Computer Simulations in Stroke Prevention: Design Tools and Virtual Strategies Towards Procedure Planning
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- Iannaccone, F., De Beule, M., Verhegghe, B. et al. Cardiovasc Eng Tech (2013) 4: 291. doi:10.1007/s13239-013-0134-x
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Stroke is a heterogeneous disease caused by a sustained interruption of the blood supply to part of the brain. Prevention and treatment of this disease is of primary importance as it has been estimated to be the second leading cause of death worldwide. Due to the large number of possible origins there is no general strategy for preventive treatment and evidence based recommendations are given. However major causes of stroke can be confined to few vascular districts. More and more evidence is supporting the hypothesis that biomechanical and hemodynamic parameters can be related to catastrophic cerebrovascular events. In this context structural and fluidodynamic computer simulations offer an optimal tool to quantify these predictors. On the other hand the advances in medical imaging allow providing realistic in vivo conditions (such as reliable anatomical geometries and initial mechanical state) for patient specific analysis. This paper reviews the progress and the state of art of numerical simulation used to analyze the early stages and the progression of the disease as well as their potential as tool for risk assessment, for treatment outcome and procedure planning.
KeywordsStrokeNumerical simulationsPlaque ruptureCerebral aneurysmIntracranial atherosclerosis
Stroke is a heterogeneous disease caused by a sustained interruption of the blood supply to part of the brain due to blockage (ischemic stroke) of an artery to the brain or to hemorrhage after the rupture of a vessel mainly located in the cerebral circulation. Prevention and treatment of this disease is of primary importance as it has been estimated to be the second leading cause of death worldwide.110 Of all strokes, 85–87% are ischemic while the remaining are intra-cerebral and subarachnoid hemorrhage strokes.4,125,138 The source of the occluding embolus in ischemic stroke may be cerebrovascular atherosclerosis, lacunar (related to small penetrating brain arteries) or cardiogenic, but the definite cause cannot be identified for a large amount of ischemic strokes (cryptogenic).4,82
Due to the large number of possible embolic origins there is no general strategy for preventive treatment and evidence-based recommendations are given.57,145 Thrombolytic therapy is normally preferred for cardio embolism, anti-platelet agents for non-cardioembolic stroke.57,145 Recently the use of a new class of temporary thrombectomy devices (the so called stent retrievers, which have a similar design to stents used in stent supported coiling) showed to be effective in the treatment of acute ischemic strokes.127,149
Endovascular treatment is possible in case of cerebral aneurysm (ruptured and/or unruptured) by clipping, coiling, stent supported coiling or flow diverters. The exact treatment strategy will depend on the location, shape, and dimension of the aneurysm.
The use of an interventional approach or revascularization using endovascular devices for atherosclerotic disease is still controversial (at least in certain cases, mainly due to the lack of knowledge on the long term effects of the endovascular devices) and is normally performed for patients who have sustained symptoms despite medical therapies.57,145
For patients with hemodynamically significant intracranial stenosis, endovascular treatment (angioplasty and/or stenting) is an effective solution to improve cerebral blood flow.109,137,145 Symptomatic extracranial vertebral stenosis without ulceration can be successfully treated with stenting reducing the risk of elastic recoil and restenosis compared to balloon angioplasty alone.34 For atherosclerotic carotid diseases, while low degree of stenosis does not seem to have preferential therapy, carotid endarterectomy (CEA) is still the recommended procedure for the majority of cases, except for symptomatic severe stenosis and in patients with high risk for surgery that are suited for carotid artery stenting (CAS).16,22,62,122,139
Computer Simulations in Stroke Prevention
Many cerebrovascular diseases have been associated with the specific hemodynamic and biomechanical “milieu” in stroke related vessel diseases. Examples are the specific flow patterns in the carotid bifurcation region (characterized by low and oscillatory wall shear stress (WSS)) which have been associated with an atherosclerosis-prone environment, or mechanical stress profiles in vulnerable plaque types, or the influence of low shear stresses in the growth of cerebral aneurysms. Numerical biomechanical analysis has been introduced to analyze and quantify these biomechanical actors, and has become an extra tool to study and understand the development of some vascular diseases. More and more, the potential of this numerical analysis is recognized as possible diagnostic or risk assessment tool, and to evaluate clinical procedures.
Structural FE simulations (FEA), only based on structural mechanics to study critical stress/stretch conditions.
Computational fluidodynamics (CFD), for the study of the fluid domain in order to analyze potential hemodynamic factors.
Fluid structure interactions (FSI), a combination of both FEA and CFD that takes into account the relative effects of both the structural and fluid domain, in general leading to more realistic solution.
