Biomechanical Rupture Risk Assessment of Abdominal Aortic Aneurysms: Model Complexity versus Predictability of Finite Element Simulations

Geometrical Factors Affect Wall Shear Stress in Saccular Aneurysms of the Infrarenal Abdominal Aorta

OBJECTIVES

Low wall shear stress (WSS) is predictive of aortic aneurysm growth and rupture. Yet, estimating WSS in a clinical setting is impractical whereas measuring aneurysm geometry is feasible. This study investigates the association between saccular aneurysm geometry of the infrarenal aorta and WSS.

METHODS

Starting with a non- aneurysmal, patient-specific, computational fluid dynamics model of the aorta, saccular aneurysms of varying geometry were created by incrementally increasing the neck width and sac depth from 1cm to 4cm. The aspect ratio (the ratio between sac depth and neck width) varied between 0.25 and 4. The peak WSS, time- averaged WSS (TAWSS), and oscillatory shear index (OSI) were measured within the aneurysm sac.

RESULTS

Decreasing the neck width from 4cm to 1cm decreased the peak WSS by 69% and the TAWSS by 83%. Increasing the sac depth from 1cm to 4cm decreased the peak WSS by 55% and OSI by 37%. The aspect ratio was negatively correlated to peak WSS (Rs -0.85, p<0.001).

CONCLUSIONS

In saccular aneurysms of the infrarenal aorta, a smaller neck width, deeper aneurysm sac, and larger aspect ratio are associated with lower peak WSS.

Computation for biomechanical analysis of aortic aneurysms: the importance of computational grid

Aortic wall stress is the most common variable of interest in abdominal aortic aneurysm (AAA) rupture risk assessment. Computation of such stress has been dominated by finite element analysis. However, the effects of finite element (FE) formulation, element quality, and methods of FE mesh construction on the efficiency, robustness, and accuracy of such computation have attracted little attention. In this study, we fill this knowledge gap by comparing the results of the calculated aortic wall stress for ten AAA patients using tetrahedral and hexahedral meshes when varying the FE formulation (displacement-based and hybrid), FE shape functions, spatial integration scheme, and number of elements through the wall thickness.

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.

Unraveling the complexity of vascular tone regulation: a multiscale computational approach to integrating chemo-mechano-biological pathways with cardiovascular biomechanics

Vascular tone regulation is a crucial aspect of cardiovascular physiology, with significant implications for overall cardiovascular health. However, the precise physiological mechanisms governing smooth muscle cell contraction and relaxation remain uncertain. The complexity of vascular tone regulation stems from its multiscale and multifactorial nature, involving global hemodynamics, local flow conditions, tissue mechanics, and biochemical pathways. Bridging this knowledge gap and translating it into clinical practice presents a challenge. In this paper, a computational model is presented to integrate chemo-mechano-biological pathways with cardiovascular biomechanics, aiming to unravel the intricacies of vascular tone regulation. The computational framework combines an algebraic description of global hemodynamics with detailed finite element analyses at the scale of vascular segments for describing their passive and active mechanical response, as well as the molecular transport problem linked with chemo-biological pathways triggered by wall shear stresses. Their coupling is accounted for by considering a two-way interaction. Specifically, the focus is on the role of nitric oxide-related molecular pathways, which play a critical role in modulating smooth muscle contraction and relaxation to maintain vascular tone. The computational framework is employed to examine the interplay between localized alterations in the biomechanical response of a specific vessel segment-such as those induced by calcifications or endothelial dysfunction-and the broader global hemodynamic conditions-both under basal and altered states. The proposed approach aims to advance our understanding of vascular tone regulation and its impact on cardiovascular health. By incorporating chemo-mechano-biological mechanisms into in silico models, this study allows us to investigate cardiovascular responses to multifactorial stimuli and incorporate the role of adaptive homeostasis in computational biomechanics frameworks.

Computational Study of Abdominal Aortic Aneurysm Walls Accounting for Patient-Specific Non-Uniform Intraluminal Thrombus Thickness and Distinct Material Models: A Pre- and Post-Rupture Case

An intraluminal thrombus (ILT) is present in the majority of abdominal aortic aneurysms, playing a crucial role in their growth and rupture. Although most computational studies do not include the ILT, in the present study, this is taken into account, laying out the whole simulation procedure, namely, from computed tomography scans to medical image segmentation, geometry reconstruction, mesh generation, biomaterial modeling, finite element analysis, and post-processing, all carried out in open software. By processing the tomography scans of a patient's aneurysm before and after rupture, digital twins are reconstructed assuming a uniform aortic wall thickness. The ILT and the aortic wall are assigned different biomaterial models; namely, the first is modeled as an isotropic linear elastic material, and the second is modeled as the Mooney-Rivlin hyperelastic material as well as the transversely isotropic hyperelastic Holzapfel-Gasser-Ogden nonlinear material. The implementation of the latter requires the designation of local Cartesian coordinate systems in the aortic wall, suitably oriented in space, for the proper orientation of the collagen fibers. The composite aneurysm geometries (ILT and aortic wall structures) are loaded with normal and hypertensive static intraluminal pressure. Based on the calculated stress and strain distributions, ILT seems to be protecting the aneurysm from a structural point of view, as the highest stresses appear in the thrombus-free areas of the aneurysmal wall.

Using averaged models from 4D ultrasound strain imaging allows to significantly differentiate local wall strains in calcified regions of abdominal aortic aneurysms

Abdominal aortic aneurysms are a degenerative disease of the aorta associated with high mortality. To date, in vivo information to characterize the individual elastic properties of the aneurysm wall in terms of rupture risk is lacking. We have used time-resolved 3D ultrasound strain imaging to calculate spatially resolved in-plane strain distributions characterized by mean and local maximum strains, as well as indices of local variations in strains. Likewise, we here present a method to generate averaged models from multiple segmentations. Strains were then calculated for single segmentations and averaged models. After registration with aneurysm geometries based on CT-A imaging, local strains were divided into two groups with and without calcifications and compared. Geometry comparison from both imaging modalities showed good agreement with a root mean squared error of 1.22 ± 0.15 mm and Hausdorff Distance of 5.45 ± 1.56 mm (mean ± sd, respectively). Using averaged models, circumferential strains in areas with calcifications were 23.2 ± 11.7% (mean ± sd) smaller and significantly distinguishable at the 5% level from areas without calcifications. For single segmentations, this was possible only in 50% of cases. The areas without calcifications showed greater heterogeneity, larger maximum strains, and smaller strain ratios when computed by use of the averaged models. Using these averaged models, reliable conclusions can be made about the local elastic properties of individual aneurysm (and long-term observations of their change), rather than just group comparisons. This is an important prerequisite for clinical application and provides qualitatively new information about the change of an abdominal aortic aneurysm in the course of disease progression compared to the diameter criterion.

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.

