A decoupled fluid structure approach for estimating wall stress in abdominal aortic aneurysms

Narrative Review of Risk Assessment of Abdominal Aortic Aneurysm Rupture Based on Biomechanics-Related Morphology

CLINICAL IMPACT

Studies have shown that the biomechanical indicators based on multi-scale models are more effective in accurately assessing the rupture risk of AAA. To meet the need for clinical monitoring and rapid decision making, the typical morphological parameters associated with AAA rupture and their relationships with the mechanical environment have been summarized, which provide a reference for clinical preoperative risk assessment of AAA.

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.

Numerical investigation of the effects of blood rheology and wall elasticity in abdominal aortic aneurysm under pulsatile flow conditions

BACKGROUND

Previous studies on aneurysm modeling have focused on the blood rheology and vessel elasticity separately. The combined effects of blood shear thinning properties and wall elasticity need to be revealed.

OBJECTIVE

To provide insights on how pulsatile hemodynamics vary with blood rheology and vessel elasticity for a developed abdominal aortic aneurysm (AAA).

METHOD

An Arbitrary Lagrangian-Eulerian fluid-solid interaction method is adopted with the Newtonian and the shear thinning Carreau constitutive models for the fluid with the linearly elastic and the hyperelastic Yeoh models for the vessel. Finite element based numerical solver is used to simulate the blood flow in the AAA.

RESULTS

Newtonian model overestimates the velocity values compared to the Carreau model and the difference in the velocity field increases as the shear rate decreases at the instances of the cardiac cycle. The rigid walled simulations display higher deviations in the velocity and wall shear stress with the fluid rheology. The risk indicators show that Newtonian assumption combined with the linearly elastic model may overlook degeneration risk of arterial tissue.

CONCLUSIONS

Newtonian assumption for the blood as well as modelling the arterial wall as linearly elastic lead to significant differences in oscillatory hemodynamic properties with respect to the use of Carreau fluid together with hyperelastic vessel model, even in large vessel aneurysms.

Biomechanical Investigation of Disturbed Hemodynamics-Induced Tissue Degeneration in Abdominal Aortic Aneurysms Using Computational and Experimental Techniques

Abdominal aortic aneurysm (AAA) is the dilatation of the aorta beyond 50% of the normal vessel diameter. It is reported that 4-8% of men and 0.5-1% of women above 50 years of age bear an AAA and it accounts for ~15,000 deaths per year in the United States alone. If left untreated, AAA might gradually expand until rupture; the most catastrophic complication of the aneurysmal disease that is accompanied by a striking overall mortality of 80%. The precise mechanisms leading to AAA rupture remains unclear. Therefore, characterization of disturbed hemodynamics within AAAs will help to understand the mechanobiological development of the condition which will contribute to novel therapies for the condition. Due to geometrical complexities, it is challenging to directly quantify disturbed flows for AAAs clinically. Two other approaches for this investigation are computational modeling and experimental flow measurement. In computational modeling, the problem is first defined mathematically, and the solution is approximated with numerical techniques to get characteristics of flow. In experimental flow measurement, once the setup providing physiological flow pattern in a phantom geometry is constructed, velocity measurement system such as particle image velocimetry (PIV) enables characterization of the flow. We witness increasing number of applications of these complimentary approaches for AAA investigations in recent years. In this paper, we outline the details of computational modeling procedures and experimental settings and summarize important findings from recent studies, which will help researchers for AAA investigations and rupture mechanics.

Near-Wall Flow in Cerebral Aneurysms

The region where the vascular lumen meets the surrounding endothelium cell layer, hence the interface region between haemodynamics and cell tissue, is of primary importance in the physiological functions of the cardiovascular system. The functions include mass transport to/from the blood and tissue, and signalling via mechanotransduction, which are primary functions of the cardiovascular system and abnormalities in these functions are known to affect disease formation and vascular remodelling. This region is denoted by the near-wall region in the present work, and we outline simple yet effective numerical recipes to analyse the near-wall flow field. Computational haemodynamics solutions are presented for six patient specific cerebral aneurysms, at three instances in the cardiac cycle: peak systole, end systole (taken as dicrotic notch) and end diastole. A sensitivity study, based on Newtonian and non-Newtonian rheological models, and different flow rate profiles, is effected for a selection of aneurysm cases. The near-wall flow field is described by the wall shear stress (WSS) and the divergence of wall shear stress (WSSdiv), as descriptors of tangential and normal velocity components, respectively, as well as the wall shear stress critical points. Relations between near-wall and free-stream flow fields are discussed.

Mechanical and geometrical determinants of wall stress in abdominal aortic aneurysms: A computational study

An aortic aneurysm (AA) is a focal dilatation of the aortic wall. Occurrence of AA rupture is an all too common event that is associated with high levels of patient morbidity and mortality. The decision to surgically intervene prior to AA rupture is made with recognition of significant procedural risks, and is primarily based on the maximal diameter and/or growth rate of the AA. Despite established thresholds for intervention, rupture occurs in a notable subset of patients exhibiting sub-critical maximal diameters and/or growth rates. Therefore, a pressing need remains to identify better predictors of rupture risk and ultimately integrate their measurement into clinical decision making. In this study, we use a series of finite element-based computational models that represent a range of plausible AA scenarios, and evaluate the relative sensitivity of wall stress to geometrical and mechanical properties of the aneurysmal tissue. Taken together, our findings encourage an expansion of geometrical parameters considered for rupture risk assessment, and provide perspective on the degree to which tissue mechanical properties may modulate peak stress values within aneurysmal tissue.

