A model for saccular cerebral aneurysm growth by collagen fibre remodelling

The first structural model for saccular cerebral aneurysm growth is proposed. It is assumed that the development of the aneurysm is accompanied by a loss of the media, and that only collagen fibres provide load-bearing capacity to the aneurysm wall. The aneurysm is modelled as an axisymmetric multi-layered membrane, exposed to an inflation pressure. Each layer is characterized by an orientation angle, which changes between different layers. The collagen fibres and fibroblasts within a specific layer are perfectly aligned. The growth and the morphological changes of the aneurysm are accomplished by the turnover of collagen. Fibroblasts are responsible for collagen production, and the related deformations are assumed to govern the collagen production rate. There are four key parameters in the model: a normalized pressure, the number of layers in the wall, an exponent in the collagen mass production rate law, and the pre-stretch under which the collagen is deposited. The influence of the model parameters on the aneurysmal response is investigated, and a stability analysis is performed. The model is able to predict clinical observations and mechanical test results, for example, in terms of predicted aneurysm size, shape, wall stress and wall thickness.     

Reduced M2 macrophages and adventitia collagen dampen the structural integrity of blood blister–like aneurysms and induce preoperative rerupture

ObjectiveBlood blister–like aneurysms (BBAs) are extremely rare aneurysms. They are predisposed to preoperative rerupture with a high case‐fatality rate. Here, we attempt to interrogate the distinct clinicopathology and the histological basis underlying its clinical rerupture.MethodsThree middle meningeal arteries, 11 BBA (5 reruptured, 6 non‐rerupture) and 19 saccular aneurysm samples were obtained for histopathological investigation. Three reruptured BBAs, 3 non‐reruptured BBAs and 6 saccular (3 ruptured, 3 unruptured) aneurysms were obtained for quantitative flow cytometry analysis.ResultsCompared with true saccular aneurysms, the BBA aneurysm wall lacks arterial stroma cells including CD31+ endothelial cells and α‐SMA + smooth muscle cells. Only fibroblasts and adventitial collagen were observed in the BBA aneurysm wall. Meanwhile, BBAs were enriched with infiltrated inflammatory cells, especially polarized macrophages. Based on the rerupture status, those reruptured BBAs showed drastically reduced fibroblasts and adventitia collagen. Moreover, M2‐polarized macrophages were observed dominant in BBAs and exhibit repairing cellular functions based on their interplays with arterial fibroblasts. Reduced M2 macrophages and arterial tissue repairing modulation may be responsible for the decreasing collagen synthesis and fibrosis repairment, which potentially dampens the aneurysm integrity and induces BBA aneurysm reruputre.ConclusionsBBAs poses histopathological features of occult pseudoaneurysms or dissecting aneurysms. Reduced M2 macrophages and adventitia collagen may dampen the structural integrity of BBAs and induce preoperative rerupture.     

An inelastic multi-mechanism constitutive equation for cerebral arterial tissue

Intracranial aneurysms (ICA) are abnormal saccular dilations of cerebral arteries, commonly found at apices of arterial bifurcations and outer walls of curved arterial segments. Histological evidence suggests the stages in ICA development include the deformation of a segment of arterial wall into a “bleb” with no identifiable neck region followed by the development of an aneurysm with a clear neck. Afterwards, the aneurysm may undergo further enlargement, possibly with significant biological response including calcification and thrombosis. Past studies of the biomechanics of cerebral aneurysm tissue have been directed at modeling elastic deformations of pre-existing aneurysms. Taking this approach, the aneurysm wall is treated as a different entity than the arterial tissue from which it developed. In the current work, a nonlinear, inelastic, dual-mechanism constitutive equation for cerebral arterial tissue is developed. It is the first to model the recruitment of collagen fibers and degradation of the internal elastic lamina, two important characteristics of early stage aneurysm formation.     

