Modeling rupture of growing aneurysms

Growth and rupture of aneurysms are driven by micro-structural alterations of the arterial wall yet precise mechanisms underlying the process remain to be uncovered. In the present work we examine a scenario when the aneurysm evolution is dominated by turnover of collagen fibers. In the latter case it is natural to hypothesize that rupture of individual fibers (or their bonds) causes the overall aneurysm rupture. We examine this hypothesis in computer simulations of growing aneurysms in which constitutive equations describe both collagen evolution and failure. Failure is enforced in constitutive equations by limiting strain energy that can be accumulated in a fiber. Within the proposed theoretical framework we find a range of parameters that lead to the aneurysm rupture. We conclude in a qualitative agreement with clinical observations that some aneurysms will rupture while others will not.     

Morphological Parameters Associated with Ruptured Posterior Communicating Aneurysms

The rupture risk of unruptured intracranial aneurysms is known to be dependent on the size of the aneurysm. However, the association of morphological characteristics with ruptured aneurysms has not been established in a systematic and location specific manner for the most common aneurysm locations. We evaluated posterior communicating artery (PCoA) aneurysms for morphological parameters associated with aneurysm rupture in that location. CT angiograms were evaluated to generate 3-D models of the aneurysms and surrounding vasculature. Univariate and multivariate analyses were performed to evaluate morphological parameters including aneurysm volume, aspect ratio, size ratio, distance to ICA bifurcation, aneurysm angle, vessel angles, flow angles, and vessel-to-vessel angles. From 2005–2012, 148 PCoA aneurysms were treated in a single institution. Preoperative CTAs from 63 patients (40 ruptured, 23 unruptured) were available and analyzed. Multivariate logistic regression revealed that smaller volume (p = 0.011), larger aneurysm neck diameter (0.048), and shorter ICA bifurcation to aneurysm distance (p = 0.005) were the most strongly associated with aneurysm rupture after adjusting for all other clinical and morphological variables. Multivariate subgroup analysis for patients with visualized PCoA demonstrated that larger neck diameter (p = 0.018) and shorter ICA bifurcation to aneurysm distance (p = 0.011) were significantly associated with rupture. Intracerebral hemorrhage was associated with smaller volume, larger maximum height, and smaller aneurysm angle, in addition to lateral projection, male sex, and lack of hypertension. We found that shorter ICA bifurcation to aneurysm distance is significantly associated with PCoA aneurysm rupture. This is a new physically intuitive parameter that can be measured easily and therefore be readily applied in clinical practice to aid in the evaluation of patients with PCoA aneurysms.     

A nonlinear dynamical mechanism for bruit generation by an intracranial saccular aneurysm

 Intracranial saccular aneurysms have been clinically observed to emit a transient sound, a bruit, on each heartbeat. The mechanism causing the bruits has been a matter of contention. A qualitative analysis of the nonlinear dynamical properties of the Shah-Humphrey model for periodic pressure forcing of a thin-necked saccular aneurysm, using the Fung nonlinear constitutive model for the aneurysm material, shows that a small blood pressure jump on each beat, whether the pressure is weakly aperiodic or periodic, induces transients in the radial deformation response of the aneurysmal wall on each heartbeat. These transient vibrations, which have a component with frequency near the natural frequency of the system but are not resonant phenomena and which decay rapidly to a limit cycle during each distinct forcing pressure cycle, can generate the bruits. Received: 21 November 2000 / Revised version: 9 August 2001 / Published online: 23 August 2002 Mathematics Subject Classification (2000): 92B99, 70K40, 70K05 Key words or phrases: Intracranial saccular aneurysm – Bruit – Spectrum – Nonlinear dynamics – Transients – Vortex shedding – Fung model     

Morphological and Hemodynamic Discriminators for Rupture Status in Posterior Communicating Artery Aneurysms

Background and Purpose

The conflicting findings of previous morphological and hemodynamic studies on intracranial aneurysm rupture may be caused by the relatively small sample sizes and the variation in location of the patient-specific aneurysm models. We aimed to determine the discriminators for aneurysm rupture status by focusing on only posterior communicating artery (PCoA) aneurysms.

Materials and Methods

In 129 PCoA aneurysms (85 ruptured, 44 unruptured), clinical, morphological and hemodynamic characteristics were compared between the ruptured and unruptured cases. Multivariate logistic regression analysis was performed to determine the discriminators for rupture status of PCoA aneurysms.