Tetralogy of Fallot Surgical Repair: Shunt Configurations, Ductus Arteriosus and the Circle of Willis

In this study, hemodynamic performance of three novel shunt configurations that are considered for the surgical repair of tetralogy of Fallot (TOF) disease are investigated in detail. Clinical experience suggests that the shunt location, connecting angle, and its diameter can influence the post-operative physiology and the neurodevelopment of the neonatal patient. An experimentally validated second order computational fluid dynamics (CFD) solver and a parametric neonatal diseased great artery model that incorporates the ductus arteriosus (DA) and the full patient-specific circle of Willis (CoW) are employed. Standard truncated resistance CFD boundary conditions are compared with the full cerebral arterial system, which resulted 21, -13, and 37% difference in flow rate at the brachiocephalic, left carotid, and subclavian arteries, respectively. Flow splits at the aortic arch and cerebral arteries are calculated and found to change with shunt configuration significantly for TOF disease. The central direct shunt (direct shunt) has pulmonary flow 5% higher than central oblique shunt (oblique shunt) and 23% higher than modified Blalock Taussig shunt (RPA shunt) while the DA is closed. Maximum wall shear stress (WSS) in the direct shunt configuration is 9 and 60% higher than that of the oblique and RPA shunts, respectively. Patent DA, significantly eliminated the pulmonary flow control function of the shunt repair. These results suggests that, due to the higher flow rates at the pulmonary arteries, the direct shunt, rather than the central oblique, or right pulmonary artery shunts could be preferred by the surgeon. This extended model introduced new hemodynamic performance indices for the cerebral circulation that can correlate with the post-operative neurodevelopment quality of the patient.

An Euler–Lagrange approach for studying blood flow in an aneurysmal geometry

To numerically study blood flow in an aneurysm, the development of an approach that tracks the moving tissue and accounts for its interaction with the fluid is required. This study presents a mathematical approach that expands fluid mechanics principles, taking into consideration the domain’s motion. The initial fluid equations, derived in Euler form, are expanded to a mixed Euler–Lagrange formulation to study blood flow in the aneurysm during the cardiac cycle. Transport equations are transformed into a moving body-fitted reference frame using generalized curvilinear coordinates. The equations of motion consist of a coupled and nonlinear system of partial differential equations (PDEs). The PDEs are discretized using the finite volume method. Owing to strong coupling and nonlinear terms, a simultaneous solution approach is applied. The results show that velocity is substantially influenced by the pulsating wall. Intensification of polymorphic flow patterns is observed. Increments of Reynolds and Womersley numbers are evident as pulsatility increases. The pressure field reveals areas of a lateral pressure gradient at the aneurysm. As pulsatility increases, the diastolic flow vortex shifts towards the aortic wall, distal to the aneurysmal neck. Wall shear stress is amplified at the shoulders of the moving wall compared with that of the rigid one.

A Methodology for the Derivation of Unloaded Abdominal Aortic Aneurysm Geometry With Experimental Validation

In this work, we present a novel method for the derivation of the unloaded geometry of an abdominal aortic aneurysm (AAA) from a pressurized geometry in turn obtained by 3D reconstruction of computed tomography (CT) images. The approach was experimentally validated with an aneurysm phantom loaded with gauge pressures of 80, 120, and 140 mm Hg. The unloaded phantom geometries estimated from these pressurized states were compared to the actual unloaded phantom geometry, resulting in mean nodal surface distances of up to 3.9% of the maximum aneurysm diameter. An in-silico verification was also performed using a patient-specific AAA mesh, resulting in maximum nodal surface distances of 8 μm after running the algorithm for eight iterations. The methodology was then applied to 12 patient-specific AAA for which their corresponding unloaded geometries were generated in 5-8 iterations. The wall mechanics resulting from finite element analysis of the pressurized (CT image-based) and unloaded geometries were compared to quantify the relative importance of using an unloaded geometry for AAA biomechanics. The pressurized AAA models underestimate peak wall stress (quantified by the first principal stress component) on average by 15% compared to the unloaded AAA models. The validation and application of the method, readily compatible with any finite element solver, underscores the importance of generating the unloaded AAA volume mesh prior to using wall stress as a biomechanical marker for rupture risk assessment.

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.

A Review of Computational Methods to Predict the Risk of Rupture of Abdominal Aortic Aneurysms

Computational methods have played an important role in health care in recent years, as determining parameters that affect a certain medical condition is not possible in experimental conditions in many cases. Computational fluid dynamics (CFD) methods have been used to accurately determine the nature of blood flow in the cardiovascular and nervous systems and air flow in the respiratory system, thereby giving the surgeon a diagnostic tool to plan treatment accordingly. Machine learning or data mining (MLD) methods are currently used to develop models that learn from retrospective data to make a prediction regarding factors affecting the progression of a disease. These models have also been successful in incorporating factors such as patient history and occupation. MLD models can be used as a predictive tool to determine rupture potential in patients with abdominal aortic aneurysms (AAA) along with CFD-based prediction of parameters like wall shear stress and pressure distributions. A combination of these computer methods can be pivotal in bridging the gap between translational and outcomes research in medicine. This paper reviews the use of computational methods in the diagnosis and treatment of AAA.

