A simple, effective and clinically applicable method to compute abdominal aortic aneurysm wall stress

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.

The predictive capability of aortic stiffness index for aortic dissection among dilated ascending aortas

OBJECTIVE

We created a finite element model to predict the probability of dissection based on imaging-derived aortic stiffness and investigated the link between stiffness and wall tensile stress using our model.

METHODS

Transthoracic echocardiogram measurements were used to calculate aortic diameter change over the cardiac cycle. Aortic stiffness index was subsequently calculated based on diameter change and blood pressure. A series of logistic models were developed to predict the binary outcome of aortic dissection using 1 or more series of predictor parameters such as aortic stiffness index or patient characteristics. Finite element analysis was performed on a subset of diameter-matched patients exhibiting patient-specific material properties.

RESULTS

Transthoracic echocardiogram scans of patients with type A aortic dissection (n = 22) exhibited elevated baseline aortic stiffness index when compared with aneurysmal patients' scans with tricuspid aortic valve (n = 83, P < .001) and bicuspid aortic valve (n = 80, P < .001). Aortic stiffness index proved an excellent discriminator for a future dissection event (area under the curve, 0.9337, odds ratio, 2.896). From the parametric finite element study, we found a correlation between peak longitudinal wall tensile stress and stiffness index (ρ = .6268, P < .001, n = 28 pooled).

CONCLUSIONS

Noninvasive transthoracic echocardiogram-derived aortic stiffness measurements may serve as an impactful metric toward predicting aortic dissection or quantifying dissection risk. A correlation between longitudinal stress and stiffness establishes an evidence-based link between a noninvasive stiffness parameter and stress state of the aorta with clinically apparent dissection events.

Peak wall rupture index is associated with risk of rupture of abdominal aortic aneurysms, independent of size and sex

BACKGROUND

Information on the predictive determinants of abdominal aortic aneurysm rupture from CT angiography are scarce. The aim of this study was to investigate biomechanical parameters in abdominal aortic aneurysms and their association with risk of subsequent rupture.

METHODS

In this retrospective study, the digital radiological archive was searched for 363 patients with ruptured abdominal aortic aneurysms. All patients who underwent at least one CT angiography examination before aneurysm rupture were included. CT angiography results were analysed to determine maximum aneurysm diameter, aneurysm volume, and biomechanical parameters (peak wall stress and peak wall rupture index). In the primary survival analysis, patients with abdominal aortic aneurysms less than 70 mm were considered. Sensitivity analyses including control patients and abdominal aortic aneurysms of all sizes were performed.

RESULTS

A total of 67 patients who underwent 109 CT angiography examinations before aneurysm rupture were identified. The majority were men (47, 70%) and the median age at the time of CTA examination was 77 (71-83) years. The median maximum aneurysm diameter was 56 (interquartile range 46-65) mm and the median time to rupture was 2.13 (interquartile range 0.64-4.72) years. In univariable analysis, maximum aneurysm diameter, aneurysm volume, peak wall stress, and peak wall rupture index were all associated with risk of rupture. Women had an increased HR for rupture when adjusted for maximum aneurysm diameter or aneurysm volume (HR 2.16, 95% c.i. 1.23 to 3.78 (P = 0.007) and HR 1.92, 95% c.i. 1.06 to 3.50 (P = 0.033) respectively). In multivariable analysis, the peak wall rupture index was associated with risk of rupture. The HR for peak wall rupture index was 1.05 (95% c.i. 1.03 to 1.08) per % (P < 0.001) when adjusted for maximum aneurysm diameter and 1.05 (95% c.i. 1.02 to 1.08) per % (P < 0.001) when adjusted for aneurysm volume.

CONCLUSION

Biomechanical factors appear to be important in the prediction of abdominal aortic aneurysm rupture. Women are at increased risk of rupture when adjustments are made for maximum aneurysm diameter alone.

Correlation of four-dimensional ultrasound strain analysis with computed tomography angiography wall stress simulations in abdominal aortic aneurysms

Objective

Biomechanical modeling of infrarenal aortic aneurysms seeks to predict ruptures in advance, thereby reducing aneurysm-related deaths. As individual methods focusing on strain and stress analysis lack adequate discretization power, this study aims to explore multifactorial characterization for progressive aneurysmal degeneration. The study's objective is to compare stress- and strain-related parameters in infrarenal aortic aneurysms.

Methods

Twenty-two patients with abdominal aortic aneurysms (AAAs) (mean maximum diameter, 53.2 ± 7.2 mm) were included in the exploratory study, examined by computed tomography angiography (CTA) and three-dimensional real-time speckle tracking ultrasound (4D-US). The conformity of aneurysm anatomy in 4D-US and CTA was determined with the mean point-to-point distance (MPPD). CTA was employed for each AAA to characterize stress-related indices using the semi-automated A4-clinics RE software. Five segmentations from one 4D-US examination were fused into one averaged model for strain analysis using MATLAB and the Abaqus solver.

