Wall stress and flow dynamics in abdominal aortic aneurysms: finite element analysis vs. fluid–structure interaction

Improving the efficiency of abdominal aortic aneurysm wall stress computations

An abdominal aortic aneurysm is a pathological dilation of the abdominal aorta, which carries a high mortality rate if ruptured. The most commonly used surrogate marker of rupture risk is the maximal transverse diameter of the aneurysm. More recent studies suggest that wall stress from models of patient-specific aneurysm geometries extracted, for instance, from computed tomography images may be a more accurate predictor of rupture risk and an important factor in AAA size progression. However, quantification of wall stress is typically computationally intensive and time-consuming, mainly due to the nonlinear mechanical behavior of the abdominal aortic aneurysm walls. These difficulties have limited the potential of computational models in clinical practice. To facilitate computation of wall stresses, we propose to use a linear approach that ensures equilibrium of wall stresses in the aneurysms. This proposed linear model approach is easy to implement and eliminates the burden of nonlinear computations. To assess the accuracy of our proposed approach to compute wall stresses, results from idealized and patient-specific model simulations were compared to those obtained using conventional approaches and to those of a hypothetical, reference abdominal aortic aneurysm model. For the reference model, wall mechanical properties and the initial unloaded and unstressed configuration were assumed to be known, and the resulting wall stresses were used as reference for comparison. Our proposed linear approach accurately approximates wall stresses for varying model geometries and wall material properties. Our findings suggest that the proposed linear approach could be used as an effective, efficient, easy-to-use clinical tool to estimate patient-specific wall stresses.

Functional and molecular imaging techniques in aortic aneurysm disease

PURPOSE OF REVIEW

Functional and molecular aortic imaging has shown great promise for evaluation of aortic disease, and may soon augment conventional assessment of aortic dimensions for the clinical management of patients.

RECENT FINDINGS

A range of imaging techniques is available for evaluation of patients with aortic disease. Magnetic resonance blood flow imaging can identify atherosclerosis prone aortic regions and may be useful for predicting aneurysm growth. Computational modeling can demonstrate significant differences in wall stress between abdominal aortic aneurysms of similar size and may better predict rupture than diameter alone. Metabolic imaging with fluorodeoxyglucose-PET [(FDG)-PET] can identify focal aortic wall inflammation that may portend rapid progression of disease. Molecular imaging with probes that target collagen and elastin can directly exhibit changes in the vessel wall associated with disease.

SUMMARY

The complexity of aortic disease is more fully revealed with new functional imaging techniques than with conventional anatomic analysis alone. This may better inform surveillance imaging regimens, medical management and decisions regarding early intervention for aortic disease.

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.

Pulse-wave propagation in straight-geometry vessels for stiffness estimation: theory, simulations, phantoms and in vitro findings

Pulse wave imaging (PWI) is an ultrasound-based method for noninvasive characterization of arterial stiffness based on pulse wave propagation. Reliable numerical models of pulse wave propagation in normal and pathological aortas could serve as powerful tools for local pulse wave analysis and a guideline for PWI measurements in vivo. The objectives of this paper are to (1) apply a fluid-structure interaction (FSI) simulation of a straight-geometry aorta to confirm the Moens-Korteweg relationship between the pulse wave velocity (PWV) and the wall modulus, and (2) validate the simulation findings against phantom and in vitro results. PWI depicted and tracked the pulse wave propagation along the abdominal wall of canine aorta in vitro in sequential Radio-Frequency (RF) ultrasound frames and estimates the PWV in the imaged wall. The same system was also used to image multiple polyacrylamide phantoms, mimicking the canine measurements as well as modeling softer and stiffer walls. Finally, the model parameters from the canine and phantom studies were used to perform 3D two-way coupled FSI simulations of pulse wave propagation and estimate the PWV. The simulation results were found to correlate well with the corresponding Moens-Korteweg equation. A high linear correlation was also established between PWV² and E measurements using the combined simulation and experimental findings (R² =  0.98) confirming the relationship established by the aforementioned equation.