Results

While univariate analyses showed that the size of aneurysm dome, aspect ratio (AR), size ratio (SR), dome-to-neck ratio (DN), inflow angle (IA), normalized wall shear stress (NWSS) and percentage of low wall shear stress area (LSA) were significantly associated with PCoA aneurysm rupture status. With multivariate analyses, significance was only retained for higher IA (OR = 1.539, p < 0.001) and LSA (OR = 1.393, p = 0.041).

Conclusions

Hemodynamics and morphology were related to rupture status of intracranial aneurysms. Higher IA and LSA were identified as discriminators for rupture status of PCoA aneurysms.     

Radio aneurysm coils for noninvasive detection of cerebral embolization failures: a preliminary study

The rupture of a cerebral aneurysm is the most common cause of subarachnoid hemorrhage. Endovascular embolization of the aneurysms by implantation of Guglielmi detachable coils (GDC) has become a major treatment approach in the prevention of a rupture. Implantation of the coils induces formation of tissues over the coils, embolizing the aneurysm. However, blood entry into the coiled aneurysm often occurs due to failures in the embolization process. Current diagnostic methods used for aneurysms, such as X-ray angiography and computer tomography, are ineffective for continuous monitoring of the disease and require extremely expensive equipment. Here we present a novel technique for wireless monitoring of cerebral aneurysms using implanted embolization coils as radiofrequency resonant sensors that detect the blood entry. The experiments show that commonly used embolization coils could be utilized as electrical inductors or antennas. As the blood flows into a coil-implanted aneurysm, parasitic capacitance of the coil is modified because of the difference in permittivity between the blood and the tissues grown around the coil, resulting in a change in the coil's resonant frequency. The resonances of platinum GDC-like coils embedded in aneurysm models are detected to show average responses of 224–819 MHz/ml to saline injected into the models. This preliminary demonstration indicates a new possibility in the use of implanted GDC as a wireless sensor for embolization failures, the first step toward realizing long-term, noninvasive, and cost-effective remote monitoring of cerebral aneurysms treated with coil embolization.     

Direct numerical simulation of transitional flow in a patient-specific intracranial aneurysm

In experiments turbulence has previously been shown to occur in intracranial aneurysms. The effects of turbulence induced oscillatory wall stresses could be of great importance in understanding aneurysm rupture. To investigate the effects of turbulence on blood flow in an intracranial aneurysm, we performed a high resolution computational fluid dynamics (CFD) simulation in a patient specific middle cerebral artery (MCA) aneurysm using a realistic, pulsatile inflow velocity. The flow showed transition to turbulence just after peak systole, before relaminarization occurred during diastole. The turbulent structures greatly affected both the frequency of change of wall shear stress (WSS) direction and WSS magnitude, which reached a maximum value of 41.5Pa. The recorded frequencies were predominantly in the range of 1-500Hz. The current study confirms, through properly resolved CFD simulations that turbulence can occur in intracranial aneurysms.     

Mechanical analysis of the development of left ventricular aneurysms

The left ventricle is modelled as a spherical shell with an infarcted wall segment. The mechanics of the circumstances causing this infarcted segment to develop into an aneurysm is presented. Both the wall stresses and deformations are worked out for aneurysms developing from infarcts of different sizes and percentages of wall damage. The governing equations consist of incompressibility relations, force-equilibrium relations and stress-strain relations. Newton Raphson technique is used to solve these nonlinear simultaneous algebraic equations, for the values of the myocardial stresses in the infarcted segment and the bulge values, in terms of the ventricular geometry and the damage extent (expressed in terms of the damage angle and percentage of wall damage). The results indicate that in general it is innermost layer which is severely stressed and that in the rupture of the ventricle the critical factor involved is the percentage of infarct thickness rather than the angle of damage.     

Onset and nature of flow-induced vibrations in cerebral aneurysms via fluid–structure interaction simulations

Clinical, experimental, and recent computational studies have demonstrated the presence of wall vibrations in cerebral aneurysms, thought to be induced by blood flow instability. These vibrations could induce irregular, high-rate deformation of the aneurysm wall, and potentially disrupt regular cell behavior and promote deleterious wall remodeling. In order to elucidate, for the first time, the onset and nature of such flow-induced vibrations, in this study we imposed a linearly increasing flow rate on high-fidelity fluid–structure interaction models of three anatomically realistic aneurysm geometries. Prominent narrow-band vibrations in the range of 100–500 Hz were found in two out of the three aneurysm geometries tested, while the case that did not exhibit flow instability did not vibrate. Aneurysm vibrations consisted mostly of fundamental modes of the entire aneurysm sac, with the vibrations exhibiting more frequency content at higher frequencies than the flow instabilities driving those vibrations. The largest vibrations occurred in the case which exhibited strongly banded fluid frequency content, and the vibration amplitude was highest when the strongest fluid frequency band was an integer multiple of one of the natural frequencies of the aneurysm sac. Lower levels of vibration occurred in the case which exhibited turbulent-like flow with no distinct frequency bands. The current study provides a plausible mechanistic explanation for the high-frequency sounds observed in cerebral aneurysms, and suggests that narrow-band (vortex-shedding type) flow might stimulate the wall more, or at least at lower flow rates, than broad-band, turbulent-like flow.

