Modelling evolution and the evolving mechanical environment of saccular cerebral aneurysms

An updated Lagrangian constrained mixture model of pathological cardiac growth and remodelling

Progressive left ventricular (LV) growth and remodelling (G&R) is often induced by volume and pressure overload, characterized by structural and functional adaptation through myocyte hypertrophy and extracellular matrix remodelling, which are dynamically regulated by biomechanical factors, inflammation, neurohormonal pathways, etc. When prolonged, it can eventually lead to irreversible heart failure. In this study, we have developed a new framework for modelling pathological cardiac G&R based on constrained mixture theory using an updated reference configuration, which is triggered by altered biomechanical factors to restore biomechanical homeostasis. Eccentric and concentric growth, and their combination have been explored in a patient-specific human LV model under volume and pressure overload. Eccentric growth is triggered by overstretching of myofibres due to volume overload, i.e. mitral regurgitation, whilst concentric growth is driven by excessive contractile stress due to pressure overload, i.e. aortic stenosis. Different biological constituent's adaptations under pathological conditions are integrated together, which are the ground matrix, myofibres and collagen network. We have shown that this constrained mixture-motivated G&R model can capture different phenotypes of maladaptive LV G&R, such as chamber dilation and wall thinning under volume overload, wall thickening under pressure overload, and more complex patterns under both pressure and volume overload. We have further demonstrated how collagen G&R would affect LV structural and functional adaption by providing mechanistic insight on anti-fibrotic interventions. This updated Lagrangian constrained mixture based myocardial G&R model has the potential to understand the turnover processes of myocytes and collagen due to altered local mechanical stimuli in heart diseases, and in providing mechanistic links between biomechanical factors and biological adaption at both the organ and cellular levels. Once calibrated with patient data, it can be used for assessing heart failure risk and designing optimal treatment therapies. STATEMENT OF SIGNIFICANCE: Computational modelling of cardiac G&R has shown high promise to provide insight into heart disease management when mechanistic understandings are quantified between biomechanical factors and underlying cellular adaptation processes. The kinematic growth theory has been dominantly used to phenomenologically describe the biological G&R process but neglecting underlying cellular mechanisms. We have developed a constrained mixture based G&R model with updated reference by taking into account different mechanobiological processes in the ground matrix, myocytes and collagen fibres. This G&R model can serve as a basis for developing more advanced myocardial G&R models further informed by patient data to assess heart failure risk, predict disease progression, select the optimal treatment by hypothesis testing, and eventually towards a truly precision cardiology using in-silico models.

Computational analysis of effects of clot length on Acute ischemic stroke recanalization under different cyclic aspiration loading conditions

Acute ischemic stroke, the second leading cause of death worldwide, results from occlusion of a cerebral artery by a blood clot. Application of cyclic aspiration using an aspiration catheter is a current therapy for the removal of lodged clots. In this study, we perform finite element simulations to analyze deformation of long clots, having length to radius ratio of 2-10, which corresponds to clot-length of 2.85-14.25 mm, under peak-to-peak cyclic aspiration pressures of 10-50 mmHg, and frequencies of 0.5, 1, and 2 Hz. Our computational system comprises of a nonlinear viscoelastic solid clot, a hyperelastic artery, and a nonlinear viscoelastic cohesive zone, the latter modeling the clot-artery interface. We observe that clots having length-to-radius ratio approximately greater than two separate from the inner arterial surface somewhere between the axial and distal ends, irrespective of the cyclic aspiration loading conditions. The stress distribution within the clot shows large tensile stresses in the clot interior, indicating the possibility of simultaneous fragmentation of the clot. Thus, this study shows us the various failure mechanisms simultaneously present in the clot during cyclic aspiration. Similarly, the stress distribution within the artery implies a possibility of endothelial damage to the arterial wall near the end where the aspiration pressure is applied. This framework provides a foundation for further investigation to clot fracture and adhesion characterization.

