ABSTRACT: Objectives: Previous works have shown that maximum diameter is not a reliable determinant of abdominal aortic aneurysm (AAA) rupture; however, it is currently the most widely accepted indicator. Wall stress may be a better indicator, and promising patient-specific results from structural models using static pressure have been published. The purpose of this study is to investigate changes in internal static pressure, blood flow, and wall shear stress (WSS) when the AAA increases in diameter from 10 mm to 50 mm. Understanding how this stress is distributed and which factors influence their distribution is critical in evaluating the potential for rupture. Methods: Three male patients, diagnosed with AAA at different stages, were selected to reproduce the growing process of an aneurysm. Diagnostic information obtained included the geometry of the AAA lumen, material property of the wall, and flow conditions at the model boundaries. All patients were scanned with a spiral computed tomography scanner, and the obtained data were imported in a finite element code software. A linear law was speculated to predict the growth of the aneurysm from 10 mm to 50 mm diameter. Five representative finite element models were created and imported in a computational fluid dynamics code to perform fluid dynamics analyses. Patient informed consent and IRB approval were obtained. Results: The results of fluid dynamics analyses evidenced peaks of pressure ranging from about 17 MPa for a diameter of 10 mm, to 19 MPa for a diameter of 50 mm. Depression zones can be identified under the neck of the aneurysms. Pressure distribution decreases from the borders to the center. Vectors of fluid velocity localized on the whole artery evidence peaks from 3.08 m/s for a diameter of 10 mm to 2.66 m/s for a diameter of 50 mm. Analyses show flow separation streamline regions on the neck of the aneurysm, in which recirculation eddies are formed, while separation domains of velocity vectors can be easily individuated between center and periphery of the aneurysm, in which pressure radially increases while velocity decreases. Wall shear stress registered on the top of the caps of the 5 AAAs show values ranging from 0.15 Pa to 0.50 Pa. Conclusions: Knowledge of the regional distribution of wall thickness and failure properties in an AAA can help in understanding its natural history, developing methods to predict rupture risk, and designing vascular prostheses. The relationship between thickness and local pressure allows identification of areas at risk of rupture and can inform design of vascular prosthesis.

VASCULAR DISEASE MANAGEMENT 2015;12(5):E84-E95
Key words: abdominal aortic aneurysm, computer-aided design, computational fluid dynamics code 

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An aneurysm is the focal dilation of the wall of a blood vessel, typically an artery. The typical progression of an aneurysm in the aorta begins with high blood pressure, which increases the pressure waves of blood against the walls of the aorta. Smoking causes damage to the aortic wall, weakening it.¹ The presence of atherosclerotic disease also causes the wall of the aorta to lose its elasticity so that its ability to dilate and recoil with each pressure wave of blood created by the heartbeat is decreased.² Eventually, the elastic membranes and smooth muscle within the aortic wall deteriorate and the vessel diameter increases.  

There are two types of aneurysm: fusiform, which is a diffuse dilation of the vessel wall, and saccular, which is a focal, large dilation of the vessel wall that is attached to a stalk that communicates with the vessel lumen. Saccular aneurysms are generally larger than fusiform aneurysms. The shape of an aneurysm is not specific to a particular disease.^3,4 Saccular aneurysms are spherical in shape and involve only a portion of the vessel wall; they vary in size from 5 cm to 20 cm (8 in) in diameter, and are often filled, either partially or fully, by thrombus. 

Abdominal aortic aneurysm (AAA), is an abnormal dilation of the aorta, and is related to weakening of vessel wall usually as a consequence of atherosclerotic disease.⁵ Current repair techniques are risky, so surgeons adopt a conservative method to operate when the risk of rupture is higher than the risk of surgery.⁶ The main clinical indicators used to assess the risk for rupture are the maximum diameter and expansion rate of the AAA, obtained from ultrasound or CT scans. Surgery is recommended when the maximum diameter of the AAA measures 55 mm and greater or when the maximum diameter increases more than 10 mm a year for smaller AAAs.^7,8 The decision regarding the time to intervene for an AAA is related to risk of rupture vs. risk of surgery. Surgical intervention is appropriate when the cumulative risk of rupture exceeds the risk of repair, within the context of overall life expectancy. The rupture risk for an AAA is clearly related to its maximal diameter,^9,10 but small AAAs are known to rupture.^11,12 In some series, 10% to 24% of the ruptured aneurysms were 5 cm or less in maximal diameter.^12,13 The decision regarding the appropriate diameter for intervention has not been made easier with the advent of the less invasive endovascular repair because older and sicker patients may have an option other than observation.¹⁴