Fracture of the porcine aorta. Part 2: FEM modelling and inverse parameter identification

The mechanics of vascular tissue, particularly its fracture properties, are crucial in the onset and progression of vascular diseases. Vascular tissue properties are complex, and the identification of fracture mechanical properties relies on robust and efficient numerical tools. In this study, we propose a parameter identification pipeline to extract tissue properties from force-displacement and digital image correlation (DIC) data. The data has been acquired by symconCT testing porcine aorta wall specimens. Vascular tissue is modelled as a non-linear viscoelastic isotropic solid, and an isotropic cohesive zone model describes tissue fracture. The model closely replicated the experimental observations and identified the fracture energies of 1.57±0.82 kJ m^-2 and 0.96±0.34 kJ m^-2 for rupturing the porcine aortic media along the axial and circumferential directions, respectively. The identified strength was always below 350 kPa, a value significantly lower than identified through classical protocols, such as simple tension, and sheds new light on the resilience of the aorta. Further refinements to the model, such as considering rate effects in the fracture process zone and tissue anisotropy, could have improved the simulation results. STATEMENT OF SIGNIFICANCE: This paper identified porcine aorta's biomechanical properties using data acquired through a previously developed experimental protocol, the symmetry-constraint compact tension test. An implicit finite element method model mimicked the test, and a two-step approach identified the material's elastic and fracture properties directly from force-displacement curves and digital image correlation-based strain measurements. Our findings show a lower strength of the abdominal aorta as compared to the literature, which may have significant implications for the clinical evaluation of the risk of aortic rupture.

Three-dimensional growth and biomechanical risk progression of abdominal aortic aneurysms under serial computed tomography assessment

Growth of abdominal aortic aneurysms (AAAs) is often described as erratic and discontinuous. This study aimed at describing growth patterns of AAAs with respect to maximal aneurysm diameter (Dmax) and aneurysm volume, and to characterize changes in the intraluminal thrombus (ILT) and biomechanical indices as AAAs grow. 384 computed tomography angiographies (CTAs) from 100 patients (mean age 70.0, standard deviation, SD = 8.5 years, 22 women), who had undergone at least three CTAs, were included. The mean follow-up was 5.2 (SD = 2.5) years. Growth of Dmax was 2.64 mm/year (SD = 1.18), volume 13.73 cm³/year (SD = 10.24) and PWS 7.3 kPa/year (SD = 4.95). For Dmax and volume, individual patients exhibited linear growth in 87% and 77% of cases. In the tertile of patients with the slowest Dmax-growth (< 2.1 mm/year), only 67% belonged to the slowest tertile for volume-growth, and 52% and 55% to the lowest tertile of PWS- and PWRI-increase, respectively. The ILT-ratio (ILT-volume/aneurysm volume) increased with time (2.6%/year, p < 0.001), but when adjusted for volume, the ILT-ratio was inversely associated with biomechanical stress. In contrast to the notion that AAAs grow in an erratic fashion most AAAs displayed continuous and linear growth. Considering only change in Dmax, however, fails to capture the biomechanical risk progression, and parameters such as volume and the ILT-ratio need to be considered.

Abdominal aortic aneurysm volume and relative intraluminal thrombus volume might be auxiliary predictors of rupture-an observational cross-sectional study

Objectives

The study aimed to identify differences and compare anatomical and biomechanical features between elective and ruptured abdominal aortic aneurysms (AAAs).

Methods

Data (clinical, anatomical, and biomechanical) of 98 patients with AAA, 75 (76.53%) asymptomatic (Group aAAA) and 23 (23.46%) ruptured AAA (Group rAAA), were prospectively collected and analyzed. Anatomical, morphological, and biomechanical imaging markers like peak wall stress (PWS) and rupture risk equivalent diameter (RRED), comorbid conditions, and demographics were compared between the groups. Biomechanical features were assessed by analysis of Digital Imaging and Communication in Medicine images by A4clinics (Vascops), and anatomical features were assessed by 3Surgery (Trimensio). Binary and multiple logistic regression analysis were used and adjusted for confounders. Accuracy was assessed using receiving operative characteristic (ROC) curve analysis.

Results

In a multivariable model, including gender and age as confounder variables, maximal aneurysm diameter [MAD, odds ratio (OR) = 1.063], relative intraluminal thrombus (rILT, OR = 1.039), and total aneurysm volume (TAV, OR = 1.006) continued to be significant predictors of AAA rupture with PWS (OR = 1.010) and RRED (OR = 1.031). Area under the ROC curve values and correct classification (cc) for the same parameters and the model that combines MAD, TAV, and rILT were measured: MAD (0.790, cc = 75%), PWS (0.713, cc = 73%), RRED (0.717, cc = 55%), TAV (0.756, cc = 79%), rILT (0.656, cc = 60%), and MAD + TAV + rILT (0.797, cc = 82%).

Conclusion

Based on our results, in addition to MAD, other important predictors of rupture that might be used during aneurysm surveillance are TAV and rILT. Biomechanical parameters (PWS, RRED) as valuable predictors should be assessed in prospective clinical trials. Similar studies on AAA smaller than 55 mm in diameter, even difficult to organize, would be of even greater clinical value.

A quarter of a century biomechanical rupture risk assessment of abdominal aortic aneurysms. Achievements, clinical relevance, and ongoing developments

Abdominal aortic aneurysm (AAA) disease, the local enlargement of the infrarenal aorta, is a serious condition that causes many deaths, especially in men exceeding 65 years of age. Over the past quarter of a century, computational biomechanical models have been developed towards the assessment of AAA risk of rupture, technology that is now on the verge of being integrated within the clinical decision-making process. The modeling of AAA requires a holistic understanding of the clinical problem, in order to set appropriate modeling assumptions and to draw sound conclusions from the simulation results. In this article we summarize and critically discuss the proposed modeling approaches and report the outcome of clinical validation studies for a number of biomechanics-based rupture risk indices. Whilst most of the aspects concerning computational mechanics have already been settled, it is the exploration of the failure properties of the AAA wall and the acquisition of robust input data for simulations that has the greatest potential for the further improvement of this technology.

Inverse material parameter estimation of patient-specific finite element models at the carotid bifurcation: The impact of excluding the zero-pressure configuration and residual stress

The carotid bifurcation experiences a complex loading environment due to its anatomical structure. Previous in-vivo material parameter estimation methods often use simplified model geometries, isotropic hyperelastic constitutive equations or neglect key aspects of the vessel, such as the zero-pressure configuration or residual stress, all of which have independently been shown to alter the stress environment of the vessel wall. Characterizing the location of high stress in the vessel wall has often been proposed as a potential indicator of structural weakness. However, excluding the afore-mentioned zero-pressure configuration, residual stress and patient-specific material parameters can lead to an incorrect estimation of the true stress values observed, meaning that stress alone as a risk indicator of rupture is insufficient. In this study, we investigate how the estimated material parameters and overall stress distributions in geometries of carotid bifurcations, extracted from in-vivo MR images, alter with the inclusion of the zero-pressure configuration and residual stress. This approach consists of the following steps: (1) geometry segmentation and hexahedral meshing from in-vivo magnetic resonance images (MRI) at two known phases; (2) computation of the zero-pressure configuration and the associated residual stresses; (3) minimization of an objective function built on the difference between the stress states of an "almost true" stress field at two known phases and a "deformed" stress field by altering the input material parameters to determine patient-specific material properties; and (4) comparison of the stress distributions throughout these carotid bifurcations for all cases with estimated material parameters. This numerical approach provides insights into the need for estimation of both the zero-pressure configuration and residual stress for accurate material property estimation and stress analysis for the carotid bifurcation, establishing the reliability of stress as a rupture risk metric.