     

Further evidence for the dynamic stability of intracranial saccular aneurysms

It has long been thought that intracranial saccular aneurysms enlarge and rupture because of mechanical instabilities. Recent nonlinear analyses suggest, however, that at least certain sub-classes of aneurysms do not exhibit quasi-static limit point instabilities or dynamic instabilities in response to periodic loading, and consequently, that the natural history of these lesions is likely governed by growth and remodeling processes. In this paper, we present additional results that support the finding that one particular sub-class of saccular aneurysms is dynamically stable. Specifically, we extended recent results of Shah and Humphrey, which are based on the assumption that some saccular aneurysms can be modeled as spherical elastic membranes surrounded by a viscous cerebrospinal fluid, to account for a viscohyperelastic behavior of the aneurysm. It is shown that inclusion of a "short-term" viscoelastic contribution to the mechanical behavior of an aneurysm serves to increase its dynamic stability against various disturbances.     

Numerical simulation of saccular aneurysm hemodynamics: influence of morphology on rupture risk

The governing equations for pulsatile fluid flow were solved in their finite volume formulation in order to simulate blood flow in a variety of three-dimensional aneurysm geometries. The influence of geometric factors on flow patterns and fluid mechanical forces was studied with the goal of identifying the risk of aneurysm rupture. Aneurysm morphology was characterized by quantitative shape indices reflecting the three dimensionality of the vasculature derived from clinical studies. Recirculation zones and secondary flows were observed in aneurysms and arteries. Regions of extreme and alternating shear stress were observed and identified as sites for potential aneurysm rupture. The ellipticity of an aneurysm was observed to be strongly correlated with wall shear stress at the aneurysm fundus, while its non-sphericity, volume, and degree of undulation were more weakly correlated.     

The effects of variable mass and geometry, pretwist, shear deformation and rotatory inertia on the resonant frequencies of intact long bones: A finite element model analysis

The influence of pretwist, nonuniformities in mass and flexural stiffness, rotatory inertia and shear deformation on the natural frequencies of intact bones is evaluated by means of a linear elastic, finite-element model which has been programmed for solution on the digital computer. Theoretical results are compared to the results on the forced vibration of intact canine radii obtained experimentally by Thompson. Surprisingly, inclusion of fairly large pretwist angles (from −14° to 12° for one specimen) had little affect on the first three frequencies of transverse vibration in either the cranial or lateral directions. Inclusion of shear deformation reduced the third-mode frequency in the stiffest (lateral) direction by about six per cent, otherwise shear deformation played a minor role in determining natural frequencies. Similarly, rotatory inertia had negligible influence up to the third natural frequency.

The predominant influence on the first three natural frequencies of transverse vibration could be attributed to the variations in mass and flexural stiffness along the length of the test specimens. Different effective moduli of elasticity are required to yield correct absolute values for the frequencies which correspond to experimental findings, thus implying the presence of some inhomogeneities in material properties around the bone cross-section and/or along its length.     

Fluid-structure interaction of a patient-specific abdominal aortic aneurysm treated with an endovascular stent-graft

Background  

Abdominal aortic aneurysms (AAA) are local dilatations of the infrarenal aorta. If left untreated they may rupture and lead to death. One form of treatment is the minimally invasive insertion of a stent-graft into the aneurysm. Despite this effective treatment aneurysms may occasionally continue to expand and this may eventually result in post-operative rupture of the aneurysm. Fluid-structure interaction (FSI) is a particularly useful tool for investigating aneurysm biomechanics as both the wall stresses and fluid forces can be examined.     

