How does hemodynamics affect rupture tissue mechanics in abdominal aortic aneurysm: Focus on wall shear stress derived parameters, time-averaged wall shear stress, oscillatory shear index, endothelial cell activation potential, and relative residence time

An abdominal aortic aneurysm (AAA) is a critical health condition with a risk of rupture, where the diameter of the aorta enlarges more than 50% of its normal diameter. The incidence rate of AAA has increased worldwide. Currently, about three out of every 100,000 people have aortic diseases. The diameter and geometry of AAAs influence the hemodynamic forces exerted on the arterial wall. Therefore, a reliable assessment of hemodynamics is crucial for predicting the rupture risk. Wall shear stress (WSS) is an important metric to define the level of the frictional force on the AAA wall. Excessive levels of WSS deteriorate the remodeling mechanism of the arteries and lead to abnormal conditions. At this point, WSS-related hemodynamic parameters, such as time-averaged WSS (TAWSS), oscillatory shear index (OSI), endothelial cell activation potential (ECAP), and relative residence time (RRT) provide important information to evaluate the shear environment on the AAA wall in detail. Calculation of these parameters is not straightforward and requires a physical understanding of what they represent. In addition, computational fluid dynamics (CFD) solvers do not readily calculate these parameters when hemodynamics is simulated. This review aims to explain the WSS-derived parameters focusing on how these represent different characteristics of disturbed hemodynamics. A representative case is presented for spatial and temporal formulation that would be useful for interested researchers for practical calculations. Finally, recent hemodynamics investigations relating WSS-related parameters with AAA rupture risk assessment are presented. This review will be useful to understand the physical representation of WSS-related parameters in cardiovascular flows and how they can be calculated practically for AAA investigations.

A predictive hemodynamic model based on risk factors for ruptured mirror aneurysms

Objectives

To identify hemodynamic risk factors for intracranial aneurysm rupture and establish a predictive model to aid evaluation.

Methods

We analyzed the hemodynamic parameters of 91 pairs of ruptured mirror aneurysms. A conditional univariate analysis was used for the continuous variables. A conditional multivariate logistic regression analysis was performed to identify the independent risk factors. Differences where p < 0.05 were statistically significant. A predictive model was established based on independent risk factors. Odds ratios (ORs) were used to score points. The validation cohort consisted of 189 aneurysms. Receiver operating characteristic curves were generated to determine the cutoff values and area under the curves (AUCs) of the predictive model and independent risk factors.

Results

The conditional multivariate logistic analysis showed that the low shear area (LSA) (OR = 70.322, p = 0.044, CI = 1.112–4,445.256), mean combined hemodynamic parameter (CHP) (>0.087) (OR = 3.171, p = 0.034, CI = 1.089–9.236), and wall shear stress gradient (WSSG) ratio (>893.180) (OR = 5.740, p = 0.003, CI = 1.950–16.898) were independent risk factors. A prediction model was established: 23^*LSA + 1^*CHP mean (>0.087: yes = 1, no = 0) + 2 ^* WSSG ratio (>893.180: yes = 1, no = 0). The AUC values of the predictive model, LSA, mean CHP (>0.087), and WSSG ratio (>893.180) were 0.748, 0.700, 0.654, and 0.703, respectively. The predictive model and LSA cutoff values were 1.283 and 0.016, respectively. In the validation cohort, the predictive model, LSA, CHP (>0.087), and WSSG ratio (>893.180) were 0.736, 0.702, 0.689, and 0.706, respectively.

Conclusions

LSA, CHP (>0.087), and WSSG ratio (>893.180) were independent risk factors for aneurysm rupture. Our predictive model could aid practical evaluation.

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.