Intracranial aneurysm wall (in)stability-current state of knowledge and clinical perspectives

Intracranial aneurysm (IA), a local outpouching of cerebral arteries, is present in 3 to 5% of the population. Once formed, an IA can remain stable, grow, or rupture. Determining the evolution of IAs is almost impossible. Rupture of an IA leads to subarachnoid hemorrhage and affects mostly young people with heavy consequences in terms of death, disabilities, and socioeconomic burden. Even if the large majority of IAs will never rupture, it is critical to determine which IA might be at risk of rupture. IA (in)stability is dependent on the composition of its wall and on its ability to repair. The biology of the IA wall is complex and not completely understood. Nowadays, the risk of rupture of an IA is estimated in clinics by using scores based on the characteristics of the IA itself and on the anamnesis of the patient. Classification and prediction using these scores are not satisfying and decisions whether a patient should be observed or treated need to be better informed by more reliable biomarkers. In the present review, the effects of known risk factors for rupture, as well as the effects of biomechanical forces on the IA wall composition, will be summarized. Moreover, recent advances in high-resolution vessel wall magnetic resonance imaging, which are promising tools to discriminate between stable and unstable IAs, will be described. Common data elements recently defined to improve IA disease knowledge and disease management will be presented. Finally, recent findings in genetics will be introduced and future directions in the field of IA will be exposed.

A pilot study on biaxial mechanical, collagen microstructural, and morphological characterizations of a resected human intracranial aneurysm tissue

Intracranial aneurysms (ICAs) are focal dilatations that imply a weakening of the brain artery. Incidental rupture of an ICA is increasingly responsible for significant mortality and morbidity in the American’s aging population. Previous studies have quantified the pressure-volume characteristics, uniaxial mechanical properties, and morphological features of human aneurysms. In this pilot study, for the first time, we comprehensively quantified the mechanical, collagen fiber microstructural, and morphological properties of one resected human posterior inferior cerebellar artery aneurysm. The tissue from the dome of a right posterior inferior cerebral aneurysm was first mechanically characterized using biaxial tension and stress relaxation tests. Then, the load-dependent collagen fiber architecture of the aneurysm tissue was quantified using an in-house polarized spatial frequency domain imaging system. Finally, optical coherence tomography and histological procedures were used to quantify the tissue’s microstructural morphology. Mechanically, the tissue was shown to exhibit hysteresis, a nonlinear stress-strain response, and material anisotropy. Moreover, the unloaded collagen fiber architecture of the tissue was predominantly aligned with the testing Y-direction and rotated towards the X-direction under increasing equibiaxial loading. Furthermore, our histological analysis showed a considerable damage to the morphological integrity of the tissue, including lack of elastin, intimal thickening, and calcium deposition. This new unified characterization framework can be extended to better understand the mechanics-microstructure interrelationship of aneurysm tissues at different time points of the formation or growth. Such specimen-specific information is anticipated to provide valuable insight that may improve our current understanding of aneurysm growth and rupture potential.

Adaptive Remodeling in the Elastase-induced Rabbit Aneurysms

BACKGROUND

Rupture of brain aneurysms is associated with high fatality and morbidity rates. Through remodeling of the collagen matrix, many aneurysms can remain unruptured for decades, despite an enlarging and evolving geometry.

OBJECTIVE

Our objective was to explore this adaptive remodeling for the first time in an elastase induced aneurysm model in rabbits.

METHODS

Saccular aneurysms were created in 22 New Zealand white rabbits and remodeling was assessed in tissue harvested 2, 4, 8 and 12 weeks after creation.

RESULTS

The intramural principal stress ratio doubled after aneurysm creation due to increased longitudinal loads, triggering a remodeling response. A distinct wall layer with multi-directional collagen fibers developed between the media and adventitia as early as 2 weeks, and in all cases by 4 weeks with an average thickness of 50.6 ± 14.3 μm. Collagen fibers in this layer were multi-directional (AI = 0.56 ± 0.15) with low tortuosity (1.08 ± 0.02) compared with adjacent circumferentially aligned medial fibers (AI = 0.78 ± 0.12) and highly tortuous adventitial fibers (1.22 ± 0.03). A second phase of remodeling replaced circumferentially aligned fibers in the inner media with longitudinal fibers. A structurally motivated constitutive model with both remodeling modes was introduced along with methodology for determining material parameters from mechanical testing and multiphoton imaging.