The organization of this paper is as follows. First, imaging techniques are reviewed, as these provide the essential information (geometrical data and boundary conditions) underlying the patient-specific models, followed by segmentation methods to extract the model geometry. Next, computer model generation strategies are reviewed, including techniques to obtain material properties. Finally, applications are addressed, with (i) initiation and progression of (carotid) atherosclerotic diseases, (ii) atherosclerotic plaque rupture, (iii) endovascular carotid treatments, (iv) initiation, progression and rupture of intracranial aneurysm, (v) aneurysm coiling, (vi) aneurysm stenting, (vii) intracranial atherosclerosis.
We would like to highlight that to our knowledge, there are no numerical studies about stent retrievers. These devices perform a mechanical recanalization: they are deployed at the occluded location, incorporate the clot material, and then are retrieved in the microcatheter used for the delivery. Numerical simulations could help to understand and improve the clot integration and optimize the device design to reduce and avoid any potential damage to the vessel during retrieval.
Imaging Techniques for Numerical Modelling
Evaluation of vascular disease and related causes of stroke is mainly performed using medical imaging techniques thanks to the improvements of high-resolution in vivo imaging. Conventional angiography and in particular digital subtraction angiography (DSA), both 2D and 3D, is the gold-standard to detect cerebral aneurysms and to evaluate the degree of stenosis of carotid arteries because of the high resolution and accuracy. It is, however, associated with high costs and high risk of morbidity and mortality due its invasive nature and is therefore performed almost exclusively in the perioperative procedure.15
On the other hand, ultrasonography (US) is the primary noninvasive test to evaluate extra-cranial cerebral vessels due to its simplicity, low cost, and ability to distinguish different structures. The presence of dense calcification of plaques, however, affects its accuracy and due to operator dependence, vascular tortuosity and the proximity of the transducer to the tissue of interest, good images are not necessarily obtained. Thus US requires to be complemented with other diagnostic techniques when suspicious conditions are detected. In most cases, a diagnostic evaluation for cerebral vascular disease can be performed by using either magnetic resonance angiography (MRA) or computer tomography angiography (CTA). Contrast-enhanced (CE) MRA or CTA offer full anatomic depiction of the cervical and cerebral portions of the common and internal carotid artery.159
The strength of current MRI techniques, however, is the ability to identify key determinants of plaques using multi-contrast imaging (typically time-of-flight angiography, T1, T2, and proton density weighted sequences).141
As the prevalence of stroke (for untreated atherosclerotic patients, after CAS or CEA) has demonstrated to be higher in patients with carotid plaques containing fragile components,18,45,61,133,179 it is important to evaluate the plaque characteristics of a carotid artery accurately before endovascular treatment. US, MRA, and multi-detector-row CTA all seem to be able to differentiate plaque composition (and thus identify vulnerable plaques) when compared with histological results and among each other.45,63,194 In particular CT and MR angiography offer high-resolution images and can demonstrate the entire circumference of the carotid arterial wall with excellent visualization of calcification (CTA) and a lipid-necrotic core intra plaque hemorrhage, ulcers, fibrous cap (MRA).63 Moreover MRA and CTA can both provide measurements of the arterial wall thickness143,144,194,198 showing good agreement with the intima-media thickness measured by US,107,142 a parameter for cardiovascular risk assessment in general and for risk of carotid stenosis progression in particular.81,96 Intracranial atherosclerosis is normally detected by CTA,15 but new high resolution MR techniques also demonstrated to be efficacious for intracranial plaque detection.96 Due to their reproducibility, three-dimensional nature and the ability to discriminate different structures, CTA and MRA are the most used techniques for image-based numerical simulations.159,178 In addition to its ability to define the vessel lumen and wall, phase contrast (PC) MRI is one of the most powerful techniques for time resolved blood flow quantification in vivo.159 Due to this feature PC-MRI is largely used in image-based CFD for providing in vivo inlet and outlet flow or velocity boundary conditions of the vessel geometries. However, the presence of complex flow patterns, such as at the carotid bifurcation, or turbulence, can introduce artifacts on the velocity measurements.160
US imaging of vascular anatomy, though widely used in the clinic, has relevance in image-based numerical analysis, mainly due to the lack of reference to a fixed coordinate system, making it difficult to reconstruct 3D geometries.159 However the advantage of US to retrieve real-time blood flow measurements make it suitable to provide realistic boundary condition for fluidodynamic simulations.64,111 On the other hand 3D US systems have served for image reconstruction and CFD simulations.10,53 Intravascular US (IVUS) has a higher potential in image-based CFD modeling studies50,140,192 due to its capability to acquire detailed images of the vessel structure. Due to the invasiveness of the procedures, IVUS has been limited to patients already referred for catheterization and is still uncommon for patient with high risk of plaque rupture even though IVUS can well evaluate the result of stenting procedures.36 In addition US and IVUS coupled with FEA can be used to derive wall elasticity by tuning the computational model with the displacements acquired by the US technique.33,188,201 Intravascular optical coherence tomography (OCT) has also been proved to be an effective tool to study stent strut apposition in carotid arteries but it is also experimental.132,151