Cell signaling model for arterial mechanobiology

Arterial growth and remodeling at the tissue level is driven by mechanobiological processes at cellular and sub-cellular levels. Although it is widely accepted that cells seek to promote tissue homeostasis in response to biochemical and biomechanical cues—such as increased wall stress in hypertension—the ways by which these cues translate into tissue maintenance, adaptation, or maladaptation are far from understood. In this paper, we present a logic-based computational model for cell signaling within the arterial wall, aiming to predict changes in extracellular matrix turnover and cell phenotype in response to pressure-induced wall stress, flow-induced wall shear stress, and exogenous sources of angiotensin II, with particular interest in mouse models of hypertension. We simulate a number of experiments from the literature at both the cell and tissue level, involving single or combined inputs, and achieve high qualitative agreement in most cases. Additionally, we demonstrate the utility of this modeling approach for simulating alterations (in this case knockdowns) of individual nodes within the signaling network. Continued modeling of cellular signaling will enable improved mechanistic understanding of arterial growth and remodeling in health and disease, and will be crucial when considering potential pharmacological interventions.

Biological soft tissues are characterized by continuous production and removal of material, which endows them with a remarkable ability to adapt to changes in their biochemical and biomechanical environments. For arteries, mechanical stimuli result primarily from changes in blood pressure or flow, and biochemical changes are induced by multiple factors, including pharmacological intervention. In order to understand how arterial properties are maintained in health, or how they adapt or fail to adapt in disease, we must understand better how these diverse stimuli affect material turnover. Extracellular matrix is tightly regulated by mechano-sensing and mechano-regulation, and therefore cell signaling, thus we present a computational model of relevant signaling pathways within the vascular wall, with the aim of predicting changes in wall composition and function in response to three main inputs: pressure-induced wall stress, flow-induced wall shear stress, and exogenous angiotensin II. We obtain qualitative agreement with a range of experimental studies from the literature, and provide illustrative examples demonstrating how such models can be used to further our understanding of arterial remodeling.

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.

Degradation and erosion mechanisms of bioresorbable porous acellular vascular grafts: an in vitro investigation

A fundamental mechanism of in situ tissue regeneration from biodegradable synthetic acellular vascular grafts is the effective interplay between graft degradation, erosion and the production of extracellular matrix. In order to understand this crucial process of graft erosion and degradation, we conducted an in vitro investigation of grafts (n = 4 at days 1, 4, 7, 10 each) exposed to enzymatic degradation. Herein, we provide constitutive relationships for mass loss and mechanical properties based on much-needed experimental data. Furthermore, we formulate a mathematical model to provide a physics-based framework for understanding graft erosion. A novel finding is that despite their porous nature, grafts lost mass exponentially via surface erosion demonstrating a 20% reduction in outer diameter and no significant change in apparent density. A diffusion based, concentration gradient-driven mechanistic model of mass loss through surface erosion was introduced which can be extended to an in vivo setting through the use of two degradation parameters. Furthermore, notably, mechanical properties of degrading grafts did not scale with mass loss. Thus, we introduced a damage function scaling a neo-Hookean model to describe mechanical properties of the degrading graft; a refinement to existing mass-dependent growth and remodelling (G&R) models. This framework can be used to improve accuracy of well-established G&R theories in biomechanics; tools that predict evolving structure-function relationships of neotissues and guide graft design.

Understanding Angiography-Based Aneurysm Flow Fields through Comparison with Computational Fluid Dynamics

BACKGROUND AND PURPOSE

Hemodynamics is thought to be an important factor for aneurysm progression and rupture. Our aim was to evaluate whether flow fields reconstructed from dynamic angiography data can be used to realistically represent the main flow structures in intracranial aneurysms.

MATERIALS AND METHODS

DSA-based flow reconstructions, obtained during interventional treatment, were compared qualitatively with flow fields obtained from patient-specific computational fluid dynamics models and quantitatively with projections of the computational fluid dynamics fields (by computing a directional similarity of the vector fields) in 15 cerebral aneurysms.

RESULTS

The average similarity between the DSA and the projected computational fluid dynamics flow fields was 78% in the parent artery, while it was only 30% in the aneurysm region. Qualitatively, both the DSA and projected computational fluid dynamics flow fields captured the location of the inflow jet, the main vortex structure, the intrasaccular flow split, and the main rotation direction in approximately 60% of the cases.

