A reduced-order model for wall shear stress in abdominal aortic aneurysms by proper orthogonal decomposition

In this paper, we introduce a method to construct a Reduced-Order Model (ROM) to study the physiological flow and the Wall Shear Stress (WSS) conditions in Abdominal Aortic Aneurysms (AAA). We start the process by running a training case using Computational Fluid Dynamics (CFD) simulations with time-varying flow parameters, such that these parameters cover the range of parameters that we would like to consider in our ROM. We use the inflow angle as the variable parameter in the current study. Then we use the snapshot Proper Orthogonal Decomposition (POD) to construct the reduced-order bases, which are subsequently enhanced using a QR-factorization technique to satisfy the relevant fluid boundary conditions. The resulting ROM enables us to study the flow pattern and the WSS distribution over a range of system parameters computationally very efficiently. We have used this method to show how the WSS varies significantly for an AAA with a simplified geometry, over a range of inflow angles usually considered mild in clinical terms. We have validated the ROM results with CFD results. This approach enables comprehensive analysis of the model system across a range of inflow angles and frequencies without the need to re-compute the simulation for small changes.     

Including surrounding tissue improves ultrasound-based 3D mechanical characterization of abdominal aortic aneurysms

ObjectivesIn this study the influence of surrounding tissues including the presence of the spine on wall stress analysis and mechanical characterization of abdominal aortic aneurysms using ultrasound imaging has been investigated.MethodsGeometries of 7 AAA patients and 11 healthy volunteers were acquired using 3-D ultrasound and converted to finite element based models. Model complexity of externally unsupported (aorta-only) models was complemented with inclusion of both soft tissue around the aorta and a spine support dorsal to the aorta. Computed 3-D motion of the aortic wall was verified by means of ultrasound speckle tracking. Resulting stress, strain, and estimated shear moduli were analyzed to quantify the effect of adding surrounding material supports.ResultsAn improved agreement was shown between the ultrasound measurements and the finite element tissue and spine models compared to the aorta-only models. Peak and 99-percentile Von Mises stress showed an overall decrease of 23–30%, while estimated shear modulus decreased with 12–20% after addition of the soft tissue. Shear strains in the aortic wall were higher in areas close to the spine compared to the anterior region.ConclusionsImproving model complexity with surrounding tissue and spine showed a homogenization of wall stresses, reduction in homogeneity of shear strain at the posterior side of the AAA, and a decrease in estimated aortic wall shear modulus. Future research will focus on the importance of a patient-specific spine geometry and location.     

Stochastic modelling of wall stresses in abdominal aortic aneurysms treated by a gene therapy

A stochastic mechanical model using the membrane theory was used to simulate the in vivo mechanical behaviour of abdominal aortic aneurysms (AAAs) in order to compute the wall stresses after stabilisation by gene therapy. For that, both length and diameter of AAAs rats were measured during their expansion. Four groups of animals, control and treated by an endovascular gene therapy during 3 or 28 days were included. The mechanical problem was solved analytically using the geometric parameters and assuming the shape of aneurysms by a ‘parabolic–exponential curve’. When compared to controls, stress variations in the wall of AAAs for treated arteries during 28 days decreased, while they were nearly constant at day 3. The measured geometric parameters of AAAs were then investigated using probability density functions (pdf) attributed to every random variable. Different trials were useful to define a reliable confidence region in which the probability to have a realisation is equal to 99%. The results demonstrated that the error in the estimation of the stresses can be greater than 28% when parameters uncertainties are not considered in the modelling. The relevance of the proposed approach for the study of AAA growth may be studied further and extended to other treatments aimed at stabilisation AAAs, using biotherapies and pharmacological approaches.     