More than 50% of aneurysms greater than 5.5 cm will rupture when surgery is deferred because of high operative risk.⁸ In this high-risk group, the median time to rupture was only 19 months for patients with 5.5 cm to 5.9 cm AAAs, and only 9 months for patients with AAAs of more than 7 cm. Recently, large studies have been conducted to determine whether observation of AAAs with a maximal diameter less than 5.5 cm is safe.^8,15,16 Morphologic analysis of AAAs with indices of body habitus have been proposed to better characterize rupture risk but have not gained wide acceptance.¹⁷ More recently, a mathematic analysis of AAA geometry has been suggested to be a theoretically better way to estimate wall stress and the risk of rupture. Other factors, such as hypertension and smoking, may increase sick but are not a justification for surgery.¹⁸ Maximum diameter does have a relationship with the probability of rupture;¹⁰ however, the lack of randomized data makes this association unclear.¹⁹ A screening trial showed that about 5% of the patients in the watchful surveillance group died from aneurysm-related causes, some after emergency surgery.¹⁹ Clearly, a more accurate indicator is needed to reduce the incidence of rupture. Rupture is a mechanical failure that occurs when the stress experienced by the vessel wall exceeds wall strength.

A patient-specific study has demonstrated that maximum wall stress was 12% more accurate and 13% more sensitive in predicting AAA rupture than maximum diameter.²⁰ Studies using idealized fusiform and saccular models have shown that wall stress increases with aneurysmal bulge diameter and asymmetry.²¹ From a purely mechanical point of view, rupture of AAA occurs when the mechanical stresses (internal forces per unit area) acting on the aneurysm exceeds the ability of the wall tissue to withstand these stresses (i.e., the wall’s failure strength). 

Materials and Methods

Three male patients, aged 65, 66, and 70, affected by AAA (diameters of 35 mm, 58 mm, and 51 mm), were selected for this study. Patient informed consent and IRB approval were obtained. Data obtained included the geometry of the AAA lumen, material property of the wall, and flow conditions at the model boundaries. All patients were given contrast agent and scanned with a spiral computed tomography (CT) scanner (Mx 8000 IDT; Philips), for their routine AAA examinations. AAA geometries were reconstructed, by the distinguishable lumen, from the entire set of 2D CT slices. The lumen boundaries were segmented automatically by the region growing method (RGM).²² Before applying RGM, noise in the image was reduced using a Gaussian filter, with a 3 × 3 kernel, to clarify the lumen boundaries.²³

Because the lumen borders were obtained automatically, the geometric models reconstructed were reproducible and convertible as IGES files, a computer-aided design (CAD) format usable to create finite element (FE) models. Median thicknesses calculated were 1.81 mm, 0.55 mm, and 0.6 mm for diameters of 35 mm, 58 mm, and 51 mm respectively. Wall stress plays a pivotal role in aneurysm failure. Understanding how these stresses are distributed and which factors influence stress distribution is critical in evaluating the potential for rupture. 

Five representative FE models were created with Hypermesh, an FE code by Altair (Figure 1), in order to simulate the growth of the AAA from 10 mm to 50 mm in diameter, using information previously described. The FE method involves dividing the domain of the problem into a collection of subdomains, with each subdomain represented by a set of element equations to the original problem, followed by systematically recombining all sets of element equations into a global system of equations for the final calculation. The global system of equations has known solution techniques and can be calculated from the initial values of the original problem to obtain a numerical answer. 

The obtained FE models were used as input to perform computational fluid dynamics (CFD) analyses. An alternative means for invasive flow measurements is presented by the calculation of models in which blood flow can be virtually simulated. Computational fluid dynamics is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows and the interaction of liquids and gases with surfaces defined by boundary conditions. The unsteady 3-dimensional incompressible Navier-Stokes equations were used for blood-flow simulations with the CFD software Fluent (v. 6.1.22; Fluent Inc.). Blood was considered a Newtonian fluid. For simplicity, the vessel walls were assumed to be rigid and no slip boundary condition was imposed. Pressure and velocity inlets were defined at 16 Pa and 2.5 m/s, while the outlets were defined as outflow conditions. The simulations were performed with the following material constants: blood density 1,041 kg/m3, blood dynamic viscosity .004 Pa. Turbulence intensity at the inlet boundary was set to .05 kg/ms, simulating a disturbance-free inlet, and grid independence was established for all cases. The convective terms in the momentum and turbulence equations were discretized using second-order upwinding and pressure-velocity coupling was achieved using the SIMPLEC solver. All computations were converged to residuals less than 10E-05. 

