Stanislav Polzer

The impact of intraluminal thrombus failure on the mechanical stress in the wall of abdominal aortic aneurysms.

OBJECTIVES The role of the intraluminal thrombus (ILT) in abdominal aortic aneurysm (AAA) rupture is controversial, and it is still not clear if an ILT increases or decreases AAA rupture risk. Specifically, signs of bleeding in the ILT are considered to increase AAA rupture risk. To further explore this hypothesis, intact AAAs (n = 4) with clear signs of fissures in the ILT, identified by computed tomography angiography (CTA) were investigated. METHODS Two different cases of ILT fissuring were investigated, where (1) ILT fissures were extracted directly from the CTA data and (2) a hypothetical fissure was introduced in the otherwise-intact ILT tissue. Wall stress distributions were predicted based on detailed Finite Element (FE) models. RESULTS ILT fissures extracted from CTA data locally increase the mechanical stress in the underlying wall by up to 30%. The largest impact on wall stress was observed if the ILT crack reaches the aneurysm wall, or if it involves large parts of the ILT. By contrast, a concentric failure in the medial ILT, which does not reach the aneurysm wall, has almost no impact on wall stress distribution. Hypothetical ILT fissures that connect the lumen with the wall cause a twofold increase of the stress in the underlying wall. CONCLUSIONS ILT fissures increase the stress in the underlying wall, whereas regions other than that remain unaffected. If ILT fissures reach the wall or involve large parts of the ILT, the resulting increase in wall stress could possibly cause AAA rupture.

Importance of material model in wall stress prediction in abdominal aortic aneurysms

BACKGROUND Results of biomechanical simulation of the abdominal aortic aneurysm (AAA) depend on the constitutive description of the wall. Based on in vitro and in vivo experimental data several constitutive models for the AAA wall have been proposed in the literature. Those models differ strongly from each other and their impact on the computed stress in biomechanical simulation is not clearly understood. METHODS Finite element (FE) models of AAAs from 7 patients who underwent elective surgical repair were used to compute wall stresses. AAA geometry was reconstructed from CT angiography (CT-A) data and patient-specific (PS) constitutive descriptions of the wall were derived from planar biaxial testing of anterior wall tissue samples. In total 28 FE models were used, where the wall was described by either patient-specific or previously reported study-average properties. This data was derived from either uniaxial or biaxial in vitro testing. Computed wall stress fields were compared on node-by-node basis. RESULTS Different constitutive models for the AAA wall cause significantly different predictions of wall stress. While study-average data from biaxial testing gives globally the same stress field as the patient-specific wall properties, the material model based on uniaxial test data overestimates the wall stress on average by 30 kPa or about 67% of the mean stress. A quasi-linear description based on the in vivo measured distensibility of the AAA wall leads to a completely altered stress field and overestimates the wall stress by about 75 kPa or about 167% of the mean stress. CONCLUSION The present study demonstrated that the constitutive description of the wall is crucial for AAA wall stress prediction. Consequently, results obtained using different models should not be mutually compared unless different stress gradients across the wall are not taken into account. Highly nonlinear material models should be preferred when the response of AAA to increased blood pressure is investigated, while the quasi-linear model with high initial stiffness produces negligible stress gradients across the wall and thus, it is more appropriate when response to mean blood pressure is calculated.

Structure-based constitutive model can accurately predict planar biaxial properties of aortic wall tissue

Structure-based constitutive models might help in exploring mechanisms by which arterial wall histology is linked to wall mechanics. This study aims to validate a recently proposed structure-based constitutive model. Specifically, the models ability to predict mechanical biaxial response of porcine aortic tissue with predefined collagen structure was tested. Histological slices from porcine thoracic aorta wall (n=9) were automatically processed to quantify the collagen fiber organization, and mechanical testing identified the non-linear properties of the wall samples (n=18) over a wide range of biaxial stretches. Histological and mechanical experimental data were used to identify the model parameters of a recently proposed multi-scale constitutive description for arterial layers. The model predictive capability was tested with respect to interpolation and extrapolation. Collagen in the media was predominantly aligned in circumferential direction (planar von Mises distribution with concentration parameter bM=1.03 ± 0.23), and its coherence decreased gradually from the luminal to the abluminal tissue layers (inner media, b=1.54 ± 0.40; outer media, b=0.72 ± 0.20). In contrast, the collagen in the adventitia was aligned almost isotropically (bA=0.27 ± 0.11), and no features, such as families of coherent fibers, were identified. The applied constitutive model captured the aorta biaxial properties accurately (coefficient of determination R(2)=0.95 ± 0.03) over the entire range of biaxial deformations and with physically meaningful model parameters. Good predictive properties, well outside the parameter identification space, were observed (R(2)=0.92 ± 0.04). Multi-scale constitutive models equipped with realistic micro-histological data can predict macroscopic non-linear aorta wall properties. Collagen largely defines already low strain properties of media, which explains the origin of wall anisotropy seen at this strain level. The structure and mechanical properties of adventitia are well designed to protect the media from axial and circumferential overloads.