Biomechanical wall properties of human intracranial aneurysms resected following surgical clipping (IRRAs Project)

Background and purposeIndividual rupture risk assessment of intracranial aneurysms is a major issue in the clinical management of asymptomatic aneurysms. Aneurysm rupture occurs when wall tension exceeds the strength limit of the wall tissue. At present, aneurysmal wall mechanics are poorly understood and thus, risk assessment involving mechanical properties is inexistent. Aneurysm computational hemodynamics studies make the assumption of rigid walls, an arguable simplification. We therefore aim to assess mechanical properties of ruptured and unruptured intracranial aneurysms in order to provide the foundation for future patient-specific aneurysmal risk assessment. This work also challenges some of the currently held hypotheses in computational flow hemodynamics research.MethodsA specific conservation protocol was applied to aneurysmal tissues following clipping and resection in order to preserve their mechanical properties. Sixteen intracranial aneurysms (11 female, 5 male) underwent mechanical uniaxial stress tests under physiological conditions, temperature, and saline isotonic solution. These represented 11 unruptured and 5 ruptured aneurysms. Stress/strain curves were then obtained for each sample, and a fitting algorithm was applied following a 3-parameter (C₁₀, C₀₁, C₁₁) Mooney–Rivlin hyperelastic model. Each aneurysm was classified according to its biomechanical properties and (un)rupture status.ResultsTissue testing demonstrated three main tissue classes: Soft, Rigid, and Intermediate. All unruptured aneurysms presented a more Rigid tissue than ruptured or pre-ruptured aneurysms within each gender subgroup. Wall thickness was not correlated to aneurysmal status (ruptured/unruptured). An Intermediate subgroup of unruptured aneurysms with softer tissue characteristic was identified and correlated with multiple documented risk factors of rupture.ConclusionThere is a significant modification in biomechanical properties between ruptured aneurysm, presenting a soft tissue and unruptured aneurysms, presenting a rigid material. This finding strongly supports the idea that a biomechanical risk factor based assessment should be utilized in the to improve the therapeutic decision making.     

Analysis of Morphological Parameters to Differentiate Rupture Status in Anterior Communicating Artery Aneurysms

In contrast to size, the association of morphological characteristics of intracranial aneurysms with rupture has not been established in a systematic manner. We present an analysis of the morphological variables that are associated with rupture in anterior communicating artery aneurysms to determine site-specific risk variables. One hundred and twenty-four anterior communicating artery aneurysms were treated in a single institution from 2005 to 2010, and CT angiograms (CTAs) or rotational angiography from 79 patients (42 ruptured, 37 unruptured) were analyzed. Vascular imaging was evaluated with 3D Slicer© to generate models of the aneurysms and surrounding vasculature. Morphological parameters were examined using univariate and multivariate analysis and included aneurysm volume, aspect ratio, size ratio, distance to bifurcation, aneurysm angle, vessel angle, flow angle, and parent-daughter angle. Multivariate logistic regression revealed that size ratio, flow angle, and parent-daughter angle were associated with aneurysm rupture after adjustment for age, sex, smoking history, and other clinical risk factors. Simple morphological parameters such as size ratio, flow angle, and parent-daughter angle may thus aid in the evaluation of rupture risk of anterior communicating artery aneurysms.     

犬囊状动脉瘤模型的制作

本文报道用“静脉囊镶嵌技术·制成犬的囊状动脉瘤模型。18个模型(6个单侧型,6个分叉型,6个末梢型)造型后2周经IA DSA检查。本模型在分型、血流动力学改变方面与人类囊状脑动脉瘤类似。不同类型的动脉瘤模型既有相同的血流动力学特征,又有各自的特点,这与动脉瘤与载瘤动脉的角度有关。我们认为该模型可应用于研究动脉瘤的血流动力学与血管内栓塞治疗。     

An Analysis of 1256 Cases of Sporadic Ruptured Cerebral Aneurysm in a Single Chinese Institution

Background

To review the epidemiology of sporadic ruptured cerebral aneurysm.

Methods

This is a retrospective study of consecutive 1256 Chinese patients between January 2006 and January 2013, who were admitted to the Second Hospital of Hebei Medical University, China, for spontaneous subarachnoid hemorrhage due to a rupture of cerebral artery aneurysm. In 288 males and 478 females, the size of aneurysms was measured by a neuroradiologist on DSA. In 123 males and 184 females, the size of the ruptured aneurysms was not measured. The remaining patients, with 61 males and 122 females, had multiple aneurysms, and the medical record could not reliably determine the specific aneurysm responsible for the rupture.

Results

In total there were 784 females and 472 males with a female/male ratio of 1.66. The female/male ratio was down to 0.50 for patients younger than 35 yrs. For both males and females, aneurysm rupture was most common during the age of 50–59 yrs. Ruptured aneurysms were mostly of 2 mm–5 mm in size (47.1%), followed by 5 mm–10 mm (39.7%). Ruptured single cerebral aneurysm occurred in anterior circulation in 95.0% of the cases, with 5.0% occurred in posterior circulation. Ruptured aneurysm most commonly occurred at posterior communicating artery (34.9%) and anterior communicating artery (29.5%). 183 cases (14.6%) had multiple aneurysms.

