Simulation of abdominal aortic aneurysm growth with updating hemodynamic loads using a realistic geometry

Computational approaches for mechanobiology in cardiovascular development and diseases

The cardiovascular development in vertebrates evolves in response to genetic and mechanical cues. The dynamic interplay among mechanics, cell biology, and anatomy continually shapes the hydraulic networks, characterized by complex, non-linear changes in anatomical structure and blood flow dynamics. To better understand this interplay, a diverse set of molecular and computational tools has been used to comprehensively study cardiovascular mechanobiology. With the continual advancement of computational capacity and numerical techniques, cardiovascular simulation is increasingly vital in both basic science research for understanding developmental mechanisms and disease etiologies, as well as in clinical studies aimed at enhancing treatment outcomes. This review provides an overview of computational cardiovascular modeling. Beginning with the fundamental concepts of computational cardiovascular modeling, it navigates through the applications of computational modeling in investigating mechanobiology during cardiac development. Second, the article illustrates the utility of computational hemodynamic modeling in the context of treatment planning for congenital heart diseases. It then delves into the predictive potential of computational models for elucidating tissue growth and remodeling processes. In closing, we outline prevailing challenges and future prospects, underscoring the transformative impact of computational cardiovascular modeling in reshaping cardiovascular science and clinical practice.

A review on the biomechanical behaviour of the aorta

Large aortic aneurysm and acute and chronic aortic dissection are pathologies of the aorta requiring surgery. Recent advances in medical intervention have improved patient outcomes; however, a clear understanding of the mechanisms leading to aortic failure and, hence, a better understanding of failure risk, is still missing. Biomechanical analysis of the aorta could provide insights into the development and progression of aortic abnormalities, giving clinicians a powerful tool in risk stratification. The complexity of the aortic system presents significant challenges for a biomechanical study and requires various approaches to analyse the aorta. To address this, here we present a holistic review of the biomechanical studies of the aorta by categorising articles into four broad approaches, namely theoretical, in vivo, experimental and combined investigations. Experimental studies that focus on identifying mechanical properties of the aortic tissue are also included. By reviewing the literature and discussing drawbacks, limitations and future challenges in each area, we hope to present a more complete picture of the state-of-the-art of aortic biomechanics to stimulate research on critical topics. Combining experimental modalities and computational approaches could lead to more comprehensive results in risk prediction for the aortic system.

Fluid-structure interaction study for biomechanics and risk factors in Stanford type A aortic dissection

Aortic dissection is a life-threatening condition with a rising prevalence in the elderly population, possibly as a consequence of the increasing population life expectancy. Untreated aortic dissection can lead to myocardial infarction, aortic branch malperfusion or occlusion, rupture, aneurysm formation and death. This study aims to assess the potential of a biomechanical model in predicting the risks of a non-dilated thoracic aorta with Stanford type A dissection. To achieve this, a fully coupled fluid-structure interaction model was developed under realistic blood flow conditions. This model of the aorta was developed by considering three-dimensional artery geometry, multiple artery layers, hyperelastic artery wall, in vivo-based physiological time-varying blood velocity profiles, and non-Newtonian blood behaviours. The results demonstrate that in a thoracic aorta with Stanford type A dissection, the wall shear stress (WSS) is significantly low in the ascending aorta and false lumen, leading to potential aortic dilation and thrombus formation. The results also reveal that the WSS is highly related to blood flow patterns. The aortic arch region near the brachiocephalic and left common carotid artery is prone to rupture, showing a good agreement with the clinical reports. The results have been translated into their potential clinical relevance by revealing the role of the stress state, WSS and flow characteristics as the main parameters affecting lesion progression, including rupture and aneurysm. The developed model can be tailored for patient-specific studies and utilised as a predictive tool to estimate aneurysm growth and initiation of wall rupture inside the human thoracic aorta.