Fluid-solid interaction in arteries incorporating the autoregulation concept in boundary conditions

In pre-surgery decisions in hospital emergency cases, fast and reliable results of the solid and fluid mechanics problems are of great interest to clinicians. In the current investigation, an iterative process based on a pressure-type boundary condition is proposed in order to reduce the computational costs of blood flow simulations in arteries, without losing control of the important clinical parameters. The incorporation of cardiovascular autoregulation, together with the well-known impedance boundary condition, forms the basis of the proposed methodology. With autoregulation, the instabilities associated with conventional pressure-type or impedance boundary conditions are avoided without an excessive increase in computational costs. The general behaviour of pulsatile blood flow in arteries, which is important from the clinical point of view, is well reproduced through this new methodology. In addition, the interaction between the blood and the arterial walls occurs via a modified weak coupling, which makes the simulation more stable and computationally efficient. Based on in vitro experiments, the hyperelastic behaviour of the wall is characterised and modelled. The applications and benefits of the proposed pressure-type boundary condition are shown in a model of an idealised aortic arch with and without an ascending aorta dissection, which is a common cardiovascular disorder.

The Effects That Cardiac Motion has on Coronary Hemodynamics and Catheter Trackability Forces for the Treatment of Coronary Artery Disease: An In Vitro Assessment

The coronary arterial tree experiences large displacements due to the contraction and expansion of the cardiac muscle and may influence coronary haemodynamics and stent placement. The accurate measurement of catheter trackability forces within physiological relevant test systems is required for optimum catheter design. The effects of cardiac motion on coronary flowrates, pressure drops, and stent delivery has not been previously experimentally assessed. A cardiac simulator was designed and manufactured which replicates physiological coronary flowrates and cardiac motion within a patient-specific geometry. A motorized delivery system delivered a commercially available coronary stent system and monitored the trackability forces along three phantom patient-specific thin walled compliant coronary vessels supported by a dynamic cardiac phantom model. Pressure drop variation is more sensitive to cardiac motion than outlet flowrates. Maximum pressure drops varied from 7 to 49 mmHg for a stenosis % area reduction of 56 to 90%. There was a strong positive linear correlation of cumulative trackability force with the cumulative curvature. The maximum trackability forces and curvature ranged from 0.24 to 0.87 N and 0.06 to 0.22 mm(-1) respectively for all three vessels. There were maximum and average percentage differences in trackability forces of (23-49%) and (1.9-5.2%) respectively when comparing a static pressure case with the inclusion of pulsatile flow and cardiac motion. Cardiac motion with pulsatile flow significantly altered (p value <0.001) the trackability forces along the delivery pathways with high local percentage variations and pressure drop measurements.

Progression of abdominal aortic aneurysm towards rupture: refining clinical risk assessment using a fully coupled fluid-structure interaction method

Rupture of abdominal aortic aneurysm (AAA) is associated with high mortality rates. Risk of rupture is multi-factorial involving AAA geometric configuration, vessel tortuosity, and the presence of intraluminal pathology. Fluid structure interaction (FSI) simulations were conducted in patient based computed tomography scans reconstructed geometries in order to monitor aneurysmal disease progression from normal aortas to non-ruptured and contained ruptured AAA (rAAA), and the AAA risk of rupture was assessed. Three groups of 8 subjects each were studied: 8 normal and 16 pathological (8 non-ruptured and 8 rAAA). The AAA anatomical structures segmented included the blood lumen, intraluminal thrombus (ILT), vessel wall, and embedded calcifications. The vessel wall was described with anisotropic material model that was matched to experimental measurements of AAA tissue specimens. A statistical model for estimating the local wall strength distribution was employed to generate a map of a rupture potential index (RPI), representing the ratio between the local stress and local strength distribution. The FSI simulations followed a clear trend of increasing wall stresses from normal to pathological cases. The maximal stresses were observed in the areas where the ILT was not present, indicating a potential protective effect of the ILT. Statistically significant differences were observed between the peak systolic stress and the peak stress at the mean arterial pressure between the three groups. For the ruptured aneurysms, where the geometry of intact aneurysm was reconstructed, results of the FSI simulations clearly depicted maximum wall stress at the a priori known location of rupture. The RPI mapping indicated several distinct regions of high RPI coinciding with the actual location of rupture. The FSI methodology demonstrates that the aneurysmal disease can be described by numerical simulations, as indicated by a clear trend of increasing aortic wall stresses in the studied groups, (normal aortas, AAAs and rAAAs). Ultimately, the results demonstrate that FSI wall stress mapping and RPI can be used as a tool for predicting the potential rupture of an AAA by predicting the actual rupture location, complementing current clinical practice by offering a predictive diagnostic tool for deciding whether to intervene surgically or spare the patient from an unnecessary risky operation.