CONCLUSIONS

A new mechanism was identified by which aneurysm walls can rapidly adapt to changes in load, ensuring the structural integrity of the aneurysm until a slower process of medial reorganization occurs. The rabbit model can be used to evaluate therapies to increase aneurysm wall stability.

Modeling intracranial aneurysm stability and growth: an integrative mechanobiological framework for clinical cases

We present a novel patient-specific fluid-solid-growth framework to model the mechanobiological state of clinically detected intracranial aneurysms (IAs) and their evolution. The artery and IA sac are modeled as thick-walled, non-linear elastic fiber-reinforced composites. We represent the undulation distribution of collagen fibers: the adventitia of the healthy artery is modeled as a protective sheath whereas the aneurysm sac is modeled to bear load within physiological range of pressures. Initially, we assume the detected IA is stable and then consider two flow-related mechanisms to drive enlargement: (1) low wall shear stress; (2) dysfunctional endothelium which is associated with regions of high oscillatory flow. Localized collagen degradation and remodelling gives rise to formation of secondary blebs on the aneurysm dome. Restabilization of blebs is achieved by remodelling of the homeostatic collagen fiber stretch distribution. This integrative mechanobiological modelling workflow provides a step towards a personalized risk-assessment and treatment of clinically detected IAs.

Computational modeling of cardiac growth and remodeling in pressure overloaded hearts-Linking microstructure to organ phenotype

Cardiac growth and remodeling (G&R) refers to structural changes in myocardial tissue in response to chronic alterations in loading conditions. One such condition is pressure overload where elevated wall stresses stimulate the growth in cardiomyocyte thickness, associated with a phenotype of concentric hypertrophy at the organ scale, and promote fibrosis. The initial hypertrophic response can be considered adaptive and beneficial by favoring myocyte survival, but over time if pressure overload conditions persist, maladaptive mechanisms favoring cell death and fibrosis start to dominate, ultimately mediating the transition towards an overt heart failure phenotype. The underlying mechanisms linking biological factors at the myocyte level to biomechanical factors at the systemic and organ level remain poorly understood. Computational models of G&R show high promise as a unique framework for providing a quantitative link between myocardial stresses and strains at the organ scale to biological regulatory processes at the cellular level which govern the hypertrophic response. However, microstructurally motivated, rigorously validated computational models of G&R are still in their infancy. This article provides an overview of the current state-of-the-art of computational models to study cardiac G&R. The microstructure and mechanosensing/mechanotransduction within cells of the myocardium is discussed and quantitative data from previous experimental and clinical studies is summarized. We conclude with a discussion of major challenges and possible directions of future research that can advance the current state of cardiac G&R computational modeling. STATEMENT OF SIGNIFICANCE: The mechanistic links between organ-scale biomechanics and biological factors at the cellular size scale remain poorly understood as these are largely elusive to investigations using experimental methodology alone. Computational G&R models show high promise to establish quantitative links which allow more mechanistic insight into adaptation mechanisms and may be used as a tool for stratifying the state and predict the progression of disease in the clinic. This review provides a comprehensive overview of research in this domain including a summary of experimental data. Thus, this study may serve as a basis for the further development of more advanced G&R models which are suitable for making clinical predictions on disease progression or for testing hypotheses on pathogenic mechanisms using in-silico models.

Plasma Soluble Human Elastin Fragments as an Intra-Aneurysmal Localized Biomarker for Ruptured Intracranial Aneurysm

Background Fragmentation of the tunica media is a hallmark of intracranial aneurysm formation, often leading to aneurysmal progression and subsequent rupture. The objective of this study is to determine the plasma level of elastin fragments in the lumen of ruptured versus unruptured human intracranial aneurysms. Methods and Results One hundred consecutive patients with/without ruptured saccular intracranial aneurysms undergoing endovascular coiling or stent-assisted coiling were recruited. Blood samples were collected from the lumen of intracranial aneurysm using a microcatheter. The tip of the microcatheter was placed inside the aneurysm's sac in close proximity to the inner wall of the dome. Plasma levels of elastin fragments were measured using an ELISA -based method. Mean plasma level of soluble human elastin fragments was significantly greater in ruptured aneurysms when compared with nonruptured aneurysms (102.0±15.5 versus 39.3±9.6 ng/mL; P<0.001). Mean plasma level of soluble human elastin fragments did not have significant correlation with age, sex, size, or aneurysm location. Conclusions The present study revealed that a significantly higher concentration of soluble human elastin fragments in the lumen of ruptured intracranial aneurysms when compared with nonruptured ones.