Estimation of aneurysm wall stresses created by treatment with a shape memory polymer foam device

In this study, compliant latex thin-walled aneurysm models are fabricated to investigate the effects of expansion of shape memory polymer foam. A simplified cylindrical model is selected for the in-vitro aneurysm, which is a simplification of a real, saccular aneurysm. The studies are performed by crimping shape memory polymer foams, originally 6 and 8 mm in diameter, and monitoring the resulting deformation when deployed into 4-mm-diameter thin-walled latex tubes. The deformations of the latex tubes are used as inputs to physical, analytical, and computational models to estimate the circumferential stresses. Using the results of the stress analysis in the latex aneurysm model, a computational model of the human aneurysm is developed by changing the geometry and material properties. The model is then used to predict the stresses that would develop in a human aneurysm. The experimental, simulation, and analytical results suggest that shape memory polymer foams have potential of being a safe treatment for intracranial saccular aneurysms. In particular, this work suggests oversized shape memory foams may be used to better fill the entire aneurysm cavity while generating stresses below the aneurysm wall breaking stresses.     

Modelling evolution and the evolving mechanical environment of saccular cerebral aneurysms

A fluid–solid-growth (FSG) model of saccular cerebral aneurysm evolution is developed. It utilises a realistic two-layered structural model of the internal carotid artery and explicitly accounts for the degradation of the elastinous constituents and growth and remodelling (G&R) of the collagen fabric. Aneurysm inception is prescribed: a localised degradation of elastin results in a perturbation in the arterial geometry; the collagen fabric adapts, and the artery achieves a new homeostatic configuration. The perturbation to the geometry creates an altered haemodynamic environment. Subsequent degradation of elastin is explicitly linked to low wall shear stress (WSS) in a confined region of the arterial domain. A sidewall saccular aneurysm develops, the collagen fabric adapts and the aneurysm stabilises in size. A quasi-static analysis is performed to determine the geometry at diastolic pressure. This enables the cyclic stretching of the tissue to be quantified, and we propose a novel index to quantify the degree of biaxial stretching of the tissue. Whilst growth is linked to low WSS from a steady (systolic) flow analysis, a pulsatile flow analysis is performed to compare steady and pulsatile flow parameters during evolution. This model illustrates the evolving mechanical environment for an idealised saccular cerebral aneurysm developing on a cylindrical parent artery and provides the guidance to more sophisticated FSG models of aneurysm evolution which link G&R to the local mechanical stimuli of vascular cells.     

Mechanical instability of normal and aneurysmal arteries

Tortuous arteries associated with aneurysms have been observed in aged patients with atherosclerosis and hypertension. However, the underlying mechanism is poorly understood. The objective of this study was to determine the effect of aneurysms on arterial buckling instability and the effect of buckling on aneurysm wall stress. We investigated the mechanical buckling and post-buckling behavior of normal and aneurysmal carotid arteries and aorta’s using computational simulations and experimental measurements to elucidate the interrelationship between artery buckling and aneurysms. Buckling tests were done in porcine carotid arteries with small aneurysms created using elastase treatment. Parametric studies were done for model aneurysms with orthotropic nonlinear elastic walls using finite element simulations. Our results demonstrated that arteries buckled at a critical buckling pressure and the post-buckling deflection increased nonlinearly with increasing pressure. The presence of an aneurysm can reduce the critical buckling pressure of arteries, although the effect depends on the aneurysm’s dimensions. Buckled aneurysms demonstrated a higher peak wall stress compared to unbuckled aneurysms under the same lumen pressure. We conclude that aneurysmal arteries are vulnerable to mechanical buckling and mechanical buckling could lead to high stresses in the aneurysm wall. Buckling could be a possible mechanism for the development of tortuous aneurysmal arteries such as in the Loeys–Dietz syndrome.     