Interaction of the Blood Components with Ascending Thoracic Aortic Aneurysm Wall: Biomechanical and Fluid Analyses

Background: Ascending thoracic aortic aneurysm (ATAA) is an asymptomatic localized dilation of the aorta that is prone to rupture with a high rate of mortality. While diameter is the main risk factor for rupture assessment, it has been shown that the peak wall stress from finite element (FE) simulations may contribute to refinement of clinical decisions. In FE simulations, the intraluminal boundary condition is a single-phase blood flow that interacts with the thoracic aorta (TA). However, the blood is consisted of red blood cells (RBCs), white blood cells (WBCs), and plasma that interacts with the TA wall, so it may affect the resultant stresses and strains in the TA, as well as hemodynamics of the blood. Methods: In this study, discrete elements were distributed in the TA lumen to represent the blood components and mechanically coupled using fluid–structure interaction (FSI). Healthy and aneurysmal human TA tissues were subjected to axial and circumferential tensile loadings, and the hyperelastic mechanical properties were assigned to the TA and ATAA FE models. Results: The ATAA showed larger tensile and shear stresses but smaller fluid velocity compared to the ATA. The blood components experienced smaller shear stress in interaction with the ATAA wall compared to TA. The computational fluid dynamics showed smaller blood velocity and wall shear stress compared to the FSI. Conclusions: This study is a first proof of concept, and future investigations will aim at validating the novel methodology to derive a more reliable ATAA rupture risk assessment considering the interaction of the blood components with the TA wall.

The Detrimental Role of Intraluminal Thrombus Outweighs Protective Advantage in Abdominal Aortic Aneurysm Pathogenesis: The Implications for the Anti-Platelet Therapy

Abdominal aortic aneurysm (AAA) is a common cardiovascular disease resulting in morbidity and mortality in older adults due to rupture. Currently, AAA treatment relies entirely on invasive surgical treatments, including open repair and endovascular, which carry risks for small aneurysms (diameter < 55 mm). There is an increasing need for the development of pharmacological intervention for early AAA. Over the last decade, it has been increasingly recognized that intraluminal thrombus (ILT) is involved in the growth, remodeling, and rupture of AAA. ILT has been described as having both biomechanically protective and biochemically destructive properties. Platelets are the second most abundant cells in blood circulation and play an integral role in the formation, expansion, and proteolytic activity of ILT. However, the role of platelets in the ILT-potentiated AAA progression/rupture remains unclear. Researchers are seeking pharmaceutical treatment strategies (e.g., anti-thrombotic/anti-platelet therapies) to prevent ILT formation or expansion in early AAA. In this review, we mainly focus on the following: (a) the formation/deposition of ILT in the progression of AAA; (b) the dual role of ILT in the progression of AAA (protective or detrimental); (c) the function of platelet activity in ILT formation; (d) the application of anti-platelet drugs in AAA. Herein, we present challenges and future work, which may motivate researchers to better explain the potential role of ILT in the pathogenesis of AAA and develop anti-platelet drugs for early AAA.

An accurate, robust, and efficient finite element framework with applications to anisotropic, nearly and fully incompressible elasticity

Fiber-reinforced soft biological tissues are typically modeled as hyperelastic, anisotropic, and nearly incompressible materials. To enforce incompressibility a multiplicative split of the deformation gradient into a volumetric and an isochoric part is a very common approach. However, the finite element analysis of such problems often suffers from severe volumetric locking effects and numerical instabilities. In this paper, we present novel methods to overcome volumetric locking phenomena for using stabilized P1-P1 elements. We introduce different stabilization techniques and demonstrate the high robustness and computational efficiency of the chosen methods. In two benchmark problems from the literature as well as an advanced application to cardiac electromechanics, we compare the approach to standard linear elements and show the accuracy and versatility of the methods to simulate anisotropic, nearly and fully incompressible materials. We demonstrate the potential of this numerical framework to accelerate accurate simulations of biological tissues to the extent of enabling patient-specific parameterization studies, where numerous forward simulations are required.

The effects of viscoelasticity on residual strain in aortic soft tissues

Residual stress is thought to play a critical role in modulating stress distributions in soft biological tissues and in maintaining the mechanobiological stress environment of cells. Residual stresses in arteries and other tissues are classically assessed through opening angle experiments, which demonstrate the continuous release of residual stresses over hours. These results are then assessed through nonlinear biomechanical models to provide estimates of the residual stresses in the intact state. Although well studied, these analyses typically focus on hyperelastic material models despite significant evidence of viscoelastic phenomena over both short and long timescales. In this work, we extended the state-of-the-art structural tensor model for arterial tissues from Holzapfel and Ogden for fractional viscoelasticity. Models were tuned to capture consistent levels of hysteresis observed in biaxial experiments, while also minimizing the fractional viscoelastic weighting and opening angles to correctly capture opening angle dynamics. Results suggest that a substantial portion of the human abdominal aorta is viscoelastic, but exhibits a low fractional order (i.e. more elastically). Additionally, a significantly larger opening angle in the fully unloaded state is necessary to produce comparable hysteresis in biaxial testing. As a consequence, conventional estimates of residual stress using hyperelastic approaches over-estimate their viscoelastic counterparts by a factor of 2. Thus, a viscoelastic approach, such as the one illustrated in this study, in combination with an additional source of rate-controlled viscoelastic data is necessary to accurately analyze the residual stress distribution in soft biological tissues. STATEMENT OF SIGNIFICANCE: Residual stress plays a crucial role in achieving a homeostatic stress environment in soft biological tissues. However, the analysis of residual stress typically focuses on hyperelastic material models despite evidence of viscoelastic behavior. This work is the first attempt at analyzing the effects of viscoelasticity on residual stress. The application of viscoelasticity was crucial for producing realistic opening dynamics in arteries. The overall residual stresses were estimated to be 50% less than those from using hyperelastic material models, while the opening angles were projected to be 25% more than those measured after 16 hours, suggesting underestimated residual strain. This study highlights the importance viscoelasticity in the analysis of residual stress even in weakly dissipative materials like the human aorta.

On stress in abdominal aortic aneurysm: Linear versus non-linear analysis and aneurysm rupture risk

We present comprehensive biomechanical analyses of abdominal aortic aneurysms (AAA) for 43 patients. We compare stress magnitudes and stress distributions within arterial walls of abdominal aortic aneurysms (AAA) obtained using two simulation and modelling methods: (a) Fully automated and computationally very efficient linear method embedded in the software platform Biomechanics based Prediction of Aneurysm Rupture Risk (BioPARR), freely available from https://bioparr.mech.uwa.edu.au/; (b) More complex and much more computationally demanding Non-Linear Iterative Stress Analysis (Non-LISA) that uses a non-linear inverse iterative approach and strongly non-linear material model. Both methods predicted localised high stress zones with over 90% of AAA model volume fraction subjected to stress below 20% of the 99th percentile maximum principal stress. However, for the non-linear iterative method, the peak maximum principal stress (and 99th percentile maximum principal stress) was higher and the stress magnitude in the low stress area lower than for the automated linear method embedded in BioPARR. Differences between the stress distributions obtained using the two methods tended to be particularly pronounced in the areas where the AAA curvature was large. Performance of the selected characteristic features of the stress fields (we used 99th percentile maximum principal stress) obtained using BioPARR and Non-LISA in distinguishing between the AAAs that would rupture and remain intact was for practical purposes the same for both methods.