Results

The results of the examinations are shown in Tables 1 to 3. Table 1 reports maximum and minimum values of static pressure on the whole artery at the different aneurysmal growth stages, at the peak systole along the axial direction. Peaks of maximum static pressure increase, relative to the aneurysm’s growth, from about 16.8 MPa for 10 mm of diameter to 19 MPa for 50 mm of diameter, while peaks of minimum static pressure range from 14.6 MPa to 16.5 MPa. 

Figure 2 shows contours of static pressure on the whole artery at different stages of aneurysm growth. Depression zones can be identified under the neck of the aneurysm. As the fluid lines are addressed inside the aneurysm, depressurized areas are induced under the inlet point of aneurysm. Figure 3 shows maximum and minimum static pressure values localized on the whole artery at different diameters of the aneurysm and the correspondent linear trend curves. A more detailed analysis of the effects localized on the aneurysm’s cap can be seen in Table 2,which reports the same results of Table 1 with a focus on the single aneurysms. Data exhibit linear increases of pressure that increase the aneurysm’s diameter. Table 2 shows, for each aneurysm’s volume, the corresponding value extrapolated by the obtained linear trend curves, as shown also by Figure 4. Also in this case, data exhibit increases in linear pressure that increase the aneurysm’s diameter and consequently its volume. The corresponding maximum percentage error, around 5%, is also reported in Table 2. 

The figures and tables show that pressure increases with dimensions and concentrates on the spherical borders, discharging the central area of the aneurysm. Figure 5 and Table 3 show, respectively, vectors of fluid velocity localized on the whole artery and on the single aneurysms for each increasing diameter. Values range from 3.08 m/s for 10 mm of diameter to 2.66 m/s for 50 mm of diameter, on the whole artery. For the single aneurysms, values range from 0.63 m/s for 10 mm of diameter to 1.59 m/s for 50 mm of diameter. Flow separation streamline regions are shown in the figures, on the inlet neck of the aneurysms, where recirculation eddies are formed. Separation domains can be easily individuated between the center and periphery of the aneurysms, in which pressure radially increases while velocity decreases. Table 3 shows, for each aneurysm’s diameter, the corresponding value extrapolated by the obtained linear trend curves, as shown also in Figure 6. Also in this case the data exhibit linear growth of the maximum velocity aging on the aneurysms and a linear decrease for maximum velocity aging on the whole artery. The corresponding maximum percentage error, around 4%, is also reported in Table 3. Moreover, Table 3 reports WSS values registered on the top of the caps of the 5 AAAs analyzed. Stress increases as thickness of the cap decreases, from 0.25 Pa for the diameter of 10 mm to 0.50 Pa in the case of 50 mm (Figure 7). 

Discrepancies in the obtained results may be due to numerous variables present. No information has been evaluated regarding modifications concerning the inlet channel of the aneurysm, and moreover, the way that every stage of the growing aneurysm modifies the geometry of the whole artery. 

Discussion

Many investigators have used CFD to study blood flow in AAAs.^24,25 In many cases, regions of high pressure or high WSS have been singled out as potentially important to pathogenesis, though with little direct reference to the underlying mechanobiology. Like their intracranial counterparts, the natural history of AAAs includes pathogenesis, enlargement, and rupture. Again, there is considerable debate over pathogenesis. Some suggest that AAAs initiate due to inflammation and a local weakening of the wall (e.g., early loss of elastin), which in turn leads to atherosclerotic involvement and intraluminal thrombus; others suggest that AAAs are a consequence of a ruptured atherosclerotic plaque and associated formation of a thrombus and revascularization from the vasa vasorum. Regardless, AAAs expand at rates up to 0.25 cm to 0.75 cm per year, initially slower, then faster. If untreated, many lesions continue to enlarge until rupture (e.g., 50% of untreated AAAs in patients with high surgical risk will rupture, often within 1 year.²⁶ Although patients with a ruptured antero-lateral wall often succumb to sudden death, those with a ruptured postero-lateral wall can survive to hospitalization. Regardless, AAAs tend to have up to 90% less elastin, much of which is fragmented, and concomitantly few smooth muscle cells.²⁷