Nonlinear anisotropic stress analysis of anatomically realistic cerebral aneurysms

BACKGROUND: Static deformation analysis and estimation of wall stress distribution of patient-specific cerebral aneurysms can provide useful insights into the disease process and rupture. METHOD OF APPROACH: The three-dimensional geometry of saccular cerebral aneurysms from 27 patients (18 unruptured and nine ruptured) was reconstructed based on computer tomography angiography images. The aneurysm wall tissue was modeled using a nonlinear, anisotropic, hyperelastic material model (Fung-type) which was incorporated in a user subroutine in ABAQUS. Effective material fiber orientations were assumed to align with principal surface curvatures. Static deformation of the aneurysm models were simulated assuming uniform wall thickness and internal pressure load of 100 mm Hg. RESULTS: The numerical analysis technique was validated by quantitative comparisons to results in the literature. For the patient-specific models, in-plane stresses in the aneurysm wall along both the stiff and weak fiber directions showed significant regional variations with the former being higher. The spatial maximum of stress ranged from as low as 0.30 MPa in a small aneurysm to as high as 1.06 MPa in a giant aneurysm. The patterns of distribution of stress, strain, and surface curvature were found to be similar. Sensitivity analyses showed that the computed stress is mesh independent and not very sensitive to reasonable perturbations in model parameters, and the curvature-based criteria for fiber orientations tend to minimize the total elastic strain energy in the aneurysms wall. Within this small study population, there were no statistically significant differences in the spatial means and maximums of stress and strain values between the ruptured and unruptured groups. However, the ratios between the stress components in the stiff and weak fiber directions were significantly higher in the ruptured group than those in the unruptured group. CONCLUSIONS: A methodology for nonlinear, anisotropic static deformation analysis of geometrically realistic aneurysms was developed, which can be used for a more accurate estimation of the stresses and strains than previous methods and to facilitate prospective studies on the role of stress in aneurysm rupture.     

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。     

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     

Hemodynamic stress in lateral saccular aneurysms

The flow velocities in glass and silastic lateral aneurysm models were quantitatively measured with the non-invasive laser Doppler method. The influences of the elasticity of the wall, the pulse wave and the properties of the perfusion medium on the intra-aneurysmal circulation were investigated. As shown previously, the inflow into the aneurysm arose from the downstream lip and was directed toward the center of the fundus. Backflow to the parent vessel took place along the walls of the fundus. With non-pulsatile perfusion, flow velocities in the center of the standardized aneurysms varied between 0.4 and 2% of the maximum velocity in the parent vessel. With pulsatile perfusion, flow velocities in the center of the fundus ranged between 8 and 13% of the flow velocity in the axis of the parent vessel. Flow velocities in the aneurysms were slower with a polymer suspension with blood-like properties compared to a glycerol/water solution. Flow velocity measurements near the aneurysmal wall allowed the estimation of the shear stresses at critical locations. The maximum shear stresses at the downstream lip of the aneurysm were in the range of the stresses measured at the flow divider of an arterial bifurcation. The present results suggest that in human saccular aneurysms intra-aneurysmal flow and shear stress on the wall are directly related to the pulsatility of perfusion, i.e. the systolic/diastolic pressure difference and that the tendency to spontaneous thrombosis depends on the viscoelastic properties of the blood, namely the hematocrit.     

Structure of pulsatile flow in a model of elastic cerebral aneurysm

This study examines the effect of aneurysmal wall elasticity on the structure of flow within an elastic aneurysm during pulsatile flow. We visualized flow structure in a model of an elastic saccular aneurysm located at the bifurcation of the anterior cerebral artery and extending to the anterior communicating artery, and measured changes in the diameter of the aneurysm wall during pulsatile flow using particle imaging velocimetry (PIV). We similarly measured these features during steady flow by PIV and found that dilation of the aneurysmal wall absorbed the dynamic energy within the aneurysm. Accordingly, aneurysm wall elasticity functions as a biocompatible reaction that relieves wall shear stress acting on the vascular wall during pulsatile flow, and should thus inhibit the development and rupture of an aneurysm.     