Conclusions

With younger patients, there is a male predominance in our series. Ninety percent of patients have ruptured aneurysms less than 10 mm in size.     

Impact of stents and flow diverters on hemodynamics in idealized aneurysm models

Cerebral aneurysms constitute a major medical challenge as treatment options are limited and often associated with high risks. Statistically, up to 3% of patients with a brain aneurysm may suffer from bleeding for each year of life. Eight percent of all strokes are caused by ruptured aneurysms. In order to prevent this rupture, endovascular stenting using so called flow diverters is increasingly being regarded as an alternative to the established coil occlusion method in minimally invasive treatment. Covering the neck of an aneurysm with a flow diverter has the potential to alter the hemodynamics in such a way as to induce thrombosis within the aneurysm sac, stopping its further growth, preventing its rupture and possibly leading to complete resorption. In the present study the influence of different flow diverters is quantified considering idealized patient configurations, with a spherical sidewall aneurysm placed on either a straight or a curved parent vessel. All important hemodynamic parameters (exchange flow rate, velocity, and wall shear stress) are determined in a quantitative and accurate manner using computational fluid dynamics when varying the key geometrical properties of the aneurysm. All simulations are carried out using an incompressible, Newtonian fluid with steady conditions. As a whole, 72 different cases have been considered in this systematic study. In this manner, it becomes possible to compare the efficiency of different stents and flow diverters as a function of wire density and thickness. The results show that the intra-aneurysmal flow velocity, wall shear stress, mean velocity, and vortex topology can be considerably modified thanks to insertion of a suitable implant. Intra-aneurysmal residence time is found to increase rapidly with decreasing stent porosity. Of the three different implants considered in this study, the one with the highest wire density shows the highest increase of intra-aneurysmal residence time for both the straight and the curved parent vessels. The best hemodynamic modifications are always obtained for a small aneurysm diameter.     

Inflation of an artery leading to aneurysm formation and rupture

Formation and rupture of aneurysms due to the inflation of an artery with collagen fibers distributed in two preferred directions, subjected to internal pressure and axial stretch are examined within the framework of nonlinear elasticity. A two layer tube model with a fiber-reinforced composite based incompressible anisotropic hyperelastic constitutive material is employed to model the stress-strain behavior of the artery wall with distributed collagen fibers. The artery wall takes up a uniform inflation deformation, and there are no aneurysms in the artery under the normal condition. But an aneurysm may be formed in arteries when the stiffness of the fibers is decreased to a certain value or the direction of the fibers is changed to a certain degree towards the circumferential direction. The aneurysm may expand to much large extent and become complex in shape. One portion of the aneurysm becomes highly distended as a bubble while the rest remains lightly inflated. The rupture of the aneurysm is discussed along with the distribution of stresses. Critical pressures and the rupture pressures are given for different collagen fiber orientations or stiffness. Furthermore, the stability of the solutions is discussed to explain the formation of aneurysm.     

Flow instability detected in ruptured versus unruptured cerebral aneurysms at the internal carotid artery

Flow instability has emerged as a new hemodynamic metric hypothesized to have potential value in assessing the rupture risk of cerebral aneurysms. However, diverse findings have been reported in the literature. In the present study, high-resolution hemodynamic simulations were performed retrospectively on 35 aneurysms (10 ruptured & 25 unruptured) located at the internal carotid artery (ICA). Simulated hemodynamic parameters were statistically compared between the ruptured and unruptured aneurysms, with emphasis on examining the correlation of flow instability with the status of aneurysm rupture. Pronounced flow instability was detected in 20% (2 out of 10) of the ruptured aneurysms, whereas in 44% (11 out of 25) of the unruptured aneurysms. Statistically, the flow instability metric (quantified by the temporally and spatially averaged fluctuating kinetic energy over the aneurysm sac) did not differ significantly between the ruptured and unruptured aneurysms. In contrast, low wall shear stress area (LSA) and pressure loss coefficient (PLC) exhibited significant correlations with the status of aneurysm rupture. In conclusion, the present study suggests that the presence of flow instability may not correlate closely with the status of aneurysm rupture, at least for ICA aneurysms. On the other hand, the retrospective nature of the study and the small sample size may have to some extent compromised the reliability of the conclusion, and therefore large-scale prospective studies would be needed to further address the issue.