Impact of poroelasticity of intraluminal thrombus on wall stress of abdominal aortic aneurysms

BackgroundThe predictions of stress fields in Abdominal Aortic Aneurysm (AAA) depend on constitutive descriptions of the aneurysm wall and the Intra-luminal Thrombus (ILT). ILT is a porous diluted structure (biphasic solid–fluid material) and its impact on AAA biomechanics is controversially discussed in the literature. Specifically, pressure measurements showed that the ILT cannot protect the wall from the arterial pressure, while other (numerical and experimental) studies showed that at the same time it reduces the stress in the wall.MethodTo explore this phenomenon further a poroelastic description of the ILT was integrated in Finite Element (FE) Models of the AAA. The AAA model was loaded by a pressure step and a cyclic pressure wave and their transition into wall tension was investigated. To this end ILT’s permeability was varied within a microstructurally motivated range.ResultsThe two-phase model verified that the ILT transmits the entire mean arterial pressure to the wall while, at the same time, it significantly reduces the stress in the wall. The predicted mean stress in the AAA wall was insensitive to the permeability of the ILT and coincided with the results of AAA models using a single-phase ILT description.ConclusionAt steady state, the biphasic ILT behaves like a single-phase material in an AAA model. Consequently, computational efficient FE single-phase models, as they have been exclusively used in the past, accurately predict the wall stress in AAA models.

Automatic identification and validation of planar collagen organization in the aorta wall with application to abdominal aortic aneurysm.

Arterial physiology relies on a delicate three-dimensional (3D) organization of cells and extracellular matrix, which is remarkably altered by vascular diseases like abdominal aortic aneurysms (AAA). The ability to explore the micro-histology of the aorta wall is important in the study of vascular pathologies and in the development of vascular constitutive models, i.e., mathematical descriptions of biomechanical properties of the wall. The present study reports and validates a fast image processing sequence capable of quantifying collagen fiber organization from histological stains. Powering and re-normalizing the histogram of the classical fast Fourier transformation (FFT) is a key step in the proposed analysis sequence. This modification introduces a powering parameter w, which was calibrated to best fit the reference data obtained using classical FFT and polarized light microscopy (PLM) of stained histological slices of AAA wall samples. The values of w = 3 and 7 give the best correlation (Pearsons correlation coefficient larger than 0.7, R 2 about 0.7) with the classical FFT approach and PLM measurements. A fast and operator independent method to identify collagen organization in the arterial wall was developed and validated. This overcomes severe limitations of currently applied methods like PLM to identify collagen organization in the arterial wall.

Biomechanical rupture risk assessment of abdominal aortic aneurysms based on a novel probabilistic rupture risk index.

A rupture risk assessment is critical to the clinical treatment of abdominal aortic aneurysm (AAA) patients. The biomechanical AAA rupture risk assessment quantitatively integrates many known AAA rupture risk factors but the variability of risk predictions due to model input uncertainties remains a challenging limitation. This study derives a probabilistic rupture risk index (PRRI). Specifically, the uncertainties in AAA wall thickness and wall strength were considered, and wall stress was predicted with a state-of-the-art deterministic biomechanical model. The discriminative power of PRRI was tested in a diameter-matched cohort of ruptured (n = 7) and intact (n = 7) AAAs and compared to alternative risk assessment methods. Computed PRRI at 1.5 mean arterial pressure was significantly (p = 0.041) higher in ruptured AAAs (20.21(s.d. 14.15%)) than in intact AAAs (3.71(s.d. 5.77)%). PRRI showed a high sensitivity and specificity (discriminative power of 0.837) to discriminate between ruptured and intact AAA cases. The underlying statistical representation of stochastic data of wall thickness, wall strength and peak wall stress had only negligible effects on PRRI computations. Uncertainties in AAA wall stress predictions, the wide range of reported wall strength and the stochastic nature of failure motivate a probabilistic rupture risk assessment. Advanced AAA biomechanical modelling paired with a probabilistic rupture index definition as known from engineering risk assessment seems to be superior to a purely deterministic approach.