Mathematical modeling of mammary ducts in lactating human females

This work studies a model for milk transport through lactating human breast ducts and describes mathematically the mass transfer from alveolar sacs through the mammary ducts to the nipple. In this model, both the phenomena of diffusion in the sacs and conventional flow in ducts have been considered. The ensuing analysis reveals that there is an optimal range of bifurcation numbers leading to the easiest milk flow based on the minimum flow resistance. This model formulates certain difficult-to-measure values like diameter of the alveolar sacs and the total length of the milk path as a function of easy-to-measure properties such as milk fluid properties and macroscopic measurements of the breast. Alveolar dimensions from breast tissues of six lactating women are measured and reported in this paper. The theoretically calculated alveoli diameters for optimum milk flow (as a function of bifurcation numbers) show excellent match with our biological data on alveolar dimensions. Also, the mathematical model indicates that for minimum milk flow resistance the glandular tissue must be within a short distance from the base of the nipple, an observation that matches well with the latest anatomical and physiological research.

The influence of computational assumptions on analysing abdominal aortic aneurysm haemodynamics

The variation in computational assumptions for analysing abdominal aortic aneurysm haemodynamics can influence the desired output results and computational cost. Such assumptions for abdominal aortic aneurysm modelling include static/transient pressures, steady/transient flows and rigid/compliant walls. Six computational methods and these various assumptions were simulated and compared within a realistic abdominal aortic aneurysm model with and without intraluminal thrombus. A full transient fluid-structure interaction was required to analyse the flow patterns within the compliant abdominal aortic aneurysms models. Rigid wall computational fluid dynamics overestimates the velocity magnitude by as much as 40%-65% and the wall shear stress by 30%-50%. These differences were attributed to the deforming walls which reduced the outlet volumetric flow rate for the transient fluid-structure interaction during the majority of the systolic phase. Static finite element analysis accurately approximates the deformations and von Mises stresses when compared with transient fluid-structure interaction. Simplifying the modelling complexity reduces the computational cost significantly. In conclusion, the deformation and von Mises stress can be approximately found by static finite element analysis, while for compliant models a full transient fluid-structure interaction analysis is required for acquiring the fluid flow phenomenon.

Advancements in identifying biomechanical determinants for abdominal aortic aneurysm rupture

Abdominal aortic aneurysms are a common health problem and currently the need for surgical intervention is determined based on maximum diameter and growth rate criteria. Since these universal variables often fail to predict accurately every abdominal aortic aneurysms evolution, there is a considerable effort in the literature for other markers to be identified towards individualized rupture risk estimations and growth rate predictions. To this effort, biomechanical tools have been extensively used since abdominal aortic aneurysm rupture is in fact a material failure of the diseased arterial wall to compensate the stress acting on it. The peak wall stress, the role of the unique geometry of every individual abdominal aortic aneurysm as well as the mechanical properties and the local strength of the degenerated aneurysmal wall, all confer to rupture risk. In this review article, the assessment of these variables through mechanical testing, advanced imaging and computational modeling is reviewed and the clinical perspective is discussed.

Fluid-structure interaction modeling of abdominal aortic aneurysms: the impact of patient-specific inflow conditions and fluid/solid coupling

Rupture risk assessment of abdominal aortic aneurysms (AAA) by means of biomechanical analysis is a viable alternative to the traditional clinical practice of using a critical diameter for recommending elective repair. However, an accurate prediction of biomechanical parameters, such as mechanical stress, strain, and shear stress, is possible if the AAA models and boundary conditions are truly patient specific. In this work, we present a complete fluid-structure interaction (FSI) framework for patient-specific AAA passive mechanics assessment that utilizes individualized inflow and outflow boundary conditions. The purpose of the study is two-fold: (1) to develop a novel semiautomated methodology that derives velocity components from phase-contrast magnetic resonance images (PC-MRI) in the infrarenal aorta and successfully apply it as an inflow boundary condition for a patient-specific fully coupled FSI analysis and (2) to apply a one-way-coupled FSI analysis and test its efficiency compared to transient computational solid stress and fully coupled FSI analyses for the estimation of AAA biomechanical parameters. For a fully coupled FSI simulation, our results indicate that an inlet velocity profile modeled with three patient-specific velocity components and a velocity profile modeled with only the axial velocity component yield nearly identical maximum principal stress (σ1), maximum principal strain (ε1), and wall shear stress (WSS) distributions. An inlet Womersley velocity profile leads to a 5% difference in peak σ1, 3% in peak ε1, and 14% in peak WSS compared to the three-component inlet velocity profile in the fully coupled FSI analysis. The peak wall stress and strain were found to be in phase with the systolic inlet flow rate, therefore indicating the necessity to capture the patient-specific hemodynamics by means of FSI modeling. The proposed one-way-coupled FSI approach showed potential for reasonably accurate biomechanical assessment with less computational effort, leading to differences in peak σ1, ε1, and WSS of 14%, 4%, and 18%, respectively, compared to the axial component inlet velocity profile in the fully coupled FSI analysis. The transient computational solid stress approach yielded significantly higher differences in these parameters and is not recommended for accurate assessment of AAA wall passive mechanics. This work demonstrates the influence of the flow dynamics resulting from patient-specific inflow boundary conditions on AAA biomechanical assessment and describes methods to evaluate it through fully coupled and one-way-coupled fluid-structure interaction analysis.