CONCLUSIONS

Several factors affect the reconstruction of 2D flow fields from dynamic angiography sequences. The most important factors are the 3-dimensionality of the intrasaccular flow patterns and inflow jets, the alignment of the main vortex structure with the line of sight, the overlapping of surrounding vessels, and possibly frame rate undersampling. Flow visualization with DSA from >1 projection is required for understanding of the 3D intrasaccular flow patterns. Although these DSA-based flow quantification techniques do not capture swirling or secondary flows in the parent artery, they still provide a good representation of the mean axial flow and the corresponding flow rate.

Endoleak Assessment Using Computational Fluid Dynamics and Image Processing Methods in Stented Abdominal Aortic Aneurysm Models

Endovascular aortic aneurysm repair (EVAR) is a predominant surgical procedure to reduce the risk of aneurysm rupture in abdominal aortic aneurysm (AAA) patients. Endoleak formation, which eventually requires additional surgical reoperation, is a major EVAR complication. Understanding the etiology and evolution of endoleak from the hemodynamic perspective is crucial to advancing the current posttreatments for AAA patients who underwent EVAR. Therefore, a comprehensive flow assessment was performed to investigate the relationship between endoleak and its surrounding pathological flow fields through computational fluid dynamics and image processing. Six patient-specific models were reconstructed, and the associated hemodynamics in these models was quantified three-dimensionally to calculate wall stress. To provide a high degree of clinical relevance, the mechanical stress distribution calculated from the models was compared with the endoleak positions identified from the computed tomography images of patients through a series of imaging processing methods. An endoleak possibly forms in a location with high local wall stress. An improved stent graft (SG) structure is conceived accordingly by increasing the mechanical strength of the SG at peak wall stress locations. The presented analytical paradigm, as well as numerical analysis using patient-specific models, may be extended to other common human cardiovascular surgeries.

Stability analysis of a continuum-based constrained mixture model for vascular growth and remodeling

A stabilizing criterion is derived for equations governing vascular growth and remodeling. We start from the integral state equations of the continuum-based constrained mixture theory of vascular growth and remodeling and obtain a system of time-delayed differential equations describing vascular growth. By employing an exponential form of the constituent survival function, the delayed differential equations can be reduced to a nonlinear ODE system. We demonstrate the degeneracy of the linearized system about the homeostatic state, which is a fundamental cause of the neutral stability observations reported in prior studies. Due to this degeneracy, stability conclusions for the original nonlinear system cannot be directly inferred. To resolve this problem, a sub-system is constructed by recognizing a linear relation between two states. Subsequently, Lyapunov's indirect method is used to connect stability properties between the linearized system and the original nonlinear system, to rigorously establish the neutral stability properties of the original system. In particular, this analysis leads to a stability criterion for vascular expansion in terms of growth and remodeling kinetic parameters, geometric quantities and material properties. Numerical simulations were conducted to evaluate the theoretical stability criterion under broader conditions, as well as study the influence of key parameters and physical factors on growth properties. The theoretical results are also compared with prior numerical and experimental findings in the literature.

Transitional flow in aneurysms and the computation of haemodynamic parameters

Haemodynamic forces appear to play an influential role in the evolution of aneurysms. This has led to numerous studies, usually based on computational fluid dynamics. Their focus is predominantly on the wall shear stress (WSS) and associated derived parameters, attempting to find correlations between particular patterns of haemodynamic indices and regions subjected to disease formation and progression. The indices are generally determined by integration of flow properties over a single cardiac cycle. In this study, we illustrate that in some cases the transitional flow in aneurysms can lead to significantly different WSS distributions in consecutive cardiac cycles. Accurate determination of time-averaged haemodynamic indices may thus require simulation of a large number of cycles, which contrasts with the common approach to determine parameters using data from a single cycle. To demonstrate the role of transitional flow, two exemplary cases are considered: flow in an abdominal aortic aneurysm and in an intracranial aneurysm. The key differences that are observed between these cases are explained in terms of the integral timescale of the transitional flows in comparison with the cardiac cycle duration: for relatively small geometries, transients will decay before the next cardiac cycle. In larger geometries, transients are still present when the systolic phase produces new instabilities. These residual fluctuations serve as random initial conditions and thus seed different flow patterns in each cycle. To judge whether statistics are converged, the derived indices from at least two successive cardiac cycles should be compared.