In vivo development of tissue engineered vascular grafts: a fluid-solid-growth model

Methods of tissue engineering continue to advance, and multiple clinical trials are underway evaluating tissue engineered vascular grafts (TEVGs). Whereas initial concerns focused on suture retention and burst pressure, there is now a pressing need to design grafts to have optimal performance, including an ability to grow and remodel in response to changing hemodynamic loads. Toward this end, there is similarly a need for computational methods that can describe and predict the evolution of TEVG geometry, composition, and material properties while accounting for changes in hemodynamics. Although the ultimate goal is a fluid-solid-growth (FSG) model incorporating fully 3D growth and remodeling and 3D hemodynamics, lower fidelity models having high computational efficiency promise to play important roles, especially in the design of candidate grafts. We introduce here an efficient FSG model of in vivo development of a TEVG based on two simplifying concepts: mechanobiologically equilibrated growth and remodeling of the graft and an embedded control volume analysis of the hemodynamics. Illustrative simulations for a model Fontan conduit reveal the utility of this approach, which promises to be particularly useful in initial design considerations involving formal methods of optimization which otherwise add considerably to the computational expense.

Constrained Mixture Models of Soft Tissue Growth and Remodeling - Twenty Years After

Soft biological tissues compromise diverse cell types and extracellular matrix constituents, each of which can possess individual natural configurations, material properties, and rates of turnover. For this reason, mixture-based models of growth (changes in mass) and remodeling (change in microstructure) are well-suited for studying tissue adaptations, disease progression, and responses to injury or clinical intervention. Such approaches also can be used to design improved tissue engineered constructs to repair, replace, or regenerate tissues. Focusing on blood vessels as archetypes of soft tissues, this paper reviews a constrained mixture theory introduced twenty years ago and explores its usage since by contrasting simulations of diverse vascular conditions. The discussion is framed within the concept of mechanical homeostasis, with consideration of solid-fluid interactions, inflammation, and cell signaling highlighting both past accomplishments and future opportunities as we seek to understand better the evolving composition, geometry, and material behaviors of soft tissues under complex conditions.

Coupling hemodynamics with mechanobiology in patient-specific computational models of ascending thoracic aortic aneurysms

BACKGROUND AND OBJECTIVE

The prevention of ascending thoracic aortic aneurysms (ATAAs), which affect thousands of persons every year worldwide, remains a major issue. ATAAs may be caused by anything that weakens the aortic wall. Altered hemodynamics, which concerns a majority of patients with bicuspid aortic valves, has been shown to be related to such weakening and to contribute to ATAA development and progression. However the underlying mechanisms remain unclear and computational modeling in this field could help significantly to elucidate how hemodynamics and mechanobiology interact in ATAAs.

METHODS

Accordingly, we propose a numerical framework combining computational fluid dynamics and 4D flow magnetic resonance imaging (MRI) coupled with finite element (FE) analyses to simulate growth and remodeling (G&R) occurring in patient-specific aortas in relation with altered hemodynamics. The geometries and the blood velocities obtained from 4D flow MRI are used as boundary conditions for CFD simulations. CFD simulations provide an estimation of the wall shear stress (WSS) and relative residence time (RRT) distribution across the luminal surface of the wall. An initial insult is then applied to the FE model of the aortic wall, assuming that the magnitude of the insult correlates spatially with the normalized RRT distribution obtained from CFD simulations. G&R simulations are then performed. The material behavior of each Gauss point in these FE models is evolved continuously to compensate for the deviation of the actual wall stress distribution from the homeostatic state after the initial insult. The whole approach is illustrated on two healthy and two diseased subjects. The G&R parameters are calibrated against previously established statistical models of ATAA growth rates.

RESULTS

Among the variety of results provided by G&R simulations, the analysis focused especially on the evolution of the wall stiffness, which was shown to be a major risk factor for ATAAs. It was shown that the G&R parameters, such as for instance the rate of collagen production or cell mechanosensitivity, play a critical role in ATAA progression and remodeling.

CONCLUSIONS

These preliminary findings show that patient-specific computational modeling coupling hemodynamics with mechanobiology is a promising approach to explore aneurysm progression.

Weighted Gene Co-Expression Network Analysis Reveals Key Genes and Potential Drugs in Abdominal Aortic Aneurysm

Abdominal aortic aneurysm (AAA) is a prevalent aortic disease that causes high mortality due to asymptomatic gradual expansion and sudden rupture. The underlying molecular mechanisms and effective pharmaceutical therapy for preventing AAA progression have not been fully identified. In this study, we identified the key modules and hub genes involved in AAA growth from the GSE17901 dataset in the Gene Expression Omnibus (GEO) database through the weighted gene co-expression network analysis (WGCNA). Key genes were further selected and validated in the mouse dataset (GSE12591) and human datasets (GSE7084, GSE47472, and GSE57691). Finally, we predicted drug candidates targeting key genes using the Drug-Gene Interaction database. Overall, we identified key modules enriched in the mitotic cell cycle, GTPase activity, and several metabolic processes. Seven key genes (CCR5, ADCY5, ADCY3, ACACB, LPIN1, ACSL1, UCP3) related to AAA progression were identified. A total of 35 drugs/compounds targeting the key genes were predicted, which may have the potential to prevent AAA progression.