The role of geometric and biomechanical factors in abdominal aortic aneurysm rupture risk assessment

The current clinical management of abdominal aortic aneurysm (AAA) disease is based to a great extent on measuring the aneurysm maximum diameter to decide when timely intervention is required. Decades of clinical evidence show that aneurysm diameter is positively associated with the risk of rupture, but other parameters may also play a role in causing or predisposing the AAA to rupture. Geometric factors such as vessel tortuosity, intraluminal thrombus volume, and wall surface area are implicated in the differentiation of ruptured and unruptured AAAs. Biomechanical factors identified by means of computational modeling techniques, such as peak wall stress, have been positively correlated with rupture risk with a higher accuracy and sensitivity than maximum diameter alone. The objective of this review is to examine these factors, which are found to influence AAA disease progression, clinical management and rupture potential, as well as to highlight on-going research by our group in aneurysm modeling and rupture risk assessment.

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.

New insights into the understanding of flow dynamics in an in vitro model for abdominal aortic aneurysms

An in vitro dynamics set-up of the flow in a compliant abdominal aortic aneurysm (AAA) model with an anterior posterior asymmetry, aorto-iliac bifurcation, and physiological inlet flow rate and outlet pressure waveforms was developed. The aims were first to show that the structural mechanical behavior of the used material to mimic the AAA wall was similar to this of patients with AAA and then to study the influence of the aorto-iliac bifurcation presence and to study the influence of the imbalanced flow rate in the iliac branches on the AAA flow field. 3D visualizations, never performed in the literature, have clearly put into evidence the development of a vortex ring generated at the AAA proximal neck during the decelerating phase of flow rate, which detaches and progresses downstream during the cardiac cycle, impinges on the anterior wall in the distal AAA region, breaks up, and separates into two vortices of which one rolls on upstream along the anterior wall. 2D particle image velocimetry measurements, swirling strength and enstrophy calculations allowed quantification of the vorticity, vortex trajectory and energy for the different geometrical and hydrodynamical conditions. The main results show that the instant and the intensity of the vortex ring impingement depend on the presence of the aorto-iliac bifurcation, with higher intensity, by about 90%, for an AAA without bifurcation. The imbalance of the flow rates into the iliac branches induces different propagation velocities of the vortex ring and lowers the intensity of the vortex impact by about 60%. The potential influence of the AAA dynamics is discussed in terms of AAA remodeling and rupture.

A literature review of the numerical analysis of abdominal aortic aneurysms treated with endovascular stent grafts

The purpose of this paper is to present the basic principles and relevant advances in the computational modeling of abdominal aortic aneurysms and endovascular aneurysm repair, providing the community with up-to-date state of the art in terms of numerical analysis and biomechanics. Frameworks describing the mechanical behavior of the aortic wall already exist. However, intraluminal thrombus nonhomogeneous structure and porosity still need to be well characterized. Also, although the morphology and mechanical properties of calcifications have been investigated, their effects on wall stresses remain controversial. Computational fluid dynamics usually assumes a rigid artery wall, whereas fluid-structure interaction accounts for artery compliance but is still challenging since arteries and blood have similar densities. We discuss alternatives to fluid-structure interaction based on dynamic medical images that address patient-specific hemodynamics and geometries. We describe initial stresses, elastic boundary conditions, and statistical strength for rupture risk assessment. Special emphasis is accorded to workflow development, from the conversion of medical images into finite element models, to the simulation of catheter-aorta interactions and stent-graft deployment. Our purpose is also to elaborate the key ingredients leading to virtual stenting and endovascular repair planning that could improve the procedure and stent-grafts.

Characterization of the transport topology in patient-specific abdominal aortic aneurysm models

Abdominal aortic aneurysm (AAA) is characterized by disturbed blood flow patterns that are hypothesized to contribute to disease progression. The transport topology in six patient-specific abdominal aortic aneurysms was studied. Velocity data were obtained by image-based computational fluid dynamics modeling, with magnetic resonance imaging providing the necessary simulation parameters. Finite-time Lyapunov exponent (FTLE) fields were computed from the velocity data, and used to identify Lagrangian coherent structures (LCS). The combination of FTLE fields and LCS was used to characterize topological flow features such as separation zones, vortex transport, mixing regions, and flow impingement. These measures offer a novel perspective into AAA flow. It was observed that all aneurysms exhibited coherent vortex formation at the proximal segment of the aneurysm. The evolution of the systolic vortex strongly influences the flow topology in the aneurysm. It was difficult to predict the vortex dynamics from the aneurysm morphology, motivating the application of image-based flow modeling.

Fluid, solid and fluid-structure interaction simulations on patient-based abdominal aortic aneurysm models

This article describes the use of fluid, solid and fluid-structure interaction simulations on three patient-based abdominal aortic aneurysm geometries. All simulations were carried out using OpenFOAM, which uses the finite volume method to solve both fluid and solid equations. Initially a fluid-only simulation was carried out on a single patient-based geometry and results from this simulation were compared with experimental results. There was good qualitative and quantitative agreement between the experimental and numerical results, suggesting that OpenFOAM is capable of predicting the main features of unsteady flow through a complex patient-based abdominal aortic aneurysm geometry. The intraluminal thrombus and arterial wall were then included, and solid stress and fluid-structure interaction simulations were performed on this, and two other patient-based abdominal aortic aneurysm geometries. It was found that the solid stress simulations resulted in an under-estimation of the maximum stress by up to 5.9% when compared with the fluid-structure interaction simulations. In the fluid-structure interaction simulations, flow induced pressure within the aneurysm was found to be up to 4.8% higher than the value of peak systolic pressure imposed in the solid stress simulations, which is likely to be the cause of the variation in the stress results. In comparing the results from the initial fluid-only simulation with results from the fluid-structure interaction simulation on the same patient, it was found that wall shear stress values varied by up to 35% between the two simulation methods. It was concluded that solid stress simulations are adequate to predict the maximum stress in an aneurysm wall, while fluid-structure interaction simulations should be performed if accurate prediction of the fluid wall shear stress is necessary. Therefore, the decision to perform fluid-structure interaction simulations should be based on the particular variables of interest in a given study.