Computational Model Generation
It is a challenging step to go from a segmented geometry to a meshed 3D geometrical model that is suitable for numerical analysis (Fig. 1c). Structured meshes (characterized by regular connectivity that can be expressed as a two or three dimensional array) can be relatively easily built for simple vessel segments. For more complex geometries with bifurcations and/or branching vessels, unstructured meshes (tetrahedral, hexahedral) are more easily generated58 using widely available mesh generators mainly intended for CFD simulations. A survey of unstructured mesh generators, though not up to date, can be found in Owen.129 Many of these software packages start from the segmented geometry to discretize the volume using 3D elements. However, the resulting meshes can be over- or under-resolved relative to the requirements of the solution178 dramatically affecting the extraction of relevant hemodynamic parameters.131 Only few tools for structured grids are described in literature due to the complexity of creating acceptable quality elements over the complete domain of complex geometrical structures.6,43,99,148 Structured grids can be built to organize the elements along the main flow direction in order to assure more accurate numerical solutions especially when solving the blood flow in large vessels where the blood motion is highly directional.6 It has been shown that a structured mesh have faster convergence compared to an unstructured mesh.148 An alternative is the use of tetrahedral quadratic elements with refined boundary layers composed of prismatic elements7 or adaptive refinement methods.20,131,147
3D mesh generation becomes more difficult when bifurcations, wall thickness and multiple structures need to be included (i.e., plaques and calcifications), which is typical for structural and FSI analysis. In-house solutions have been developed to solve these issues. Even though an unstructured (tetrahedral) mesh generator can serve, it is well known that hexahedral meshes lead to a more accurate solution.190 The basic approach to create a structured mesh of the vessel-wall is to discretize the outer and inner surface and the internal structures with an equal number of key-points and to connect these. For bifurcating vessels, additional interpolation is required at the bifurcation. This process can be done either deriving the point on the contour of the 2D segmented slices40,67,69,177) or either using 3D non-uniform rational basis spline (NURBS) surface reconstructions.79 These procedures are often complex and require different software packages for every step to achieve the final mesh. 3D numerical simulations are thus time consuming and not yet really suitable for routinely procedure planning.
In order to reduce the complexity, the problem may be simplified to bi-dimensional. Despite the computational cost advantage of 2D models (especially when using FSI simulations), these models have great limitations especially when involving fluidodynamic simulations. For example, as highlighted by Tang et al.,177 2D models ignore non-uniform pressure and the drop in pressure at the stenotic region caused by the narrowing which has been shown to collapse arterial stenotic models. Axial stretch, which leads to radial contraction, is also neglected and in very asymmetric model with complex plaque structure it will introduce big errors. In addition 2D FEA models do not account for shear stresses, torques, or time-varying forces acting on the lesion in the models.
A common approach to model stent devices is the use of CAD like programs to draw the basic pattern to be meshed using additional tools.41,52,113,117 Image-based reconstruction strategies have also been proposed for semi-automated stent mesh generation119 or coils device.29,115
CFD/FSI modeling with implanted device can be extremely challenging also with powerful softwares.116,163 An interesting approach is based on embedding methods well described in a recent review by Löhner et al.97 which seems promising for CFD simulations including stent and coils.29
Implementation of adequate constitutive laws to describe the complex material behavior with correct (subject-specific) parameter values is extremely important for a correct FEA or FSI analysis. Most of the studies use one layered vessels with isotropic, incompressible material behaviour, which does not take into account differences in radial and axial behavior of the vessel and plaque. Indeed the vessel wall and plaque constituents have a highly anisotropic behavior, thus neglecting this behavior can lead to high differences in the derived biomechanical parameters.12,69 In addition not taking into account the axial in situ prestretch can also lead to incorrect stress predictions.69 This might be less critical in comparative studies, but it is important to realize that exact stress magnitudes are not reliable without a complete and accurate description of the mechanical properties of the vascular structure or the virtually implanted device. In general there is a lack of knowledge of the real values of human vessel plaque material properties (and in particular for a given subject) and only few accurate mechanical test studies have been performed.101,155 Moreover the variability between individuals and complex characteristics of the plaque due to inhomogeneities and to the remodeling process can change their morphology in the long term, making realistic simulations very challenging.