Results

The mean MPPD between the adjacent points of the 4D-US and CTA-derived geometry was 1.8 ± 0.4 mm. The interclass correlation coefficients for all raters and all measurements for the maximum AAA diameter in 2D, 4D ultrasound, and CTA indicate moderate to good reliability (interclass correlation coefficient1 0.69 with 95% confidence interval [CI], 0.49-0.84; P < .001). The peak wall stress (PWS) correlates fairly with the maximum AAA diameter in 2D-US (r = 0.54; P < .01) and 4D-US (r = 0.53; P < .05) and moderately strongly with the maximum exterior AAA diameter (r = 0.63; P < .01). The peak wall rupture risk index shows a strong correlation with the PWS (ρ > 0.9; P < .001) and is influenced by anatomical parameters with equal strength. Isolated observation of the intraluminal thrombus does not provide significant information in the determination of PWS. The maximum AAA diameter in 2D-US shows a fair negative correlation with the mean circumferential, longitudinal and in-plane shear strain (ρ = -0.46; r = -0.45; ρ = -0.47; P < .05 for all). The circumferential strain ratio as an indicator of wall motion heterogeneity increases with the aneurysm diameter (r = 0.47; P < .05). The direct comparison of wall strain and wall stress indices shows no quantitative correlation.

Conclusions

The strain and stress analyses provide independent biomechanical information of AAAs. At the current stage of development, the two methods are considered complementary and may optimize a more patient-specific rupture risk prediction in the future.

Mechanics of ascending aortic aneurysms based on a modulus of elasticity dependent on aneurysm diameter and pressure

The mechanical stresses and strains are examined, in ascending thoracic aortic aneurysm (aTAA) models, in a patient-specific aTAA as well as in healthy thoracic aortic models, via Finite Element Analysis. The aneurysms are assumed spherical, 1.5 mm thick, with diameters between 47 mm and 80 mm, eccentrically positioned. The geometry and wall thickness distribution of the aorta along its length are based on open literature data for an average patient age of 66.25 years, accounting for the Body Surface Area (BSA) parameter. The vessel wall material is assumed isotropic and incompressible, with its Young's modulus varying with the aneurysm diameter and the applied intraluminal pressure (120 mmHg to 240 mmHg). In the aTAAs, peak stresses were found to increase nonlinearly with aneurysm diameter (for a given pressure) tending to reach a plateau, appearing at the proximal area of the aneurysm, whereas lower stresses were found at its distal part and even smaller at the aneurysm maximum diameter. Regarding the patient-specific aTAA model, the peak stresses appeared at the distal part of the aneurysm where a tear of the intima layer was detected during surgical intervention. Peak strains exhibited for each pressure a maximum at a certain aneurysm diameter beyond which they dropped so that essentially the vessel wall's distensibility was thus reduced. Examining more than 100 geometry cases and employing a failure stress criterion, the rupture diameter thresholds were estimated to be 65, 52.5, 50 and 47.5 mm for a pressure of 120, 160, 200 and 240 mmHg respectively.

Biomechanical characterization of tissue types in murine dissecting aneurysms based on histology and 4D ultrasound-derived strain

Abdominal aortic aneurysm disease is the local enlargement of the aorta, typically in the infrarenal section, causing up to 200,000 deaths/year. In vivo information to characterize the individual elastic properties of the aneurysm wall in terms of rupture risk is lacking. We used a method that combines 4D ultrasound and direct deformation estimation to compute in vivo 3D Green-Lagrange strain in murine angiotensin II-induced dissecting aortic aneurysms, a commonly used mouse model. After euthanasia, histological staining of cross-sectional sections along the aorta was performed in areas where in vivo strains had previously been measured. The histological sections were segmented into intact and fragmented elastin, thrombus with and without red blood cells, and outer vessel wall including the adventitia. Meshes were then created from the individual contours based on the histological segmentations. The isolated contours of the outer wall and lumen from both imaging modalities were registered individually using a coherent point drift algorithm. 2D finite element models were generated from the meshes, and the displacements from the registration were used as displacement boundaries of the lumen and wall contours. Based on the resulting deformed contours, the strains recorded were grouped according to segmented tissue regions. Strains were highest in areas containing intact elastin without thrombus attachment. Strains in areas with intact elastin and thrombus attachment, as well as areas with disrupted elastin, were significantly lower. Strains in thrombus regions with red blood cells were significantly higher compared to thrombus regions without. We then compared this analysis to statistical distribution indices and found that the results of each aligned, elucidating the relationship between vessel strain and structural changes. This work demonstrates the possibility of advancing in vivo assessments to a microstructural level ultimately improving patient outcomes.

PyTorch-FEA: Autograd-enabled finite element analysis methods with applications for biomechanical analysis of human aorta

BACKGROUND AND OBJECTIVES

Finite-element analysis (FEA) is widely used as a standard tool for stress and deformation analysis of solid structures, including human tissues and organs. For instance, FEA can be applied at a patient-specific level to assist in medical diagnosis and treatment planning, such as risk assessment of thoracic aortic aneurysm rupture/dissection. These FEA-based biomechanical assessments often involve both forward and inverse mechanics problems. Current commercial FEA software packages (e.g., Abaqus) and inverse methods exhibit performance issues in either accuracy or speed.

METHODS

In this study, we propose and develop a new library of FEA code and methods, named PyTorch-FEA, by taking advantage of autograd, an automatic differentiation mechanism in PyTorch. We develop a class of PyTorch-FEA functionalities to solve forward and inverse problems with improved loss functions, and we demonstrate the capability of PyTorch-FEA in a series of applications related to human aorta biomechanics. In one of the inverse methods, we combine PyTorch-FEA with deep neural networks (DNNs) to further improve performance.