Analysis of the Formation of an Aneurysm in Arteries Through Finite Element Modeling Using Hyper-Elastic Model

This paper presents the stress patterns and deformation in an artery with an aneurysm under a variation of pressure. An aneurysm occurs when a weak portion of artery wall bulges out under pressure. To make a proper treatment decision, one must understand the formation and growth of the condition. In this article, finite element analysis of the formation of fusiform aneurysms in arteries is presented using the hyperelastic material model by employing ANSYS. We present the effect of different blood pressures in the deformation of the weakened arterial wall and also compare it with a normal artery. This work can be used as a reference for research in this area.

Fast, Rate-Independent, Finite Element Implementation of a 3D Constrained Mixture Model of Soft Tissue Growth and Remodeling

Constrained mixture models of soft tissue growth and remodeling can simulate many evolving conditions in health as well as in disease and its treatment, but they can be computationally expensive. In this paper, we derive a new fast, robust finite element implementation based on a concept of mechanobiological equilibrium that yields fully resolved solutions and allows computation of quasi-equilibrated evolutions when imposed perturbations are slow relative to the adaptive process. We demonstrate quadratic convergence and verify the model via comparisons with semi-analytical solutions for arterial mechanics. We further examine the enlargement of aortic aneurysms for which we identify new mechanobiological insights into factors that affect the nearby non-aneurysmal segment as it responds to the changing mechanics within the diseased segment. Because this new 3D approach can be implemented within many existing finite element solvers, constrained mixture models of growth and remodeling can now be used more widely.

Quantifying hemodynamics within an aneurysm exposed to prolonged exercise levels

BACKGROUND AND OBJECTIVE

Non-invasive treatment of unruptured Abdominal Aortic Aneurysm involves subjecting the patients to certain physiological levels of the heart. Flow topology (Re_peak = 200-1200, frequency: f = 1.18-2.41 Hz) within an aneurysm geometry (2-D) under resting and exercise (mild and moderate) conditions are explored in the present study. Blood is assumed to be Newtonian in nature. Spatio-temporal evolution of the flow patterns and vorticity are established. Hemodynamic indicators (TAWSS and OSI), movement of vortex cores and Particle Residence Index (PRI) are quantified to select an optimum exercise level in attenuating the disease.

METHODS

The finite volume method is employed for numerical solutions using ANSYS-Fluent^Ⓡ software. The SIMPLE scheme has been used for the pressure-velocity coupling. Least Square cell-based method is used for the spatial discretization of the gradients. Second order upwind scheme is considered for discretization of the pressure term. Third order upwind (QUICK) scheme is used to discretize the momentum equation. First order Implicit Scheme was used for the discretization of the temporal terms. Discrete Phase Material (DPM) technique is employed throughout, to visualize the signature of particle deposits within the aneurysm.

RESULTS

Vortex impingement induces a pressure peak within the aneurysm (moderate) while the peaks are anchored at the proximal and distal ends under resting and mild conditions. Along the averaged flow separation zone, exercise increases the maximum TAWSS from 1.21 N/m² (mild) to 9.3 N/m² (moderate). The distal site is exposed to oscillatory loading (OSI = 0.5) under mild activity whereas the loading becomes distributed almost over the entire wall, when subjected to moderate conditions. This in turn, reduces the time involved in 50 percent clearance of particles (PRI = 0.5) from 10.56 s (resting) to 3.98 s (mild) and 0.87 s (moderate), respectively.

CONCLUSIONS

Resting conditions manifests the aneurysmal wall to recirculating fluid for most of cycle time. Moderate exercise exhibits the least particle clearance time, but it exposes the aneurysmal wall and the distal end to high pressure, which otherwise has low intensity under mild activity. This in turn establishes that mild exercise for prolonged duration can be an optimum level for non-invasive aneurysmal treatment.