Numerical Simulations in Atherosclerotic Diseases
Initiation and Progression of Atherosclerosis
The propensity for plaque formation at bifurcations, branching, and curvatures (conditions common to the carotid and coronary arteries, infra-renal abdominal aorta and vessels of the lower extremities) has led to hypotheses that local mechanical factors such as WSS and wall tensile stress play a role in atherogenesis.55
First, experimental studies using in vitro models83,199 identified intimal thickening at the carotid sinus and at bifurcations (all zones where WSS is lower) and related plaque formation with low and oscillatory WSS. Next, CFD has been extensively used to demonstrate the correlation between plaque formation and both low WSS and high oscillatory shear stress in vivo for carotid arteries.98,114,161 CFD simulation of 50 normal human carotid bifurcation samples found correlations between low and oscillatory shear stresses and between indicators of disturbed flow at the normal carotid bifurcation87,88 showing a significant relationship between disturbed flow and both proximal area ratio and bifurcation tortuosity, but not bifurcation angle, planarity, or distal area ratio.87
However, as plaque progression continues, the severity of the stenosis increases and lumen narrowing induces complex flow features with separation zones100 which are associated with locally elevated shear stress conditions173,174,176 while WSS oscillations are observed downstream.100,154 These results suggest seeking other mechanical factors such as plaque wall structural stresses and other hypotheses to explain the plaque progression process.193
The interaction of mechanical forces on the upstream plaque shoulder increases the pressure on the proximal plaque region and can be measured as tensile stress. Consecutive hemodynamical changes and/or modifications of the plaque configuration increase stress on the plaque and lead to rupture depending on plaque stability.25 The relative roles of WSS, tensile stress, and the metabolism of the artery wall in the progression and complication of atherosclerosis remain to be clarified.
Plaque rupture is the direct underlying cause of many acute manifestations of cardiovascular disease associated with the most adverse events.185 This is not only the case for vascular territories associated with stroke, but also for the coronary arteries where plaque rupture leads to myocardial infarction. As the underlying mechanical mechanisms are common, and given the more extensive literature in this field, we will in this section also refer to studies on coronary plaque mechanics. Currently, the decision for intervention is based on the degree of luminal stenosis and plaque severity as suggested by large clinical trials.16,122,139 Nonetheless there was group of patients in the European Carotid Surgery Trial122 that revealed higher risk of stroke in presence of ulceration.25 Criteria of plaque vulnerability parameters were redefined126 for a better risk stratification and include active inflammation, the presence of a thin cap with a large lipid core, endothelial denudation with superficial platelet aggregation, a fissured plaque (which is likely to induce thrombus48,157) or stenosis >90%. Calcification seems to be not related to stroke symptoms.48 Compensatory remodeling associated with atherosclerotic plaques as a response to the pathological environment as first described by Glagov et al.54 in coronaries may result in angiographically normal endoluminal dimensions that hide the presence of underlying large atheromas at risk of rupture.130,135
Prediction of plaque rupture is not an easy task as it depends on many interlaced factors. Rupture is not only associated with plaque morphology (thin fibrous cap, soft lipid pool, thrombotic lesions), but also with biomechanical stresses that are induced hemodynamically.135 This suggests that, provided these biomechanical stresses can be accurately determined, there is a potential usefulness of simulations for patient-specific plaque assessment. Even though the role played by hemodynamic actors in the early manifestation of atherosclerosis has been studied extensively, there are few studies describing their role on the mature plaque and the mechanisms inducing rupture.104 The evidence that plaque rupture is likely to occur at the upstream shoulder of the plaque71,104 has suggested that high WSS is involved in the rupture. CFD studies on in vivo and ex vivo image-based stenotic carotid models have confirmed this observation.60,162 CFD simulations have been used to correlate fluidodynamic descriptors such as WSS, time averaged (TA) WSS and oscillatory shear index (OSI) with the histology of vulnerable plaques. The findings generally confirmed the general trend of previous experimental studies (i.e., lipids and macrophages correlating negatively with WSS and TAWSS and positively with OSI) even though the results were not conclusive.77 Note, however, that a recent in vivo MRI-based study of 18 atherosclerotic carotids (comparing 3D FSI simulations with histological analysis) suggested that while flow shear stresses values have good correlation with the degree of stenosis, critical plaque mechanical stresses are a better predictor of plaque rupture and the sites of occurrence.180
Structural simulations combining mechanical factors and morphological information have been introduced to study rupture in coronary and carotid plaque, in order to study patterns of tensile stresses and to define critical stress levels.