RESULTS

We applied PyTorch-FEA in four fundamental applications for biomechanical analysis of human aorta. In the forward analysis, PyTorch-FEA achieved a significant reduction in computational time without compromising accuracy compared with Abaqus, a commercial FEA package. Compared to other inverse methods, inverse analysis with PyTorch-FEA achieves better performance in either accuracy or speed, or both if combined with DNNs.

CONCLUSIONS

We have presented PyTorch-FEA, a new library of FEA code and methods, representing a new approach to develop FEA methods to forward and inverse problems in solid mechanics. PyTorch-FEA eases the development of new inverse methods and enables a natural integration of FEA and DNNs, which will have numerous potential applications.

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.

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.

Engineering analysis of aortic wall stress and root dilatation in the V-shape surgery for treatment of ascending aortic aneurysms

OBJECTIVES

The study objective was to evaluate the aortic wall stress and root dilatation before and after the novel V-shape surgery for the treatment of ascending aortic aneurysms and root ectasia.

METHODS

Clinical cardiac computed tomography images were obtained for 14 patients [median age, 65 years (range, 33-78); 10 (71%) males] who underwent the V-shape surgery. For 10 of the 14 patients, the computed tomography images of the whole aorta pre- and post-surgery were available, and finite element simulations were performed to obtain the stress distributions of the aortic wall at pre- and post-surgery states. For 6 of the 14 patients, the computed tomography images of the aortic root were available at 2 follow-up time points post-surgery (Post 1, within 4 months after surgery and Post 2, about 20-52 months from Post 1). We analysed the root dilatation post-surgery using change of the effective diameter of the root at the two time points and investigated the relationship between root wall stress and root dilatation.

RESULTS

The mean and peak max-principal stresses of the aortic root exhibit a significant reduction, P=0.002 between pre- and post-surgery for both root mean stress (median among the 10 patients presurgery, 285.46 kPa; post-surgery, 199.46 kPa) and root peak stress (median presurgery, 466.66 kPa; post-surgery, 342.40 kPa). The mean and peak max-principal stresses of the ascending aorta also decrease significantly from pre- to post-surgery, with P=0.004 for the mean value (median presurgery, 296.48 kPa; post-surgery, 183.87 kPa), and P=0.002 for the peak value (median presurgery, 449.73 kPa; post-surgery, 282.89 kPa), respectively. The aortic root diameter after the surgery has an average dilatation of 5.01% in total and 2.15%/year. Larger root stress results in larger root dilatation.

CONCLUSIONS

This study marks the first biomechanical analysis of the novel V-shape surgery. The study has demonstrated significant reduction in wall stress of the aortic root repaired by the surgery. The root was able to dilate mildly post-surgery. Wall stress could be a critical factor for the dilatation since larger root stress results in larger root dilatation. The dilated aortic root within 4 years after surgery is still much smaller than that of presurgery.

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.

Targeted drug delivery of magnetic microbubble for abdominal aortic aneurysm: an in silico study

Targeted drug delivery (TDD) to abdominal aortic aneurysm (AAA) using a controlled and efficient approach has recently been a significant challenge. In this study, by using magnetic microbubbles (MMBs) under a magnetic field, we investigated the MMBs performance in TDD to AAA based on the amount of surface density of MMBs (SDMM) adhered to the AAA lumen. The results showed that among the types of MMBs studied in the presence of the magnetic field, micromarkers are the best type of microbubble with a -[Formula: see text] increase in SDMM adhered to the critical area of AAA. The results show that applying a magnetic field causes the amount of SDMM adhered to the whole area of AAA to increase -[Formula: see text] times compared to the condition in which the magnetic field is absent. This optimal and maximum value occurs for Definity MMBs with - 3.3 μm diameter. Applying a magnetic field also increases the adhesion surface density by - [Formula: see text], - [Formula: see text], and -[Formula: see text] times for the Micromarker, Optison, and Sonovue microbubbles, respectively, relative to the condition in which the magnetic field is absent. It was shown that using MBBs under magnetic field has the best performance in delivery to AAA for patients with negative inlet blood flow. Also, we have exposed that in an efficient TDD to AAA using MMBs, decreasing the density of MMBs increases drug delivery efficiency and performance. When density is - [Formula: see text], there is the highest difference (about - 75%) between the SDMM adhered to AAA in the presence of a magnetic field and in the absence of a magnetic field.

Patient-Specific Analysis of Ascending Thoracic Aortic Aneurysm with the Living Heart Human Model

In ascending thoracic aortic aneurysms (ATAAs), aneurysm kinematics are driven by ventricular traction occurring every heartbeat, increasing the stress level of dilated aortic wall. Aortic elongation due to heart motion and aortic length are emerging as potential indicators of adverse events in ATAAs; however, simulation of ATAA that takes into account the cardiac mechanics is technically challenging. The objective of this study was to adapt the realistic Living Heart Human Model (LHHM) to the anatomy and physiology of a patient with ATAA to assess the role of cardiac motion on aortic wall stress distribution. Patient-specific segmentation and material parameter estimation were done using preoperative computed tomography angiography (CTA) and ex vivo biaxial testing of the harvested tissue collected during surgery. The lumped-parameter model of systemic circulation implemented in the LHHM was refined using clinical and echocardiographic data. The results showed that the longitudinal stress was highest in the major curvature of the aneurysm, with specific aortic quadrants having stress levels change from tensile to compressive in a transmural direction. This study revealed the key role of heart motion that stretches the aortic root and increases ATAA wall tension. The ATAA LHHM is a realistic cardiovascular platform where patient-specific information can be easily integrated to assess the aneurysm biomechanics and potentially support the clinical management of patients with ATAAs.