Regional distribution of wall thickness and failure properties of human abdominal aortic aneurysm

The regional distribution of wall thickness and failure properties in human abdominal aortic aneurysm (AAA) was explored. Three unruptured and one ruptured AAA were harvested as a whole during necropsy. Thickness was measured at about every 1.5 cm² wall surface area for an average of 100 measurement sites per AAA. Multiple longitudinally oriented rectangular specimen strips were cut at various locations from each AAA for a total of 48 strips. The strips were subjected to uniaxial extension until failure. Wall thickness varied regionally and between AAA from as low as 0.23 mm at a rupture site to 4.26 mm at a calcified site (median=1.48 mm). Wall thickness was slightly lower in the posterior and right regions. The failure tension (ultimate) of specimen strips varied regionally and between AAA from 5.5 N/cm close to a blister site in the ruptured AAA to 42.3 N/cm at the undilated neck of a 4 cm diameter unruptured AAA (median=14.8 N/cm). Failure stress (ultimate) varied from 33.6 to 235.1 N/cm² (median=126.6 N/cm²). There was no perceptible pattern in failure properties along the circumference. Failure tension of specimen strips at or close to blisters was mostly low. The rupture site in the ruptured aneurysm had the lowest recorded wall thickness of 0.23 mm with only slightly higher readings within a 1 cm radius. The failure tension of the specimen strip close to the rupture site was low (11.1 N/cm) compared to its neighborhood in the ruptured aneurysm.     

Model studies of the flow in abdominal aortic aneurysms during resting and exercise conditions

Pulsatile flow in abdominal aortic aneurysm (AAA) models has been examined in order to understand the hemodynamics that may contribute to growth of an AAA. The model studies were conducted by experiments (flow visualization and laser Doppler velocimetry) and by numerical simulation using physiologically realistic resting and exercise flow conditions. We characterize the flow for two AAA model shapes and sizes emulating early AAA development through moderate AAA growth (mean and peak Reynolds numbers of 362<Re_mean<1053 and 3308<Re_peak<5696 with Womersley parameter 16.4<<21.2). The results of our investigation indicate that AAA flow can be divided into three flow regimes: (i) Attached flow over the entire cycle in small AAAs at resting conditions, (ii) vortex formation and translation in moderate size AAAs at resting conditions, and (iii) vortex formation, translation and turbulence in moderate size AAAs under exercise conditions. The second two regimes are classified in the medical literature as disturbed flow conditions that have been correlated with atherogenesis as well as thrombogenesis. Thus, AAA disturbed hemodynamics may be a contributing factor to AAA growth by accelerating the degeneration of the arterial wall. Our investigation also concluded that vortex development is considerably weaker in an asymmetric AAA. Furthermore, turbulence was not observed in the asymmetric model. Finally, our investigation suggests a new mode of transition to turbulence: vortex ring instability and bursting to turbulence. The transition process depends on a combination of the pulsatile flow conditions and the tube cross-sectional area change.     

Automated and objective removal of bifurcation aneurysms: Incremental improvements,and validation against healthy controls

Abnormal hemodynamic stresses are thought to correlate with aneurysm initiation, growth, and rupture. We have previously investigated the role of wall shear stress (WSS) and WSS gradients (WSSG) in search for a mechanistic link to formation of sidewall aneurysms using an automated and objective tool for aneurysm removal and arterial reconstruction in combination with computational fluid dynamics (CFD). However, we warned against the use of the tool for bifurcation type aneurysms because of a potential unrealistic reconstruction of the apex. We hypothesized that inclusion of additional morphological features from the surrounding vasculature could overcome these constraints. We extended the previously published method for removal and reconstruction of the bifurcation vasculature based on diverging and converging points of the parent and daughter artery centerlines, to also include two new centerlines between the daughter vessels, one of them passed through the bifurcation center. Validation was performed by comparing the efficacy of the two algorithms, using ten healthy models of the internal carotid artery terminus as ground truth. Qualitative results showed that the bifurcation apexes became smoother relative to the original algorithm; more consistent with the reference models. This was reflected quantitatively by a reduced maximum distance between the reference and reconstructed surfaces, although not statistically significant. Furthermore, the modified algorithm also quantitatively improved CFD derived WSS and WSSG, especially the latter. In conclusion, the modified algorithm does not perfectly reconstruct the bifurcation apex, but provides an incremental improvement, especially important for the derived hemodynamic metrics of interest in vascular pathobiology.     

