Flow in simplified and real models of intracranial aneurysms

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Abstract

Numerical flow simulations have been performed on simplified artificial intracranial aneurysm models, as well as on real models obtained from rotational digital subtraction angiography images. The simplified geometries provide a basic understanding of the flow and allow the study of the influence of certain geometrical parameters with high accuracy and controllability. The real aneurysm models demonstrate that there is an infinite variety of shapes and very complex flow patterns. Nevertheless, it is proposed in this paper that the aneurysms can be divided into four basic classes corresponding to typical flow patterns. Some features of these have been identified and associated with possible causes of growth and rupture.

Introduction

Intracranial aneurysms are defined as thin-walled bulges of the arterial walls located on the basal surface of the brain. These lesions are found in approximately 5% of the population (The International Study of Unruptured Intracranial Aneurysm Investigators, 1999). Rupture of such aneurysms is the most frequent reason of subarachnoid hemorrhage, a special type of stroke that affects 0.1–0.15% of the population each year and results in death or permanent disability in 35–40% of its victims (Longstreth et al., 1985). The ethiology of intracranial aneurysms is not fully understood. Most aneurysms are thought to develop due to a combination of structural, physiological and hemodynamic factors. Similarly, little is known about the reasons of aneurysm rupture. Comparing the frequency of aneurysms (5%) with the yearly rate of subarachnoid hemorrhage (0.1–0.15%/year) it becomes evident that less than 1/3 of all aneurysms will ever rupture. Prevention of rupture can be achieved by either open skull surgery or by an intra-arterial approach. Surgical treatment requires isolation of the aneurysm and (in particular) its entry point, the “neck”. The aneurysm is then excluded from the circulation by placing a metallic clip on the aneurysm neck (Mayberg et al., 1994). Alternatively, the arterial (endovascular) technique utilizes fine platinum coils to tightly pack the aneurysm’s cavity and achieve blood stasis and subsequent aneurysm thrombosis (Guglielmi et al., 1991). Newly emerging methods aim to achieve this goal by modifying the blood flow within the parent artery and the aneurysm itself by placing a metallic endoprosthesis (stent) within the parent vessel across the entrance of the aneurysm (Szikora et al., 2006). Considering that all preventive techniques carry relatively high risk, it would be mandatory that only those lesions are treated that have a high likelihood of rupture and bleeding. Fig. 1 shows the typical locations of intracranial aneurysms. They often develop at branching points, or on the side wall of arteries, usually at the inward or outward curve of arterial bends.

Hemodynamic stress at certain points of the arterial tree might be an important factor in both triggering aneurysm growth and leading to rupture of an existing aneurysm. Medical imaging techniques, such as digital subtraction angiography (DSA), computer tomographic angiography (CTA), or magnetic resonance angiography (MRA) are now capable of providing accurate three-dimensional information on intracranial vessel geometry. Current knowledge on the risk of bleeding from a known aneurysm (and subsequent decision on invasive treatment) is derived exclusively from such morphological information. As these techniques are not yet capable of delineating flow conditions within the visualized vascular segments, hemodynamic factors are not considered in the therapeutic decision-making process.

The purpose of this study is to develop a technique that is able to simulate arterial flow in and around intracranial aneurysms in order to study the effect of local hemodynamics on aneurysm growth and risk of aneurysm rupture. This information may lead to better indication of high risk surgical procedures.

There have been several research efforts to investigate the problem using numerical simulations. There are basically two approaches: using artificial models which are supposed to reflect the important geometrical and flow characteristics of the aneurysm and working on real models derived from medical imaging techniques. In the case of artificial models the researcher has complete freedom in preparing the geometry and the numerical mesh. Because of the relative simplicity, regularity and controllability of the geometry the mesh has usually a good quality. Examples for such artificial geometries are Egelhoff et al. (1999) (abdominal aneurysms), Shipkowitz et al. (2000) (abdominal aortic branches), Paál et al. (2004) (intracranial aneurysms). In the second approach the arterial geometry is obtained in a digital format consisting of voxels. It is possible to perform simulations on this mesh consisting of small cubes but these have a rough appearance since the surfaces of all cubes are in one of the three coordinate directions. In this case, especially near the wall, the results would be unrealistic. Various strategies have been applied to obtain a smoother mesh. One possibility is to deform and smooth the original hexagonal mesh (e.g. Shojima et al., 2004). It is also possible to redefine the surfaces in a smoother form using the original point set (Di Martino et al., 2001, Oshima, 2004, Hassan et al., 2004, Steinman et al., 2003). In this paper flow simulations in both artificial and real aneurysm geometries will be presented.