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.

Aortic hemodynamics assessment prior and after valve sparing reconstruction: A patient-specific 4D flow-based FSI model

INTRODUCTION

Valve-sparing root replacement (VSRR) of the ascending aorta is a life-saving procedure for the treatment of aortic aneurysms, but patients remain at risk for post-operative events involving the downstream native aorta, the mechanism for which is uncertain. It is possible that proximal graft replacement of the ascending aorta induces hemodynamics alterations in the descending aorta, which could trigger adverse events. Herein, we present a fluid-structure interaction (FSI) protocol, based on patient-specific geometry and boundary conditions, to assess impact of proximal aortic grafts on downstream aortic hemodynamics and distensibility.

METHODS

Cardiac magnetic resonance (CMR), including MRA, cine-CMR and 4D flow sequences, was performed prior and after VSRR on one subject. Central blood pressure was non-invasively acquired at the time of the CMR: data were used to reconstruct the pre- and post-VSRR model and derive patient-specific boundary conditions for the FSI and a computational fluid dynamic (CFD) analysis with the same settings. Results were validated comparing the predicted velocity field against 4D flow dataset, over four landmarks along the aorta, and the predicted distensibility against the cine-CMR derived value.

RESULTS

Instantaneous velocity magnitudes extracted from 4D flow and FSI were similar (p > 0.05), while CFD-predicted velocity was significantly higher (p < 0.001), especially in the descending aorta of the pre-VSRR model (v_max was 73 cm/s, 76 cm/s and 99 cm/s, respectively). As measured in cine-CMR, FSI predicted an increase in descending aorta distensibility after grafting (i.e., 4.02 to 5.79 10^-3 mmHg^-1). In the descending aorta, the post-VSRR model showed increased velocity, aortic distensibility, stress and strain and wall shear stress.

CONCLUSIONS

Our Results indicate that i) the distensibility of the wall cannot be neglected, and hence the FSI method is necessary to obtain reliable results; ii) graft implantation induces alterations in the hemodynamics and biomechanics along the thoracic aorta, that may trigger adverse vessel remodeling.

Mechanical characterization of abdominal aortas using multi-perspective ultrasound imaging

Mechanical characterization of abdominal aortic aneurysms using personalized biomechanical models is being widely investigated as an alternative criterion to assess risk of rupture. These methods rely on accurate wall motion detection and appropriate model boundary conditions. In this study, multi-perspective ultrasound is combined with finite element models to perform mechanical characterization of abdominal aortas in volunteers. Multi-perspective biplane radio frequency ultrasound recordings were made under seven angles (-45° to 45°) in one phantom set-up and eight volunteers, which were merged using automatic image registration. 2-D displacement fields were estimated in the seven longitudinal ultrasound views, creating a sparse, high resolution 3-D map of the wall motion at relatively high frame rates (20-27 Hz). The displacements were used to personalize the subject-specific finite element model of which the geometry of the aorta, spine, and surrounding tissue were determined from a single 3-D ultrasound acquisition. Automatic registration of the multi-perspective images was successful in six out of eight cases with an average error of 5.4° compared to the ground truth. Displacements of the aortic wall were measured and cyclic strain of the aortic diameter was found ranging from 4.2% to 8.6%. The subject-specific mesh and inverse FE analysis was performed yielding shear moduli estimates for the wall between 104 and 215 kPa. Comparative results from a single-perspective workflow revealed very low aortic wall motion signal, which resulted in relatively high modulus estimates, between 230 and 754 kPa. Multi-perspective biplane ultrasound imaging was used to personalize finite element models of the abdominal aorta and its surroundings, and performing mechanical characterization of the aortic shear modulus. The method was found to be a more robust method compared to a single-perspective 3-D ultrasound approach. Future research will focus on investigating the use of multiple 3-D ultrasound acquisitions, the feasibility of free-hand scanning, the creation of a full 3-D automatic registration process, and with that, enable a clinical continuation of this study.

Patient-specific computational evaluation of stiffness distribution in ascending thoracic aortic aneurysm

Quantifying local aortic stiffness properties in vivo is acknowledged as essential to assess the severity of an ascending thoracic aortic aneurysm (ATAA). Recently, the LESI (local extensional stiffness identification) methodology has been established to quantify non-invasively local stiffness properties of ATAAs using electrocardiographic-gated computed tomography (ECG-gated CT) scans. The aim of the current study was to determine the most sensitive markers of local ATAA stiffness estimation with the hypothesis that direct measures of local ATAA stiffness could better detect the high-risk patients. A cohort of 30 patients (12 BAV and 18 TAV) referred for aortic size evaluation by ECG-gated CT were recruited. For each patient, the extensional stiffness Q was evaluated by the LESI methodology whilst computational flow analyses were also performed to derive hemodynamics markers such as the wall shear stress (WSS). A strong positive correlation was found between the extensional stiffness and the aortic pulse pressure (R = 0.644 and p < 0.001). Interestingly, a significant positive correlation was also found between the extensional stiffness and patients age for BAV ATAAs (R = 0.619 and p = 0.032), but not for TAV ATAAs (R = -0.117 and p = 0.645). No significant correlation was found between the extensional stiffness and WSS evaluated locally. There was no significant difference either in the extensional stiffness between BAV ATAAs and TAV ATAAs (Q = 3.6 ± 2.5 MPa.mm for BAV ATAAs vs Q = 5.3 ± 3.1 MPa.mm for TAV ATAAs, p = 0.094). Future work will focus on relating the extensional stiffness to the patient-specific rupture risk of ATAAs on larger cohorts to confirm the promising interest of the LESI methodology.