An innovative numerical approach to resolve the pulse wave velocity in a healthy thoracic aorta model

Aortic dissection and atherosclerosis are highly fatal diseases. The development of both diseases is closely associated with highly complex haemodynamics. Thus, in predicting the onset of cardiac disease, it is desirable to obtain a detailed understanding of the flowfield characteristics in the human cardiovascular circulatory system. Accordingly, in this study, a numerical model of a normal human thoracic aorta is constructed using the geometry information obtained from a phase-contrast magnetic resonance imaging (PC-MRI) technique. The interaction between the blood flow and the vessel wall dynamics is then investigated using a coupled fluid-structure interaction (FSI) analysis. The simulations focus specifically on the flowfield characteristics and pulse wave velocity (PWV) of the blood flow. Instead of using a conventional PC-MRI method to measure PWV, we present an innovative application of using the FSI approach to numerically resolve PWV for the assessment of wall compliance in a thoracic aorta model. The estimated PWV for a normal thoracic aorta agrees well with the results obtained via PC-MRI measurement. In addition, simulations which consider the FSI effect yield a lower predicted value of the wall shear stress at certain locations in the cardiac cycle than models which assume a rigid vessel wall. Consequently, the model provides a suitable basis for the future development of more sophisticated methods capable of performing the computer-aided analysis of aortic blood flows.

Computational fluid dynamics evaluation of the cross-limb stent graft configuration for endovascular aneurysm repair

The technique of crossing the limbs of bifurcated modular stent grafts for endovascular aneurysm repair (EVAR) is often employed in the face of splayed aortic bifurcations to facilitate cannulation and prevent device kinking. However, little has been reported about the implications of cross-limb EVAR, especially in comparison to conventional EVAR. Previous computational fluid dynamics studies of conventional EVAR grafts have mostly utilized simplified planar stent graft geometries. We herein examined the differences between conventional and cross-limb EVAR by comparing their hemodynamic flow fields (i.e., in the "direct" and "cross" configurations, respectively). We also added a "planar" configuration, which is commonly found in the literature, to identify how well this configuration compares to out-of-plane stent graft configurations from a hemodynamic perspective. A representative patient's cross-limb stent graft geometry was segmented using computed tomography imaging in Mimics software. The cross-limb graft geometry was used to build its direct and planar counterparts in SolidWorks. Physiologic velocity and mass flow boundary conditions and blood properties were implemented for steady-state and pulsatile transient simulations in ANSYS CFX. Displacement forces, wall shear stress (WSS), and oscillatory shear index (OSI) were all comparable between the direct and cross configurations, whereas the planar geometry yielded very different predictions of hemodynamics compared to the out-of-plane stent graft configurations, particularly for displacement forces. This single-patient study suggests that the short-term hemodynamics involved in crossing the limbs is as safe as conventional EVAR. Higher helicity and improved WSS distribution of the cross-limb configuration suggest improved flow-related thrombosis resistance in the short term. However, there may be long-term fatigue implications to stent graft use in the cross configuration when compared to the direct configuration.

Quantification of Arterial Wall Inhomogeneity Size, Distribution, and Modulus Contrast Using FSI Numerical Pulse Wave Propagation

Changes in aortic wall material properties, such as stiffness, have been shown to accompany onset and progression of various cardiovascular pathologies. Pulse Wave velocity (PWV) and propagation along the aortic wall have been shown to depend on the wall stiffness (i.e. stiffer the wall, higher the PWV), and can potentially enhance the noninvasive diagnostic techniques. Conventional clinical methods involve a global examination of the pulse traveling between femoral and carotid arteries, to provide an average PWV estimate. Such methods may not prove effective in detecting wall focal changes as entailed by a range of cardiovascular diseases. A two-way-coupled fluid-structure interaction (FSI) simulation study of pulse wave propagation along inhomogeneous aortas with focal stiffening and softening has previously proved the model reliable. In this study, simulations are performed on inhomogeneous aortic walls with hard inclusions of different numbers, size and modulus in order to further characterize the effects of focal hardening on pulse wave propagation. Spatio-temporal maps of the wall displacement were used to analyze the regional pulse wave propagations and velocities. The findings showed that the quantitative markers -such as PWVs and r² s on the pre-inclusion forward, reflected and post-inclusion waves, and the width of the standing wave- as well as qualitative markers -such as diffracted reflection zone versus single reflection wave- allow the successful and reliable distinction between the changes in inclusion numbers, size and modulus. Future studies are needed to incorporate the wall softening and physiologically-relevant wall inhomogeneities such as those seen in calcifications or aneurysms.