Stereoscopically observed deformations of a compliant abdominal aortic aneurysm model

A new experimental setup has been implemented to precisely measure the deformations of an entire model abdominal aortic aneurysm (AAA). This setup addresses a gap between the computational and experimental models of AAA that have aimed at improving the limited understanding of aneurysm development and rupture. The experimental validation of the deformations from computational approaches has been limited by a lack of consideration of the large and varied deformations that AAAs undergo in response to physiologic flow and pressure. To address the issue of experimentally validating these calculated deformations, a stereoscopic imaging system utilizing two cameras was constructed to measure model aneurysm displacement in response to pressurization. The three model shapes, consisting of a healthy aorta, an AAA with bifurcation, and an AAA without bifurcation, were also evaluated with computational solid mechanical modeling using finite elements to assess the impact of differences between material properties and for comparison against the experimental inflations. The device demonstrated adequate accuracy (surface points were located to within 0.07 mm) for capturing local variation while allowing the full length of the aneurysm sac to be observed at once. The experimental model AAA demonstrated realistic aneurysm behavior by having cyclic strains consistent with reported clinical observations between pressures 80 and 120 mm Hg. These strains are 1-2%, and the local spatial variations in experimental strain were less than predicted by the computational models. The three different models demonstrated that the asymmetric bifurcation creates displacement differences but not cyclic strain differences within the aneurysm sac. The technique and device captured regional variations of strain that are unobservable with diameter measures alone. It also allowed the calculation of local strain and removed rigid body motion effects on the strain calculation. The results of the computations show that an asymmetric aortic bifurcation created displacement differences but not cyclic strain differences within the aneurysm sac.

Computational evaluation of aortic aneurysm rupture risk: what have we learned so far?

In current clinical practice, aneurysm diameter is one of the primary criteria used to decide when to treat a patient with an abdominal aortic aneurysm (AAA). It has been shown that simple association of aneurysm diameter with the probability of rupture is not sufficient, and other parameters may also play a role in causing or predisposing to AAA rupture. Peak wall stress (PWS), intraluminal thrombus (ILT), and AAA wall mechanics are the factors most implicated with rupture risk and have been studied by computational risk evaluation techniques. The objective of this review is to examine these factors that have been found to influence AAA rupture. The prediction rate of rupture among computational models depends on the level of model complexity and the predictive value of the biomechanical parameters used to assess risk, such as PWS, distribution of ILT, wall strength, and the site of rupture. There is a need for simpler geometric analogues, including geometric parameters (e.g., lumen tortuosity and neck length and angulation) that correlate well with PWS, conjugated with clinical risk factors for constructing rupture risk predictive models. Such models should be supported by novel imaging techniques to provide the required patient-specific data and validated through large, prospective clinical trials.

In vivo three-dimensional MR wall shear stress estimation in ascending aortic dilatation

PURPOSE

To estimate surface-based wall shear stress (WSS) and evaluate flow patterns in ascending aortic dilatation (AscAD) using a high-resolution, time-resolved, three-dimensional (3D), three-directional velocity encoded, radially undersampled phase contrast MR sequence (4D PC-MRI).

MATERIALS AND METHODS

4D PC-MRI was performed in 11 patients with AscAD (46.3 ± 22.0 years) and 10 healthy volunteers (32.9 ± 13.4 years) after written informed consent and institutional review board approval. Following manual vessel wall segmentation of the ascending aorta (MATLAB, The Mathworks, Natick, MA), a 3D surface was created using spline interpolation. Spatial WSS variation based on surface division in 12 segments and temporal variation were evaluated in AscAD and normal aortas. Visual analysis of flow patterns was performed based on streamlines and particle traces using EnSight (v9.0, CEI, Apex, NC).

RESULTS

AscAD was associated with significantly increased diastolic WSS, decreased systolic to diastolic WSS ratio, and delayed onset of peak WSS (all P < 0.001). Temporally averaged WSS was increased and peak systolic WSS was decreased. The maximum WSS in AscAD was on the anterior wall of the ascending aorta. Vortical flow with highest velocities along the anterior wall and increased helical flow during diastole were observed in AscAD compared with controls.

CONCLUSION

Changes in WSS in the ascending aorta of AscAD correspond to observed alterations in flow patterns compared to controls.

Expanding Current EVAR Indications to Include Small Abdominal Aortic Aneurysms: A Glimpse of the Future

The traditional criterion of maximum transverse diameter is not sufficient to differentiate the small abdominal aortic aneurysms (AAAs) that are either prone to rupture or prone to enlarge rapidly. Wall stress may be a more reliable indicator with respect to these tasks. We review the importance of geometric features in rupture- or growth-predictive models and stress the need for further evaluation and validation of geometric indices. This study may lead to identifying those small AAAs that could justify early endovascular intervention.