Mathematical modeling and computer simulation of needle insertion into soft tissue

In this study we present a kinematic approach for modeling needle insertion into soft tissues. The kinematic approach allows the presentation of the problem as Dirichlet-type (i.e. driven by enforced motion of boundaries) and therefore weakly sensitive to unknown properties of the tissues and needle-tissue interaction. The parameters used in the kinematic approach are straightforward to determine from images. Our method uses Meshless Total Lagrangian Explicit Dynamics (MTLED) method to compute soft tissue deformations. The proposed scheme was validated against experiments of needle insertion into silicone gel samples. We also present a simulation of needle insertion into the brain demonstrating the method's insensitivity to assumed mechanical properties of tissue.

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.

Drug delivery performance of nanocarriers based on adhesion and interaction for abdominal aortic aneurysm treatment

Targeted drug delivery using nanocarriers (NCs) is one of the novel techniques that has recently been used to improve drug delivery to the Abdominal aortic aneurysm (AAA) disease. The purpose of this study is to evaluate the surface density of NCs (SDNC) adhered via ligand-receptor binding to the inner wall of AAA. For this purpose, fluid-structure interaction (FSI) analysis was first performed for the patient-specific and ideal AAA models. Then, by injecting NCs into the aortic artery, the values of SDNC adhered to and interacted with AAA wall were obtained. Two types of NCs, liposomes, and solid particles in four different diameters, were used to investigate the effect of the diameter and the type of NCs on the drug delivery. Additionally, the effect of the number of the injected NCs to the artery on the values of SDNC adhered to and interacted with AAA wall was investigated. The simulation results showed that the interaction and adhesion values of SDNC for Liposome nanoparticles were higher than the ones for the solid particles. Furthermore, as the diameter of NCs increases, the values of SDNC adhered to AAA wall increase, but the values of SDNC interacted with the inner wall of AAA decrease. In the low number of inserted NCs in the artery (1000 NCs), the interaction and adhesion values of SDNC were very slight, and by increasing the number of NCs inserted into the artery, the drug delivery was improved. By examining different AAA models, it was found that the complexity of the shape of AAA has a minor effect on the pattern of increase or decrease of the values of SDNC adhered to and interacted with AAA wall.This study's findings can improve the understanding of NCs design and propose the appropriate amount of their injection into various AAA models.

Assessing Patient-Specific Mechanical Properties of Aortic Wall and Peri-Aortic Structures From In Vivo DENSE Magnetic Resonance Imaging Using an Inverse Finite Element Method and Elastic Foundation Boundary Conditions

The establishment of in vivo, noninvasive patient-specific, and regionally resolved techniques to quantify aortic properties is key to improving clinical risk assessment and scientific understanding of vascular growth and remodeling. A promising and novel technique to reach this goal is an inverse finite element method (FEM) approach that utilizes magnetic resonance imaging (MRI)-derived displacement fields from displacement encoding with stimulated echoes (DENSE). Previous studies using DENSE MRI suggested that the infrarenal abdominal aorta (IAA) deforms heterogeneously during the cardiac cycle. We hypothesize that this heterogeneity is driven in healthy aortas by regional adventitial tethering and interaction with perivascular tissues, which can be modeled with elastic foundation boundary conditions (EFBCs) using a collection of radially oriented springs with varying stiffness with circumferential distribution. Nine healthy IAAs were modeled using previously acquired patient-specific imaging and displacement fields from steady-state free procession (SSFP) and DENSE MRI, followed by assessment of aortic wall properties and heterogeneous EFBC parameters using inverse FEM. In contrast to traction-free boundary condition, prescription of EFBC reduced the nodal displacement error by 60% and reproduced the DENSE-derived heterogeneous strain distribution. Estimated aortic wall properties were in reasonable agreement with previously reported experimental biaxial testing data. The distribution of normalized EFBC stiffness was consistent among all patients and spatially correlated to standard peri-aortic anatomical features, suggesting that EFBC could be generalized for human adults with normal anatomy. This approach is computationally inexpensive, making it ideal for clinical research and future incorporation into cardiovascular fluid-structure analyses.

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.