Computational study on hemodynamic changes in patient-specific proximal neck angulation of abdominal aortic aneurysm with time-varying velocity

Aneurysms are considered as a critical cardiovascular disease worldwide when they rupture. The clinical understanding of geometrical impact on the flow behaviour and biomechanics of abdominal aortic aneurysm (AAA) is progressively developing. Proximal neck angulations of AAAs are believed to influence the hemodynamic changes and wall shear stress (WSS) within AAAs. Our aim was to perform pulsatile simulations using computational fluid dynamics (CFD) for patient-specific geometry to investigate the influence of severe angular (≥ 60°) neck on AAA's hemodynamic and wall shear stress. The patient's geometrical characteristics were obtained from a computed tomography images database of AAA patients. The AAA geometry was reconstructed using Mimics software. In computational method, blood was assumed Newtonian fluid and an inlet varying velocity waveform in a cardiac cycle was assigned. The CFD study was performed with ANSYS software. The results of flow behaviours indicated that the blood flow through severe bending of angular neck leads to high turbulence and asymmetry of flows within the aneurysm sac resulting in blood recirculation. The high wall shear stress (WSS) occurred near the AAA neck and on surface of aneurysm sac. This study explained and showed flow behaviours and WSS progression within high angular neck AAA and risk prediction of abdominal aorta rupture. We expect that the visualization of blood flow and hemodynamic changes resulted from CFD simulation could be as an extra tool to assist clinicians during a decision making when estimation the risks of interventional procedures.

Patient-Specific Prediction of Abdominal Aortic Aneurysm Expansion Using Bayesian Calibration

Translating recent advances in abdominal aortic aneurysm (AAA) growth and remodeling (G&R) knowledge into a predictive, patient-specific clinical treatment tool requires a major paradigm shift in computational modeling. The objectives of this study are to develop a prediction framework that first calibrates the physical AAA G&R model using patient-specific serial computed tomography (CT) scan images, predicts the expansion of an AAA in the future, and quantifies the associated uncertainty in the prediction. We adopt a Bayesian calibration method to calibrate parameters in the G&R computational model and predict the magnitude of AAA expansion. The proposed Bayesian approach can take different sources of uncertainty; therefore, it is well suited to achieve our aims in predicting the AAA expansion process as well as in computing the propagated uncertainty. We demonstrate how to achieve the proposed aims by solving the formulated Bayesian calibration problems for cases with the synthetic G&R model output data and real medical patient-specific CT data. We compare and discuss the performance of predictions and computation time under different sampling cases of the model output data and patient data, both of which are simulated by the G&R computation. Furthermore, we apply our Bayesian calibration to real patient-specific serial CT data and validate our prediction. The accuracy and efficiency of the proposed method is promising, which appeals to computational and medical communities.

Fluid-Structure Interaction in Abdominal Aortic Aneurysms: Effect of Haematocrit

The Abdominal Aortic Aneurysm (AAA) is a local dilation of the abdominal aorta and it is a cause for serious concern because of the high mortality associated with its rupture. Consequently, the understanding of the phenomena related to the creation and the progression of an AAA is of crucial importance. In this work, the complicated interaction between the blood flow and the AAA wall is numerically examined using a fully coupled Fluid-Structure Interaction (FSI) method. The study investigates the possible link between the dynamic behavior of an AAA and the blood viscosity variations attributed to the haematocrit value, while it also incorporates the pulsatile blood flow, the non-Newtonian behavior of blood and the hyperelasticity of the arterial wall. It was found that blood viscosity has no significant effect on von Mises stress magnitude and distribution, whereas there is a close relation between the haematocrit value and the Wall Shear Stress (WSS) magnitude in AAAs. This WSS variation can possibly alter the mechanical properties of the arterial wall and increase its growth rate or even its rupture possibility. The relationship between haematocrit and dynamic behavior of an AAA can be helpful in designing a patient specific treatment.

Prediction of Abdominal Aortic Aneurysm Growth Using Dynamical Gaussian Process Implicit Surface

OBJECTIVE

We propose a novel approach to predict the Abdominal Aortic Aneurysm (AAA) growth in future time, using longitudinal computer tomography (CT) scans of AAAs that are captured at different times in a patient-specific way.