FEA and FSI studies on simplified models of the lumen section have provided a better understanding of the effect of the morphology on the plaque rupture. One of the first works using FEA suggested that stress concentration on the fibrous cap is associated with high local pressure, which can be a trigger of plaque rupture.136 Lumen curvature and fibrous cap thickness showed to be major determinants of plaque stress, while the size of the lipid core does not seem to influence the stress distribution when it is covered by a thick fibrous cap.94,102,187 On the other hand thin fibrous caps in presence of moderate degree of stenosis appear to increase the risk of rupture.91 Simulations based on ex vivo specimen derived from cadavers or endarterectomy have been extensively performed. Using FEA Cheng et al.35 studied 2D histological-based patient specific models of coronary arteries establishing a relation between circumferential stresses and location of plaque rupture in 1993. This study also suggested that mismatch in the exact rupture location were imputable to local defects in plaque strength which could render less stress-solicited zones prone to rupture. Huang et al.70 investigated the influence of calcification and lipid pool on the plaque stresses comparing the real morphology with different possible scenarios of the plaque composition, suggesting that the calcification did not influence plaque stability. 2D and 3D FSI models177 indicated that large lipid pools and thin plaque caps are associated with both extreme stress/strain levels. These results were also confirmed in 2D/3D FSI models compared with silicon experimental models in different flow conditions and it has been highlighted that stenosis severity, eccentricity, lipid pool size, shape, and position axial stretch, pressure, and fluid–structure interactions are factors leading to an increase of plaque stress. Moreover tube compression and collapse, negative pressure and high shear stress at the throat of the stenosis, flow recirculation, and low shear stress upstream were observed. These critical flow and mechanical conditions may be related to platelet aggregation, thrombus formation, excessive artery fatigue and possible plaque cap rupture.173–175
With the advent of high resolution imaging techniques, detailed morphological and structural characterization of carotid plaques could be performed in vivo avoiding problems that can derive from analysis on ex vivo specimens (possible structural alterations occurring during surgery, histological preparation, morphological configuration, altered material properties of the plaque components) and, as such, may provide a more accurate quantitative assessment of plaque stress.93 A significant correlation has been found between plaque stress and lumen curvature, the lumen curvature being significantly larger for symptomatic patients92,94 and ruptured plaque exhibits higher maximal stresses than unruptured.93,172,181 These studies also showed that ulcerating region were affected by higher WSS and it was noticed that stress concentration occurred at the shoulders and the thinnest fibrous cap regions.172,180 These modeling studies thus provided the initial in vivo evidence that plaque rupture may be linked to higher plaque wall stress. Local biomechanical stresses have been found to have better correlation to plaque morphological features than global maximum stress.171 Larger relative stiffness of fibrous cap to lipid pool resulted in higher stress within the cap.93
Whether numerical analysis has an added clinical value is a topic of study. Even though stress values seem to able to differentiate different groups of patients, they failed to refine risk stratification among symptomatic patient with/without hemorrhage or thrombi instead detected using stretches as markers.181 FSI was used to identify and verify the zone of pronounced stress in a pre-rupture stenosed carotid confirming the location and extension of the plaque rupture.86 The same computational strategy applied in a study on 61 patients demonstrated that biomechanical structural stresses (with geometrical models based on MRI scans), are significantly associated with the development of subsequent ipsilateral cerebrovascular ischaemic symptoms in patients with a predominantly lesser degree of carotid stenosis at baseline suggesting a possible strategy for risk stratification and selection of candidates for appropriate non-invasive or surgical treatment.146 Anyway it must taken into account that the accuracy of the boundaries in the plaque reconstruction is crucial because it can significantly change stress values51 and the lumen boundary extraction affects the reproducibility of fluidodynamic simulations.56
Besides excessive stress, plaque rupture may also be a fatigue-related process as hypothesized by some authors.14,158 Levels of pulse pressure and mean pressure (descriptors of the fatigue process—but also of stress level as such) indeed seem to be related to stroke events.103,202 Large cyclic stress/strain variations observed in FSI plaque models under pulsating pressure may lead to material fatigue and possible plaque rupture.177 FEA fatigue studies on generalized atherosclerotic cross sections related the increment of crack propagation with blood pressure and lipid stiffness.187
Endovascular Carotid Treatment
Although CEA is still the preferred procedure to treat carotid stenosis, CAS is emerging as an alternative technique. Its benefit over CEA is, however, still controversial.22,156,197 After CAS the peri-procedural risk of stroke is high156 and the implanted device induces restenosis.39 There are indications that stent design has an influence on CAS failure19 and that changes in the biomechanical environment due to stenting/angioplasty promote restenosis.192 Anyway few numerical studies are available on CAS. Numerical simulations have been used to assess comparison between different stent designs when inserted in the same vessel model. A study on an idealized carotid model comparing the effect of two stent designs showed that strut length influences the final configuration of the vessel.195 Using patient specific stenosed carotid model Auricchio et al.11 simulated the insertion of 6 different commercially available stent designs to study the impact of the design on the stress configuration of the treated vessel. They found that the laser-cut closed-cell design provides a higher lumen gain, that oversizing affects the stress induced in the vessel wall and that configuration and size have a limited impact on the vessel straightening.