Among others, Freestone et al suggest that as the media attenuates and the aorta dilates, the adventitia experiences a stress-induced thickening via a turnover of fibrillar collagen that reinforces the wall.²⁸ The combination of decreased elastin and increased collagen and collagen cross-linking increases wall stiffness and decreases distensibility to a degree that is evident clinically.^27,29 Although collagen turnover is likely a protective response to the loss of medial elastin and smooth muscle, localized imbalances between degradation and synthesis may be responsible in large part for eventual rupture.^30,31 Low flows lead to regions of low WSS, which can be detrimental to the wall endothelium. In particular, stagnant blood flow promotes thrombus formation which, when adjacent to the aneurysm wall, can lead to the release of substances that promote inflammation in the aneurysm wall.^32-34 Inflammation can be associated with structural degradation through the release of numerous types of destructive enzymes.^35,36

High intravascular blood flow causes an elevation of WSS. At high levels of WSS, the endothelium releases nitrous oxide that leads to remodeling of the arterial wall in a system that seeks to maintain the WSS within an acceptable range.^37-39 excessive levels of WSS, the endothelium becomes dysfunctional and can be destroyed.⁴⁰

Walraevens et al used uniaxial unconfined compression tests to distinguish the mechanical properties of healthy tissue from calcified tissue in the aorta.⁴¹ More recently, Ebenstein et al used nanoindentation to measure the mechanical properties of blood clots, fibrous tissue, partially calcified fibrous tissue, and bulk calcifications of human atherosclerotic plaque tissue.⁴² The results demonstrated that the stiffness of plaque tissue largely depends on the mineral content. 

Most of these previous studies focused on the fibrous cap and are based on monoaxial tests under compression or elongation. It is well known that atherosclerotic plaques also have fiber-oriented multilayered structures. Different layers display different direction-dependent mechanical behaviors.⁴³ Accurate knowledge of ultimate strength of arteries will provide the mechanical loading threshold for plaque vulnerability assessment based on computational stress/strain predictions.^44,45 Di Martino et al were the first to report patient-specific wall stress results of a fully coupled fluid-solid interaction (FSI) simulation and suggested that the fluid dynamic field could affect wall stress.⁴⁶ The pressure acting on the inner wall is the major determinant of wall stress. It is debated that pressure variations, due to fluid motion, can significantly affect wall stress results. Taylor and Yamaguchi have shown in ideal rigid wall models that the vortices at the distal end of the AAA models caused regions of high pressure.⁴⁷ However, Finol et al found in 2 patient-specific AAA models that hemodynamic pressure variation is insignificant along the inner AAA wall at any stage of the cardiac cycle and that its magnitude and distribution are dependent on the shape and size of an aneurysm.⁴⁸ Scottie et al furthered the study and compared idealized FSI models and static solid models with varying wall thickness and asymmetry.⁴⁹ Although flow patterns in the asymmetric and axisymmetric models are different, affecting the internal pressure field, their results show that the predicted wall stress is insensitive to flow-induced pressure variation. 

Results reported in this paper have evidenced that if a regular spherical shape and no localized material differences are considered, the static pressure inside the aneurysm increases with its dimensions (almost 17 Pa to 19 Pa).

Papaharilaou et al used a decoupled FSI approach to study a highly asymmetric 100 mm realistic AAA model with a uniform wall thickness (2.0 mm).⁵⁰ For comparison they calculated wall stress by applying a static pressure and found peak wall stress was 12.5% less than the result obtained with the decoupled FSI model, which is consistent with findings of Scotti et al.⁴⁹ Flow patterns of the human aortic arch have been extensively studied through MR velocity mapping.^51-53 Helical and retrograde secondary flows were found to be consistent features of the intra-aortic flow in healthy subjects. The vortex that originates in the center of the growing aneurysm may be explained by the radial pressure gradient in association with the Bernoulli equation, where for irrotational flow the velocity is inversely proportional to the radius of curvature of the streamline, so it is larger at the inside of the bend.⁵⁴ Inertial effects then cause the higher velocity flow to be swept away from the inner bend. Flow separation streamlines regions can be identified on the inlet of aneurysm in which recirculation eddies are formed. 