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 morphological applicability of a novel endovascular aneurysm sealing (EVAS) system (Nellix) in patients with abdominal aortic aneurysms

OBJECTIVE

Endovascular aneurysm sealing (EVAS) using the Nellix system is a promising alternative to endovascular repair (EVR) and open surgery for abdominal aortic aneurysms (AAA). The aim of this study was to investigate the proportion of patients with AAA who are morphologically suitable for treatment with Nellix.

METHODS

Patients presenting with AAA were investigated at two regionalised vascular units. Separate cohorts were identified, who had undergone infrarenal EVR, open aneurysm repair, fenestrated endovascular repair (FEVR) or non-operative management. Pre-operative morphology was quantified using three-dimensional computed tomography according to a validated protocol. Each aneurysm was assessed for compliance with the instructions for use (IFU) of Nellix

RESULTS

776 patients were identified with mean age 75 ± 9 years. 730/776 (94.1%) had undergone infrarenal EVR, 6/776 (0.8%) open repair, 27/776 (3.5%) FEVR and 13/776 (1.7%) had been managed non-operatively. 544/776 (70.1%) of all AAA were morphologically suitable for Nellix. 533/730 (73.0%) of patients who had undergone infrarenal EVR were compliant with Nellix IFU, compared with 497/730 (68.1%), 379/730 (51.9%) and 214/730 (29.3%) with the IFU for Medtronic Endurant (p = .04) or Cook Zenith (p < .01) and Gore C3 Excluder (p < .01) endografts respectively.

CONCLUSIONS

Nellix technology appears widely applicable to contemporary infrarenal AAA practice, and may provide an option for patients that are outside current EVR device instructions for use. However, formal outcomes study is still required, and will ultimately dictate the clinical relevance of this feasibility study. The major limitation to anatomic suitability for Nellix is currently the maximum patent lumen diameter of large AAA.

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.

Predicting aortic complications after endovascular aneurysm repair

Background

Lifelong surveillance is standard after endovascular repair of abdominal aortic aneurysm (EVAR), but remains costly, heterogeneous and poorly calibrated. This study aimed to develop and validate a scoring system for aortic complications after EVAR, informing rationalized surveillance.

Methods

Patients undergoing EVAR at two centres were studied from 2004 to 2010. Preoperative morphology was quantified using three-dimensional computed tomography according to a validated protocol, by investigators blinded to outcomes. Proportional hazards modelling was used to identify factors predicting aortic complications at the first centre, and thereby derive a risk score. Sidak tests between risk quartiles dichotomized patients to low- or high-risk groups. Aortic complications were reported by Kaplan–Meier analysis and risk groups were compared by log rank test. External validation was by comparison of aortic complications between risk groups at the second centre.

Results

Some 761 patients, with a median age of 75 (interquartile range 70–80) years, underwent EVAR. Median follow-up was 36 (range 11–94) months. Physiological variables were not associated with aortic complications. A morphological risk score incorporating maximum aneurysm diameter (P &lt; 0·001) and largest common iliac diameter (measured 10 mm from the internal iliac origin; P = 0·004) allocated 75 per cent of patients to a low-risk group, with excellent discrimination between 5-year rates of aortic complication in low- and high-risk groups at both centres (centre 1: 12 versus 31 per cent, P &lt; 0·001; centre 2: 12 versus 45 per cent, P = 0·002).