As mentioned above the factors leading to aneurysm growth and rupture are not clear. Many authors emphasize the potentially key role of the wall shear stress. However, there is considerable disagreement among researchers whether the high or the low values, or the oscillation of shear (especially if associated with directional changes) are to blame. To the best knowledge of the authors, there is no convincing evidence supporting any of these hypotheses. Shojima et al. (2004) reported about 20 processed cases which all have more or less similar geometries. Out of these cases three have ruptured. They identified three groups of aneurysms, according to the locations of maximum shear stress. They tried to relate the aspect ratio of the sac with the wall shear stress but found only a very weak correlation. No significant correlation has been found between the magnitude of shear stress and the probability of rupture. Gonzalez et al. (1992) performed simulations on a sidewall aneurysm with curved parent vessel. They found that the flow pattern varies during the cycle with reverse flow in diastole near the aneurysm. Based on this they hypothesised a mechanism of aneurysm growth – namely that at the locations of largest shear stress oscillation the vessel wall is weakened and the aneurysm is prone to grow. Another idea is that the locally increased pressure due to a jet impinging on the aneurysm wall could be responsible for the growth. Hassan et al. (2004) simulated the flow in a giant vertebrobasilar aneurysm before and after therapeutic occlusion of one of the vertebral arteries. They detected an increased local pressure at the point of impingement of the jet on the aneurysm wall from the other vertebral artery. In the clinical follow-up it turned out that the aneurysm grew further exactly on this spot. This result looks encouraging; the question is what the relationship is between growth and rupture.

Another interesting question is to what extent the elasticity of the vessel walls plays a role in the flow in and around the aneurysms. Very few coupled (fluid–structure interaction = FSI) simulations have been performed. Di Martino et al. (2001) performed coupled fluid–structure interaction simulations for aortic aneurysms but conclude that their linearly elastic mechanical model contains too many uncertainties to make clinical decisions. Our research group performed some coupled simulations on simplified geometries which will not be shown here. Preliminary results indicate that the flow field is influenced only a very little by the elasticity of the wall so that the rigid wall approximation might be justified. However, further research is needed in this direction.

Similarly to the computational studies, there are two approaches to building flow models of aneurysms: simplified models and scaled-up real models extracted from angiography data. The models are usually made of transparent acrylic or Perspex blocks. Laser-based optical methods are almost exclusively used since the flow field is very complicated and the usage of intrusive probes would not only be cumbersome but would also disturb the flow while providing much less information. To avoid unwanted refractions at curved surfaces refractive index matching techniques are used. One of the central questions of these experiments is to determine to what extent the qualitative flow pattern changes during the cardiac cycle. The results are controversial and it is very likely that the answer is largely influenced by the exact shape of the unsteady input flow function. Liou and Liao (1997) investigated the flow field with particle tracking velocimetry (PTV) and by means of flow visualisation for varying curvature of the parent vessel and concluded that the intra-aneurysm velocities increase with increasing curvature. They also found that the qualitative appearance of the flow field is affected. Liou et al. (1997) measured velocity fields inside a model sidewall aneurysm using laser-Doppler velocimetry (LDV). They found slight variations in the inflow angle during the cycle but otherwise the flow field was similar. The peak shear stress was at the distal lip (as found in this paper) and the magnitude of the shear stress increased with decreasing sac size. Liou et al. (2004) used PTV and flow visualisation to study the unsteady flow pattern in an (artificial) model aneurysm with and without stents. It could be expected that the average flow velocity and the shear stresses are significantly reduced with the insertion of stents. However, they obtained a surprising result. In the unstented case the flow pattern remained unchanged throughout the cycle except for the velocity magnitude. Stent deployment across the neck of the aneurysm, however, produced qualitative changes of the flow pattern during the cycle. These changes were characteristic for the particular stent design. Tateshima et al. (2003) reported on LDV and particle image velocimetry (PIV) measurements in a real aneurysm model. Detailed time-resolved flow velocities were obtained and the variation of in- and outflow zones during the cycle identified. Benard et al. (2003) determined possible zones of very low shear stress caused by the insertion of a stent.

Healthy arteries are highly deformable complex structures, characterised by a nonlinear strain–stress curve with exponential rigidity in the higher strain ranges. This rigidity effect, characteristic for all biological tissues, is the result of rough collagen fibres which show typical anisotropic behaviour. Under normal circumstances the artery wall shows cylindrical orthotropy, generally accepted in the scientific literature. The material characteristics are either derived from in vivo experiments or from in vitro tests reflecting real conditions. Researchers would naturally prefer in vivo experiments; however, the data originating from physical reactions of the artery wall can only be measured by in vitro experiments at present. Under ex vivo conditions mechanical properties are subject to change due to biological degeneration, therefore arteries should be tested in a physiological saline solution properly oxygenated and at controlled temperature.