Local aortic aneurysm wall expansion measured with automated image analysis

Background

Assessment of regional aortic wall deformation (RAWD) might better predict for abdominal aortic aneurysm (AAA) rupture than the maximal aortic diameter or growth rate. Using sequential computed tomography angiograms (CTAs), we developed a streamlined, semiautomated method of computing RAWD using deformable image registration (dirRAWD).

Methods

Paired sequential CTAs performed 1 to 2 years apart of 15 patients with AAAs of various shapes and sizes were selected. Using each patient’s initial CTA, the luminal and aortic wall surfaces were segmented both manually and semiautomatically. Next, the same patient’s follow-up CTA was aligned with the first using automated rigid image registration. Deformable image registration was then used to calculate the local aneurysm wall expansion between the sequential scans (dirRAWD). To measure technique accuracy, the deformable registration results were compared with the local displacement of anatomic landmarks (fiducial markers), such as the origin of the inferior mesenteric artery and/or aortic wall calcifications. Additionally, for each patient, the maximal RAWD was manually measured for each aneurysm and was compared with the dirRAWD at the same location.

Results

The technique was successful in all patients. The mean landmark displacement error was 0.59 ± 0.93 mm with no difference between true landmark displacement and deformable registration landmark displacement by Wilcoxon rank sum test (P = .39). The absolute difference between the manually measured maximal RAWD and dirRAWD was 0.27 ± 0.23 mm, with a relative difference of 7.9% and no difference using the Wilcoxon rank sum test (P = .69). No differences were found in the maximal dirRAWD when derived using a purely manual AAA segmentation compared with using semiautomated AAA segmentation (P = .55).

Conclusions

We found accurate and automated RAWD measurements were feasible with clinically insignificant errors. Using semiautomated AAA segmentations for deformable image registration methods did not alter maximal dirRAWD accuracy compared with using manual AAA segmentations. Future work will compare dirRAWD with finite element analysis–derived regional wall stress and determine whether dirRAWD might serve as an independent predictor of rupture risk.

Current abdominal aortic aneurysm (AAA) surveillance methods are limited to assessments of the maximal diameter, which cannot accurately predict for AAA expansion and rupture risk. Automated assessment of AAA expansion across the entire three-dimensional geometry of the aneurysm could better describe aneurysm growth and could substantially inform management decisions, including the indications for repair. We have developed an accurate and streamlined approach to assessing local three-dimensional AAA expansion with submillimeter accuracy using computed tomography imaging obtained during routine aneurysm surveillance. This novel process does not require significant user expertise nor computer processing power and can be performed using open-source software readily accessible to both scientists and clinicians.

Low Shear Stress at Baseline Predicts Expansion and Aneurysm-Related Events in Patients With Abdominal Aortic Aneurysm

BACKGROUND

Low shear stress has been implicated in abdominal aortic aneurysm (AAA) expansion and clinical events. We tested the hypothesis that low shear stress in AAA at baseline is a marker of expansion rate and future aneurysm-related events.

METHODS

Patients were imaged with computed tomography angiography at baseline and followed up every 6 months >24 months with ultrasound measurements of maximum diameter. From baseline computed tomography angiography, we reconstructed 3-dimensional models for automated computational fluid dynamics simulations and computed luminal shear stress. The primary composite end point was aneurysm repair and/or rupture, and the secondary end point was aneurysm expansion rate.

RESULTS

We included 295 patients with median AAA diameter of 49 mm (interquartile range, 43-54 mm) and median follow-up of 914 (interquartile range, 670-1112) days. There were 114 (39%) aneurysm-related events, with 13 AAA ruptures and 98 repairs (one rupture was repaired). Patients with low shear stress (<0.4 Pa) experienced a higher number of aneurysm-related events (44%) compared with medium (0.4-0.6 Pa; 27%) and high (>0.6 Pa; 29%) shear stress groups (P=0.010). This association was independent of known risk factors (adjusted hazard ratio, 1.72 [95% CI, 1.08-2.73]; P=0.023). Low shear stress was also independently associated with AAA expansion rate (β=+0.28 mm/y [95% CI, 0.02-0.53]; P=0.037).

CONCLUSIONS

We show for the first time that low shear stress (<0.4 Pa) at baseline is associated with both AAA expansion and future aneurysm-related events. Aneurysms within the lowest tertile of shear stress, versus those with higher shear stress, were more likely to rupture or reach thresholds for elective repair. Larger prospective validation trials are needed to confirm these findings and translate them into clinical management.

Stress Analysis in AAA does not Predict Rupture Location Correctly in Patients with Intraluminal Thrombus

BACKGROUND

A biomechanical approach to the rupture risk of an abdominal aortic aneurysm could be a solution to ensure a personalized estimate of this risk. It is still difficult to know in what conditions, the assumptions made by biomechanics, are valid. The objective of this work was to determine the individual biomechanical rupture threshold and to assess the correlation between their rupture sites and the locations of their maximum stress comparing two computed tomography scan (CT) before and at time of rupture.

METHODS

We included 5 patients who had undergone two CT; one within the last 6 months period before rupture and a second CT scan just before the surgical procedure for the rupture. All DICOM data, both pre- and rupture, were processed following the same following steps: generation of a 3D geometry of the abdominal aortic aneurysm, meshing and computational stress analysis using the finite element method. We used two different modelling scenarios to study the distribution of the stresses, a "wall" model without intraluminal thrombus (ILT) and a "thrombus" model with ILT.

RESULTS

The average time between the pre-rupture and rupture CT scans was 44 days (22-97). The median of the maximum stresses applied to the wall between the pre-rupture and rupture states were 0.817 MPa (0.555-1.295) and 1.160 MPa (0.633-1.625) for the "wall" model; and 0.365 MPa (0.291-0.753) and 0.390 MPa (0.343-0.819) for the "thrombus" model. There was an agreement between the site of rupture and the location of maximum stress for only 1 patient, who was the only patient without ILT.

CONCLUSIONS

We observed a large variability of stress values at rupture sites between patients. The rupture threshold strongly varied between individuals depending on the intraluminal thrombus. The site of rupture did not correlate with the maximum stress except for 1 patient.

Geometric and biomechanical modeling aided by machine learning improves the prediction of growth and rupture of small abdominal aortic aneurysms

It remains difficult to predict when which patients with abdominal aortic aneurysm (AAA) will require surgery. The aim was to study the accuracy of geometric and biomechanical analysis of small AAAs to predict reaching the threshold for surgery, diameter growth rate and rupture or symptomatic aneurysm. 189 patients with AAAs of diameters 40–50 mm were included, 161 had undergone two CTAs. Geometric and biomechanical variables were used in prediction modelling. Classifications were evaluated with area under receiver operating characteristic curve (AUC) and regressions with correlation between observed and predicted growth rates. Compared with the baseline clinical diameter, geometric-biomechanical analysis improved prediction of reaching surgical threshold within four years (AUC 0.80 vs 0.85, p = 0.031) and prediction of diameter growth rate (r = 0.17 vs r = 0.38, p = 0.0031), mainly due to the addition of semiautomatic diameter measurements. There was a trend towards increased precision of volume growth rate prediction (r = 0.37 vs r = 0.45, p = 0.081). Lumen diameter and biomechanical indices were the only variables that could predict future rupture or symptomatic AAA (AUCs 0.65–0.67). Enhanced precision of diameter measurements improves the prediction of reaching the surgical threshold and diameter growth rate, while lumen diameter and biomechanical analysis predicts rupture or symptomatic AAA.