Coupled Simulation of Hemodynamics and Vascular Growth and Remodeling in a Subject-Specific Geometry

A computational framework to couple vascular growth and remodeling (G&R) with blood flow simulation in a 3D patient-specific geometry is presented. Hyperelastic and anisotropic properties are considered for the vessel wall material and a constrained mixture model is used to represent multiple constituents in the vessel wall, which was modeled as a membrane. The coupled simulation is divided into two time scales-a longer time scale for G&R and a shorter time scale for fluid dynamics simulation. G&R is simulated to evolve the boundary of the fluid domain, and fluid simulation is in turn used to generate wall shear stress and transmural pressure data that regulates G&R. To minimize required computation cost, the fluid dynamics are only simulated when G&R causes significant vascular geometric change. For demonstration, this coupled model was used to study the influence of stress-mediated growth parameters, and blood flow mechanics, on the behavior of the vascular tissue growth in a model of the infrarenal aorta derived from medical image data.

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.

Which spring is the best? Comparison of methods for virtual stenting

This paper presents a methodology for modeling the deployment of implantable devices used in minimally invasive vascular interventions. Motivated by the clinical need to perform preinterventional rehearsals of a stent deployment, we have developed methods enabling virtual device placement inside arteries, under the constraint of real-time application. This requirement of rapid execution narrowed down the search for a suitable method to the concept of a dynamic mesh. Inspired by the idea of a mesh of springs, we have found a novel way to apply it to stent modeling. The experiments conducted in this paper investigate properties of the stent models based on three different spring types: lineal, semitorsional, and torsional springs. Furthermore, this paper compares the results of various deployment scenarios for two different classes of devices: a stent graft and a flow diverter. The presented results can be of a high-potential clinical value, enabling the predictive evaluation of the outcome of a stent deployment treatment.

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.

Mechanics of the brain: perspectives, challenges, and opportunities

The human brain is the continuous subject of extensive investigation aimed at understanding its behavior and function. Despite a clear evidence that mechanical factors play an important role in regulating brain activity, current research efforts focus mainly on the biochemical or electrophysiological activity of the brain. Here, we show that classical mechanical concepts including deformations, stretch, strain, strain rate, pressure, and stress play a crucial role in modulating both brain form and brain function. This opinion piece synthesizes expertise in applied mathematics, solid and fluid mechanics, biomechanics, experimentation, material sciences, neuropathology, and neurosurgery to address today’s open questions at the forefront of neuromechanics. We critically review the current literature and discuss challenges related to neurodevelopment, cerebral edema, lissencephaly, polymicrogyria, hydrocephaly, craniectomy, spinal cord injury, tumor growth, traumatic brain injury, and shaken baby syndrome. The multi-disciplinary analysis of these various phenomena and pathologies presents new opportunities and suggests that mechanical modeling is a central tool to bridge the scales by synthesizing information from the molecular via the cellular and tissue all the way to the organ level.

Effects of intraluminal thrombus on patient-specific abdominal aortic aneurysm hemodynamics via stereoscopic particle image velocity and computational fluid dynamics modeling

The pathology of the human abdominal aortic aneurysm (AAA) and its relationship to the later complication of intraluminal thrombus (ILT) formation remains unclear. The hemodynamics in the diseased abdominal aorta are hypothesized to be a key contributor to the formation and growth of ILT. The objective of this investigation is to establish a reliable 3D flow visualization method with corresponding validation tests with high confidence in order to provide insight into the basic hemodynamic features for a better understanding of hemodynamics in AAA pathology and seek potential treatment for AAA diseases. A stereoscopic particle image velocity (PIV) experiment was conducted using transparent patient-specific experimental AAA models (with and without ILT) at three axial planes. Results show that before ILT formation, a 3D vortex was generated in the AAA phantom. This geometry-related vortex was not observed after the formation of ILT, indicating its possible role in the subsequent appearance of ILT in this patient. It may indicate that a longer residence time of recirculated blood flow in the aortic lumen due to this vortex caused sufficient shear-induced platelet activation to develop ILT and maintain uniform flow conditions. Additionally, two computational fluid dynamics (CFD) modeling codes (Fluent and an in-house cardiovascular CFD code) were compared with the two-dimensional, three-component velocity stereoscopic PIV data. Results showed that correlation coefficients of the out-of-plane velocity data between PIV and both CFD methods are greater than 0.85, demonstrating good quantitative agreement. The stereoscopic PIV study can be utilized as test case templates for ongoing efforts in cardiovascular CFD solver development. Likewise, it is envisaged that the patient-specific data may provide a benchmark for further studying hemodynamics of actual AAA, ILT, and their convolution effects under physiological conditions for clinical applications.