Mechanical properties of the aneurysm sac were analysed by Scott et al., 1972, Steiger et al., 1989, Tóth et al., 1998. Tóth et al. (1998) measured the elasticity of cerebral saccular aneurysms assuming spherical symmetry and homogenous elastic properties within the wall. They also considered the viscoelastic behaviour in the wall. Tóth et al. (2005) performed laboratory experiments, measuring the stress–strain functions of the arterial wall material using uniaxial and biaxial stretching tests. Human arterial strips were cut from both surgery and cadavers, from aneurysms and from normal arteries as control samples. The original location of the wall sample within the aneurysm was also taken into consideration in evaluating the measured results, to achieve precise description of the inhomogeneous and anisotropic nature of the material response. Longitudinal and circumferential, as well as thick (near to neck) and thin (near to the top – this is where rupture usually takes place) strips of human cerebral aneurysms were investigated.

The results show that the values of elastic modulus are higher for women in each case. The tensile strength of thin strips is higher in both circumferential and longitudinal direction than that of the thick ones but the difference between them is much larger in the circumferential than in the longitudinal direction.

In comparison with control human arteries the aneurysm samples experienced reduced elasticity in stretching at the beginning and the difference increased by further stretching. The aneurysm tissue reaches maximum extension relative to the control specimen at considerably smaller tensile strength.

We follow here a double research strategy. First, well-controlled, simple, artificial aneurysm models are investigated. This allows the generation of high-quality numerical meshes and carrying out highly accurate flow simulations. Then, further flow simulations are performed using real geometries obtained from DSA and an in-house mesh generation code. For both cases rigid wall geometry has been assumed. It turns out that the flow is significantly more complex in the real geometries than in the simplified ones. Also, because of the infinite variability of the shapes there are a number of different flow patterns even in similar geometries. Therefore, after examining a number of geometries, certain morphological classes are set up leading to flow pattern classes. The objective is to establish a correlation between flow pattern and aneurysm rupture risk. Another approach is to perform fully coupled flow–vessel wall deformation simulations (we shall present this work in a later publication). This way we can obtain additional information about wall stresses which might also be related to aneurysm growth and rupture.

Section snippets

The software

The ANSYS ICEM CFD commercial software was applied to generate the geometries of the artificial models and their computational meshes. The setup of the physical problem, the solution and the presentation and post-processing of the results was performed by various modules of ANSYS CFX. The tetrahedral meshes of the real artery geometries were created with an in-house code on the basis of the DSA data.

Geometries and meshes

Initially several simplified two-dimensional (2D) and three-dimensional (3D) geometries were

Parametric studies in 2D

The purpose of the parametric studies in 2D was to quantify the effect of the neck width. First the velocity distribution is shown for a medium neck width (d = 4 mm) in Fig. 6. It is clear that the dominant motion is rotation with the highest velocity at the downstream (distal) end of the cavity. The inflow into the cavity takes place mainly also at the distal end whereas the outflow at the proximal end. Generally, however, there is little exchange of fluid between the main flow and the cavity

Results for real geometries

Having inspected and simulated a large number of real aneurysms we found that they have an infinite variety of morphologies. Yet, it was possible to establish typical groups among them. These are

  • (a)

    Aneurysm on the outer side of a bend;

  • (b)

    Aneurysm on the inner side of a bend;

  • (c)

    Bifurcating aneurysm;

  • (d)

    Atypical aneurysm.

One example of each case is presented in the form of the geometry, the wall shear stress distribution the pressure distribution and a picture demonstrating the flow. This latter picture is

Discussion

As mentioned in Section 1, there is no conclusive evidence concerning what physical processes contribute most to the growth and rupture of aneurysms. The four proposals put forward in the literature are (i) increased wall shear stress; (ii) reduced wall shear stress; (iii) high amplitude oscillation (possibly reversal of direction) of wall shear stress; and (iv) locally high pressure on the aneurysm wall. In this paper a crude classification of aneurysms was proposed and in a tentative way we

Conclusions

Numerical simulations have been performed for simplified and real models of intracranial aneurysms. The simulations on simplified models are more accurate because of the better quality mesh and they provide a basic understanding of the underlining flow pattern in typical aneurysm geometries. It has been found that decreasing neck width reduces the amount of rotation in the aneurysm sac and increasing neck length has the same effect but in addition the structure of the flow changes. The flow in

Acknowledgement

This work was partially supported by the GE Hungary Rt. – Healthcare Division within the framework of the project “Development of medical imaging solutions”. We sincerely appreciate the help of András Lassó. Partial support was provided by the Hungarian National Fund for Science and Research under grant Nr. OTKA T047150 OPR. Ádám Ugron wishes to thank for the support of his participation at the CMFF’06 by the SZEFH Foundation.

References (23)

  • W.T. Longstreth et al.

    Risk factors for subarachnoid hemorrhage

    Stroke

    (1985)
  • Cited by (0)

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