A Predictive Analysis of Wall Stress in Abdominal Aortic Aneurysms Using a Neural Network Model

Rupture risk assessment of abdominal aortic aneurysms (AAAs) by means of quantifying wall stress is a common biomechanical strategy. However, the clinical translation of this approach has been greatly limited due to the complexity associated with the computational tools required for its implementation. Thus, being able to estimate wall stress using nonbiomechanical markers that can be quantified as a direct outcome of clinical image segmentation would be advantageous in improving the potential implementation of said strategy. In the present work, we investigated the use of geometric indices to predict patient-specific AAA wall stress by means of a novel neural network (NN) modeling approach. We conducted a retrospective review of existing clinical images of two patient groups: 98 asymptomatic and 50 symptomatic AAAs. The images were subject to a protocol consisting of image segmentation, processing, volume meshing, finite element modeling, and geometry quantification, from which 53 geometric indices and the spatially averaged wall stress (SAWS) were calculated. SAWS estimated from finite element analysis was considered the gold standard for the predictions. We developed feed-forward NN models composed of an input layer, two dense layers, and an output layer using Keras, a deep learning library in python. The NN models were trained, tested, and validated independently for both AAA groups using all geometric indices, as well as a reduced set of indices resulting from a variable reduction procedure. We compared the performance of the NN models with two standard machine learning algorithms (MARS: multivariate adaptive regression splines and GAM: generalized additive model) and a linear regression model (GLM: generalized linear model). With the reduced sets of indices, the NN-based approach exhibited the highest mean goodness-of-fit (for the symptomatic group 0.71 and for the asymptomatic group 0.79) and lowest mean relative error (17% for both groups). In contrast, MARS yielded a mean goodness-of-fit of 0.59 for the symptomatic group and 0.77 for the asymptomatic group, with relative errors of 17% for the symptomatic group and 22% for the asymptomatic group. GAM had a mean goodness-of-fit of 0.70 for the symptomatic group and 0.80 for the asymptomatic group, with relative errors of 16% for the symptomatic group and 20% for the asymptomatic group. GLM did not perform as well as the other algorithms, with a mean goodness-of-fit of 0.53 for the symptomatic group and 0.70 for the asymptomatic group, with relative errors of 19% for the symptomatic group and 23% for the asymptomatic group. Nevertheless, the NN models required a reduced set of 15 and 13 geometric indices to predict SAWS for the symptomatic and asymptomatic AAA groups, respectively. This was in contrast to the reduced set of nine and eight geometric indices required to predict SAWS with the MARS and GAM algorithms for each AAA group, respectively. The use of NN modeling represents a promising alternative methodology for the estimation of AAA wall stress using geometric indices as surrogates, in lieu of finite element modeling. The performance metrics of NN models are expected to improve with significantly larger group sizes, given the suitability of NN modeling for "big data" applications.

Comparison of peak wall stress and peak wall rupture index in ruptured and asymptomatic intact abdominal aortic aneurysms

BACKGROUND

Previous studies have suggested that finite element analysis (FEA) can estimate the rupture risk of an abdominal aortic aneurysm (AAA); however, the value of biomechanical estimates over measurement of AAA diameter alone remains unclear. This study aimed to compare peak wall stress (PWS) and peak wall rupture index (PWRI) in participants with ruptured and asymptomatic intact AAAs.

METHODS

The reproducibility of semiautomated methods for estimating aortic PWS and PWRI from CT images was assessed. PWS and PWRI were estimated in people with ruptured AAAs and those with asymptomatic intact AAAs matched by orthogonal diameter on a 1 : 2 basis. Spearman's correlation coefficient was used to assess the association between PWS or PWRI and AAA diameter. Independent associations between PWS or PWRI and AAA rupture were identified by means of logistic regression analyses.

RESULTS

Twenty individuals were included in the analysis of reproducibility. The main analysis included 50 patients with an intact AAA and 25 with a ruptured AAA. Median orthogonal diameter was similar in ruptured and intact AAAs (82·3 (i.q.r. 73·5-92·0) versus 81·0 (73·2-92·4) mm respectively; P = 0·906). Median PWS values were 286·8 (220·2-329·6) and 245·8 (215·2-302·3) kPa respectively (P = 0·192). There was no significant difference in PWRI between the two groups (P = 0·982). PWS and PWRI correlated positively with orthogonal diameter (both P < 0·001). Participants with high PWS, but not PWRI, were more likely to have a ruptured AAA after adjusting for potential confounders (odds ratio 5·84, 95 per cent c.i. 1·22 to 27·95; P = 0·027). This association was not maintained in all sensitivity analyses.

CONCLUSION

High aortic PWS had an inconsistent association with greater odds of aneurysm rupture in patients with a large AAA.

Mechanical role of intraluminal thrombus in aneurysm growth: A computational study

Models that seek to improve our current understanding of biochemical processes and predict disease progression have been increasingly in use over the last decades. Recently, we proposed a finite element implementation of arterial wall growth and remodeling with application to abdominal aortic aneurysms (AAAs). The study focused on changes within the aortic wall and did not include the complex role of intraluminal thrombus (ILT) during the AAA evolution. Thus, in this work, we extend the model with a gradual deposition of ILT and its mechanical influence on AAA growth. Despite neglecting the increased biochemical activity due to the presence of a proteolytically active luminal layer of ILT, and thus underestimating rupture risk potential, we show that ILT helps to slow down the growth of the aneurysm in the axial direction by redirecting blood pressure loading from the axial-radial plane to predominately radial direction. This very likely lowers rupture potential. We also show that the ratio of ILT volume to volume sac is an important factor in AAA stabilization and that fully thrombosed aneurysms could stabilize quicker and at smaller maximum diameters compared to partially thrombosed ones. Furthermore, we show that ILT formation and the associated mural stress decrease negatively impact the wall constituent production and thickness. Although further studies that include increased biochemical degradation of the wall after the formation of ILT and ILT deposition based on hemodynamics are needed, the present findings highlight the dual role an ILT plays during AAA progression.

Systematic Review and Meta-Analysis of Peak Wall Stress and Peak Wall Rupture Index in Ruptured and Asymptomatic Intact Abdominal Aortic Aneurysms

Background Prior studies have suggested aortic peak wall stress (PWS) and peak wall rupture index (PWRI) can estimate the rupture risk of an abdominal aortic aneurysm (AAA), but whether these measurements have independent predictive ability over assessing AAA diameter alone is unclear. The aim of this systematic review was to compare PWS and PWRI in participants with ruptured and asymptomatic intact AAAs of similar diameter. Methods and Results Web of Science, Scopus, Medline, and The Cochrane Library were systematically searched to identify studies assessing PWS and PWRI in ruptured and asymptomatic intact AAAs of similar diameter. Random-effects meta-analyses were performed using inverse variance-weighted methods. Leave-one-out sensitivity analyses were conducted to assess the robustness of findings. Risk of bias was assessed using a modification of the Newcastle-Ottawa scale and standard quality assessment criteria for evaluating primary research papers. Seven case-control studies involving 309 participants were included. Meta-analyses suggested that PWRI (standardized mean difference, 0.42; 95% CI, 0.14-0.70; P=0.004) but not PWS (standardized mean difference, 0.13; 95% CI, -0.18 to 0.44; P=0.418) was greater in ruptured than intact AAAs. Sensitivity analyses suggested that the findings were not dependent on the inclusion of any single study. The included studies were assessed to have a medium to high risk of bias. Conclusions Based on limited evidence, this study suggested that PWRI, but not PWS, is greater in ruptured than asymptomatic intact AAAs of similar maximum aortic diameter.