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.

AneuSearch: a software prototype for intracranial aneurysm searching and clinical decision support

PURPOSE

Clinical decisions for treating intracranial aneurysms (IA) require integrating information in various forms and from multiple sources. We aim to establish a framework namely AneuSearch to integrate relevant information in IA management and also allow for efficient IA searching based on carefully designed criteria.

METHODS

The backbone of AneuSearch is an open-source three-tier DICOM image management system called DCM4Chee, which is a Java implementation for PACS. A supplementary database (AneuSearchDB) was developed to contain morphological features, hemodynamic and histological data. The relational tables in AneuSearchDB correspond to the most fundamental questions raised by neurosurgeons during IA treatment. The system was developed through collaborations between bioengineers and neurosurgeons.

RESULTS

The prototype software has been deployed to computers in a Mianyang Central Hospital in China. Currently, the system contains the data of 105 IA patients, seven hemodynamic simulation results and nine histological section images. This system was queried as per given criteria and can also provide blood flow data after running an external computational fluid dynamics software.

CONCLUSIONS

The prototype software provides a novel tool to IA management. Future works include incorporating IA treatment criteria in IA rupture risk assessment.

Characterization of pressure reduction in coil-filled aneurysm under flow of human blood with and without anti-coagulant

Filling aneurysms with embolization coils is a widely used part of the treatment to stop intracranial aneurysm from rupturing. However, the effect of coiling on aneurysmal pressure has not been established. In this study, the effect of intra-aneurysmal coiling on pressure reduction was characterized. Coil deployment in the aneurysm will disturb flow and may induce aneurysmal coagulation. These effects were experimentally examined in this study using silicone rubber saccular aneurysm models. Changes in aneurysmal blood pressure under pulsatile flow were characterized. With coils in the aneurysm, results showed that flow reduction of anti-coagulated blood in the aneurysm did not reduce aneurysmal pressure. Significant pressure reduction was observed only when the blood's coagulation ability is restored to normal. These results suggest that blood coagulation is pivotal to pressure reduction and concomitant with rupture risk reduction in treatments of aneurysm with coils.

Biochemomechanics of intraluminal thrombus in abdominal aortic aneurysms

Most computational models of abdominal aortic aneurysms address either the hemodynamics within the lesion or the mechanics of the wall. More recently, however, some models have appropriately begun to account for the evolving mechanics of the wall in response to the changing hemodynamic loads. Collectively, this large body of work has provided tremendous insight into this life-threatening condition and has provided important guidance for current research. Nevertheless, there has yet to be a comprehensive model that addresses the mechanobiology, biochemistry, and biomechanics of thrombus-laden abdominal aortic aneurysms. That is, there is a pressing need to include effects of the hemodynamics on both the development of the nearly ubiquitous intraluminal thrombus and the evolving mechanics of the wall, which depends in part on biochemical effects of the adjacent thrombus. Indeed, there is increasing evidence that intraluminal thrombus in abdominal aortic aneurysms is biologically active and should not be treated as homogeneous inert material. In this review paper, we bring together diverse findings from the literature to encourage next generation models that account for the biochemomechanics of growth and remodeling in patient-specific, thrombus-laden abdominal aortic aneurysms.