Important is also the scaffolding provided by the stent in order to confine the plaque. There is not standardized vessel scaffolding definition and the proposed parameters123 compare the stents in their free-expanded configuration not taking into account the actual configuration of a stent implanted in a tortuous carotid bifurcation. Conti et al.38 validated their numerical simulation with a stented carotid silicon model (with the geometry based on patient data) showing good agreement with the experimental results. They evaluated two different stent design and their ability to scaffold the vessel measuring the inter-strut angles of the stents. The closed-cell design provided superior vessel scaffolding compared to the open-cell but reduced the stent’s ability to accommodate to the irregular eccentric profile of the vessel cross section, leading to a gap between the stent surface and the vessel wall. Using a similar strategy and the same model they compared four designs and analyzed the deformed cell area along the stent (as a measure of the scaffolding). This study suggested that evaluation of the expanded configuration of the stent neglects the post-implant variability, which seems to be more pronounced in open-cell designs, especially at the bifurcation segment.12
Stent implantation in a simplified model associated the effect of calcification on the stenting procedure with severe residual stenosis, dogboning effect, and corresponding edge stress concentrations after stenting, which requires pre- and/or post-surgical management.200 The hemodynamic effect of incomplete stent apposition to the vessel wall was demonstrated in a CFD study. A virtual stent implantation in a realistic carotid model showed that malapposed stent struts can cause disturbing flow and potentially lead to trombo-embolic events.42 This is confirmed in a study performed in vivo on stented coronary arteries, which related neo-intimal response with WSS and other hemodynamic parameters derived from CFD.116 Remarkable in both studies is that the implanted geometry was derived from structural analysis. Incomplete stent apposition was previously assessed using FEA for coronary stents.118,121 Cebral et al.30 also performed CFD in a stented carotid geometry by use of virtual geometrical implantation describing flow patterns changes. Hayase et al.64via virtual prototyping performed CFD to recommend the best design for surgical reconstruction during a carotid treatment. In addition FEA has been used to study the behavior of an embolic protection device for carotid stenting in different configuration and computing the apposition of the device in a straight vessel.37
The effect of balloon angioplasty has been rarely analyzed for carotid arteries. Lee et al.89 using 2D FEA, could predict the location of plaque rupture after angioplasty, which was simulated by simply applying pressure on the plaque. More accurate simulations of balloon angioplasty (also combined with stenting) have been reported for other districts. The effect of balloon angioplasty in a very accurate iliac artery model (both from the anatomical and material point of view) has been studied with and without stenting.67–69 Coronary balloon-expandable stents have been also virtually implanted.113
Anyway in these studies the balloon itself was either neglected or simplified. Mortier et al.120 simulated the entire procedure for coronary balloon-expandable stents with side branch access, emulating the real mechanics of the balloon inflation. They reported that the procedure may compromise the downstream branch lumen. Similarly Gastaldi et al.52 modelled the provisional side-branch stenting technique in atherosclerotic coronary bifurcations analyzing effects of stent positioning, after in vitro model validation.
Unfortunately, in vivo validation of these numerical studies is rare and not performed on a statistically relevant number of cases.
Numerical Simulations in Intracranial Aneurysm Treatment
Formation, Development, and Rupture of the Aneurysm
The initiation, progression, and rupture of aneurysms are also related to complex interactions of flow-dependent biomechanical factors, acting with similar underlying mechanisms of the atherosclerotic disease. Hemodynamic characteristics, such as recirculation, secondary flow, and jet impingement may be relevant to assess. In particular WSS has emerged as a biomechanical flow-related parameter of interest for aneurysm assessment and CFD is a valid tool for providing this information.75 A recent review75 analyzed in detail the added value of CFD in aneurysm assessment. The most important factor for accurate calculation of intraaneurysmal flow patterns is the vessel geometry.26 The improvements in medical imaging for detailed depiction of the brain and cerebral blood vessels have produced an increase of CFD studies on patient specific aneurysms derived from angiographic information with clinical purposes. The current review complements and extends the above mentioned interesting review paper and focuses also on relevant studies including structural simulations.
