Circumferential vascular deformation after stent implantation alters wall shear stress evaluated with time-dependent 3D computational fluid dynamics models.

The success of vascular stents in the restoration of blood flow is limited by restenosis. Recent data generated from computational fluid dynamics (CFD) models suggest that stent geometry may cause local alterations in wall shear stress (WSS) that have been associated with neointimal hyperplasia and subsequent restenosis. However, previous CFD studies have ignored histological evidence of vascular straightening between circumferential stent struts. We tested the hypothesis that consideration of stent-induced vascular deformation may more accurately predict alterations in indexes of WSS that may subsequently account for histological findings after stenting. We further tested the hypothesis that the severity of these alterations in WSS varies with the degree of vascular deformation after implantation. Steady-state and time-dependent simulations of three-dimensional CFD arteries based on canine coronary artery measurements of diameter and blood flow were conducted, and WSS and WSS gradients were calculated. Circumferential straightening introduced areas of high WSS between stent struts that were absent in stented vessels of circular cross section. The area of vessel exposed to low WSS was dependent on the degree of circumferential vascular deformation and axial location within the stent. Stents with four vs. eight struts increased the intrastrut area of low WSS in vessels, regardless of cross-sectional geometry. Elevated WSS gradients were also observed between struts in vessels with polygonal cross sections. The results obtained using three-dimensional CFD models suggest that changes in vascular geometry after stent implantation are important determinants of WSS distributions that may be associated with subsequent neointimal hyperplasia.     

Alterations in regional vascular geometry produced by theoretical stent implantation influence distributions of wall shear stress: analysis of a curved coronary artery using 3D computational fluid dynamics modeling

Background  

The success of stent implantation in the restoration of blood flow through areas of vascular narrowing is limited by restenosis. Several recent studies have suggested that the local geometric environment created by a deployed stent may influence regional blood flow characteristics and alter distributions of wall shear stress (WSS) after implantation, thereby rendering specific areas of the vessel wall more susceptible to neointimal hyperplasia and restenosis. Stents are most frequently implanted in curved vessels such as the coronary arteries, but most computational studies examining blood flow patterns through stented vessels conducted to date use linear, cylindrical geometric models. It appears highly probable that restenosis occurring after stent implantation in curved arteries also occurs as a consequence of changes in fluid dynamics that are established immediately after stent implantation.     

Allometric scaling of wall shear stress from mice to humans: quantification using cine phase-contrast MRI and computational fluid dynamics

Allometric scaling laws relate structure or function between species of vastly different sizes. They have rarely been derived for hemodynamic parameters known to affect the cardiovascular system, e.g., wall shear stress (WSS). This work describes noninvasive methods to quantify and determine a scaling law for WSS. Geometry and blood flow velocities in the infrarenal aorta of mice and rats under isoflurane anesthesia were quantified using two-dimensional magnetic resonance angiography and phase-contrast magnetic resonance imaging at 4.7 tesla. Three-dimensional models constructed from anatomic data were discretized and used for computational fluid dynamic simulations using phase-contrast velocity imaging data as inlet boundary conditions. WSS was calculated along the infrarenal aorta and compared between species to formulate an allometric equation for WSS. Mean WSS along the infrarenal aorta was significantly greater in mice and rats compared with humans (87.6, 70.5, and 4.8 dyn/cm(2), P < 0.01), and a scaling exponent of -0.38 (R(2) = 0.92) was determined. Manipulation of the murine genome has made small animal models standard surrogates for better understanding the healthy and diseased human cardiovascular system. It has therefore become increasingly important to understand how results scale from mouse to human. This noninvasive methodology provides the opportunity to serially quantify changes in WSS during disease progression and/or therapeutic intervention.     

Optimization of cardiovascular stent design using computational fluid dynamics

Coronary stent design affects the spatial distribution of wall shear stress (WSS), which can influence the progression of endothelialization, neointimal hyperplasia, and restenosis. Previous computational fluid dynamics (CFD) studies have only examined a small number of possible geometries to identify stent designs that reduce alterations in near-wall hemodynamics. Based on a previously described framework for optimizing cardiovascular geometries, we developed a methodology that couples CFD and three-dimensional shape-optimization for use in stent design. The optimization procedure was fully-automated, such that solid model construction, anisotropic mesh generation, CFD simulation, and WSS quantification did not require user intervention. We applied the method to determine the optimal number of circumferentially repeating stent cells (N(C)) for slotted-tube stents with various diameters and intrastrut areas. Optimal stent designs were defined as those minimizing the area of low intrastrut time-averaged WSS. Interestingly, we determined that the optimal value of N(C) was dependent on the intrastrut angle with respect to the primary flow direction. Further investigation indicated that stent designs with an intrastrut angle of approximately 40 deg minimized the area of low time-averaged WSS regardless of vessel size or intrastrut area. Future application of this optimization method to commercially available stent designs may lead to stents with superior hemodynamic performance and the potential for improved clinical outcomes.     

Alterations in wall shear stress predict sites of neointimal hyperplasia after stent implantation in rabbit iliac arteries

Restenosis resulting from neointimal hyperplasia (NH) limits the effectiveness of intravascular stents. Rates of restenosis vary with stent geometry, but whether stents affect spatial and temporal distributions of wall shear stress (WSS) in vivo is unknown. We tested the hypothesis that alterations in spatial WSS after stent implantation predict sites of NH in rabbit iliac arteries. Antegrade iliac artery stent implantation was performed under angiography, and blood flow was measured before casting 14 or 21 days after implantation. Iliac artery blood flow domains were obtained from three-dimensional microfocal X-ray computed tomography imaging and reconstruction of the arterial casts. Indexes of WSS were determined using three-dimensional computational fluid dynamics. Vascular histology was unchanged proximal and distal to the stent. Time-dependent NH was localized within the stented region and was greatest in regions exposed to low WSS and acute elevations in spatial WSS gradients. The lowest values of WSS spatially localized to the stented area of a theoretical artery progressively increased after 14 and 21 days as NH occurred within these regions. This NH abolished spatial disparity in distributions of WSS. The results suggest that stents may introduce spatial alterations in WSS that modulate NH in vivo.     