Mechanotransduction in embryonic vascular development

A plethora of biochemical signals provides spatial and temporal cues that carefully orchestrate the complex process of vertebrate embryonic development. The embryonic vasculature develops not only in the context of these biochemical cues, but also in the context of the biomechanical forces imparted by blood flow. In the mature vasculature, different blood flow regimes induce distinct genetic programs, and significant progress has been made toward understanding how these forces are perceived by endothelial cells and transduced into biochemical signals. However, it cannot be assumed that paradigms that govern the mature vasculature are pertinent to the developing embryonic vasculature. The embryonic vasculature can respond to the mechanical forces of blood flow, and these responses are critical in vascular remodeling, certain aspects of sprouting angiogenesis, and maintenance of arterial-venous identity. Here, we review data regarding mechanistic aspects of endothelial cell mechanotransduction, with a focus on the response to shear stress, and elaborate upon the multifarious effects of shear stress on the embryonic vasculature. In addition, we discuss emerging predictive vascular growth models and highlight the prospect of combining signaling pathway information with computational modeling. We assert that correlation of precise measurements of hemodynamic parameters with effects on endothelial cell gene expression and cell behavior is required for fully understanding how blood flow-induced loading governs normal vascular development and shapes congenital cardiovascular abnormalities.

Perspectives on biomechanical growth and remodeling mechanisms in glaucoma()

Glaucoma is a blinding diseases in which damage to the axons results in loss of retinal ganglion cells. Experimental evidence indicates that chronic intraocular pressure elevation initiates axonal insult at the level of the lamina cribrosa. The lamina cribrosa is a porous collagen structure through which the axons pass on their path from the retina to the brain. Recent experimental studies revealed the extensive structural changes of the lamina cribrosa and its surrounding tissues during the development and progression of glaucoma. In this perspective paper we review the experimental evidence for growth and remodeling mechanisms in glaucoma including adaptation of tissue anisotropy, tissue thickening/thinning, tissue elongation/shortening and tissue migration. We discuss the existing predictive computational approaches that try to elucidate the potential biomechanical basis of theses growth and remodeling mechanisms and highlight open questions, challenges, and avenues for further development.

Importance of initial aortic properties on the evolving regional anisotropy, stiffness and wall thickness of human abdominal aortic aneurysms

Complementary advances in medical imaging, vascular biology and biomechanics promise to enable computational modelling of abdominal aortic aneurysms to play increasingly important roles in clinical decision processes. Using a finite-element-based growth and remodelling model of evolving aneurysm geometry and material properties, we show that regional variations in material anisotropy, stiffness and wall thickness should be expected to arise naturally and thus should be included in analyses of aneurysmal enlargement or wall stress. In addition, by initiating the model from best-fit material parameters estimated for non-aneurysmal aortas from different subjects, we show that the initial state of the aorta may influence strongly the subsequent rate of enlargement, wall thickness, mechanical behaviour and thus stress in the lesion. We submit, therefore, that clinically reliable modelling of the enlargement and overall rupture-potential of aneurysms may require both a better understanding of the mechanobiological processes that govern the evolution of these lesions and new methods of determining the patient-specific state of the pre-aneurysmal aorta (or correlation to currently unaffected portions thereof) through knowledge of demographics, comorbidities, lifestyle, genetics and future non-invasive or minimally invasive tests.

Mechanics, mechanobiology, and modeling of human abdominal aorta and aneurysms

Biomechanical factors play fundamental roles in the natural history of abdominal aortic aneurysms (AAAs) and their responses to treatment. Advances during the past two decades have increased our understanding of the mechanics and biology of the human abdominal aorta and AAAs, yet there remains a pressing need for considerable new data and resulting patient-specific computational models that can better describe the current status of a lesion and better predict the evolution of lesion geometry, composition, and material properties and thereby improve interventional planning. In this paper, we briefly review data on the structure and function of the human abdominal aorta and aneurysmal wall, past models of the mechanics, and recent growth and remodeling models. We conclude by identifying open problems that we hope will motivate studies to improve our computational modeling and thus general understanding of AAAs.

Wall shear stress distribution inside growing cerebral aneurysm

BACKGROUND AND PURPOSE

Hemodynamic stimulation has been suggested to affect the growth of cerebral aneurysms. The present study examined the effects of intra-aneurysmal hemodynamics on aneurysm growth.

MATERIALS AND METHODS

Velocity profiles were measured for 2 cases of AcomA aneurysms. Realistically shaped models of these aneurysms were constructed, based on CT angiograms. Flow fields and WSS in the models were measured by using particle image velocimetry and LDV. In 1 case, hemodynamic changes were observed in 4 stages of growth over a 27-month period, whereas no development was observed in the other case.