As shown by fluidodynamic modeling, complex hemodynamic forces, alteration of the WSS,5,170 may induce pathologic remodeling of the vascular structure, transmitted by the endothelial cells.134,150 An in vivo animal model, complemented with CFD showed that localization of destructive wall remodeling, is correlated with high WSS and high WSS gradients.112 Similar results have been found in a recent study that suggested patients with zones of localized high WSS (>5 times the parental vessel) to be prone to aneurysm formation.84 On the other hand low WSS has been observed in many aneurysm studies and could potentially be involved in the growth of the aneurysm.152,183 Comparing in vivo aneurysm with virtually reconstructed parental vessels prior aneurysm formation, numerical simulations revealed an area of relatively low WSS at the location at which each aneurysm had developed.108 Similarly another study with in vivo intracranial aneurysm at two time points of seven patients,21 found that aneurysm growth is likely to occur in regions where the endothelial layer lining the vessel wall is exposed to abnormally low WSS which might lead to rupture.76,84,196 Omodaka et al.128 found that the rupture point is located in a low WSS region of the aneurysm wall in six patients with ruptured aneurysm. In a study on 20 cerebral aneurysm it has been found that ruptured aneurysms had higher averaged WSS of aneurysm region than unruptured aneurysms, markedly low WSS in their tip and high WSS in the body of the aneurysm. In this work the authors speculated that the proximity of high and low WSS in a small aneurysm region promotes degeneration of the aneurysm wall.152 A study on 62 patients (classified into different categories, depending on the complexity and stability of the flow pattern, the location and size of the flow impingement region, and the size of the inflow jet) demonstrated an association between the size and stability of the inflow to the aneurysm and its propensity of rupture.27 On a larger number of patients, they also found that concentrated inflow jets, small impingement regions, complex, and unstable flow patterns are correlated with a clinical history of prior aneurysm rupture.32 A recent CFD study on 100 patients suggested pressure loss coefficient, a parameter characterizing energy expenditure and the geometric shape of vessels, as a better discriminant of aneurysm rupture than WSS.169
The geometrical characteristic also seems to play a role in the rupture. As the arterial curvature increased, flow impingement on the distal side of the neck intensified, leading to elevations in the WSS and enlargement of the impact zone at the distal side of the aneurysm neck.66 The morphological parameters of the aneurysm sac (discriminants of rupture such as size ratio, undulation index, ellipticity index, and nonsphericity index) have shown on a large population study high correlation with computationally derived hemodynamic descriptors (low WSS, high OSI which have been linked to rupture105) suggesting a possible role as clinical predictors.196
As cerebral artery aneurysms rupture occurs when wall tension exceeds the strength of the wall tissue, FSI simulations seem more appropriate for predicting rupture.73 Using FSI the effect of hypertension was studied, suggesting that blood pressure and deformation of the aneurysm wall can influence aneurysm rupture3 and they are closely related to the aneurysm shape.182 Similarly a study on seven patient-specific aneurysm found that flow patterns, pressure, WSS, and displacement of the aneurysm wall showed large variations, depending on the morphology of the artery.184
These results seem to suggest that WSS is not directly responsible for the aneurysm rupture but rather for a vascular remodeling process leading to rupture that is often related to low values of WSS, while other hemodynamic factors (such as pressure or flow impingement) can lead to rupture.
A further challenge for the simulations is to account for the presence of endovascular devices to treat cerebral aneurysms such as coils and/or stents/flow diverters that promotes clot formation and thrombosis to prevent rupture. For clinical purpose, a prior knowledge of the mechanical and hemodynamic effects of the implantation is useful to evaluate and optimize treatment options for example to compute the amounts of coils and their optimal placement for flow occlusion.28,29 A CFD study of 17 patients demonstrated that after occlusion induced by coil embolization the increase of maximum WSS and partially averaged WSS can discriminate recanalized (a typical adverse event deriving from coils compaction) and stable aneurysm.95 Numerical simulation including coils have been developed using different strategies. The simplest approach is to model the coils as blocked cells in the aneurysm lumen mesh.59 The relative pressure amplitudes did not change under different simulated aneurysm filling conditions. They reported that coils can relieve the influx of pulsating blood and allow for initial clotting provided that at least 20% of the volume is filled. Byun and Rhee24 analyzed the blood flow fields of lateral aneurysm models for different coil locations (modeled as a sphere) and parent vessel geometries suggesting that distal neck coiling better promotes embolization. Ahmed et al.2 with a similar modelling strategy used FSI to study inflow rate, WSS, apparent viscosity, and effective stress of coiled aneurysm models as a possible tool to address additional treatment. An interesting approach was developed by Kakalis et al.78 modeling the coiled part of the aneurysm as a porous media which characteristics dimensions determined by the coil sizes. CFD results showed that insertion of coils rapidly changes intra-aneurysmal blood flow and causes reduction in mural pressure and blood velocity up to stagnation, providing favorable conditions for thrombus formation. Cebral et al.29 showed more realistic technique for coil implantation based on in vivo data and embedding grid technique. Morales et al.115 used a virtual coiling technique based on dynamic path planning approach to insert one-by-one the coils inside a closed geometry consecutively selecting the next position of the coil tip. They found that coils configuration reduce its influence on the hemodynamics as the packing density increases. Due to the complexity of the procedure, real-time simulation of coils insertion as a possible training tool have been proposed based on FEA44 and a combination of a novel method to solve fluidodynamic problems and FEA that takes into account the relative interaction between flow and coils.191