Biomechanics of aortic wall failure with a focus on dissection and aneurysm: A review

Aortic dissections and aortic aneurysms are fatal events characterized by structural changes to the aortic wall. The maximum diameter criterion, typically used for aneurysm rupture risk estimations, has been challenged by more sophisticated biomechanically motivated models in the past. Although these models are very helpful for the clinicians in decision-making, they do not attempt to capture material failure. Following a short overview of the microstructure of the aorta, we analyze the failure mechanisms involved in the dissection and rupture by considering also traumatic rupture. We continue with a literature review of experimental studies relevant to quantify tissue strength. More specifically, we summarize more extensively uniaxial tensile, bulge inflation and peeling tests, and we also specify trouser, direct tension and in-plane shear tests. Finally we analyze biomechanically motivated models to predict rupture risk. Based on the findings of the reviewed studies and the rather large variations in tissue strength, we propose that an appropriate material failure criterion for aortic tissues should also reflect the microstructure in order to be effective. STATEMENT OF SIGNIFICANCE: Aortic dissections and aortic aneurysms are fatal events characterized by structural changes to the aortic wall. Despite the advances in medical, biomedical and biomechanical research, the mortality rates of aneurysms and dissections remain high. The present review article summarizes experimental studies that quantify the aortic wall strength and it discusses biomechanically motivated models to predict rupture risk. We identified contradictory observations and a large variation within and between data sets, which may be due to biological variations, different sample sizes, differences in experimental protocols, etc. Based on the findings of the reviewed literature and the rather large variations in tissue strength, it is proposed that an appropriate criterion for aortic failure should also reflect the microstructure.

A deep learning approach to estimate stress distribution: a fast and accurate surrogate of finite-element analysis

Structural finite-element analysis (FEA) has been widely used to study the biomechanics of human tissues and organs, as well as tissue-medical device interactions, and treatment strategies. However, patient-specific FEA models usually require complex procedures to set up and long computing times to obtain final simulation results, preventing prompt feedback to clinicians in time-sensitive clinical applications. In this study, by using machine learning techniques, we developed a deep learning (DL) model to directly estimate the stress distributions of the aorta. The DL model was designed and trained to take the input of FEA and directly output the aortic wall stress distributions, bypassing the FEA calculation process. The trained DL model is capable of predicting the stress distributions with average errors of 0.492% and 0.891% in the Von Mises stress distribution and peak Von Mises stress, respectively. This study marks, to our knowledge, the first study that demonstrates the feasibility and great potential of using the DL technique as a fast and accurate surrogate of FEA for stress analysis.

Estimation of in vivo constitutive parameters of the aortic wall using a machine learning approach

The patient-specific biomechanical analysis of the aorta requires the quantification of the in vivo mechanical properties of individual patients. Current inverse approaches have attempted to estimate the nonlinear, anisotropic material parameters from in vivo image data using certain optimization schemes. However, since such inverse methods are dependent on iterative nonlinear optimization, these methods are highly computation-intensive. A potential paradigm-changing solution to the bottleneck associated with patient-specific computational modeling is to incorporate machine learning (ML) algorithms to expedite the procedure of in vivo material parameter identification. In this paper, we developed an ML-based approach to estimate the material parameters from three-dimensional aorta geometries obtained at two different blood pressure (i.e., systolic and diastolic) levels. The nonlinear relationship between the two loaded shapes and the constitutive parameters are established by an ML-model, which was trained and tested using finite element (FE) simulation datasets. Cross-validations were used to adjust the ML-model structure on a training/validation dataset. The accuracy of the ML-model was examined using a testing dataset.

Wall Stress and Geometry Measures in Electively Repaired Abdominal Aortic Aneurysms

Abdominal aortic aneurysm (AAA) is a vascular disease characterized by the enlargement of the infrarenal segment of the aorta. A ruptured AAA can cause internal bleeding and carries a high mortality rate, which is why the clinical management of the disease is focused on preventing aneurysm rupture. AAA rupture risk is estimated by the change in maximum diameter over time (i.e., growth rate) or if the diameter reaches a prescribed threshold. The latter is typically 5.5 cm in most clinical centers, at which time surgical intervention is recommended. While a size-based criterion is suitable for most patients who are diagnosed at an early stage of the disease, it is well known that some small AAA rupture or patients become symptomatic prior to a maximum diameter of 5.5 cm. Consequently, the mechanical stress in the aortic wall can also be used as an integral component of a biomechanics-based rupture risk assessment strategy. In this work, we seek to identify geometric characteristics that correlate strongly with wall stress using a sample space of 100 asymptomatic, unruptured, electively repaired AAA models. The segmentation of the clinical images, volume meshing, and quantification of up to 45 geometric measures of each AAA were done using in-house Matlab scripts. Finite element analysis was performed to compute the first principal stress distributions from which three global biomechanical parameters were calculated: peak wall stress, 99th percentile wall stress and spatially averaged wall stress. Following a feature reduction approach consisting of Pearson's correlation matrices with Bonferroni correction and linear regressions, a multivariate stepwise regression analysis was conducted to find the geometric measures most highly correlated with each of the biomechanical parameters. Our findings indicate that wall stress can be predicted by geometric indices with an accuracy of up to 94% when AAA models are generated with uniform wall thickness and up to 67% for patient specific, non-uniform wall thickness AAA. These geometric predictors of wall stress could be used in lieu of complex finite element models as part of a geometry-based protocol for rupture risk assessment.