Tan et al found flow velocity values in systole, inside the aneurysm, of about 2 m/s, while in this paper they are about 1.6 m/s, for an aneurysm bigger than 50 mm of diameter.⁵⁵ his study showed a statistically significant elevated peak stress for ruptured AAAs (46.8 ± 4.5 N/cm²) as compared with electively repaired AAAs (38.1 ± 1.3 N/cm²), even when adjusted for maximum diameter. Roloff et al found in a cerebral aneurysm of 20 mm a velocity of flow of 0.20 m/s and a pressure of more than 15000 Pa,⁵⁶ while our values in a similar case are 0.89 m/s and a static pressure of 16080 Pa. It must be noted that different locations, and thus different lumens and inlet and outlet conditions, are involved. Soudah et al found velocity between 1 m/s and 2 m/s for aneurysms larger than 50 mm in diameter.⁵⁷ The location of maximal stress evidenced by CFD analyses was not at the site of maximal AAA diameter but rather in the top of the cap enclosing the growing stacking blood, where most ruptures occur. Fillinger found for an inlet pressure of 120 mm Hg (16.000 Pa) a peak on the WSS of 0.47 Pa. calculated for aneurysm of 55 mm diameter.⁵⁸ Raghavan et al analyzed a series of AAAs and calculated a WSS of 0.44 Pa, for aneurysms of 55 mm diameter.⁵⁹

Pacanowski et al created an in vitro model to study the phenomenon of endotension.⁶⁰ They furnished a potential method of testing the ability of computer-simulated finite element models to accurately compare sac stress/strain distribution, or demonstrate regional variations in expression of genes in the arterial wall which can predict risk for rupture. 

Conclusions

A qualitative hemodynamic analysis of cerebral aneurysms using image-based patient-specific geometries has shown that concentrated inflow jets, small impingement regions, complex flow patterns, and unstable flow patterns are correlated with a clinical history of prior aneurysm rupture. Analyses described in this paper highlight the potential for CFD to play an important role in the clinical determination of aneurysm risks. The choice of boundary conditions, mesh and time resolution, segmentation methods and parameters, location of vessel truncation, and so forth can affect the quantitative hemodynamic results. Conclusions drawn in this study report a general increase of static pressure and velocity of blood, due to the central vertex generations, inside the cap of aneurysm. Moreover, as the aneurysm grows, the cap thickness decreases, influencing the resulting WSS, which in turn reaches values close to the ultimate tensile stress of the material for a diameter of 50 mm. 

Several limitations of this study need to be mentioned. First, all aneurysms considered were saccular whereas most are fusiform. In a sphere subjected to an internal pressure, stress spreads almost uniformly on the entire surface because of the constant camber, while in a flat shape, areas with a smaller camber are more stressed than larger ones. Also, the assumption of uniform wall thickness is certainly a convenience. While the tension is dictated primarily by surface geometry, the actual stress depends inversely on the thickness. Furthermore, no information has been evaluated regarding modifications concerning the inlet channel of the aneurysm and how each stage of the growing aneurysm modifies the geometry of the whole artery. 

Clinical Relevance

The present research is articulated in two principal steps, the first one focused in this paper regards the evaluation of the static pressure range inside the growing aneurysm. In a second step the obtained data will be used to evaluate the critical stress range on the cap of aneurysm by finite element analysis. The aim is to identify a criterion that considers the uncorrupted thickness of the blood vessel evaluated closely to the aneurysm, the relationship between the decreasing of thickness and the increasing of the aneurysm’s diameter, the static pressure inside the cap, and finally the resultant stress on the aneurysm.  

Editor’s note: Disclosure: The author has completed and returned the ICMJE Form for Disclosure of Potential Conflicts of Interest. The author reports no disclosures related to the content herein.

Manuscript received November 4, 2014; provisional acceptance given February 9, 2015; final version accepted February 12, 2015. 

Address for correspondence: Vincenzo Filardi, PhD, University of Messina, CARECI, Via Consolato del Mare 41, Messina 98168, Italy. Email: vfilardi@unime.it.

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