Stent supported coiling is used as a treatment option for fusiform and wide-neck aneurysms to avoid coil protrusion in the parent vessel or, in case of flow diverters (stents with low porosity), the stent is used alone to reduce the flow in the aneurysm. Stent placement induces hemodynamic changes in the aneurysm dome which effects are not known prior thrombus formation. CFD simulation used to analyze the effect of flow diverters in actual cases showed that rupture of giant aneurysm is influenced by an increase of pressure in the aneurysm.31 This effect has been also described in a CFD study comparing different idealized stent designs (both braided and laser cut) in an internal carotid aneurysm model.49 Two commercial stents were deployed at various locations and the computed residence times were evaluated and compared, demonstrating the advantage associated with a lower stent porosity with respect to the maximum WSS in the aneurysm sac.74 A different approach used by Augsburger et al.9 is to model the stent as a porous medium, which seems to give results comparable with real stent geometries. Even though these CFD studies are appealing from a clinical point of view they suffer of a major limitation in the stent placement technique. The stent in fact is often deployed using geometrical projection methods to the vessel wall8,74,85 that neglect the stent mechanics and do not reckon with the actual behavior of the stent and its effects on the vessel wall. It has been shown in vitro that the deployment method used to deliver the vascular reconstruction device plays a critical role in stent apposition to the vessel wall65 which has already been associated with adverse effects such as late stent thrombosis in the coronary circulation.153 Moreover stent placement induces changes in the vessel geometry72 that are not reflected using geometrical fitting of the stent for the numerical simulations. FEA can reproduce the real mechanics of stent deployment. Bernardini et al.17 compared different stenting techniques (FEA vs. geometrical) showing that the final configuration of the stent is affected by neglecting mechanical properties of materials. Results showed how open stent designs—while inducing negligible geometrical changes of the vascular geometry—suffers from incomplete stent apposition and show effects of “fish-scaling.” A FEA simulating the insertion of pipeline-like flow diverter mimicking a complete endovascular procedure highlighted the importance of retraction and pushing steps of the device to obtain maximal flow diversion and best apposition.106 A CFD study validated in vitro showed that stent configuration has a strong impact on the flow in the aneurysm dome, primarily due to strut protrusion,13 confirming the importance of a realistic virtual stent insertion. An interesting FEA study on vessel ring geometry studied the effect of the arterial clamping and validated it with in vivo animal experiment.46
There are only few studies investigating cerebral stenosis. The reason is partially due to the limited resolution of stenotic lumen imaged by current imaging techniques which precludes the development of a realistic geometry for use in finite element modeling and CFD analysis.165 CEMRI-based CFD modelling was used to determine WSS in one patient.165 They reported an increase of WSS at the stenotic region and they suggested that the borderzone infarct in the patient may have corresponded to thromboembolism that developed at the plaque surface under the influence of hypo-perfusion. This shows the main difference with larger arteries where the plaque vulnerability is more likely leading to stroke. Using pre and post stenting vessel geometries in one patient164 a decrease in WSS has been shown after stenting which could predict minimal chance of restenosis and intimal hyperplasia.124 Main limitation of the study was the lack of stent in the model.
Numerical analysis is gaining importance as a tool for clinical purposes. CFD, FEA, and FSI allow studying different facets of and the interactions between the pathophysiological biomechanical environment and the risk of stroke. With the advancement in imaging techniques it is possible to acquire non-invasively the complex structure of pathological vessels and this under in vivo conditions. Numerical simulations are able to study the relationship of biomechanical factors with initiation and development of the disease leading to major catastrophic cerebrovascular events. WSS has an assumed important role in the first stages of atherosclerotic disease and possibly in the aneurysm formation while structural analysis has the potential to be a predictor of plaque rupture and could be involved in the risk stratification in the clinical arena. Also for patient treatment using endovascular devices, there is a possible role for numerical simulations in the choice of the treatment or the selection of the best device design according to the patient specific conditions. Nevertheless, the numbers of studies supporting the inclusion of numerical simulations in the clinical decision making process is still scarce and further in vivo validation is absolutely required. In addition, for efficient inclusion in clinical practice there some still some issues to be solved. Computational cost of the 3D simulation, especially involving fluid–structure interactions are a big limitation for diagnostic and procedure planning routine. Regarding assessment of plaque rupture there are missing tools for automated segmentation of the plaque components, which is still highly time consuming and operator dependent. Moreover realistic material properties and boundary conditions, ideally specific for the individual patient, are needed for a correct evaluation. Mesh generation is still highly challenging for complex in vivo structures and in the presence of endovascular devices. Image resolution is still suboptimal to retrieve correct geometrical information or information on the vessel wall structure in the cerebral circulation. An additional major issue is the lack of a reliable, well established strategy to include mechanobiology which can take into account the remodeling response of the vessel and could predict the long term effect of the mechanical changes in pathological conditions and in presence of devices.
The authors acknowledge the Research Foundation of Flanders (FWO) for the financial support of this research activity.
Conflict of interest
Matthieu De Beule and Benedict Verhegghe are shareholders of FEops, an engineering consultancy spin-off from Ghent University, and have served as consultants for several medical device companies. The other authors have no conflict of interest to declare.