RESULTS

The growing model had a smaller and more stagnant recirculation area than that in the nongrowth model. The WSS was markedly reduced in the enlarging region in the growing models, whereas extremely low WSS was not found in the nongrowth model. In addition, a higher WSSG was consistently observed adjacent to the enlarging region during aneurysm growth.

CONCLUSIONS

The results indicated that the flow structure of recirculation itself does not necessarily lead to high likelihood of cerebral aneurysm. However, WSSG and WSS were distinctly different between the 2 cases. Higher WSSG was found surrounding the growing region, and extremely low WSS was found at the growing region of the growing cerebral aneurysm.

Computational hemodynamic optimization predicts dominant aortic arch selection is driven by embryonic outflow tract orientation in the chick embryo

In the early embryo, a series of symmetric, paired vessels, the aortic arches, surround the foregut and distribute cardiac output to the growing embryo and fetus. During embryonic development, the arch vessels undergo large-scale asymmetric morphogenesis to form species-specific adult great vessel patterns. These transformations occur within a dynamic biomechanical environment, which can play an important role in the development of normal arch configurations or the aberrant arch morphologies associated with congenital cardiac defects. Arrested migration and rotation of the embryonic outflow tract during late stages of cardiac looping has been shown to produce both outflow tract and several arch abnormalities. Here, we investigate how changes in flow distribution due to a perturbation in the angular orientation of the embryonic outflow tract impact the morphogenesis and growth of the aortic arches. Using a combination of in vivo arch morphometry with fluorescent dye injection and hemodynamics-driven bioengineering optimization-based vascular growth modeling, we demonstrate that outflow tract orientation significantly changes during development and that the associated changes in hemodynamic load can dramatically influence downstream aortic arch patterning. Optimization reveals that balancing energy expenditure with diffusive capacity leads to multiple arch vessel patterns as seen in the embryo, while minimizing energy alone led to the single arch configuration seen in the mature arch of aorta. Our model further shows the critical importance of the orientation of the outflow tract in dictating morphogenesis to the adult single arch and accurately predicts arch IV as the dominant mature arch of aorta. These results support the hypothesis that abnormal positioning of the outflow tract during early cardiac morphogenesis may lead to congenital defects of the great vessels due to altered hemodynamic loading.

A fluid-structure interaction-based numerical investigation on the evolution of stress, strength and rupture potential of an abdominal aortic aneurysm

An abdominal aortic aneurysm (AAA) is an irreversible dilation of the abdominal artery. Once an aneurysm is detected by doctors, clinical intervention is usually recommended. The interventions involve traditional open surgery repair and endovascular aneurysm repair with a stent graft. Both types of prophylactic procedures are expensive and not without any risk to the patient. It is very difficult to balance the risk of aneurysm repair and the chance of rupture. The reason lies in that the changing trend of characteristic physical quantities with the evolution of AAA and the mechanisms that give rise to it are still not completely clear. In this study, computational 3D patient-specific model for investigating AAA development was established based on computed tomography (CT) images. Results showed that as the aneurysm evolved, peak wall stress and time-averaged wall shear stress distribution patterns changed. The expansion of AAA wall resulted in the increment of peak stress. The AAA wall compliance not only showed different magnitudes at different cross-sections of the aneurismal body, but also changed with the development of the aneurysm. Furthermore, minimum wall strength and rupture potential index during the three stages of AAA evolution were also investigated in detail. This study might provide valuable information on how to further explore the mechanical basis and the rupture potential during AAA evolution, and that it may assist clinical diagnostic procedures and avoid the potential risk of unnecessary surgical intervention.