Structural modelling of the cardiovascular system

Computational modelling of the cardiovascular system offers much promise, but represents a truly interdisciplinary challenge, requiring knowledge of physiology, mechanics of materials, fluid dynamics and biochemistry. This paper aims to provide a summary of the recent advances in cardiovascular structural modelling, including the numerical methods, main constitutive models and modelling procedures developed to represent cardiovascular structures and pathologies across a broad range of length and timescales; serving as an accessible point of reference to newcomers to the field. The class of so-called hyperelastic materials provides the theoretical foundation for the modelling of how these materials deform under load, and so an overview of these models is provided; comparing classical to application-specific phenomenological models. The physiology is split into components and pathologies of the cardiovascular system and linked back to constitutive modelling developments, identifying current state of the art in modelling procedures from both clinical and engineering sources. Models which have originally been derived for one application and scale are shown to be used for an increasing range and for similar applications. The trend for such approaches is discussed in the context of increasing availability of high performance computing resources, where in some cases computer hardware can impact the choice of modelling approach used.

Phase-contrast MRI versus numerical simulation to quantify hemodynamical changes in cerebral aneurysms after flow diverter treatment

Cerebral aneurysms are a major risk factor for intracranial bleeding with devastating consequences for the patient. One recently established treatment is the implantation of flow-diverters (FD). Methods to predict their treatment success before or directly after implantation are not well investigated yet. The aim of this work was to quantitatively study hemodynamic parameters in patient-specific models of treated cerebral aneurysms and its correlation with the clinical outcome. Hemodynamics were evaluated using both computational fluid dynamics (CFD) and phase contrast (PC) MRI. CFD simulations and in vitro MRI measurements were done under similar flow conditions and results of both methods were comparatively analyzed. For preoperative and postoperative distribution of hemodynamic parameters, CFD simulations and PC-MRI velocity measurements showed similar results. In both cases where no occlusion of the aneurysm was observed after six months, a flow reduction of about 30-50% was found, while in the clinically successful case with complete occlusion of the aneurysm after 6 months, the flow reduction was about 80%. No vortex was observed in any of the three models after treatment. The results are in agreement with recent studies suggesting that CFD simulations can predict post-treatment aneurysm flow alteration already before implantation of a FD and PC-MRI could validate the predicted hemodynamic changes right after implantation of a FD.

A homogenized constrained mixture (and mechanical analog) model for growth and remodeling of soft tissue

Most mathematical models of the growth and remodeling of load-bearing soft tissues are based on one of two major approaches: a kinematic theory that specifies an evolution equation for the stress-free configuration of the tissue as a whole or a constrained mixture theory that specifies rates of mass production and removal of individual constituents within stressed configurations. The former is popular because of its conceptual simplicity, but relies largely on heuristic definitions of growth; the latter is based on biologically motivated micromechanical models, but suffers from higher computational costs due to the need to track all past configurations. In this paper, we present a temporally homogenized constrained mixture model that combines advantages of both classical approaches, namely a biologically motivated micromechanical foundation, a simple computational implementation, and low computational cost. As illustrative examples, we show that this approach describes well both cell-mediated remodeling of tissue equivalents in vitro and the growth and remodeling of aneurysms in vivo. We also show that this homogenized constrained mixture model suggests an intimate relationship between models of growth and remodeling and viscoelasticity. That is, important aspects of tissue adaptation can be understood in terms of a simple mechanical analog model, a Maxwell fluid (i.e., spring and dashpot in series) in parallel with a "motor element" that represents cell-mediated mechanoregulation of extracellular matrix. This analogy allows a simple implementation of homogenized constrained mixture models within commercially available simulation codes by exploiting available models of viscoelasticity.