Intraluminal thrombus thickness is not related to lower concentrations of trace elements in the wall of infrarenal abdominal aortic aneurysms

BackgroundIntraluminal thrombus (ILT) formation plays a significant role in the progression of infrarenal abdominal aortic aneurysms (AAA). Potentially, as ILT thickness increases the availability of trace elements in the aneurysm wall could decrease thereby leading to oxidative stress and intensifying pro-inflammatory cytokine generation.AimTo determine if thrombus thickness is related to the concentration of trace elements in the wall of infrarenal AAA.Patients and methodsThe concentrations of trace elements in the wall of the aneurysm sack and ILT obtained from 19 consecutive patients during surgery for infrarenal AAA were determined using emission spectrometry.ResultsThe concentrations of magnesium, zinc, manganese, and lead in the wall of AAA were significantly greater than in the ILT. Only the concentration of copper was lower in the AAA wall compared with the thrombus. The concentration of calcium, phosphorus, zinc, lead, copper, and magnesium increased with ILT thickness. The concentrations of no other trace elements in the wall of AAA were found to be related to the ILT thickness.ConclusionsIntraluminal thrombus thickness is not associated with a lower concentration of trace elements in the wall of the infrarenal AAA. Thus, the intraluminal thrombus participates in the progression of AAA by mechanisms independent of trace element supply to the wall of the aneurysm sack.     

Filling the void: A coalescent numerical and experimental technique to determine aortic stent graft mechanics

The presented study details a combined experimental and computational method to assess and compare the mechanical behavior of the main body of 4 different stent graft designs. The mechanical response to a flat plate compression and radial crimping of the devices is derived and related to geometrical and material features of different stent designs. The finite element modeling procedure is used to complement the experimental results and conduct a solution sensitivity study. Finite element evaluations of the mechanical behavior match well with experimental findings and are used as a quantitative basis to discuss design characteristics of the different devices.     

Computational comparison of aortic root stresses in presence of stentless and stented aortic valve bio-prostheses

We provide a computational comparison of the performance of stentless and stented aortic prostheses, in terms of aortic root displacements and internal stresses. To this aim, we consider three real patients; for each of them, we draw the two prostheses configurations, which are characterized by different mechanical properties and we also consider the native configuration. For each of these scenarios, we solve the fluid–structure interaction problem arising between blood and aortic root, through Finite Elements. In particular, the Arbitrary Lagrangian–Eulerian formulation is used for the numerical solution of the fluid-dynamic equations and a hyperelastic material model is adopted to predict the mechanical response of the aortic wall and the two prostheses. The computational results are analyzed in terms of aortic flow, internal wall stresses and aortic wall/prosthesis displacements; a quantitative comparison of the mechanical behavior of the three scenarios is reported. The numerical results highlight a good agreement between stentless and native displacements and internal wall stresses, whereas higher/non-physiological stresses are found for the stented case.     

Finite element and photoelastic modelling of an abdominal aortic aneurysm: a comparative study

Rupture prediction of abdominal aortic aneurysms (AAAs) remains a clinical challenge. Finite element analysis (FEA) may allow for improved identification for intervention timing, but the method needs further substantiation. In this study, experimental photoelastic method and finite element techniques were compared using an idealised AAA geometry. There was good agreement between the numerical and experimental results. At the proximal and distal end of the AAA model, the maximum differences in principle strain for an internal pressure of 120 mmHg had differences ranging from 0.03 to 10.01%. The maximum difference in principle strain for the photoelastic and the finite element model at a pressure of 120 mmHg was 0.167 and 0.158, respectively. The current research strengthens the case for using FEA as an adjunct to the current clinical practice of utilising diameter measurement for intervention timing.     