METHODS

We adopt a formulation that considers a surface of the AAA as a manifold embedded in a scalar field over the three dimensional (3D) space. For this formulation, we develop our Dynamical Gaussian Process Implicit Surface (DGPIS) model based on observed surfaces of 3D AAAs as visible variables while the scalar fields are hidden. In particular, we use Gaussian process regression to construct the field as an observation model from CT training image data. We then learn a dynamic model to represent the evolution of the field. Finally, we derive the predicted AAA surface from the predicted field along with uncertainty quantified in future time.

RESULTS

A dataset of 7 subjects (4-7 scans) was collected and used to evaluate the proposed method by comparing its prediction Hausdorff distance errors against those of simple extrapolation. In addition, we evaluate the prediction results with respect to a conventional shape analysis technique such as Principal Component Analysis (PCA). All comparative results show the superior prediction performance of the proposed approach.

CONCLUSION

We introduce a novel approach to predict the AAA growth and its predicted uncertainty in future time, using longitudinal CT scans in a patient-specific fashion.

SIGNIFICANCE

The capability to predict the AAA shape and its confidence region by our approach establish the potential for guiding clinicians with informed decision in conducting medical treatment and monitoring of AAAs.

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.

Fluid-Structure Interaction in Abdominal Aortic Aneurysm: Effect of Modeling Techniques

In this work, the impact of modeling techniques on predicting the mechanical behaviors of abdominal aortic aneurysm (AAA) is systematically investigated. The fluid-structure interaction (FSI) model for simultaneously capturing the transient interaction between blood flow dynamics and wall mechanics was compared with its simplified techniques, that is, computational fluid dynamics (CFD) or computational solid stress (CSS) model. Results demonstrated that CFD exhibited relatively smaller vortexes and tends to overestimate the fluid wall shear stress, compared to FSI. On the contrary, the minimal differences in wall stresses and deformation were observed between FSI and CSS models. Furthermore, it was found that the accuracy of CSS prediction depends on the applied pressure profile for the aneurysm sac. A large pressure drop across AAA usually led to the underestimation of wall stresses and thus the AAA rupture. Moreover, the assumed isotropic AAA wall properties, compared to the anisotropic one, will aggravate the difference between the simplified models with the FSI approach. The present work demonstrated the importance of modeling techniques on predicting the blood flow dynamics and wall mechanics of the AAA, which could guide the selection of appropriate modeling technique for significant clinical implications.

Prior Distributions of Material Parameters for Bayesian Calibration of Growth and Remodeling Computational Model of Abdominal Aortic Wall

For the accurate prediction of the vascular disease progression, there is a crucial need for developing a systematic tool aimed toward patient-specific modeling. Considering the interpatient variations, a prior distribution of model parameters has a strong influence on computational results for arterial mechanics. One crucial step toward patient-specific computational modeling is to identify parameters of prior distributions that reflect existing knowledge. In this paper, we present a new systematic method to estimate the prior distribution for the parameters of a constrained mixture model using previous biaxial tests of healthy abdominal aortas (AAs). We investigate the correlation between the estimated parameters for each constituent and the patient's age and gender; however, the results indicate that the parameters are correlated with age only. The parameters are classified into two groups: Group-I in which the parameters ce, ck1, ck2, cm2,Ghc, and ϕe are correlated with age, and Group-II in which the parameters cm1, Ghm, G1e, G2e, and α are not correlated with age. For the parameters in Group-I, we used regression associated with age via linear or inverse relations, in which their prior distributions provide conditional distributions with confidence intervals. For Group-II, the parameter estimated values were subjected to multiple transformations and chosen if the transformed data had a better fit to the normal distribution than the original. This information improves the prior distribution of a subject-specific model by specifying parameters that are correlated with age and their transformed distributions. Therefore, this study is a necessary first step in our group's approach toward a Bayesian calibration of an aortic model. The results from this study will be used as the prior information necessary for the initialization of Bayesian calibration of a computational model for future applications.