Growth and Remodeling of Load-Bearing Biological Soft Tissues

The past two decades reveal a growing role of continuum biomechanics in understanding homeostasis, adaptation, and disease progression in soft tissues. In this paper, we briefly review the two primary theoretical approaches for describing mechano-regulated soft tissue growth and remodeling on the continuum level as well as hybrid approaches that attempt to combine the advantages of these two approaches while avoiding their disadvantages. We also discuss emerging concepts, including that of mechanobiological stability. Moreover, to motivate and put into context the different theoretical approaches, we briefly review findings from mechanobiology that show the importance of mass turnover and the prestressing of both extant and new extracellular matrix in most cases of growth and remodeling. For illustrative purposes, these concepts and findings are discussed, in large part, within the context of two load-bearing, collagen dominated soft tissues - tendons/ligaments and blood vessels. We conclude by emphasizing further examples, needs, and opportunities in this exciting field of modeling soft tissues.

Characterizations and Correlations of Wall Shear Stress in Aneurysmal Flow

Wall shear stress (WSS) is one of the most studied hemodynamic parameters, used in correlating blood flow to various diseases. The pulsatile nature of blood flow, along with the complex geometries of diseased arteries, produces complicated temporal and spatial WSS patterns. Moreover, WSS is a vector, which further complicates its quantification and interpretation. The goal of this study is to investigate WSS magnitude, angle, and vector changes in space and time in complex blood flow. Abdominal aortic aneurysm (AAA) was chosen as a setting to explore WSS quantification. Patient-specific computational fluid dynamics (CFD) simulations were performed in six AAAs. New WSS parameters are introduced, and the pointwise correlation among these, and more traditional WSS parameters, was explored. WSS magnitude had positive correlation with spatial/temporal gradients of WSS magnitude. This motivated the definition of relative WSS gradients. WSS vectorial gradients were highly correlated with magnitude gradients. A mix WSS spatial gradient and a mix WSS temporal gradient are proposed to equally account for variations in the WSS angle and magnitude in single measures. The important role that WSS plays in regulating near wall transport, and the high correlation among some of the WSS parameters motivates further attention in revisiting the traditional approaches used in WSS characterizations.

Biology of Saccular Cerebral Aneurysms: A Review of Current Understanding and Future Directions

Understanding the biology of intracranial aneurysms is a clinical quandary. How these aneurysms form, progress, and rupture is poorly understood. Evidence indicates that well-established risk factors play a critical role, along with immunologic factors, in their development and clinical outcomes. Much of the expanding knowledge of the inception, progression, and rupture of intracranial aneurysms implicates inflammation as a critical mediator of aneurysm pathogenesis. Thus, therapeutic targets exploiting this arm of aneurysm pathogenesis have been implemented, often with promising outcomes.

On the effect of preload and pre-stretch on hemodynamic simulations: an integrative approach

In this work, we address the simulation of three-dimensional arterial blood flow and its effect on the stress state of arterial walls. The novel contribution is the unprecedented combination of several modeling techniques to account for (1) the fact that known configurations for the arterial wall are in a preloaded state, (2) the compliance of the vessel segments, (3) proper boundary data over the non-physical interfaces resulting from the isolation of an arterial district from the rest of the arterial tree, (4) the presence of surrounding tissues in which the vessel is embedded and (5) residual stress state due to pre-stretch. Firstly, we formulate both the forward mechanical problem when the reference (zero-load) configuration is assumed to be known and, the preload problem arising when the known domain is a configuration at equilibrium with a certain load state (typically due to internal pressure and tethering forces). Then, two additional complexities are faced: the fluid-structure interaction problem that follows when the compliant vessels are coupled with the blood flow, and the introduction of non-physical boundaries coming from the artificial isolation of the arterial district from the original vessel. This, in turn, posses the problem of coupling dimensionally heterogeneous models to incorporate the effect of upstream and downstream systemic impedances. Additionally, a viscoelastic support on the external surface of the vessel is also incorporated. Two examples are presented to quantify in a physiologically consistent scenario the differences in simulation results when either considering or not the preload state of arterial walls. These computational simulations shed light on the validity of simplifying hypotheses in most hemodynamic models.

