics and vascular growth and remodeling in a subject-specific geometry. Ann Biomed Eng 2015;43 (7):1543-54.  Back to cited text no. 37
Humphrey JD, Rajagopal KR. A constrained mixture model for arterial adaptations to a sustained step change in blood flow. Biomech Model Mechanobiol 2003;2 (2):109-26.  Back to cited text no. 38
Sheidaei A, Hunley SC, Zeinali-Davarani S, Raguin LG, Baek S. Simulation of abdominal aortic aneurysm growth with updating hemodynamic loads using a realistic geometry. Med Eng Phys 2011;33 (1):80-8.  Back to cited text no. 39
Figueroa CA, Baek S, Taylor CA, Humphrey JD. A computational framework for fluid-solid-growth modeling in cardiovascular simulations. Comput Methods Appl Mech Eng 2009;198 (45-46):3583-602.  Back to cited text no. 40
Menashi S, Campa JS, Greenhalgh RM, Powell JT. Collagen in abdominal aortic aneurysm: Typing, content, and degradation. J Vasc Surg 1987;6 (6):578-82.  Back to cited text no. 41
Drews JD, Pepper VK, Best CA, Szafron JM, Cheatham JP, Yates AR, Hor KN, Zbinden JC, Chang YC, Mirhaidari GJ, Ramachandra AB, Miyamoto S, Blum KM, Onwuka EA, Zakko J, Kelly J, Cheatham SJ, King N, Reinhardt JW, Sugiura T, Miyachi H, Matsuzaki Y, Breuer J, Heuer ED, West TA, Shoji T, Berman D, Boe BA, Asnes J, Galantowicz M, Matsumura G, Hibino N, Marsden AL, Pober JS, Humphrey JD, Shinoka T, Breuer CK. Spontaneous reversal of stenosis in tissue-engineered vascular grafts. Sci Transl Med 2020;12 (537):eaax 6919.  Back to cited text no. 42
Donadoni F, Pichardo-Almarza C, Bartlett M, Dardik A, Homer-Vanniasinkam S, Díaz-Zuccarini V. Patient-specific, multi-scale modeling of neointimal hyperplasia in vein grafts. Front Physiol 2017;8:226.  Back to cited text no. 43
Stevens RR, Grytsan A, Biasetti J, Roy J, Lindquist Liljeqvist M, Gasser TC. Biomechanical changes during abdominal aortic aneurysm growth. PLoS One 2017;12 (11):e0187421.  Back to cited text no. 44
Indrakusuma R, Jalalzadeh H, Planken RN, Marquering HA, Legemate DA, Koelemay MJ, Balm R. Biomechanical imaging markers as predictors of abdominal aortic aneurysm growth or rupture: A systematic review. Eur J Vasc Endovasc Surg 2016;52 (4):475-86.  Back to cited text no. 45
Vorp DA, Lee PC, Wang DH, Makaroun MS, Nemoto EM, Ogawa S, Webster MW. Association of intraluminal thrombus in abdominal aortic aneurysm with local hypoxia and wall weakening. J Vasc Surg 2001;34 (2):291-9.  Back to cited text no. 46
Doyle B, Sun Z, Jansen S, Norman P. Commentary: Computational modeling of contemporary stent-grafts. J Endovasc Ther 2015;22 (4):591-3.  Back to cited text no. 47
Joly F, Soulez G, Garcia D, Lessard S, Kauffmann C. Flow stagnation volume and abdominal aortic aneurysm growth: Insights from patient-specific computational flow dynamics of Lagrangian-coherent structures. Comput Biol Med 2018;92:98-109.  Back to cited text no. 48
Zambrano BA, Gharahi H, Lim C, Jaberi FA, Choi J, Lee W, Baek S. Association of intraluminal thrombus, hemodynamic forces, and abdominal aortic aneurysm expansion using longitudinal CT images. Ann Biomed Eng 2016;44 (5):1502-14.  Back to cited text no. 49
Fillinger MF, Marra SP, Raghavan ML, Kennedy FE. Prediction of rupture risk in abdominal aortic aneurysm during observation: Wall stress versus diameter. J Vasc Surg 2003;37 (4):724-32.  Back to cited text no. 50
Kontopodis N, Metaxa E, Papaharilaou Y, Tavlas E, Tsetis D, Ioannou C. Advancements in identifying biomechanical determinants for abdominal aortic aneurysm rupture. Vascular 2015;23 (1):65-77.  Back to cited text no. 51
Boyd AJ, Kuhn DC, Lozowy RJ, Kulbisky GP. Low wall shear stress predominates at sites of abdominal aortic aneurysm rupture. J Vasc Surg 2016;63 (6):1613-9.  Back to cited text no. 52
Gasser TC. Biomechanical rupture risk assessment: A consistent and objective decision-making tool for abdominal aortic aneurysm patients. Aorta (Stamford) 2016;4 (2):42-60.  Back to cited text no. 53
Polzer S, Gasser TC. Biomechanical rupture risk assessment of abdominal aortic aneurysms based on a novel probabilistic rupture risk index. J R Soc Interface 2015;12 (113):20150852.  Back to cited text no. 54
Shang EK, Nathan DP, Woo EY, Fairman RM, Wang GJ, Gorman RC, Gorman JH 3rd, Jackson BM. Local wall thickness in finite element models improves prediction of abdominal aortic aneurysm growth. J Vasc Surg 2015;61 (1):217-23.  Back to cited text no. 55
Vad S, Eskinazi A, Corbett T, McGloughlin T, Vande Geest JP. Determination of coefficient of friction for self-expanding stent-grafts. J Biomech Eng 2010;132 (12):121007.  Back to cited text no. 56
Prasad A, Xiao N, Gong XY, Zarins CK, Figueroa CA. A computational framework for investigating the positional stability of aortic endografts. Biomech Model Mechanobiol 2013;12 (5):869-87.  Back to cited text no. 57