Conclusion

The risk score uses commonly available morphological data to stratify the rate of complications after EVAR. The proposals for rationalized surveillance could provide clinical and economic benefits.

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.

Peak wall stress predicts expansion rate in descending thoracic aortic aneurysms

BACKGROUND

Aortic diseases, including aortic aneurysms, are the 12th leading cause of death in the United States. The incidence of descending thoracic aortic aneurysms is estimated at 10.4 per 100,000 patient-years. Growing evidence suggests that stress measurements derived from structural analysis of aortic geometries predict clinical outcomes better than diameter alone.

METHODS

Twenty-five patients undergoing clinical and radiologic surveillance for thoracic aortic aneurysms were retrospectively identified. Custom MATLAB algorithms were employed to extract aortic wall and intraluminal thrombus geometry from computed tomography angiography scans. The resulting reconstructions were loaded with 120 mm Hg of pressure using finite element analysis. Relationships among peak wall stress, aneurysm growth, and clinical outcome were examined.

RESULTS

The average patient age was 71.6 ± 10.0 years, and average follow-up time was 17.5 ± 9 months (range, 6 to 43). The mean initial aneurysm diameter was 47.8 ± 8.0 mm, and the final diameter was 52.1 ± 10.0 mm. Mean aneurysm growth rate was 2.9 ± 2.4 mm per year. A stronger correlation (r = 0.894) was found between peak wall stress and aneurysm growth rate than between maximal aortic diameter and growth rate (r = 0.531). Aneurysms undergoing surgical intervention had higher peak wall stresses than aneurysms undergoing continued surveillance (300 ± 75 kPa versus 229 ± 47 kPa, p = 0.01).

CONCLUSIONS

Computational peak wall stress in thoracic aortic aneurysms was found to be strongly correlated with aneurysm expansion rate. Aneurysms requiring surgical intervention had significantly higher peak wall stresses. Peak wall stress may better predict clinical outcome than maximal aneurysmal diameter, and therefore may guide clinical decision-making.

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.

Chronic contained abdominal aortic aneurysm rupture after suprarenal fixation fatigue fracture

Chronic contained rupture (CCR) of an abdominal aortic aneurysm is a rare condition, and differential diagnosis might be difficult. We present a clinical case of a hemodynamically stable octogenarian who presented with intermittent pain in the left lower abdomen. The patient had a history of diverticulitis, and 6 years ago, he had undergone endovascular abdominal aortic aneurysm repair (EVAR) with a Talent bifurcated prosthesis. Additionally, 20 days before his admission to our hospital, he had undergone a secondary iliac limb extension for treatment of post-EVAR rupture. On admission, abdominal plain radiography identified suprarenal fixation fracture as a possible reason for CCR, but computed tomographic angiography failed to confirm any endoleak or "active" bleeding and rupture. The patient received medication treatment for possible diverticulitis and was kept under close monitoring for suspected failure of recently performed secondary endovascular procedure and CCR. A day later, the abdominal pain symptoms worsened, and a new computed tomographic angiography confirmed the suspected CCR. The patient was treated successfully by "open" repair using a Y prosthesis. To our knowledge, this is the first reported case of post-EVAR CCR due to suprarenal fixation fatigue fracture. Lifelong post-EVAR follow-up with high level of both clinical and imaging diagnostic accuracy is essential for the early recognition and proper treatment of EVAR pitfalls.

NUMERICAL ANALYSIS OF THE WALL STRESS IN ABDOMINAL AORTIC ANEURYSM: INFLUENCE OF THE MATERIAL MODEL NEAR-INCOMPRESSIBILITY