A 3D MODEL FOR MURAL-CELL-MEDIATED DESTRUCTIVE REMODELING DURING EARLY DEVELOPMENT OF A CEREBRAL ANEURYSM

Development of a diagnostic tool for predicting the behavior of cerebral aneurysms was the inspiration of many research groups in recent years. In the present study a fluid–solid-growth (FSG) model for the early development of a cerebral aneurysm was presented in a 3D model of the internal carotid artery (ICA). This model is the result of two parallel mechanisms: first, defining arterial wall as a living tissue with the ability of degradation, growth and remodeling and second, full coupling of the wall and the blood flow. Taking into account the shear dependent nature of elastin degradation and mural-cell-mediated destructive activities, here, the degradation process has been linked to high effective stress of the vascular wall. The evolving properties of the elastinous and collagenous constituents have been predicted during the early development of the aneurysm and the code is applicable to more complicated aneurismal growth models.

A Thick-Walled Fluid–Solid-Growth Model of Abdominal Aortic Aneurysm Evolution: Application to a Patient-Specific Geometry

We propose a novel thick-walled fluid–solid-growth (FSG) computational framework for modeling vascular disease evolution. The arterial wall is modeled as a thick-walled nonlinearly elastic cylindrical tube consisting of two layers corresponding to the media-intima and adventitia, where each layer is treated as a fiber-reinforced material with the fibers corresponding to the collagenous component. Blood is modeled as a Newtonian fluid with constant density and viscosity; no slip and no-flux conditions are applied at the arterial wall. Disease progression is simulated by growth and remodeling (G&R) of the load bearing constituents of the wall. Adaptions of the natural reference configurations and mass densities of constituents are driven by deviations of mechanical stimuli from homeostatic levels. We apply the novel framework to model abdominal aortic aneurysm (AAA) evolution. Elastin degradation is initially prescribed to create a perturbation to the geometry which results in a local decrease in wall shear stress (WSS). Subsequent degradation of elastin is driven by low WSS and an aneurysm evolves as the elastin degrades and the collagen adapts. The influence of transmural G&R of constituents on the aneurysm development is analyzed. We observe that elastin and collagen strains evolve to be transmurally heterogeneous and this may facilitate the development of tortuosity. This multiphysics framework provides the basis for exploring the influence of transmural metabolic activity on the progression of vascular disease.

Investigation of material modeling in fluid-structure interaction analysis of an idealized three-layered abdominal aorta: aneurysm initiation and fully developed aneurysms

Different material models for an idealized three-layered abdominal aorta are compared using computational techniques to study aneurysm initiation and fully developed aneurysms. The computational model includes fluid-structure interaction (FSI) between the blood vessel and the blood. In order to model aneurysm initiation, the medial region was degenerated to mimic the medial loss occurring in the inception of an aneurysm. Various cases are considered in order to understand their effects on the initiation of an abdominal aortic aneurysm. The layers of the blood vessel were modeled using either linear elastic materials or Mooney-Rivlin (otherwise known as hyperelastic) type materials. The degenerated medial region was also modeled in either linear elastic or hyperelastic-type materials and assumed to be in the shape of an arc with a thin width or a circular ring with different widths. The blood viscosity effect was also considered in the initiation mechanism. In addition, dynamic analysis of the blood vessel was performed without interaction with the blood flow by applying time-dependent pressure inside the lumen in a three-layered abdominal aorta. The stresses, strains, and displacements were compared for a healthy aorta, an initiated aneurysm and a fully developed aneurysm. The study shows that the material modeling of the vessel has a sizable effect on aneurysm initiation and fully developed aneurysms. Different material modeling of degeneration regions also affects the stress-strain response of aneurysm initiation. Additionally, the structural analysis without considering FSI (called noFSI) overestimates the peak von Mises stress by 52% at the interfaces of the layers.

Microstructural modelling of cerebral aneurysm evolution through effective stress mediated destructive remodelling

Recently, researchers have shown an increased interest in the biomechanical modelling of cerebral aneurysm development. In the present study a fluid-solid-growth model for the formation of a fusiform aneurysm has been presented in an axi-symmetric geometry of the internal carotid artery. This model is the result of two parallel mechanisms: first, defining arterial wall as a living tissue with the ability of degradation, growth and remodelling and second, full coupling of the wall and the blood flow. Here for the first time the degradation of elastin has been defined as a function of vascular wall effective stress to take into account the shear dependent nature of degradation and the mural-cell-mediated destructive activities. The model has been stabilized in size and mechanical properties and is consistent with other computational or clinical studies. Furthermore, the evolving microstructural properties of the wall during the evolution process have been predicted.