Hemodynamic Study of Flow Remodeling Stent Graft for the Treatment of Highly Angulated Abdominal Aortic Aneurysm

This study investigates the effect of a novel flow remodeling stent graft (FRSG) on the hemodynamic characteristics in highly angulated abdominal aortic aneurysm based on computational fluid dynamics (CFD) approach. An idealized aortic aneurysm with varying aortic neck angulations was constructed and CFD simulations were performed on nonstented models and stented models with FRSG. The influence of FRSG intervention on the hemodynamic performance is analyzed and compared in terms of flow patterns, wall shear stress (WSS), and pressure distribution in the aneurysm. The findings showed that aortic neck angulations significantly influence the velocity flow field in nonstented models, with larger angulations shifting the mainstream blood flow towards the center of the aorta. By introducing FRSG treatment into the aneurysm, erratic flow recirculation pattern in the aneurysm sac diminishes while the average velocity magnitude in the aneurysm sac was reduced in the range of 39% to 53%. FRSG intervention protects the aneurysm against the impacts of high velocity concentrated flow and decreases wall shear stress by more than 50%. The simulation results highlighted that FRSG may effectively treat aneurysm with high aortic neck angulations via the mechanism of promoting thrombus formation and subsequently led to the resorption of the aneurysm.

Multi-scale Modeling of the Cardiovascular System: Disease Development, Progression, and Clinical Intervention

Cardiovascular diseases (CVDs) are the leading cause of death in the western world. With the current development of clinical diagnostics to more accurately measure the extent and specifics of CVDs, a laudable goal is a better understanding of the structure-function relation in the cardiovascular system. Much of this fundamental understanding comes from the development and study of models that integrate biology, medicine, imaging, and biomechanics. Information from these models provides guidance for developing diagnostics, and implementation of these diagnostics to the clinical setting, in turn, provides data for refining the models. In this review, we introduce multi-scale and multi-physical models for understanding disease development, progression, and designing clinical interventions. We begin with multi-scale models of cardiac electrophysiology and mechanics for diagnosis, clinical decision support, personalized and precision medicine in cardiology with examples in arrhythmia and heart failure. We then introduce computational models of vasculature mechanics and associated mechanical forces for understanding vascular disease progression, designing clinical interventions, and elucidating mechanisms that underlie diverse vascular conditions. We conclude with a discussion of barriers that must be overcome to provide enhanced insights, predictions, and decisions in pre-clinical and clinical applications.

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.

Association of Intraluminal Thrombus, Hemodynamic Forces, and Abdominal Aortic Aneurysm Expansion Using Longitudinal CT Images

While hemodynamic forces and intraluminal thrombus (ILT) are believed to play important roles on abdominal aortic aneurysm (AAA), it has been suggested that hemodynamic forces and ILT also interact with each other, making it a complex problem. There is, however, a pressing need to understand relationships among three factors: hemodynamics, ILT accumulation, and AAA expansion for AAA prognosis. Hence this study used longitudinal computer tomography scans from 14 patients and analyzed the relationship between them. Hemodynamic forces, represented by wall shear stress (WSS), were obtained from computational fluid dynamics; ILT accumulation was described by ILT thickness distribution changes between consecutives scans, and ILT accumulation and AAA expansion rates were estimated from changes in ILT and AAA volume. Results showed that, while low WSS was observed at regions where ILT accumulated, the rate at which ILT accumulated occurred at the same rate as the aneurysm expansion. Comparison between AAAs with and without thrombus showed that aneurysm with ILT recorded lower values of WSS and higher values of AAA expansion than those without thrombus. Findings suggest that low WSS may promote ILT accumulation and submit the idea that by increasing WSS levels ILT accumulation may be prevented.

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 Computational Model of Biochemomechanical Effects of Intraluminal Thrombus on the Enlargement of Abdominal Aortic Aneurysms

Abdominal aortic aneurysms (AAAs) typically develop an intraluminal thrombus (ILT), yet most computational models of AAAs have focused on either the mechanics of the wall or the hemodynamics within the lesion, both in the absence of ILT. In the few cases wherein ILT has been modeled directly, as, for example, in static models that focus on the state of stress in the aortic wall and the associated rupture risk, thrombus has been modeled as an inert, homogeneous, load-bearing material. Given the biochemomechanical complexity of an ILT, there is a pressing need to consider its diverse effects on the evolving aneurysmal wall. Herein, we present the first growth and remodeling model that addresses together the biomechanics, mechanobiology, and biochemistry of thrombus-laden AAAs. Whereas it has been shown that aneurysmal enlargement in the absence of ILT depends primarily on the stiffness and turnover of fibrillar collagen, we show that the presence of a thrombus within lesions having otherwise the same initial wall composition and properties can lead to either arrest or rupture depending on the biochemical effects (e.g., release of proteases) and biomechanical properties (e.g., stiffness of fibrin) of the ILT. These computational results suggest that ILT should be accounted for when predicting the potential enlargement or rupture risk of AAAs and highlight specific needs for further experimental and computational research.