Bisdas T, Weiss K, Eisenack M, Austermann M, Torsello G, Donas KP. Durability of the Endurant stent graft in patients undergoing endovascular abdominal aortic aneurysm repair. J Vasc Surg 2014;60 (5):1125-31.  Back to cited text no. 58
AbuRahma AF, Yacoub M, Mousa AY, Abu-Halimah S, Hass SM, Kazil J, AbuRahma ZT, Srivastava M, Dean LS, Stone PA. Aortic neck anatomic features and predictors of outcomes in endovascular repair of abdominal aortic aneurysms following vs not following instructions for use. J Am Coll Surg 2016;222 (4):579-89.  Back to cited text no. 59
Dias NV, Ivancev K, Resch TA, Malina M, Sonesson B. Endoleaks after endovascular aneurysm repair lead to nonuniform intra-aneurysm sac pressure. J Vasc Surg 2007;46 (2):197-203.  Back to cited text no. 60
Amblard A, Berre HW, Bou-Saïd B, Brunet M. Analysis of type I endoleaks in a stented abdominal aortic aneurysm. Med Eng Phys 2009;31 (1):27-33.  Back to cited text no. 61
Lu YH, Mani K, Panigrahi B, Hsu WT, Chen CY. Endoleak assessment using computational fluid dynamics and image processing methods in stented abdominal aortic aneurysm models. Comput Math Methods Med 2016;2016:9567294.  Back to cited text no. 62
Chong CK, How TV, Gilling-Smith GL, Harris PL. Modeling endoleaks and collateral reperfusion following endovascular AAA exclusion. J Endovasc Ther 2003;10 (3):424-32.  Back to cited text no. 63
Li Z, Kleinstreuer C. Computational analysis of type II endoleaks in a stented abdominal aortic aneurysm model. J Biomech 2006;39 (14):2573-82.  Back to cited text no. 64
Baum RA, Carpenter JP, Tuite CM, Velazquez OC, Soulen MC, Barker CF, Golden MA, Pyeron AM, Fairman RM. Diagnosis and treatment of inferior mesenteric arterial endoleaks after endovascular repair of abdominal aortic aneurysms. Radiology 2000;215 (2):409-13.  Back to cited text no. 65
Cantisani V, Ricci P, Grazhdani H, Napoli A, Fanelli F, Catalano C, Galati G, D'Andrea V, Biancari F, Passariello R. Prospective comparative analysis of colour-Doppler ultrasound, contrast-enhanced ultrasound, computed tomography and magnetic resonance in detecting endoleak after endovascular abdominal aortic aneurysm repair. Eur J Vasc Endovasc Surg 2011;41 (2):186-92.  Back to cited text no. 66
Ou C, Huang W, Yuen MM. A computational model based on fibrin accumulation for the prediction of stasis thrombosis following flow-diverting treatment in cerebral aneurysms. Med Biol Eng Comput 2017;55 (1):89-99.  Back to cited text no. 67
Nauta FJ, Lau KD, Arthurs CJ, Eagle KA, Williams DM, Trimarchi S, Patel HJ, Figueroa CA. Computational fluid dynamics and aortic thrombus formation following thoracic endovascular aortic repair. Ann Thorac Surg 2017;103 (6):1914-21.  Back to cited text no. 68
Hansen KB, Arzani A, Shadden SC. Mechanical platelet activation potential in abdominal aortic aneurysms. J Biomech Eng 2015;137 (4):041005.  Back to cited text no. 69
Menichini C, Xu XY. Mathematical modeling of thrombus formation in idealized models of aortic dissection: Initial findings and potential applications. J Math Biol 2016;73 (5):1205-26.  Back to cited text no. 70
Usai MV, Torsello G, Donas KP. Current evidence regarding chimney graft occlusions in the endovascular treatment of pararenal aortic pathologies: A systematic review with pooled data analysis. J Endovasc Ther 2015;22930:396-400.  Back to cited text no. 71
Tricarico R, He Y, Laquian L, Scali ST, Tran-Son-Tay R, Beck AW, Berceli SA. Hemodynamic and anatomic predictors of renovisceral stent-graft occlusion following chimney endovascular repair of juxtarenal aortic aneurysms. J Endovasc Ther 2017;24 (6):880-8.  Back to cited text no. 72
Polzer S, Gasser TC, Vlachovský R, Kubíček L, Lambert L, Man V, Novák K, Slažanský M, Burša J, Staffa R. Biomechanical indices are more sensitive than diameter in predicting rupture of asymptomatic abdominal aortic aneurysms. J Vasc Surg 2020;71 (2):617-26.e6.  Back to cited text no. 73
Tossas-Betancourt C, van Bakel TM, Arthurs CJ, Coleman DM, Eliason JL, Figueroa CA, Stanley JC. Computational analysis of renal artery flow characteristics by modeling aortoplasty and aortic bypass interventions for abdominal aortic coarctation. J Vasc Surg 2020;71 (2):505-16.e4.  Back to cited text no. 74
Rahmani S, Jarrahi A, Navidbakhsh M, Alizadeh M. Investigating the performance of four specific types of material grafts and their effects on hemodynamic patterns as well as on von Mises stresses in a grafted three-layer aortic model using fluid-structure interaction analysis. J Med Eng Technol 2017;41 (8):630-43.  Back to cited text no. 75
Spranger K, Capelli C, Bosi GM, Schievano S, Ventikos Y. Comparison and calibration of a real-time virtual stenting algorithm using finite element analysis and genetic algorithms. Comput Methods Appl Mech Eng 2015;293:462-80.  Back to cited text no. 76


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