Recently, hyperelastic mechanical models were proposed to well capture the aneurismal arterial wall anisotropic and nonlinear features experimentally observed. These models were formulated assuming the material incompressibility. However in numerical analysis, a nearly incompressible approach, i.e., a mixed formulation pressure-displacement, is usually adopted to perform finite element stress analysis of abdominal aortic aneurysm (AAA). Therefore, volume variations of the material are controlled through the volumetric energy which depends on the initial bulk modulus κ. In this paper, an analytical analysis of the influence of κ on the mechanical response of two invariant-based anisotropic models is first performed in the case of an equibiaxial tensile test. This analysis shows that for the strongly nonlinear anisotropic model, even in a restricted range of deformations, large values of κ are necessary to ensure the incompressibility condition, in order to estimate the wall stress with a reasonable precision. Finite element simulations on idealized AAA geometries are then performed. Results from these simulations show that the maximum stress in the AAA wall is underestimated in previous works, committed errors vary from 26% to 58% depending on the geometrical model complexity. In addition to affect the magnitude of the maximum stress in the aneurysm, we found that too small value of κ may also affect the location of this stress.

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.

The association of wall mechanics and morphology: a case study of abdominal aortic aneurysm growth

The purpose of this study is to evaluate the potential correlation between peak wall stress (PWS) and abdominal aortic aneurysm (AAA) morphology and how it relates to aneurysm rupture potential. Using in-house segmentation and meshing software, six 3-dimensional (3D) AAA models from a single patient followed for 28 months were generated for finite element analysis. For the AAA wall, both isotropic and anisotropic materials were used, while an isotropic material was used for the intraluminal thrombus (ILT). These models were also used to calculate 36 geometric indices characteristic of the aneurysm morphology. Using least squares regression, seven significant geometric features (p < 0.05) were found to characterize the AAA morphology during the surveillance period. By means of nonlinear regression, PWS estimated with the anisotropic material was found to be highly correlated with three of these features: maximum diameter (r = 0.992, p = 0.002), sac volume (r = 0.989, p = 0.003) and diameter to diameter ratio (r = 0.947, p = 0.033). The correlation of wall mechanics with geometry is nonlinear and reveals that PWS does not increase concomitantly with aneurysm diameter. This suggests that a quantitative characterization of AAA morphology may be advantageous in assessing rupture risk.

Application of Bioengineering Modalities in Vascular Research: Evaluating the Clinical Gain

Using knowledge gained from bioengineering studies, current vascular research focuses on the delineation of the natural history and risk assessment of clinical vascular entities with significant morbidity and mortality, making the development of new, more accurate predictive criteria a great challenge. Additionally, conclusions derived from computational simulation studies have enabled the improvement and modification of many biotechnology products that are used routinely in the treatment of vascular diseases. This review highlights the promising role of the bioengineering applications in the vascular field.

Detection of Aortic Wall Inclusion Using Regional Pulse Wave Propagation and Velocity In Silico

Monitoring of the regional stiffening of the arterial wall may prove important in the diagnosis of various vascular pathologies. The pulse wave velocity (PWV) along the aortic wall has been shown to be dependent on the wall stiffness and has played a fundamental role in a range of diagnostic methods. Conventional clinical methods involve a global examination of the pulse traveling between two remote sites, e.g. femoral and carotid arteries, to provide an average PWV estimate. However, the majority of vascular diseases entail regional vascular changes and therefore may not be detected by a global PWV estimate. In this paper, a fluid-structure interaction study of straight-geometry aortas was carried out to examine the effects of regional stiffness changes on PWV. Five homogeneous aortas with increasing wall stiffness as well as two aortas with soft and hard inclusions were considered. In each case, spatio-temporal maps of the wall motion were used to analyze the regional pulse wave propagation. On the homogeneous aortas, increasing PWVs were found to increase with the wall moduli (R² = 0.9988), indicating the reliability of the model to accurately represent the wave propagation. On the inhomogeneous aortas, formation of reflected and standing waves was observed at the site of the hard and soft inclusions, respectively. Neither the hard nor the soft inclusion had a significant effect on the velocity of the traveling pulse beyond the inclusion site, which supported the hypothesis that a global measurement of the average PWV could fail to detect regional abnormalities.

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.