Oxidative Stress and Inflammatory Markers in Abdominal Aortic Aneurysm

Abdominal aortic aneurysm (AAA) is increasing due to aging of the population and is a major cause of death among the elderly. Ultrasound screening programs are useful in early diagnosis, but aneurysm size is not always a good predictor of rupture. Our aim was to analyze the value of circulating molecules related to oxidative stress and inflammation as new biomarkers to assist the management of AAA. The markers were quantified by ELISA, and their expression in the aneurysmal wall was studied by real-time PCR and by immunostaining. Correlation analysis of the studied markers with aneurysm diameter and peak wall stress (PWS), obtained by finite element analysis, and multivariate regression analysis to assess potential confounding factors were performed. Our study shows an extensive inflammatory infiltration in the aneurysmal wall, mainly composed by T-cells, macrophages and B-cells and altered levels of reactive oxygen species (ROS), IgM, IgG, CD38, GDF15, S100A4 and CD36 in plasma and in the aneurysmal tissue of AAA patients compared with controls. Circulating levels of IgG, CD38 and GDF15 positively correlated with abdominal aortic diameter, and CD38 was correlated with PWS. Our data show that altered levels of IgG, CD38 and GDF15 have potential diagnostic value in the assessment of AAA.

Statistical techniques for predicting rupture risk in abdominal aortic aneurysms: A contribution based on bootstrap

The morphometry of abdominal aortic aneurysms (AAA) has been recognized as one of the main factors that may predispose them to rupture. The need to quantify the morphometry of AAA on a patient-specific basis constitutes a valuable tool for assisting in rupture risk prediction. Previous results of this research group have determined the correlations between hemodynamic stresses and aneurysm morphometry by means of the Pearson coefficient. The present work aims to find how the AAA morphology correlates with the hemodynamic stresses acting on the arterial wall. To do so, the potential of the bootstrap technique has been explored. Bootstrap works appropriately in applications where few data are available (13 patient-specific AAA models were simulated). The methodology developed can be considered a contribution to predicting the hemodynamic stresses from the size and shape indices. The present work explores the use of a specific statistical technique (the bootstrap technique) to predict, based on morphological correlations, the patient-specific aneurysm rupture risk, provide greater understanding of this complex phenomenon that can bring about improvements in the clinical management of aneurysmatic patients. The results obtained using the bootstrap technique have greater reliability and robustness than those obtained by regression analysis using the Pearson coefficient, thus allowing to obtain more reliable results from the characteristics of the samples used, such as their small size and high variability. Additionally, it could be an indicator that other indices, such as AAA length, deformation rate, saccular index, and asymmetry, are important.

Enhancing Lateral Contrast Using Multi-perspective Ultrasound Imaging of Abdominal Aortas

Vascular ultrasound imaging is inherently hampered by low lateral resolution and contrast. Steering of the ultrasound beams can be used to overcome these limitations in superficial artery imaging because the aperture-to-depth ratio is relatively high. However, in arteries located at larger depths, the steered beams do not overlap for larger steering angles. In this study, the ultrasound probe is physically translated over the abdomen to create large angles between acquisitions, while maintaining overlap on the abdominal aorta. In one phantom setup and 11 volunteers, 2-D cross-sectional multi-perspective ultrasound images of the abdominal aorta were acquired using seven angles between -45° and +45°. Automatic registration of the recorded images was performed by automatic feature detection of the aorta and spine. This automatic detection was successful in 62 out of 77 image sets. Compounded multi-perspective images showed an increase of contrast-to-noise ratios from 0.6 ± 0.1 to 1.2 ± 0.2 over the entire heart cycle in volunteers.

Methodology for Estimation of Annual Risk of Rupture for Abdominal Aortic Aneurysm

BACKGROUND AND OBJECTIVE

Estimating patient specific annual risk of rupture of abdominal aortic aneurysm (AAA) is currently based only on population. More accurate knowledge based on patient specific data would allow surgical treatment of only those AAAs with significant risk of rupture. This would be beneficial for both patients and health care system.

METHODS

A methodology for estimating annual risk of rupture (EARR) of abdominal aortic aneurysms (AAA) that utilizes Bayesian statistics, mechanics and patient-specific blood pressure monitoring data is proposed. EARR estimation takes into consideration, peak wall stress in AAA computed by patient-specific finite element modeling, the probability distributions of wall thickness, wall strength, systolic blood pressure and the period of time that the patient is known to have already survived with the intact AAA. Initial testing of proposed approach was performed on fifteen patients with intact AAA (mean maximal diameter 51mm±8mm). They were equipped with a pressure holter and their blood pressure was recorded over 24 hours. Then, we calculated EARR values for four possible scenarios - without considering any days of survival prior identification of AAA at computed tomography scans (EARR_0), considering past survival of 30 (EARR_30), 90 (EARR_90) and 180 days (EARR_180). Finally, effect of patient-specific blood pressure variability was analyzed.

RESULTS

Consideration of past survival does indeed significantly improve predictions of future risk: EARR_30 (1.04%± 0.87%), EARR_90 (0.67%± 0.56%) and EARR_180 (0.47%± 0.39%) which are unrealistically high otherwise (EARR_0 5.02%± 5.24%). Finally, EARR values were observed to vary by an order as a consequence of blood pressure variability and by factor of two as a consequence of neglected growth.

CONCLUSIONS

Methodology for computing annual risk of rupture of AAA was developed for the first time. Sensitivity analyses showed respecting patient specific blood pressure is important factor and should be included in the AAA rupture risk assessment. Obtained EARR values were generally low and in good agreement with confirmed survival time of investigated patients so proposed method should be further clinically validated.

Estimating aortic thoracic aneurysm rupture risk using tension-strain data in physiological pressure range: an in vitro study

Previous studies have shown that the rupture properties of an ascending thoracic aortic aneurysm (ATAA) are strongly correlated with the pre-rupture response features. In this work, we present a two-step machine learning method to predict where the rupture is likely to occur in ATAA and what safety reserve the structure may have. The study was carried out using ATAA specimens from 15 patients who underwent surgical intervention. Through inflation test, full-field deformation data and post-rupture images were collected, from which the wall tension and surface strain distributions were computed. The tension-strain data in the pressure range of 9-18 kPa were fitted to a third-order polynomial to characterize the response properties. It is hypothesized that the region where rupture is prone to initiate is associated with a high level of tension buildup. A machine learning method is devised to predict the peak risk region. The predicted regions were found to match the actual rupture sites in 13 samples out of the total 15. In the second step, another machine learning model is utilized to predict the tissue's rupture strength in the peak risk region. Results suggest that the ATAA rupture risk can be reasonably predicted using tension-strain response in the physiological range. This may open a pathway for evaluating the ATAA rupture propensity using information of in vivo response.