Patient-based abdominal aortic aneurysm rupture risk prediction with fluid structure interaction modeling

Elective repair of abdominal aortic aneurysm (AAA) is warranted when the risk of rupture exceeds that of surgery, and is mostly based on the AAA size as a crude rupture predictor. A methodology based on biomechanical considerations for a reliable patient-specific prediction of AAA risk of rupture is presented. Fluid-structure interaction (FSI) simulations conducted in models reconstructed from CT scans of patients who had contained ruptured AAA (rAAA) predicted the rupture location based on mapping of the stresses developing within the aneurysmal wall, additionally showing that a smaller rAAA presented a higher rupture risk. By providing refined means to estimate the risk of rupture, the methodology may have a major impact on diagnostics and treatment of AAA patients.

Identification of rupture locations in patient-specific abdominal aortic aneurysms using experimental and computational techniques

In the event of abdominal aortic aneurysm (AAA) rupture, the outcome is often death. This paper aims to experimentally identify the rupture locations of in vitro AAA models and validate these rupture sites using finite element analysis (FEA). Silicone rubber AAA models were manufactured using two different materials (Sylgard 160 and Sylgard 170, Dow Corning) and imaged using computed tomography (CT). Experimental models were inflated until rupture with high speed photography used to capture the site of rupture. 3D reconstructions from CT scans and subsequent FEA of these models enabled the wall stress and wall thickness to be determined for each of the geometries. Experimental models ruptured at regions of inflection, not at regions of maximum diameter. Rupture pressures (mean+/-SD) for the Sylgard 160 and Sylgard 170 models were 650.6+/-195.1mmHg and 410.7+/-159.9mmHg, respectively. Computational models accurately predicted the locations of rupture. Peak wall stress for the Sylgard 160 and Sylgard 170 models was 2.15+/-0.26MPa at an internal pressure of 650mmHg and 1.69+/-0.38MPa at an internal pressure of 410mmHg, respectively. Mean wall thickness of all models was 2.19+/-0.40mm, with a mean wall thickness at the location of rupture of 1.85+/-0.33 and 1.71+/-0.29mm for the Sylgard 160 and Sylgard 170 materials, respectively. Rupture occurred at the location of peak stress in 80% (16/20) of cases and at high stress regions but not peak stress in 10% (2/20) of cases. 10% (2/20) of models had defects in the AAA wall which moved the rupture location away from regions of elevated stress. The results presented may further contribute to the understanding of AAA biomechanics and ultimately AAA rupture prediction.

A two-system, single-analysis, fluid—structure interaction technique for modelling abdominal aortic aneurysms

This work reports on the implementation and validation of a two-system, single-analysis, fluid—structure interaction (FSI) technique that uses the finite volume (FV) method for performing simulations on abdominal aortic aneurysm (AAA) geometries. This FSI technique, which was implemented in OpenFOAM, included fluid and solid mesh motion and incorporated a non-linear material model to represent AAA tissue. Fully implicit coupling was implemented, ensuring that both the fluid and solid domains reached convergence within each time step. The fluid and solid parts of the FSI code were validated independently through comparison with experimental data, before performing a complete FSI simulation on an idealized AAA geometry. Results from the FSI simulation showed that a vortex formed at the proximal end of the aneurysm during systolic acceleration, and moved towards the distal end of the aneurysm during diastole. Wall shear stress (WSS) values were found to peak at both the proximal and distal ends of the aneurysm and remain low along the centre of the aneurysm. The maximum von Mises stress in the aneurysm wall was found to be 408 kPa, and this occurred at the proximal end of the aneurysm, while the maximum displacement of 2.31 mm occurred in the centre of the aneurysm. These results were found to be consistent with results from other FSI studies in the literature.

Accelerated time-resolved three-dimensional MR velocity mapping of blood flow patterns in the aorta using SENSE and k-t BLAST

PURPOSE

To assess the feasibility and potential limitations of the acceleration techniques SENSE and k-t BLAST for time-resolved three-dimensional (3D) velocity mapping of aortic blood flow. Furthermore, to quantify differences in peak velocity versus heart phase curves.

MATERIALS AND METHODS

Time-resolved 3D blood flow patterns were investigated in eleven volunteers and two patients suffering from aortic diseases with accelerated PC-MR sequences either in combination with SENSE (R=2) or k-t BLAST (6-fold). Both sequences showed similar data acquisition times and hence acceleration efficiency. Flow-field streamlines were calculated and visualized using the GTFlow software tool in order to reconstruct 3D aortic blood flow patterns. Differences between the peak velocities from single-slice PC-MRI experiments using SENSE 2 and k-t BLAST 6 were calculated for the whole cardiac cycle and averaged for all volunteers.

RESULTS

Reconstruction of 3D flow patterns in volunteers revealed attenuations in blood flow dynamics for k-t BLAST 6 compared to SENSE 2 in terms of 3D streamlines showing fewer and less distinct vortices and reduction in peak velocity, which is caused by temporal blurring. Solely by time-resolved 3D MR velocity mapping in combination with SENSE detected pathologic blood flow patterns in patients with aortic diseases. For volunteers, we found a broadening and flattering of the peak velocity versus heart phase diagram between the two acceleration techniques, which is an evidence for the temporal blurring of the k-t BLAST approach.