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.

Evolving anisotropy and degree of elastolytic insult in abdominal aortic aneurysms: potential clinical relevance?

Accurately estimating patient-specific rupture risk remains a primary challenge in timing interventions for abdominal aortic aneurysms (AAAs). By re-analyzing published biaxial mechanical testing data from surgically repaired human AAAs, material anisotropy emerged as a potentially important determinant of patient-specific lesion progression. That is, based on a new classification scheme, we discovered that anisotropic aneurysmal specimens correlated with increased patient age at surgery when compared with more isotropic specimens (79.7 vs. 70.9 years, p<0.002), despite no significant difference in maximum diameter. Furthermore, using an idealized axisymmetric, finite-element growth and remodeling model of AAA progression, we found that both the initial axial extent of elastin loss and ongoing damage to elastin in the shoulder region of the AAA directly affected the degree of anisotropy as the lesion evolved, with more extensive insults increasing the anisotropy. This effect appeared to be mediated by alterations in axial loading and subsequent differences in orientation of deposited collagen fibers. While the observed increased age before surgical intervention may suggest a potential benefit of anisotropic remodeling, future biaxial tests coupled with pre-surgical data on expansion rates and detailed theoretical analyses of the biostability of a lesion as a function of anisotropy will be required to verify its clinical relevance to patient-specific rupture risk.

Engineering of arteries in vitro

This review will focus on two elements that are essential for functional arterial regeneration in vitro: the mechanical environment and the bioreactors used for tissue growth. The importance of the mechanical environment to embryological development, vascular functionality, and vascular graft regeneration will be discussed. Bioreactors generate mechanical stimuli to simulate biomechanical environment of arterial system. This system has been used to reconstruct arterial grafts with appropriate mechanical strength for implantation by controlling the chemical and mechanical environments in which the grafts are grown. Bioreactors are powerful tools to study the effect of mechanical stimuli on extracellular matrix architecture and mechanical properties of engineered vessels. Hence, biomimetic systems enable us to optimize chemo-biomechanical culture conditions to regenerate engineered vessels with physiological properties similar to those of native arteries. In addition, this article reviews various bioreactors designed especially to apply axial loading to engineered arteries. This review will also introduce and examine different approaches and techniques that have been used to engineer biologically based vascular grafts, including collagen-based grafts, fibrin-gel grafts, cell sheet engineering, biodegradable polymers, and decellularization of native vessels.

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.

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.

Review: the role of biomechanical modeling in the rupture risk assessment for abdominal aortic aneurysms

AAA disease is a serious condition and a multidisciplinary approach including biomechanics is needed to better understand and more effectively treat this disease. A rupture risk assessment is central to the management of AAA patients, and biomechanical simulation is a powerful tool to assist clinical decisions. Central to such a simulation approach is a need for robust and physiologically relevant models. Vascular tissue senses and responds actively to changes in its mechanical environment, a crucial tissue property that might also improve the biomechanical AAA rupture risk assessment. Specifically, constitutive modeling should not only focus on the (passive) interaction of structural components within the vascular wall, but also how cells dynamically maintain such a structure. In this article, after specifying the objectives of an AAA rupture risk assessment, the histology and mechanical properties of AAA tissue, with emphasis on the wall, are reviewed. Then a histomechanical constitutive description of the AAA wall is introduced that specifically accounts for collagen turnover. A test case simulation clearly emphasizes the need for constitutive descriptions that remodels with respect to the mechanical loading state. Finally, remarks regarding modeling of realistic clinical problems and possible future trends conclude the article.