A study of wall shear stress in 12 aneurysms with respect to different viscosity models and flow conditions

Recent computational fluid dynamics (CFD) studies relate abnormal blood flow to rupture of cerebral aneurysms. However, it is still debated how to model blood flow with sufficient accuracy. Common assumptions made include Newtonian behaviour of blood, traction free outlet boundary conditions and inlet boundary conditions based on available literature. These assumptions are often required since the available patient specific data is usually restricted to the geometry of the aneurysm and the surrounding vasculature. However, the consequences of these assumptions have so far been inadequately addressed.     

The biaxial mechanical behaviour of abdominal aortic aneurysm intraluminal thrombus: Classification of morphology and the determination of layer and region specific properties

Intraluminal thrombus (ILT) is present in 75% of clinically-relevant abdominal aortic aneurysms (AAAs) yet, despite much research effort, its role in AAA biomechanics remains unclear. The aim of this work is to further evaluate the biomechanics of ILT and determine if different ILT morphologies have varying mechanical properties.     

Estimation of the physiological mechanical conditioning in vascular tissue engineering by a predictive fluid-structure interaction approach

The in vitro replication of physiological mechanical conditioning through bioreactors plays a crucial role in the development of functional Small-Caliber Tissue-Engineered Blood Vessels. An in silico scaffold-specific model under pulsatile perfusion provided by a bioreactor was implemented using a fluid-structure interaction (FSI) approach for viscoelastic tubular scaffolds (e.g. decellularized swine arteries, DSA). Results of working pressures, circumferential deformations, and wall shear stress on DSA fell within the desired physiological range and indicated the ability of this model to correctly predict the mechanical conditioning acting on the cells-scaffold system. Consequently, the FSI model allowed us to a priori define the stimulation pattern, driving in vitro physiological maturation of scaffolds, especially with viscoelastic properties.     

Healthy and diseased coronary bifurcation geometries influence near-wall and intravascular flow: A computational exploration of the hemodynamic risk

Local hemodynamics has been identified as one main determinant in the onset and progression of atherosclerotic lesions at coronary bifurcations. Starting from the observation that atherosensitive hemodynamic conditions in arterial bifurcation are majorly determined by the underlying anatomy, the aim of the present study is to investigate how peculiar coronary bifurcation anatomical features influence near-wall and intravascular flow patterns. Different bifurcation angles and cardiac curvatures were varied in population-based, idealized models of both stenosed and unstenosed bifurcations, representing the left anterior descending (LAD) coronary artery with its diagonal branch. Local hemodynamics was analyzed in terms of helical flow and exposure to low/oscillatory shear stress by performing computational fluid dynamics simulations.Results show that bifurcation angle impacts lowly hemodynamics in both stenosed and unstenosed cases. Instead, curvature radius influences the generation and transport of helical flow structures, with smaller cardiac curvature radius associated to higher helicity intensity. Stenosed bifurcation models exhibit helicity intensity values one order of magnitude higher than the corresponding unstenosed cases. Cardiac curvature radius moderately affects near-wall hemodynamics of the stenosed cases, with smaller curvature radius leading to higher exposure to low shear stress and lower exposure to oscillatory shear stress. In conclusion, the proposed controlled benchmark allows investigating the effect of various geometrical features on local hemodynamics at the LAD/diagonal bifurcation, highlighting that cardiac curvature influences near wall and intravascular hemodynamics, while bifurcation angle has a minor effect.     