A methodology to generate structured computational grids from DICOM data: application to a patient-specific abdominal aortic aneurysm (AAA) model

This study presents the generation of a multi-block structured grid on a real abdominal aortic aneurysm (AAA) acquired from Digital Imaging and Communication in Medicine (DICOM) data. With the use of a computed tomography exam (or medical images in standard DICOM format), the shape of a human organ is extracted and a structured computational grid is created. The structured grid generation is done by utilising Floater's and Gopalsamy et al.'s algorithm. The proposed methodology is applied to the AAA case, but it may also be applied to other human organs, enabling the scientist to develop an advanced patient-specific model. More importantly, the proposed methodology provides a precise reconstruction of the human organs, which is required in an AAA, where small variations in the geometry may alter the flow field, the stresses exerted on the walls and finally the rupture risk of the aneurysm.

Quantitative assessment of abdominal aortic aneurysm geometry

Recent studies have shown that the maximum transverse diameter of an abdominal aortic aneurysm (AAA) and expansion rate are not entirely reliable indicators of rupture potential. We hypothesize that aneurysm morphology and wall thickness are more predictive of rupture risk and can be the deciding factors in the clinical management of the disease. A non-invasive, image-based evaluation of AAA shape was implemented on a retrospective study of 10 ruptured and 66 unruptured aneurysms. Three-dimensional models were generated from segmented, contrast-enhanced computed tomography images. Geometric indices and regional variations in wall thickness were estimated based on novel segmentation algorithms. A model was created using a J48 decision tree algorithm and its performance was assessed using ten-fold cross validation. Feature selection was performed using the χ2-test. The model correctly classified 65 datasets and had an average prediction accuracy of 86.6% (κ=0.37). The highest ranked features were sac length, sac height, volume, surface area, maximum diameter, bulge height, and intra-luminal thrombus volume. Given that individual AAAs have complex shapes with local changes in surface curvature and wall thickness, the assessment of AAA rupture risk should be based on the accurate quantification of aneurysmal sac shape and size.

Semiautomatic vessel wall detection and quantification of wall thickness in computed tomography images of human abdominal aortic aneurysms

PURPOSE

Quantitative measurements of wall thickness in human abdominal aortic aneurysms (AAAs) may lead to more accurate methods for the evaluation of their biomechanical environment.

METHODS

The authors describe an algorithm for estimating wall thickness in AAAs based on intensity histograms and neural networks involving segmentation of contrast enhanced abdominal computed tomography images. The algorithm was applied to ten ruptured and ten unruptured AAA image data sets. Two vascular surgeons manually segmented the lumen, inner wall, and outer wall of each data set and a reference standard was defined as the average of their segmentations. Reproducibility was determined by comparing the reference standard to lumen contours generated automatically by the algorithm and a commercially available software package. Repeatability was assessed by comparing the lumen, outer wall, and inner wall contours, as well as wall thickness, made by the two surgeons using the algorithm.

RESULTS

There was high correspondence between automatic and manual measurements for the lumen area (r = 0.978 and r = 0.996 for ruptured and unruptured aneurysms, respectively) and between vascular surgeons (r = 0.987 and r = 0.992 for ruptured and unruptured aneurysms, respectively). The authors' automatic algorithm showed better results when compared to the reference with an average lumen error of 3.69%, which is less than half the error between the commercially available application Simpleware and the reference (7.53%). Wall thickness measurements also showed good agreement between vascular surgeons with average coefficients of variation of 10.59% (ruptured aneurysms) and 13.02% (unruptured aneurysms). Ruptured aneurysms exhibit significantly thicker walls (1.78 +/- 0.39 mm) than unruptured ones (1.48 +/- 0.22 mm), p = 0.044.

CONCLUSIONS

While further refinement is needed to fully automate the outer wall segmentation algorithm, these preliminary results demonstrate the method's adequate reproducibility and low interobserver variability.