On the computation of in vivo transmural mean stress of patient-specific aortic wall

It is well known that residual deformations/stresses alter the mechanical behavior of arteries, e.g., the pressure-diameter curves. In an effort to enable personalized analysis of the aortic wall stress, approaches have been developed to incorporate experimentally derived residual deformations into in vivo loaded geometries in finite element simulations using thick-walled models. Solid elements are typically used to account for "bending-like" residual deformations. Yet, the difficulty in obtaining patient-specific residual deformations and material properties has become one of the biggest challenges of these thick-walled models. In thin-walled models, fortunately, static determinacy offers an appealing prospect that allows for the calculation of the thin-walled membrane stress without patient-specific material properties. The membrane stress can be computed using forward analysis by enforcing an extremely stiff material property as penalty treatment, which is referred to as the forward penalty approach. However, thin-walled membrane elements, which have zero bending stiffness, are incompatible with the residual deformations, and therefore, it is often stated as a limitation of thin-walled models. In this paper, by comparing the predicted stresses from thin-walled models and thick-walled models, we demonstrate that the transmural mean stress is approximately the same for the two models and can be readily obtained from in vivo clinical images without knowing the patient-specific material properties and residual deformations. Computation of patient-specific mean stress can be greatly simplified by using the forward penalty approach, which may be clinically valuable.

Geometric surrogates of abdominal aortic aneurysm wall mechanics

The maximum diameter criterion is the most important factor in the clinical management of abdominal aortic aneurysms (AAA). Consequently, interventional repair is recommended when an aneurysm reaches a critical diameter, typically 5.0 cm in the United States. Nevertheless, biomechanical measures of the aneurysmal abdominal aorta have long been implicated in AAA risk of rupture. The purpose of this study is to assess whether other geometric characteristics, in addition to maximum diameter, may be highly correlated with the AAA peak wall stress (PWS). Using in-house segmentation and meshing algorithms, 30 patient-specific AAA models were generated for finite element analysis using an isotropic constitutive material for the AAA wall. PWS, evaluated as the spatial maximum of the first principal stress, was calculated at a systolic pressure of 120 mmHg. The models were also used to calculate 47 geometric indices characteristic of the aneurysm geometry. Statistical analyses were conducted using a feature reduction algorithm in which the 47 indices were reduced to 11 based on their statistical significance in differentiating the models in the population (p < 0.05). A subsequent discriminant analysis was performed and 7 of these indices were identified as having no error in discriminating the AAA models with a significant nonlinear regression correlation with PWS. These indices were: D_max (maximum diameter), T (tortuosity), DDr (maximum diameter to neck diameter ratio), S (wall surface area), K_median (median of the Gaussian surface curvature), C_max (maximum lumen compactness), and M_mode (mode of the Mean surface curvature). Therefore, these characteristics of an individual AAA geometry are the highest correlated with the most clinically relevant biomechanical parameter for rupture risk assessment. We conclude that the indices can serve as surrogates of PWS in lieu of a finite element modeling approach for AAA biomechanical evaluation.

Applicability of simplified computational models in prediction of peak wall stress in abdominal aortic aneurysms

In the paper impact of different material models on the calculated peak wall stress (PWS) and peak wall rupture risk (PWRR) in abdominal aortic aneurysms (AAAs) is assessed. Computational finite element models of 70 patient-specific AAAs were created using two different material models - a realistic one based on mean population results of uniaxial tests of AAA wall considered as reference, and a 100 times stiffer artificial model. The calculated results of PWS and PWRR were tested to evaluate statistical significance of differences caused by the non-realistic material model. It was shown that for majority of AAAs the differences are insignificant but for some 10% of them their relative differences exceed 20% which may lead to incorrect decisions on their surgical treatment. This percentage of failures favours application of realistic material models in clinical practise although they are much more time-consuming.

Estimation of in vivo mechanical properties of the aortic wall: A multi-resolution direct search approach

The patient-specific biomechanical analysis of the aorta requires in vivo mechanical properties of individual patients. Existing approaches for estimating in vivo material properties often demand high computational cost and mesh correspondence of the aortic wall between different cardiac phases. In this paper, we propose a novel multi-resolution direct search (MRDS) approach for estimation of the nonlinear, anisotropic constitutive parameters of the aortic wall. Based on the finite element (FE) updating scheme, the MRDS approach consists of the following three steps: (1) representing constitutive parameters with multiple resolutions using principal component analysis (PCA), (2) building links between the discretized PCA spaces at different resolutions, and (3) searching the PCA spaces in a 'coarse to fine' fashion following the links. The estimation of material parameters is achieved by minimizing a node-to-surface error function, which does not need mesh correspondence. The method was validated through a numerical experiment by using the in vivo data from a patient with ascending thoracic aortic aneurysm (ATAA), the results show that the number of FE iterations was significantly reduced compared to previous methods. The approach was also applied to the in vivo CT data from an aged healthy human patient, and using the estimated material parameters, the FE-computed geometry was well matched with the image-derived geometry. This novel MRDS approach may facilitate the personalized biomechanical analysis of aortic tissues, such as the rupture risk analysis of ATAA, which requires fast feedback to clinicians.

On the effect of computed tomography resolution to distinguish between abdominal aortic aneurysm wall tissue and calcification: A proof of concept

PURPOSE

The purpose of this study is to determine the optimal target CT spatial resolution for accurately imaging abdominal aortic aneurysm (AAA) wall characteristics, distinguishing between tissue and calcification components, for an accurate assessment of rupture risk.

