|Year : 2019 | Volume
| Issue : 3 | Page : 39-45
Principles and clinical applications of computational fluid dynamics in aneurysms of the abdominal aorta
Haoxuan Kan, Xiaoning Sun, Yuexin Chen, Yuehong Zheng
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 Submission||08-Jul-2020|
|Date of Acceptance||16-Jul-2020|
|Date of Web Publication||25-Aug-2020|
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
Source of Support: None, Conflict of Interest: None
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 Oct 17];4:39-45. Available from: http://www.translsurg.com/text.asp?2019/4/3/39/293427
| Introduction|| |
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.
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. Two-year survival rate of TAAA patients without surgical intervention was 24%, and more than half of the patients died of ruptured aneurysms. 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%.,,
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|| |
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.
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, ITK Snap, and SimVascular. 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.
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. 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. 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. 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.
Zero and/or constant pressure were used as boundary conditions at outlets in early researches, which could not obtain the pressure field., 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, and lumped-parameter model,,, among which the three-element Windkessel model is an effective model for simulating the character of downstream vascular network.
In earlier blood flow simulations, the blood vessel walls are often treated as being rigid without deformation. 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. 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. Rational selection of the models based on the availability of clinical data can help obtain more realistic simulation results and reduce the computational load.
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). 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.,
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.,
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. The remodeling of the blood vessel together with the abnormal state of blood flow promotes the growth and rupture of the abdominal aortic aneurysms.
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.
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. 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. When WSS decreases, endothelial cells inhibit the secretion of endothelial NO synthetase and secrete endothelin-1 to reduce the vessel diameter and promote collagen synthesis by VSMCs. 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., Humphrey et al. 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.
Figueroa et al. 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. 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.,
| Growth and Rupture of Aortic Aneurysms|| |
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., 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. 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.
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. CFD researches provide theoretical support for the relationship between WSS and aneurysm progression and have application value in predicting AAA growth rate.
The undesirable consequence of the continued growth of AAA is rupture, which may lead to death. 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, 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. 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.
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., 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.
| Surgical Complications Assessment|| |
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.
The deformation of the stent and the friction between the stent graft and the vessel wall can be simulated in silico 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.
AAAs with distorted aneurysmal neck have a higher risk of proximal type I endoleak and stent displacement after operation, and this phenomenon has also been verified in the computational model. 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. 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. 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.
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. Li et al. 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. 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.
Imaging techniques including CT angiography, angiography, and contrast-enhanced ultrasound are used to detect endoleak after endovascular operations. 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. 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. 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. 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.
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., 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. 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 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., Detailed mechanical properties of artificial blood vessels, stents, and other medical devices 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.
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.
Financial support and sponsorship
Conflicts of interest
There are no conflicts of interest.
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