CONCLUSION

We demonstrated the feasibility of SENSE and detected potential limitations of k-t BLAST when used for time-resolved 3D velocity mapping. The effects of higher k-t BLAST acceleration factors have to be considered for application in 3D velocity mapping.

Evaluating patient-specific abdominal aortic aneurysm wall stress based on flow-induced loading

In this paper, we develop a physiologic wall stress analysis procedure by incorporating experimentally measured, non-uniform pressure loading in a patient-based finite element simulation. First, the distribution of wall pressure is measured in a patient-based lumen cast at a series of physiologically relevant steady flow rates. Then, using published equi-biaxial stress-deformation data from aneurysmal tissue samples, a nonlinear hyperelastic constitutive equation is used to describe the mechanical behavior of the aneurysm wall. The model accounts of the characteristic exponential stiffening due to the rapid engagement of nearly inextensible collagen fibers and assumes, as a first approximation, an isotropic behavior of the arterial wall. The results show a complex wall stress distribution with a localized maximum principal stress value of 660 kPa on the inner surface of the posterior surface of the aneurysm bulge, a considerably larger value than has generally been reported in calculations of wall stress under the assumption of uniform loading. This is potentially significant since the posterior wall has been suggested as a common site of rupture, and the aneurysmal tensile strength reported by other authors is of the same order of magnitude as the maximum stress value found here.

Abdominal aortic aneurysm risk of rupture: patient-specific FSI simulations using anisotropic model

Abdominal aortic aneurysm (AAA) rupture represents a major cardiovascular risk, combining complex vascular mechanisms weakening the abdominal artery wall coupled with hemodynamic forces exerted on the arterial wall. At present, a reliable method to predict AAA rupture is not available. Recent studies have introduced fluid structure interaction (FSI) simulations using isotropic wall properties to map regions of stress concentrations developing in the aneurismal wall as a much better alternative to the current clinical criterion, which is based on the AAA diameter alone. A new anisotropic material model of AAA that closely matches observed biomechanical AAA material properties was applied to FSI simulations of patient-specific AAA geometries in order to develop a more reliable predictor for its risk of rupture. Each patient-specific geometry was studied with and without an intraluminal thrombus (ILT) using two material models-the more commonly used isotropic material model and an anisotropic material model-to delineate the ILT contribution and the dependence of stress distribution developing within the aneurismal wall on the material model employed. Our results clearly indicate larger stress values for the anisotropic material model and a broader range of stress values as compared to the isotropic material, indicating that the latter may underestimate the risk of rupture. While the locations of high and low stresses are consistent in both material models, the differences between the anisotropic and isotropic models become pronounced at large values of strain-a range that becomes critical when the AAA risk of rupture is imminent. As the anisotropic model more closely matches the biomechanical behavior of the AAA wall and resolves directional strength ambiguities, we conclude that it offers a more reliable predictor of AAA risk of rupture.

Full dimensional computer simulations to study pulsatile blood flow in vessels, aortic arch and bifurcated veins: Investigation of blood viscosity and turbulent effects

We report computational results of blood flow through a model of the human aortic arch and a vessel of actual diameter and length. A realistic pulsatile flow is used in all simulations. Calculations for bifurcation type vessels are also carried out and presented. Different mathematical methods for numerical solution of the fluid dynamics equations have been considered. The non-Newtonian behaviour of the human blood is investigated together with turbulence effects. A detailed time-dependent mathematical convergence test has been carried out. The results of computer simulations of the blood flow in vessels of three different geometries are presented: for pressure, strain rate and velocity component distributions we found significant disagreements between our results obtained with realistic non-Newtonian treatment of human blood and the widely used method in the literature: a simple Newtonian approximation. A significant increase of the strain rate and, as a result, the wall shear stress distribution, is found in the region of the aortic arch. Turbulent effects are found to be important, particularly in the case of bifurcation vessels.

Fluid—structure interaction in axially symmetric models of abdominal aortic aneurysms

Abdominal aortic aneurysm disease progression is probably influenced by tissue stresses and blood flow conditions and so accurate estimation of these will increase understanding of the disease and may lead to improved clinical practice. In this work the blood flow and tissue stresses in axially symmetric aneurysms are calculated using a complete fluid—structure interaction as a benchmark for calculating the error introduced by simpler calculations: rigid walled for the blood flow, homogeneous pressure for the tissue stress, as well as one-way-coupled interactions. The error in the peak von Mises stress in a homogeneous pressure calculation compared with a fluid—structure interaction calculation was less than 3.5 per cent for aneurysm diameters up to 7 cm. The error in the mean wall shear stress, in a rigid-walled calculation compared with a fluid—structure interaction calculation, varied from 30 per cent to 60 per cent with increasing aneurysm diameter. These results suggest that incorporation of the fluid—structure interaction is unnecessary for purely mechanical modelling, with the aim of evaluating the current rupture probability. However, for more complex biological modelling, perhaps with the aim of predicting the progress of the disease, where accurate estimation of the wall shear stress is essential, some form of fluid—structure interaction is necessary.