Assessing the potential risk of rupture of abdominal aortic aneurysms

Abdominal aortic aneurysms (AAAs) involve complex interplays between inflammatory and biomechanical factors that can be elucidated with anatomical and functional imaging. Although AAA size has been well-established in the literature to correlate with risk of rupture (and subsequent need for vascular intervention), there are other less-well-known characteristics about AAAs that also contribute to higher risk of rupture. This review focuses on biomechanical, radiological, and epidemiological characteristics of AAAs that are associated with higher rupture risk. For clinicians, knowing and considering a wide variety of risk factors in addition to AAA size is important to initiate early and proper intervention for AAA repair. Although there is no official quantitative risk score of AAA rupture risk that takes other non-size-related variables into account, if clinicians are aware of these other parameters, it is hoped that intervention can be appropriately performed for higher-risk AAAs that have not met the size-threshold for elective repair.

Poroelastic Model of Intraluminal Thrombus in FEA of Aortic Aneurysm

The influence of the intraluminal thrombus (ILT) on the biomechanics of the abdominal aortic aneurysm (AAA) has been investigated for several years both numerically and experimentally. The FE analyses published till now simplified the material of the ILT as a homogenous continuum, but there is a contradiction between experiments and FE results. Therefore we use a poroelastic constitutive model for ILT. Poroelastic behaviour of the used finite element is based on the Biot theory of consolidation, the model consists of fluid and solid parts.

Automatic Evaluation of Collagen Fiber Directions from Polarized Light Microscopy Images.

Mechanical properties of the arterial wall depend largely on orientation and density of collagen fiber bundles. Several methods have been developed for observation of collagen orientation and density; the most frequently applied collagen-specific manual approach is based on polarized light (PL). However, it is very time consuming and the results are operator dependent. We have proposed a new automated method for evaluation of collagen fiber direction from two-dimensional polarized light microscopy images (2D PLM). The algorithm has been verified against artificial images and validated against manual measurements. Finally the collagen content has been estimated. The proposed algorithm was capable of estimating orientation of some 35 k points in 15 min when applied to aortic tissue and over 500 k points in 35 min for Achilles tendon. The average angular disagreement between each operator and the algorithm was -9.3±8.6° and -3.8±8.6° in the case of aortic tissue and -1.6±6.4° and 2.6±7.8° for Achilles tendon. Estimated mean collagen content was 30.3±5.8% and 94.3±2.7% for aortic media and Achilles tendon, respectively. The proposed automated approach is operator independent and several orders faster than manual measurements and therefore has the potential to replace manual measurements of collagen orientation via PLM.

Correlation between transversal and orthogonal maximal diameters of abdominal aortic aneurysms and alternative rupture risk predictors

PURPOSE There is no standard for measuring maximal diameter (Dmax) of abdominal aortic aneurysm (AAA) from computer tomography (CT) images although differences between Dmax evaluated from transversal (axialDmax) or orthogonal (orthoDmax) planes can be large especially for angulated AAAs. Therefore we investigated their correlations with alternative rupture risk indicators as peak wall stress (PWS) and peak wall rupture risk (PWRR) to decide which Dmax is more relevant in AAA rupture risk assessment. MATERIAL AND METHODS The Dmax values were measured by a trained radiologist from 70 collected CT scans, and the corresponding PWS and PWRR were evaluated using Finite Element Analysis (FEA). The cohort was ordered according to the difference between axialDmax and orthoDmax (Da-o) quantifying the aneurysm angulation, and Spearmans correlation coefficients between PWS/PWRR - orthoDmax/axialDmax were calculated. RESULTS The calculated correlations PWS/PWRR vs. orthoDmax were substantially higher for angulated AAAs (with Da-o≥3mm). Under this limit, the correlations were almost the same for both Dmax values. Analysis of AAAs divided into two groups of angulated (n=38) and straight (n=32) cases revealed that both groups are similar in all parameters (orthoDmax, PWS, PWRR) with the exception of axialDmax (p=0.024). CONCLUSIONS It was confirmed that orthoDmax is better correlated with the alternative rupture risk predictors PWS and PWRR for angulated AAAs (DA-O≥3mm) while there is no difference between orthoDmax and axialDmax for straight AAAs (DA-O<3mm). As angulated AAAs represent a significant portion of cases it can be recommended to use orthoDmax as the only Dmax parameter for AAA rupture risk assessment.