In vivo assessment of blood flow patterns in abdominal aorta of mice with MRI: implications for AAA localization

Abdominal aortic aneurysms (AAA) localize in the infrarenal aorta in humans, while they are found in the suprarenal aorta in mouse models. It has been shown previously that humans experience a reversal of flow during early diastole in the infrarenal aorta during each cardiac cycle. This flow reversal causes oscillatory wall shear stress (OWSS) to be present in the infrarenal aorta of humans. OWSS has been linked to a variety of proatherogenic and proinflammatory factors. The presence of reverse flow in the mouse aorta is unknown. In this study we investigated blood flow in mice, using phase-contrast magnetic resonance (PCMR) imaging. We measured blood flow in the suprarenal and infrarenal abdominal aorta of 18 wild-type C57BL/6J mice and 15 apolipoprotein E (apoE)-/- mice. Although OWSS was not directly evaluated, results indicate that, unlike humans, there is no reversal of flow in the infrarenal aorta of wild-type or apoE-/- mice. Distensibility of the mouse aortic wall in both the suprarenal and infrarenal segments is higher than reported values for the human aorta. We conclude that normal mice do not experience the reverse flow in the infrarenal aorta that is observed in humans.

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.

Three-Dimensional Geometrical Characterization of Abdominal Aortic Aneurysms: Image-Based Wall Thickness Distribution

The clinical assessment of abdominal aortic aneurysm (AAA) rupture risk is based on the quantification of AAA size by measuring its maximum diameter from computed tomography (CT) images and estimating the expansion rate of the aneurysm sac over time. Recent findings have shown that geometrical shape and size, as well as local wall thickness may be related to this risk; thus, reliable noninvasive image-based methods to evaluate AAA geometry have a potential to become valuable clinical tools. Utilizing existing CT data, the three-dimensional geometry of nine unruptured human AAAs was reconstructed and characterized quantitatively. We propose and evaluate a series of 1D size, 2D shape, 3D size, 3D shape, and second-order curvature-based indices to quantify AAA geometry, as well as the geometry of a size-matched idealized fusiform aneurysm and a patient-specific normal abdominal aorta used as controls. The wall thickness estimation algorithm, validated in our previous work, is tested against discrete point measurements taken from a cadaver tissue model, yielding an average relative difference in AAA wall thickness of 7.8%. It is unlikely that any one of the proposed geometrical indices alone would be a reliable index of rupture risk or a threshold for elective repair. Rather, the complete geometry and a positive correlation of a set of indices should be considered to assess the potential for rupture. With this quantitative parameter assessment, future research can be directed toward statistical analyses correlating the numerical values of these parameters with the risk of aneurysm rupture or intervention (surgical or endovascular). While this work does not provide direct insight into the possible clinical use of the geometric parameters, we believe it provides the foundation necessary for future efforts in that direction.

Towards patient-specific risk assessment of abdominal aortic aneurysm

Diagnosis of vascular disease and selection and planning of therapy are to a large extent based on the geometry of the diseased vessel. Treatment of a particular vascular disease is usually considered if the geometrical parameter that characterizes the severity of the disease, e.g. % vessel narrowing, exceeds a threshold. The thresholds that are used in clinical practice are based on epidemiological knowledge, which has been obtained by clinical studies including large numbers of patients. They may apply "on average", but they can be sub-optimal for individual patients. To realize more patient-specific treatment decision criteria, more detailed knowledge may be required about the vascular hemodynamics, i.e. the blood flow and pressure in the diseased vessel and the biomechanical reaction of the vessel wall to this flow and pressure. Over the last decade, a substantial number of publications have appeared on hemodynamic modeling. Some studies have provided first evidence that this modeling may indeed be used to support therapeutic decisions. The goal of the research reported in this paper is to go one step further, namely to investigate the feasibility of a patient-specific hemodynamic modeling methodology that is not only effective (improves therapeutic decisions), but that is also efficient (easy to use, fast, as much as possible automatic) and robust (insensitive to variation in the quality of the input data, same outcome for different users). A review is presented of our research performed during the last 5 years and the results that were achieved. This research focused on the risk assessment for one particular disease, namely abdominal aortic aneurysm, a life-threatening dilatation of the abdominal aorta.