Modelling the influence of endothelial heterogeneity on the progression of arterial disease: application to abdominal aortic aneurysm evolution

We sophisticate a fluid-solid growth computational framework for modelling aneurysm evolution. A realistic structural model of the arterial wall is integrated into a patient-specific geometry of the vasculature. This enables physiologically representative distributions of haemodynamic stimuli, obtained from a rigid-wall computational fluid dynamics analysis, to be linked to growth and remodelling algorithms. Additionally, a quasistatic structural analysis quantifies the cyclic deformation of the arterial wall so that collagen growth and remodelling can be explicitly linked to the cyclic deformation of vascular cells. To simulate aneurysm evolution, degradation of elastin is driven by reductions in wall shear stress (WSS) below homeostatic thresholds. Given that the endothelium exhibits spatial and temporal heterogeneity, we propose a novel approach to define the homeostatic WSS thresholds: We allow them to be spatially and temporally heterogeneous. We illustrate the application of this novel fluid-solid growth framework to model abdominal aortic aneurysm (AAA) evolution and to examine how the influence of the definition of the WSS homeostatic threshold influences AAA progression. We conclude that improved understanding and modelling of the endothelial heterogeneity is important for modelling aneurysm evolution and, more generally, other vascular diseases where haemodynamic stimuli play an important role.

Evaluation of cerebral aneurysm wall thickness in experimental aneurysms: comparison of 3T-MR imaging with direct microscopic measurements

BACKGROUND

Thin aneurysm wall thickness (AWT) is thought to portend an elevated risk of intracranial aneurysm rupture. Magnetic resonance imaging (MRI) is biased by AWT overestimations. Previously, this suspected bias has been qualitatively described but never quantified. We aimed to quantify the overestimation of AWT by MRI when compared to the gold standard of AWT as measured by light microscopy of fresh aneurysm specimens (without any embedding procedure). This analysis should help to define the clinical potential of MRI estimates of AWT.

METHODS

3-Tesla (3T) MRI (contrast-enhanced T1 Flash sequences; resolution: 0.4 x 0.4 x 1.5 mm(3)) was performed in 13 experimental aneurysms. After MR acquisition, the aneurysms were retrieved, longitudinally sectioned and calibrated micrographs were obtained immediately. AWT at the dome, AWT at the neck and parent vessel wall thickness (PVT) were measured on precisely correlated MR-images and histologic micrographs by blinded independent investigators. Parameters were statistically compared (Wilcoxon test, Spearman's correlation).

RESULTS

AWT was assessed and reliably measured using MRI. Interobserver variability was not significant for either method. MR overestimation was only significant below the image resolution threshold: AWT at the dome (0.24 ± 0.06 mm vs. MR 0.30 ± 0.08 mm; p = 0.0078; R = 0.6125), AWT at the neck (0.25 ± 0.07 mm vs. MR 0.29 ± 0.07 mm; p = 0.0469; R = 0.7451), PVT (0.46 ± 0.06 mm vs. MR 0.48 ± 0.06 mm; p = 0.5; R = 0.8568).

CONCLUSION

In this experimental setting, MR overestimations were minimal (mean 0.02 mm) above the image resolution threshold. When AWT is classified in ranges defined by the MR resolution threshold, clinical usage may be beneficial. Further quantitative and comparative experimental and human studies are warranted to confirm these findings.

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.