CFD modelling of abdominal aortic aneurysm on hemodynamic loads using a realistic geometry with CT

The objective of this study is to find a correlation between the abdominal aortic aneurysm (AAA) geometric parameters, wall stress shear (WSS), abdominal flow patterns, intraluminal thrombus (ILT), and AAA arterial wall rupture using computational fluid dynamics (CFD). Real AAA 3D models were created by three-dimensional (3D) reconstruction of in vivo acquired computed tomography (CT) images from 5 patients. Based on 3D AAA models, high quality volume meshes were created using an optimal tetrahedral aspect ratio for the whole domain. In order to quantify the WSS and the recirculation inside the AAA, a 3D CFD using finite elements analysis was used. The CFD computation was performed assuming that the arterial wall is rigid and the blood is considered a homogeneous Newtonian fluid with a density of 1050 kg/m³ and a kinematic viscosity of 4 × 10⁻³ Pa·s. Parallelization procedures were used in order to increase the performance of the CFD calculations. A relation between AAA geometric parameters (asymmetry index (β), saccular index (γ), deformation diameter ratio (χ), and tortuosity index (ε)) and hemodynamic loads was observed, and it could be used as a potential predictor of AAA arterial wall rupture and potential ILT formation.

Continuum mixture models of biological growth and remodeling: past successes and future opportunities

Biological growth processes involve mass exchanges that increase, decrease, or replace material that constitutes cells, tissues, and organs. In most cases, such exchanges alter the structural makeup of the material and consequently affect associated mechanobiological responses to applied loads. Given that the type and extent of changes in structural integrity depend on the different constituents involved (e.g., particular cytoskeletal or extracellular matrix proteins), the continuum theory of mixtures is ideally suited to model the mechanics of growth and remodeling. The goal of this review is twofold: first, to highlight a few illustrative examples that show diverse applications of mixture theory to describe biological growth and/or remodeling; second, to identify some open problems in the fields of modeling soft-tissue growth and remodeling.

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.

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.

Intrasac pressure changes and vascular remodeling after endovascular repair of abdominal aortic aneurysms: review and biomechanical model simulation

In this paper, we review existing clinical research data on post-endovascular repair (EVAR) intrasac pressure and relation with abdominal aortic aneurysm (AAA) size changes. Based on the review, we hypothesize that intrasac pressure has a significant impact on post-EVAR AAA size changes, and post-EVAR remodeling depends also on how the pressure has changed over a period of time. The previously developed model of an AAA based on a constrained mixture approach is extended to include vascular adaptation after EVAR using an idealized geometry. Computational simulation shows that the same mechanism of collagen stress-mediated remodeling in AAA expansion induces the aneurysm wall to shrink in a reduced sac-pressure after post-EVAR. Computational simulation suggests that the intrasac pressure of 60 mm Hg is a critical value. At this value, the AAA remains stable, while values above cause the AAA to expand and values below cause the AAA to shrink. There are, however, variations between individuals due to different cellular sensitivities in stress-mediated adaptation. Computer simulation also indicates that an initial decrease in intrasac pressure helps the AAA shrink even if the pressure increases after some time. The presented study suggests that biomechanics has a major effect on initial adaptation after EVAR and also illustrates the utility of a computational model of vascular growth and remodeling in predicting diameter changes during the progression and after the treatment of AAAs.

Identification of in vivo material and geometric parameters of a human aorta: toward patient-specific modeling of abdominal aortic aneurysm

Recent advances in computational modeling of vascular adaptations and the need for their extension to patient-specific modeling have introduced new challenges to the path toward abdominal aortic aneurysm modeling. First, the fundamental assumption in adaptation models, namely the existence of vascular homeostasis in normal vessels, is not easy to implement in a vessel model built from medical images. Second, subjecting the vessel wall model to the normal pressure often makes the configuration deviate from the original geometry obtained from medical images. To address those technical challenges, in this work, we propose a two-step optimization approach; first, we estimate constitutive parameters of a healthy human aorta intrinsic to the material by using biaxial test data and a weighted nonlinear least-squares parameter estimation method; second, we estimate the distributions of wall thickness and anisotropy using a 2-D parameterization of the vessel wall surface and a global approximation scheme integrated within an optimization routine. A direct search method is implemented to solve the optimization problem. The numerical optimization method results in a considerable improvement in both satisfying homeostatic condition and minimizing the deviation of geometry from the original shape based on in vivo images. Finally, the utility of the proposed technique for patient-specific modeling is demonstrated in a simulation of an abdominal aortic aneurysm enlargement.