Three-dimensional macro-scale assessment of regional and temporal wall shear stress characteristics on aortic valve leaflets

The aortic valve (AV) achieves unidirectional blood flow between the left ventricle and the aorta. Although hemodynamic stresses have been shown to regulate valvular biology, the native wall shear stress (WSS) experienced by AV leaflets remains largely unknown. The objective of this study was to quantify computationally the macro-scale leaflet WSS environment using fluid–structure interaction modeling. An arbitrary Lagrangian–Eulerian approach was implemented to predict valvular flow and leaflet dynamics in a three-dimensional AV geometry subjected to physiologic transvalvular pressure. Local WSS characteristics were quantified in terms of temporal shear magnitude (TSM), oscillatory shear index (OSI) and temporal shear gradient (TSG). The dominant radial WSS predicted on the leaflets exhibited high amplitude and unidirectionality on the ventricularis (TSM>7.50 dyn/cm², OSI < 0.17, TSG>325.54 dyn/cm² s) but low amplitude and bidirectionality on the fibrosa (TSM < 2.73 dyn/cm², OSI>0.38, TSG < 191.17 dyn/cm² s). The radial WSS component computed in the leaflet base, belly and tip demonstrated strong regional variability (ventricularis TSM: 7.50–22.32 dyn/cm², fibrosa TSM: 1.26–2.73 dyn/cm²). While the circumferential WSS exhibited similar spatially dependent magnitude (ventricularis TSM: 1.41–3.40 dyn/cm², fibrosa TSM: 0.42–0.76 dyn/cm²) and side-specific amplitude (ventricularis TSG: 101.73–184.43 dyn/cm² s, fibrosa TSG: 41.92–54.10 dyn/cm² s), its temporal variations were consistently bidirectional (OSI>0.25). This study provides new insights into the role played by leaflet–blood flow interactions in valvular function and critical hemodynamic stress data for the assessment of the hemodynamic theory of AV disease.     

Adhesion study of silicone coatings: the interaction of thickness,modulus and shear rate on adhesion force

Abstract

Interactions between coating thickness, modulus and shear rate on pseudobarnacle adhesion to a platinum-cured silicone coating were studied using a statistical experimental design. A combined design method was used for two mixture components and two process variables. The two mixture components, vinyl end-terminated polydimethylsiloxanes (V21: MW = 6 kg mole^?1 and V35: MW = 4 9.5 kg mole^?1, Gelest Inc.) were mixed at five different levels to vary the modulus. The dry coating thickness was varied from 160 – 740 μm and shear tests were performed at four different shear rates (2, 7, 12, and 22 μm s^?1). The results of the statistical analysis showed that the mixture components were significant factors on shear stress, showing an interaction with the process variable. For the soft silicone coating based on the high molecular weight polydimethylsiloxane (E = 0.08 MPa), shear stress significantly increased as coating thickness decreased, while shear rate slightly impacted shear force especially at 160 μm coating thickness. As the modulus was increased (E = 1.3 MPa), more force was required to detach the pseudobarnacle from the coatings, but thickness and rate dependence on shear stress became less important.     

Flow field and oscillatory shear stress in a tuning-fork-shaped model of the average human carotid bifurcation

The oscillatory shear index (OSI) was developed based on the hypothesis that intimal hyperplasia was correlated with oscillatory shear stresses. However, the validity of the OSI was in question since the correlation between intimal thickness and the OSI at the side walls of the sinus in the Y-shaped model of the average human carotid bifurcation (Y-AHCB) was weak. The objectives of this paper are to examine whether the reason for the weak correlation lies in the deviation in geometry of Y-AHCB from real human carotid bifurcation, and whether this correlation is clearly improved in the tuning-fork-shaped model of the average human carotid bifurcation (TF-AHCB). The geometry of the TF-AHCB model was based on observation and statistical analysis of specimens from 74 cadavers. The flow fields in both models were studied and compared by using flow visualization methods under steady flow conditions and by using laser Doppler anemometer (LDA) under pulsatile flow conditions. The TF-shaped geometry leads to a more complex flow field than the Y-shaped geometry. This added complexity includes strengthened helical movements in the sinus, new flow separation zone, and directional changes in the secondary flow patterns. The results show that the OSI-values at the side walls of the sinus in the TF-shaped model were more than two times as large as those in the Y-shaped model. This study confirmed the stronger correlation between the OSI and intimal thickness in the tuning-fork geometry of human carotid bifurcation, and the TF-AHCB model is a significant improvement over the traditional Y-shaped model.