CFD: computational fluid dynamics or confounding factor dissemination? The role of hemodynamics in intracranial aneurysm rupture risk assessment

Image-based computational fluid dynamics holds a prominent position in the evaluation of intracranial aneurysms, especially as a promising tool to stratify rupture risk. Current computational fluid dynamics findings correlating both high and low wall shear stress with intracranial aneurysm growth and rupture puzzle researchers and clinicians alike. These conflicting findings may stem from inconsistent parameter definitions, small datasets, and intrinsic complexities in intracranial aneurysm growth and rupture. In Part 1 of this 2-part review, we proposed a unifying hypothesis: both high and low wall shear stress drive intracranial aneurysm growth and rupture through mural cell-mediated and inflammatory cell-mediated destructive remodeling pathways, respectively. In the present report, Part 2, we delineate different wall shear stress parameter definitions and survey recent computational fluid dynamics studies, in light of this mechanistic heterogeneity. In the future, we expect that larger datasets, better analyses, and increased understanding of hemodynamic-biologic mechanisms will lead to more accurate predictive models for intracranial aneurysm risk assessment from computational fluid dynamics.

Physical factors effecting cerebral aneurysm pathophysiology

Many factors that are either blood-, wall-, or hemodynamics-borne have been associated with the initiation, growth, and rupture of intracranial aneurysms. The distribution of cerebral aneurysms around the bifurcations of the circle of Willis has provided the impetus for numerous studies trying to link hemodynamic factors (flow impingement, pressure, and/or wall shear stress) to aneurysm pathophysiology. The focus of this review is to provide a broad overview of such hemodynamic associations as well as the subsumed aspects of vascular anatomy and wall structure. Hemodynamic factors seem to be correlated to the distribution of aneurysms on the intracranial arterial tree and complex, slow flow patterns seem to be associated with aneurysm growth and rupture. However, both the prevalence of aneurysms in the general population and the incidence of ruptures in the aneurysm population are extremely low. This suggests that hemodynamic factors and purely mechanical explanations by themselves may serve as necessary, but never as necessary and sufficient conditions of this disease's causation. The ultimate cause is not yet known, but it is likely an additive or multiplicative effect of a handful of biochemical and biomechanical factors.

Turnover of fibrillar collagen in soft biological tissue with application to the expansion of abdominal aortic aneurysms

A better understanding of the inherent properties of vascular tissue to adapt to its mechanical environment is crucial to improve the predictability of biomechanical simulations. Fibrillar collagen in the vascular wall plays a central role in tissue adaptation owing to its relatively short lifetime. Pathological alterations of collagen turnover may fail to result in homeostasis and could be responsible for abdominal aortic aneurysm (AAA) growth at later stages of the disease. For this reason our previously reported multiscale constitutive framework (Martufi, G. & Gasser, T. C. 2011 J. Biomech. 44, 2544-2550 (doi:10.1016/j.jbiomech.2011.07.015)) has been enriched by a collagen turnover model. Specifically, the framework's collagen fibril level allowed a sound integration of vascular wall biology, and the impact of collagen turnover on the macroscopic properties of AAAs was studied. To this end, model parameters were taken from the literature and/or estimated from clinical follow-up data of AAAs (on average 50.7 mm-large). Likewise, the in vivo stretch of the AAA wall was set, such that 10 per cent of collagen fibres were engaged. Results showed that the stretch spectrum, at which collagen fibrils are deposed, is the most influential parameter, i.e. it determines whether the vascular geometry grows, shrinks or remains stable over time. Most importantly, collagen turnover also had a remarkable impact on the macroscopic stress field. It avoided high stress gradients across the vessel wall, thus predicted a physiologically reasonable stress field. Although the constitutive model could be successfully calibrated to match the growth of small AAAs, a rigorous validation against experimental data is crucial to further explore the model's descriptive and predictive capabilities.

Multiscale modeling of intracranial aneurysms: cell signaling, hemodynamics, and remodeling

The genesis, growth, and rupture of intracranial aneurysms (IAs) involve physics at the molecular, cellular, blood vessel, and organ levels that occur over time scales ranging from seconds to years. Comprehensive mathematical modeling of IAs, therefore, requires the description and integration of events across length and time scales that span many orders of magnitude. In this letter, we outline a strategy for mulstiscale modeling of IAs that involves the construction of individual models at each relevant scale and their subsequent combination into an integrative model that captures the overall complexity of IA development. An example of the approach is provided using three models operating at different length and time scales: 1) shear stress induced nitric oxide production; 2) smooth muscle cell apoptosis; and 3) fluid-structure-growth modeling. A computational framework for combining them is presented. We conclude with a discussion of the advantages and challenges of the approach.