Prediction of local strength of ascending thoracic aortic aneurysms

Knowledges of both local stress and strength are needed for a reliable evaluation of the rupture risk for ascending thoracic aortic aneurysm (ATAA). In this study, machine learning is applied to predict the local strength of ATAA tissues based on tension-strain data collected through in vitro inflation tests on tissue samples. Inputs to machine learning models are tension, strain, slope, and curvature values at two points on the low strain region of the tension-strain curve. The models are trained using data from locations where the tissue ruptured, and subsequently applied to data from intact sites to predict the local rupture strength. The predicted strengths are compared with the known strength at rupture sites as well as the highest tension the tissues experienced at the intact sites. A local rupture index, which is the ratio of the end tension to the predicted rupture strength, is computed. The 'hot spots' of the rupture index are found to match the rupture sites better than those of the peak tension. The study suggests that the strength of ATAA tissue could be reliably predicted from early phase response features defined in this work.

Sources of inconsistency in mean mechanical response of abdominal aortic aneurysm tissue

INTRODUCTION

There is a striking difference in the reported mean response of abdominal aortic aneurysm tissue in academic literature depending on the type of tests (uniaxial vs biaxial) performed. In this paper, the hypothesis variability caused by differences in experimental protocols is explored using porcine aortic tissue as a substitute for aneurysmal tissue.

METHODS

Nine samples of porcine aorta were created and both uniaxial and biaxial tests were performed. Three effects were investigated. (i) Effect of sample (non) preconditioning, (ii) effect of objective function used (normalised vs non-normalised), and (iii) effect of chosen procedure used for mean response calculation: constant averaging (CA) vs fit to averaged response (FAR) vs fit to all data (FAD). Both the overall shape of mean curve and mean initial stiffness were compared.

RESULTS

(i) Non-preconditioning led to a much stiffer response, and initial stiffness was about three times higher for a non-preconditioned response based on uniaxial data compared to a preconditioned biaxial response. (ii) CA led to a much stiffer response compared to FAR and FAD procedures which gave similar results. (iii) Normalised objective function produced a mean response with six times lower initial stiffness and more pronounced nonlinearity compared to non-normalised objective function.

DISCUSSION

It is possible to reproduce a mechanically inconsistent response purely by using the chosen experimental protocol. Non-preconditioned data from failure tests should be used for FE simulation of the elastic response of aneurysms. CA should not be used to obtain a mean response.

Biomechanical rupture risk assessment of abdominal aortic aneurysms using clinical data: A patient-specific, probabilistic framework and comparative case-control study

We present a data-informed, highly personalized, probabilistic approach for the quantification of abdominal aortic aneurysm (AAA) rupture risk. Our novel framework builds upon a comprehensive database of tensile test results that were carried out on 305 AAA tissue samples from 139 patients, as well as corresponding non-invasively and clinically accessible patient-specific data. Based on this, a multivariate regression model is created to obtain a probabilistic description of personalized vessel wall properties associated with a prospective AAA patient. We formulate a probabilistic rupture risk index that consistently incorporates the available statistical information and generalizes existing approaches. For the efficient evaluation of this index, a flexible Kriging-based surrogate model with an active training process is proposed. In a case-control study, the methodology is applied on a total of 36 retrospective, diameter matched asymptomatic (group 1, n = 18) and known symptomatic/ruptured (group 2, n = 18) cohort of AAA patients. Finally, we show its efficacy to discriminate between the two groups and demonstrate competitive performance in comparison to existing deterministic and probabilistic biomechanical indices.

Predictors of Abdominal Aortic Aneurysm Risks

Computational biomechanics via finite element analysis (FEA) has long promised a means of assessing patient-specific abdominal aortic aneurysm (AAA) rupture risk with greater efficacy than current clinically used size-based criteria. The pursuit stems from the notion that AAA rupture occurs when wall stress exceeds wall strength. Quantification of peak (maximum) wall stress (PWS) has been at the cornerstone of this research, with numerous studies having demonstrated that PWS better differentiates ruptured AAAs from non-ruptured AAAs. In contrast to wall stress models, which have become progressively more sophisticated, there has been relatively little progress in estimating patient-specific wall strength. This is because wall strength cannot be inferred non-invasively, and measurements from excised patient tissues show a large spectrum of wall strength values. In this review, we highlight studies that investigated the relationship between biomechanics and AAA rupture risk. We conclude that combining wall stress and wall strength approximations should provide better estimations of AAA rupture risk. However, before personalized biomechanical AAA risk assessment can become a reality, better methods for estimating patient-specific wall properties or surrogate markers of aortic wall degradation are needed. Artificial intelligence methods can be key in stratifying patients, leading to personalized AAA risk assessment.

Multimodality Imaging-Based Characterization of Regional Material Properties in a Murine Model of Aortic Dissection

Chronic infusion of angiotensin-II in atheroprone (ApoE-/-) mice provides a reproducible model of dissection in the suprarenal abdominal aorta, often with a false lumen and intramural thrombus that thickens the wall. Such lesions exhibit complex morphologies, with different regions characterized by localized changes in wall composition, microstructure, and properties. We sought to quantify the multiaxial mechanical properties of murine dissecting aneurysm samples by combining in vitro extension-distension data with full-field multimodality measurements of wall strain and thickness to inform an inverse material characterization using the virtual fields method. A key advance is the use of a digital volume correlation approach that allows for characterization of properties not only along and around the lesion, but also across its wall. Specifically, deformations are measured at the adventitial surface by tracking motions of a speckle pattern using a custom panoramic digital image correlation technique while deformations throughout the wall and thrombus are inferred from optical coherence tomography. These measurements are registered and combined in 3D to reconstruct the reference geometry and compute the 3D finite strain fields in response to pressurization. Results reveal dramatic regional variations in material stiffness and strain energy, which reflect local changes in constituent area fractions obtained from histology but emphasize the complexity of lesion morphology and damage within the dissected wall. This is the first point-wise biomechanical characterization of such complex, heterogeneous arterial segments. Because matrix remodeling is critical to the formation and growth of these lesions, we submit that quantification of regional material properties will increase the understanding of pathological mechanical mechanisms underlying aortic dissection.

A Comparative Study of Biomechanical and Geometrical Attributes of Abdominal Aortic Aneurysms in the Asian and Caucasian Populations

In this work, we provide a quantitative assessment of the biomechanical and geometric features that characterize abdominal aortic aneurysm (AAA) models generated from 19 Asian and 19 Caucasian diameter-matched AAA patients. 3D patient-specific finite element models were generated and used to compute peak wall stress (PWS), 99th percentile wall stress (99th WS), and spatially averaged wall stress (AWS) for each AAA. In addition, 51 global geometric indices were calculated, which quantify the wall thickness, shape, and curvature of each AAA. The indices were correlated with 99th WS (the only biomechanical metric that exhibited significant association with geometric indices) using Spearman's correlation and subsequently with multivariate linear regression using backward elimination. For the Asian AAA group, 99th WS was highly correlated (R2 = 0.77) with three geometric indices, namely tortuosity, intraluminal thrombus volume, and area-averaged Gaussian curvature. Similarly, 99th WS in the Caucasian AAA group was highly correlated (R2 = 0.87) with six geometric indices, namely maximum AAA diameter, distal neck diameter, diameter-height ratio, minimum wall thickness variance, mode of the wall thickness variance, and area-averaged Gaussian curvature. Significant differences were found between the two groups for ten geometric indices; however, no differences were found for any of their respective biomechanical attributes. Assuming maximum AAA diameter as the most predictive metric for wall stress was found to be imprecise: 24% and 28% accuracy for the Asian and Caucasian groups, respectively. This investigation reveals that geometric indices other than maximum AAA diameter can serve as predictors of wall stress, and potentially for assessment of aneurysm rupture risk, in the Asian and Caucasian AAA populations.

