Jiri Bursa

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.

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.

Poisson׳s ratio of arterial wall – Inconsistency of constitutive models with experimental data

Poisson׳s ratio of fibrous soft tissues is analyzed in this paper on the basis of constitutive models and experimental data. Three different up-to-date constitutive models accounting for the dispersion of fibre orientations are analyzed. Their predictions of the anisotropic Poisson׳s ratios are investigated under finite strain conditions together with the effects of specific orientation distribution functions and of other parameters. The applied constitutive models predict the tendency to lower (or even negative) out-of-plane Poisson׳s ratio. New experimental data of porcine arterial layer under uniaxial tension in orthogonal directions are also presented and compared with the theoretical predictions and other literature data. The results point out the typical features of recent constitutive models with fibres concentrated in circumferential-axial plane of arterial layers and their potential inconsistence with some experimental data. The volumetric (in)compressibility of arterial tissues is also discussed as an eventual and significant factor influencing this inconsistency.

Numerical implementation of constitutive model for arterial layers with distributed collagen fibre orientations

Several constitutive models have been proposed for the description of mechanical behaviour of soft tissues containing collagen fibres. Some of the commonly used approaches accounting for the dispersion of fibre orientations are based on the summation of (mechanical) contributions of differently oriented fibre families. This leads to the need of numerical integration on the sphere surface, and the related numerical consumption is the main disadvantage of this category of constitutive models. The paper is focused on the comparison of various numerical integration methods applied to a specific constitutive model applicable for arterial walls. Robustness and efficiency of several integration rules were tested with respect to application in finite element (FE) codes. Among all the analysed numerical integration rules, the best results were reached by Lebedev quadrature; the related parameters for the specific constitutive model are presented in the paper. The results were implemented into the commercial FE code ANSYS via user subroutines, and their applicability was demonstrated by an example of FE simulation with non-homogenous stress field.

Development of endothelium-denuded human umbilical veins as living scaffolds for tissue- engineered small-calibre vascular grafts

Tissue‐engineered small‐calibre vessel grafts may help to alleviate the lack of graft material for coronary and peripheral bypass grafting in an increasing number of patients. This study explored the use of endothelium‐denuded human umbilical veins (HUVs) as scaffolds for vascular tissue engineering in a perfusion bioreactor. Vessel diameter (1.2 ± 0.4 mm), wall thickness (0.38 ± 0.09 mm), uniaxial ultimate failure stress (8029 ± 1714 kPa) and burst pressure (48.4 ± 20.2 kPa, range 28.4–83.9 kPa) were determined in native samples. The effects of endothelium removal from HUVs by enzymatic digestion, hypotonic lysis and dehydration were assessed. Dehydration did not significantly affect contractile function, tetrazolium dye reduction, mechanical strength and vessel structure, whereas the other methods failed in at least one of these parameters. Denudation by dehydration retained laminin, fibronectin, collagen and elastic fibres. Denuded HUVs were seeded in a perfusion bioreactor with either allogeneic HUVs endothelial cells or with saphenous vein endothelial cells harvested from patients with coronary artery disease. Seeding in a perfusion bioreactor resulted in a confluent monolayer of endothelial cells from both sources, as judged by histology and scanning electron microscopy. Seeded cells contained von Willebrand factor and CD31. In conclusion, denuded HUVs should be considered an alternative to decellularized blood vessels, as the process keeps the smooth muscle layer intact and functional, retains proteins relevant for biomechanic properties and for cell attachment and provides a suitable scaffold for seeding an autologous and flow‐resistant endothelium. Copyright

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.

A Fiber-Bundle Pull-out Test for Surface-Modified Glass Fibers in GF/Polyester Composite

The development of high-performance polymer composites is tightly bound with the functional surface modification of reinforcements. A new method, based on the principle of the fiber-bundle pull-out test, is proposed to analyze the interfacial properties between the long fibers in the form of a bundle and the polymer matrix. Specimen geometry and a test fixture were designed using finite element analysis. The method was verified for unsized and sized glass fibers embedded in polyester resin to demonstrate its applicability for a wide range of adhesion between fibers and the polymer matrix. The pull-out test can be used for a relative comparison of different surface modifications if the bundle geometry is unknown. The results of high reproducibility and sensitivity for interfacial properties make the method attractive.

Finite element simulation of mechanical tests of individual cells

The threedimensional finite element (FE) model of eucaryotic cell presented in the paper is based on similar models published recently; it comprehends elements representing cell membrane, cytoplasm and nucleus, and a complex tensegrity structure representing cytoskeleton. In contrast to the previous models, this tensegrity structure consists of several parts. External and internal parts count 30 struts and 60 cables each and their corresponding nodes are interconnected by 30 radial members; these parts represent cortical, nuclear and deep cytoskeletons, respectively. This arrangement enables us to simulate the load transmission from the extracellular space via membrane receptors (focal adhesions) to the central part of the cell (nucleus, centrosome); this ability of the model was tested by simulation of some mechanical tests of isolated cells, in particular tension test with micropipettes, indentation test and magnetic tweezer test. Although material properties of components have been defined as realistic as possible on the base of the mechanical tests with vascular smooth muscle cells, they were not identified in fact and are not unique probably. However, simulations of the tests have shown the ability of the model to simulate the global load-deformation response of the cell under various types of loadings, as well as several substantial global features of the cell behaviour, e.g. “at a distance effect”, non-linear stiffening with increasing load, or linear dependence of stiffness on increasing prestrain.

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.