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.     

The Helsinki Rat Microsurgical Sidewall Aneurysm Model

Experimental saccular aneurysm models are necessary for testing novel surgical and endovascular treatment options and devices before they are introduced into clinical practice. Furthermore, experimental models are needed to elucidate the complex aneurysm biology leading to rupture of saccular aneurysms.Several different kinds of experimental models for saccular aneurysms have been established in different species. Many of them, however, require special skills, expensive equipment, or special environments, which limits their widespread use. A simple, robust, and inexpensive experimental model is needed as a standardized tool that can be used in a standardized manner in various institutions.The microsurgical rat abdominal aortic sidewall aneurysm model combines the possibility to study both novel endovascular treatment strategies and the molecular basis of aneurysm biology in a standardized and inexpensive manner. Standardized grafts by means of shape, size, and geometry are harvested from a donor rat''s descending thoracic aorta and then transplanted to a syngenic recipient rat. The aneurysms are sutured end-to-side with continuous or interrupted 9-0 nylon sutures to the infrarenal abdominal aorta.We present step-by-step procedural instructions, information on necessary equipment, and discuss important anatomical and surgical details for successful microsurgical creation of an abdominal aortic sidewall aneurysm in the rat.     

Mechanical stresses in abdominal aortic aneurysms: influence of diameter, asymmetry, and material anisotropy

Biomechanical studies suggest that one determinant of abdominal aortic aneurysm (AAA) rupture is related to the stress in the wall. In this regard, a reliable and accurate stress analysis of an in vivo AAA requires a suitable 3D constitutive model. To date, stress analysis conducted on AAA is mainly driven by isotropic tissue models. However, recent biaxial tensile tests performed on AAA tissue samples demonstrate the anisotropic nature of this tissue. The purpose of this work is to study the influence of geometry and material anisotropy on the magnitude and distribution of the peak wall stress in AAAs. Three-dimensional computer models of symmetric and asymmetric AAAs were generated in which the maximum diameter and length of the aneurysm were individually controlled. A five parameter exponential type structural strain-energy function was used to model the anisotropic behavior of the AAA tissue. The anisotropy is determined by the orientation of the collagen fibers (one parameter of the model). The results suggest that shorter aneurysms are more critical when asymmetries are present. They show a strong influence of the material anisotropy on the magnitude and distribution of the peak stress. Results confirm that the relative aneurysm length and the degree of aneurysmal asymmetry should be considered in a rupture risk decision criterion for AAAs.     

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.     

Influence of stent configuration on cerebral aneurysm fluid dynamics

Embolic coiling is the most popular endovascular treatment available for cerebral aneurysms. Nevertheless, the embolic coiling of wide-neck aneurysms is challenging and, in many cases, ineffective. Use of highly porous stents to support coiling of wide-neck aneurysms has become a common procedure in recent years. Several studies have also demonstrated that high porosity stents alone can significantly alter aneurysmal hemodynamics, but differences among different stent configurations have not been fully characterized. As a result, it is usually unclear which stent configuration is optimal for treatment. In this paper, we present a flow study that elucidates the influence of stent configuration on cerebral aneurysm fluid dynamics in an idealized wide-neck basilar tip aneurysm model. Aneurysmal fluid dynamics for three different stent configurations (half-Y, Y and, cross-bar) were first quantified using particle image velocimetry and then compared. Computational fluid dynamics (CFD) simulations were also conducted for selected stent configurations to facilitate validation and provide more detailed characterizations of the fluid dynamics promoted by different stent configurations. In vitro results showed that the Y stent configuration reduced cross-neck flow most significantly, while the cross-bar configuration reduced velocity magnitudes within the aneurysmal sac most significantly. The half-Y configuration led to increased velocity magnitudes within the aneurysmal sac at high parent-vessel flow rates. Experimental results were in strong agreement with CFD simulations. Simulated results indicated that differences in fluid dynamic performance among the different stent configurations can be attributed primarily to protruding struts within the bifurcation region.     