An efficient and accurate method for modeling nonlinear fractional viscoelastic biomaterials

Computational biomechanics plays an important role in biomedical engineering: using modeling to understand pathophysiology, treatment and device design. While experimental evidence indicates that the mechanical response of most tissues is viscoelastic, current biomechanical models in the computational community often assume hyperelastic material models. Fractional viscoelastic constitutive models have been successfully used in literature to capture viscoelastic material response; however, the translation of these models into computational platforms remains limited. Many experimentally derived viscoelastic constitutive models are not suitable for three-dimensional simulations. Furthermore, the use of fractional derivatives can be computationally prohibitive, with a number of current numerical approximations having a computational cost that is 𝒪 ( N T 2 ) and a storage cost that is 𝒪(N_T ) (N_T denotes the number of time steps). In this paper, we present a novel numerical approximation to the Caputo derivative which exploits a recurrence relation similar to those used to discretize classic temporal derivatives, giving a computational cost that is 𝒪(N_T ) and a storage cost that is fixed over time. The approximation is optimized for numerical applications, and an error estimate is presented to demonstrate the efficacy of the method. The method, integrated into a finite element solid mechanics framework, is shown to be unconditionally stable in the linear viscoelastic case. It was then integrated into a computational biomechanical framework, with several numerical examples verifying the accuracy and computational efficiency of the method, including in an analytic test, in an analytic fractional differential equation, as well as in a computational biomechanical model problem.

The application of computational modeling for risk prediction in type B aortic dissection

OBJECTIVE

New tools are urgently needed to help with surgical decision-making in type B aortic dissection (TBAD) that is uncomplicated at the time of initial presentation. This narrative review aims to answer the clinical question, Can computational modeling be used to predict risk in acute and chronic Stanford TBAD?

METHODS

The review (PROSPERO 2018 CRD42018104472) focused on risk prediction in TBAD. A comprehensive search of the Ovid MEDLINE database, using terms related to computational modeling and aortic dissection, was conducted to find studies of any form published between 1998 and 2018. Cohort studies, case series, and case reports of adults (older than 18 years) with computed tomography or magnetic resonance imaging diagnosis of TBAD were included. Computational modeling was applied in all selected studies.

RESULTS

There were 37 studies about computational modeling of TBAD identified from the search, and the findings were synthesized into a narrative review. Computational modeling can produce numerically calculated values of stresses, pressures, and flow velocities that are difficult to measure in vivo. Hemodynamic parameters-high or low wall shear stress, high pressure gradient between lumens during the cardiac cycle, and high false lumen flow rate-have been linked to the pathogenesis of branch malperfusion and aneurysm formation by numerous studies. Considering the major outcomes of end-organ failure, aortic rupture, and stabilization and remodeling, hypotheses have been generated about inter-relationships of measurable parameters in computational models with observable anatomic and pathologic changes, resulting in specific clinical outcomes.

CONCLUSIONS

There is consistency in study findings about computational modeling in TBAD, although a limited number of patients have been analyzed using various techniques. The mechanistic patterns of association found in this narrative review should be investigated in larger cohort prospective studies to further refine our understanding. It highlights the importance of patient-specific computational hemodynamic parameters in clinical decision-making algorithms. The current challenge is to develop and to test a risk assessment method that can be used by clinicians for TBAD.

A computational model for understanding the micro-mechanics of collagen fiber network in the tunica adventitia

Abdominal aortic aneurysm is a prevalent cardiovascular disease with high mortality rates. The mechanical response of the arterial wall relies on the organizational and structural behavior of its microstructural components, and thus, a detailed understanding of the microscopic mechanical response of the arterial wall layers at loads ranging up to rupture is necessary to improve diagnostic techniques and possibly treatments. Following the common notion that adventitia is the ultimate barrier at loads close to rupture, in the present study, a finite element model of adventitial collagen network was developed to study the mechanical state at the fiber level under uniaxial loading. Image stacks of the rabbit carotid adventitial tissue at rest and under uniaxial tension obtained using multi-photon microscopy were used in this study, as well as the force-displacement curves obtained from previously published experiments. Morphological parameters like fiber orientation distribution, waviness, and volume fraction were extracted for one sample from the confocal image stacks. An inverse random sampling approach combined with a random walk algorithm was employed to reconstruct the collagen network for numerical simulation. The model was then verified using experimental stress-stretch curves. The model shows the remarkable capacity of collagen fibers to uncrimp and reorient in the loading direction. These results further show that at high stretches, collagen network behaves in a highly non-affine manner, which was quantified for each sample. A comprehensive parameter study to understand the relationship between structural parameters and their influence on mechanical behavior is presented. Through this study, the model was used to conclude important structure-function relationships that control the mechanical response. Our results also show that at loads close to rupture, the probability of failure occurring at the fiber level is up to 2%. Uncertainties in usually employed rupture risk indicators and the stochastic nature of the event of rupture combined with limited knowledge on the microscopic determinants motivate the development of such an analysis. Moreover, this study will advance the study of coupling microscopic mechanisms to rupture of the artery as a whole.

Comparative study of variations in mechanical stress and strain of human blood vessels: mechanical reference for vascular cell mechano-biology

The diseases of human blood vessels are closely associated with local mechanical variations. A better understanding of the quantitative correlation in mechanical environment between the current mechano-biological studies and vascular physiological or pathological conditions in vivo is crucial for evaluating numerous existing results and exploring new factors for disease discovery. In this study, six representative human blood vessels with known experimental measurements were selected, and their stress and strain variations in vessel walls under different blood pressures were analyzed based on nonlinear elastic theory. The results suggest that conventional mechano-biological experiments seeking the different biological expressions of cells at high/low mechanical loadings are ambiguous as references for studying vascular diseases, because distinct "site-specific" characteristics appear in different vessels. The present results demonstrate that the inner surface of the vessel wall does not always suffer the most severe stretch under high blood pressures comparing to the outer surface. Higher tension on the outer surface of aortas supports the hypothesis of the outside-in inflammation dominated by aortic adventitial fibroblasts. These results indicate that cellular studies at different mechanical niches should be "disease-specific" as well. The present results demonstrate considerable stress gradients across the wall thickness, which indicate micro-scale mechanical variations existing around the vascular cells, and imply that the physiological or pathological changes are not static processes confined within isolated regions, but are coupled with dynamic cell behaviors such as migration. The results suggest that the stress gradients, as well as the mechanical stresses and strains, are key factors constituting the mechanical niches, which may shed new light on "factor-specific" experiments of vascular cell mechano-biology.