Lamina Cribrosa Thickening in Early Glaucoma Predicted by a Microstructure Motivated Growth and Remodeling Approach

Glaucoma is among the leading causes of blindness worldwide. The ocular disease is characterized by irreversible damage of the retinal ganglion cell axons at the level of the lamina cribrosa (LC). The LC is a porous, connective tissue structure whose function is believed to provide mechanical support to the axons as they exit the eye on their path from the retina to the brain. Early experimental glaucoma studies have shown that the LC remodels into a thicker, more posterior structure which incorporates more connective tissue after intraocular pressure (IOP) elevation. The process by which this occurs is unknown. Here we present a microstructure motivated growth and remodeling (G&R) formulation to explore a potential mechanism of these structural changes. We hypothesize that the mechanical strain experienced by the collagen fibrils in the LC stimulates the G&R response at the micro-scale. The proposed G&R algorithm controls collagen fibril synthesis/degradation and adapts the residual strains between collagen fibrils and the surrounding tissue to achieve biomechanical homeostasis. The G&R algorithm was applied to a generic finite element model of the human eye subjected to normal and elevated IOP. The G&R simulation underscores the biomechanical need for a LC at normal IOP. The numerical results suggest that IOP elevation leads to LC thickening due to an increase in collagen fibril mass, which is in good agreement with experimental observations in early glaucoma monkey eyes. This is the first study to demonstrate that a biomechanically-driven G&R mechanism can lead to the LC thickening observed in early experimental glaucoma.

Biomechanical behaviors of curved artery with flexible wall: a numerical study using fluid-structure interaction method

Studies showed that vascular diseases were prone to occur in curved arteries. In this paper, biomechanical behaviors of curved artery with flexible wall subjected to physiological flow were presented. Fluid-structure interaction effect was considered. The Von Mises stress variation and distribution patterns, the influence of artery curvature and flexibility on peak wall Von Mises stress, diameter change and cross sectional shape variation of the curved artery in the cardiac cycle were studied in detail. We believe that the findings may provide important implications for individualized treatment for patients with cardiovascular disease.

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.

Influence of parent vessel dominancy on fluid dynamics of anterior communicating artery aneurysms

BACKGROUND

Parent vessel plays an important role in aneurysm formation and rupture. The diameter of either the A1 arteries is the peculiar key controlling the flow of the anterior communicating artery (ACOMA) aneurysms (ANs).

OBJECTIVE

The purpose is to study the effect of parent vessel dominancy, that is, the diameter of the A1 artery, on the flow characteristics of the ACOMA ANs.

METHODS

Numerical simulations for the flow patterns in six artificial models have been studied. Three models are designed with aneurysms and three models without. The two A1s were equal in two models. In the other two models, the nondominant A1 diameters were decreased by 50%. Again, the nondominant A1s were decreased by another 50% in the last two models. Each pair was designed with and without aneurysms in the ACOMA.

FINDINGS

The ACOMA shows lower velocity magnitudes and wall shear stresses when the two A1s are equal. However, if one A1 is dominant with a 50% difference from the other A1, there is higher shear stress on the ACOMA itself and in the inflow zone of the aneurysm that increases more with further reduction of the nondominant A1 by another 50%. An area of high corner pressure at the bifurcation of the dominant A1 into the ACOMA and A2 exists and increases in value with the decrease of diameter of the other nondominant A1.

CONCLUSION

Aneurysms located in the ACOMA with differences of 50% or more between the two A1s are subjected to more flow stresses.

Toward integrated management of cerebral aneurysms

In the last few years, some of the visionary concepts behind the virtual physiological human began to be demonstrated on various clinical domains, showing great promise for improving healthcare management. In the current work, we provide an overview of image- and biomechanics-based techniques that, when put together, provide a patient-specific pipeline for the management of intracranial aneurysms. The derivation and subsequent integration of morphological, morphodynamic, haemodynamic and structural analyses allow us to extract patient-specific models and information from which diagnostic and prognostic descriptors can be obtained. Linking such new indices with relevant clinical events should bring new insights into the processes behind aneurysm genesis, growth and rupture. The development of techniques for modelling endovascular devices such as stents and coils allows the evaluation of alternative treatment scenarios before the intervention takes place and could also contribute to the understanding and improved design of more effective devices. A key element to facilitate the clinical take-up of all these developments is their comprehensive validation. Although a number of previously published results have shown the accuracy and robustness of individual components, further efforts should be directed to demonstrate the diagnostic and prognostic efficacy of these advanced tools through large-scale clinical trials.

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.