Finite strain elastodynamics of intracranial saccular aneurysms.

Various investigators suggest that intracranial saccular aneurysms are dynamically unstable, that they resonate in response to pulsatile blood flow. This hypothesis is based on linearized analyses or experiments on rubber "models", however, and there is a need for a more critical examination. Toward this end, we (a) derive a new nonlinear equation of motion for a pulsating spherical aneurysm that is surrounded by cerebral spinal fluid and whose behavior is described by a Fung-type pseudostrain-energy function that fits data on human lesions, and (b) use methods of nonlinear dynamics to examine the stability of such lesions against perturbations to both in vivo and in vitro conditions. The numerical results suggest that this sub-class of lesions is dynamically stable. Moreover, with the exception of transients associated with initial perturbations, inertial effects appear to be insignificant for fundamental forcing frequencies less than 10 Hz and hence for typical physiologic and laboratory conditions. We submit, therefore, that further study of the mechanics of saccular aneurysms should be focused on quasi-static stress analyses that investigate the roles of lesion geometry and material properties, including growth and remodeling.     

Tetrahedral vs. polyhedral mesh size evaluation on flow velocity and wall shear stress for cerebral hemodynamic simulation

Haemodynamic factors, in particular wall shear stresses (WSSs) may have significant impact on growth and rupture of cerebral aneurysms. Without a means to measure WSS reliably in vivo, computational fluid dynamic (CFD) simulations are frequently employed to visualise and quantify blood flow from patient-specific computational models. With increasing interest in integrating these CFD simulations into pretreatment planning, a better understanding of the validity of the calculations in respect to computation parameters such as volume element type, mesh size and mesh composition is needed. In this study, CFD results for the two most common aneurysm types (saccular and terminal) are compared for polyhedral- vs. tetrahedral-based meshes and discussed regarding future clinical applications. For this purpose, a set of models were constructed for each aneurysm with spatially varying surface and volume mesh configurations (mesh size range: 5119-258, 481 volume elements). WSS distribution on the model wall and point-based velocity measurements were compared for each configuration model. Our results indicate a benefit of polyhedral meshes in respect to convergence speed and more homogeneous WSS patterns. Computational variations of WSS values and blood velocities are between 0.84 and 6.3% from the most simple mesh (tetrahedral elements only) and the most advanced mesh design investigated (polyhedral mesh with boundary layer).     

Virtual stenting workflow with vessel-specific initialization and adaptive expansion for neurovascular stents and flow diverters

Endovascular intervention using traditional neurovascular stents and densely braided flow diverters (FDs) have become the preferred treatment strategies for traditionally challenging intracranial aneurysms. Modeling stent and FD deployment in patient-specific aneurysms and its flow modification results prior to the actual intervention can potentially predict the patient outcome and treatment optimization. We present a clinically focused, streamlined virtual stenting workflow that efficiently simulates stent and FD treatment in patient-specific aneurysms based on expanding a simplex mesh structure. The simplex mesh is generated using an innovative vessel-specific initialization technique, which uses the patient’s parent artery diameter to identify the initial position of the simplex mesh inside the artery. A novel adaptive expansion algorithm enables the acceleration of deployment process by adjusting the expansion forces based on the distance of the simplex mesh from the parent vessel. The virtual stenting workflow was tested by modeling the treatment of two patient-specific aneurysms using the Enterprise stent and the Pipeline Embolization Device (commercial FD). Both devices were deployed in the aneurysm models in a few seconds. Computational fluid dynamics analyses of pre- and post-treatment aneurysmal hemodynamics show flow reduction in the aneurysmal sac in treated aneurysms, with the FD diverting more flow than the Enterprise stent. The test results show that this workflow can rapidly simulate clinical deployment of stents and FDs, hence paving the way for its future clinical implementation.     

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.