MATERIALS AND METHODS

Ruptured and non-ruptured AAA-wall samples were acquired from eight patients undergoing open surgical aneurysm repair upon institutional review board approval and informed consent was obtained from all patients. Physical measurements of AAA-wall cross-section were made using scanning electron microscopy. Samples were scanned using high resolution micro-CT scanning. A resolution range of 15.5-155μm was used to quantify the influence of decreasing resolution on wall area measurements, in terms of tissue and calcification. A statistical comparison between the reference resolution (15.5μm) and multi-detector CT resolution (744μm) was also made.

RESULTS

Electron microscopy examination of ruptured AAAs revealed extremely thin outer tissue structure <200μm in radial distribution which is supporting the aneurysm wall along with large areas of adjacent medial calcifications far greater in area than the tissue layer. The spatial resolution of 155μm is a significant predictor of the reference AAA-wall tissue and calcification area measurements (r=0.850; p<0.001; r=0.999; p<0.001 respectively). The tissue and calcification area at 155μm is correct within 8.8%±1.86 and 26.13%±9.40 respectively with sensitivity of 87.17% when compared to the reference.

CONCLUSION

The inclusion of AAA-wall measurements, through the use of high resolution-CT will elucidate the variations in AAA-wall tissue and calcification distributions across the wall which may help to leverage an improved assessment of AAA rupture risk.

Exploring the Biological and Mechanical Properties of Abdominal Aortic Aneurysms Using USPIO MRI and Peak Tissue Stress: A Combined Clinical and Finite Element Study

Inflammation detected through the uptake of ultrasmall superparamagnetic particles of iron oxide (USPIO) on magnetic resonance imaging (MRI) and finite element (FE) modelling of tissue stress both hold potential in the assessment of abdominal aortic aneurysm (AAA) rupture risk. This study aimed to examine the spatial relationship between these two biomarkers. Patients (n = 50) > 40 years with AAA maximum diameters > = 40 mm underwent USPIO-enhanced MRI and computed tomography angiogram (CTA). USPIO uptake was compared with wall stress predictions from CTA-based patient-specific FE models of each aneurysm. Elevated stress was commonly observed in areas vulnerable to rupture (e.g. posterior wall and shoulder). Only 16% of aneurysms exhibited co-localisation of elevated stress and mural USPIO enhancement. Globally, no correlation was observed between stress and other measures of USPIO uptake (i.e. mean or peak). It is suggested that cellular inflammation and stress may represent different but complimentary aspects of AAA disease progression.

BioPARR: A software system for estimating the rupture potential index for abdominal aortic aneurysms

An abdominal aortic aneurysm (AAA) is a permanent and irreversible dilation of the lower region of the aorta. It is a symptomless condition that, if left untreated, can expand until rupture. Despite ongoing efforts, an efficient tool for accurate estimation of AAA rupture risk is still not available. Furthermore, a lack of standardisation across current approaches and specific obstacles within computational workflows limit the translation of existing methods to the clinic. This paper presents BioPARR (Biomechanics based Prediction of Aneurysm Rupture Risk), a software system to facilitate the analysis of AAA using a finite element analysis based approach. Except semi-automatic segmentation of the AAA and intraluminal thrombus (ILT) from medical images, the entire analysis is performed automatically. The system is modular and easily expandable, allows the extraction of information from images of different modalities (e.g. CT and MRI) and the simulation of different modelling scenarios (e.g. with/without thrombus). The software uses contemporary methods that eliminate the need for patient-specific material properties, overcoming perhaps the key limitation to all previous patient-specific analysis methods. The software system is robust, free, and will allow researchers to perform comparative evaluation of AAA using a standardised approach. We report preliminary data from 48 cases.

Morphological and Biomechanical Features in Abdominal Aortic Aneurysm with Long and Short Neck-Case-Control Study in 64 Abdominal Aortic Aneurysms

BACKGROUND

Both, open and endovascular, procedures are related to higher complication rate in abdominal aortic aneurysm (AAA) with shorter neck. Previous study showed that long-neck AAA might have lower risk of rupture. Estimation of biomechanical forces in AAA improves rupture risk assessment. The aim of this study was to compare morphological features and biomechanical forces in the short- and long-neck AAA with threshold of 15 mm.

METHODS

Digital Imaging and Communication in Medicine images of 64 aneurysms were prospectively collected and analyzed in a case-control study. Using commercially available software, Peak wall Stress (PWS) and Rupture Risk Equivalent Diameter (RRED) were determined. Difference between the maximal aneurysm diameter (MAD) and RRED was calculated and expressed as an absolute and relative (percentage of the MAD) value. In addition, volume of intraluminal thrombus (ILT) was calculated and expressed relative to AAA volume.

RESULTS

Study included 64 AAA divided in group with long (36, 56.25%), and short (28, 43.75%) neck. There was no correlation between neck length and MAD, PWS, and RRED (P = 0.646, P = 0.421, and P = 0.405, respectively). Relative ILT volume was greater in the short-neck aneurysms (P = 0.033). Relative difference between RRED and MAD was -4% and -14.8% in short- and long-neck aneurysms, respectively (P = 0.029). The difference between RRED and MAD was positive in 14/28 patients (50%) with short neck and in 6/35 patients (17.14%) with long neck (P = 0.011).

CONCLUSIONS

Based on our biomechanical analysis, in AAA with neck longer than 15 mm rupture risk might be lower than the risk estimated by its diameter. It might be explained with lower relative volume of ILT.