Evaluation of the effect of stent strut profile on shear stress distribution using statistical moments

Background  

In-stent restenosis rates have been closely linked to the wall shear stress distribution within a stented arterial segment, which in turn is a function of stent design. Unfortunately, evaluation of hemodynamic performance can only be evaluated with long term clinical trials. In this work we introduce a set of metrics, based on statistical moments, that can be used to evaluate the hemodynamic performance of a stent in a standardized way. They are presented in the context of a 2D flow study, which analyzes the impact of different strut profiles on the wall shear stress distribution for stented coronary arteries.     

Evaluation of the effect of stent strut profile on shear stress distribution using statistical moments

A recently developed machine learning algorithm referred to as Extreme Learning Machine (ELM) was used to classify machine control commands out of time series of spike trains of ensembles of CA1 hippocampus neurons (n = 34) of a rat, which was performing a target-to-goal task on a two-dimensional space through a brain-machine interface system. Performance of ELM was analyzed in terms of training time and classification accuracy. The results showed that some processes such as class code prefix, redundancy code suffix and smoothing effect of the classifiers' outputs could improve the accuracy of classification of robot control commands for a brain-machine interface system.     

Accuracy and reproducibility of CFD predicted wall shear stress using 3D ultrasound images

Computational fluid dynamics (CFD) flow simulation techniques have the potential to enhance our understanding of how haemodynamic factors are involved in atherosclerosis. Recently, 3D ultrasound has emerged as an alternative to other 3D imaging techniques, such as magnetic resonance angiography (MRA). The method can be used to generate realistic vascular geometry suitable for CFD simulations. In order to assess accuracy and reproducibility of the procedure from image acquisition to reconstruction to CFD simulation, a human carotid artery bifurcation phantom was scanned three times using 3D ultrasound. The geometry was reconstructed and flow simulations were carried out on the three sets as well as on a model generated using computer aided design (CAD) from the geometric information given by the manufacturer. It was found that the three reconstructed sets showed good reproducibility as well as satisfactory quantitative agreement with the CAD model. Analyzing two selected locations probably representing the 'worst cases,' accuracy comparing ultrasound and CAD reconstructed models was estimated to be between 7.2% and 7.7% of the maximum instantaneous WSS and reproducibility comparing the three scans to be between 8.2% and 10.7% of their average maximum.     

Analysis of thoracic aorta hemodynamics using 3D particle tracking velocimetry and computational fluid dynamics

Parallel to the massive use of image-based computational hemodynamics to study the complex flow establishing in the human aorta, the need for suitable experimental techniques and ad hoc cases for the validation and benchmarking of numerical codes has grown more and more.     

Semi-automated mitral valve morphometry and computational stress analysis using 3D ultrasound

In vivo human mitral valves (MV) were imaged using real-time 3D transesophageal echocardiography (rt-3DTEE), and volumetric images of the MV at mid-systole were analyzed by user-initialized segmentation and 3D deformable modeling with continuous medial representation, a compact representation of shape. The resulting MV models were loaded with physiologic pressures using finite element analysis (FEA). We present the regional leaflet stress distributions predicted in normal and diseased (regurgitant) MVs. Rt-3DTEE, semi-automated leaflet segmentation, 3D deformable modeling, and FEA modeling of the in vivo human MV is tenable and useful for evaluation of MV pathology.     

Stent design properties and deployment ratio influence indexes of wall shear stress: a three-dimensional computational fluid dynamics investigation within a normal artery.

Restenosis limits the effectiveness of stents, but the mechanisms responsible for this phenomenon remain incompletely described. Stent geometry and expansion during deployment produce alterations in vascular anatomy that may adversely affect wall shear stress (WSS) and correlate with neointimal hyperplasia. These considerations have been neglected in previous computational fluid dynamics models of stent hemodynamics. Thus we tested the hypothesis that deployment diameter and stent strut properties (e.g., number, width, and thickness) influence indexes of WSS predicted with three-dimensional computational fluid dynamics. Simulations were based on canine coronary artery diameter measurements. Stent-to-artery ratios of 1.1 or 1.2:1 were modeled, and computational vessels containing four or eight struts of two widths (0.197 or 0.329 mm) and two thicknesses (0.096 or 0.056 mm) subjected to an inlet velocity of 0.105 m/s were examined. WSS and spatial WSS gradients were calculated and expressed as a percentage of the stent and vessel area. Reducing strut thickness caused regions subjected to low WSS (<5 dyn/cm(2)) to decrease by approximately 87%. Increasing the number of struts produced a 2.75-fold increase in exposure to low WSS. Reducing strut width also caused a modest increase in the area of the vessel experiencing low WSS. Use of a 1.2:1 deployment ratio increased exposure to low WSS by 12-fold compared with stents implanted in a 1.1:1 stent-to-vessel ratio. Thinner struts caused a modest reduction in the area of the vessel subjected to elevated WSS gradients, but values were similar for the other simulations. The results suggest that stent designs that reduce strut number and thickness are less likely to subject the vessel to distributions of WSS associated with neointimal hyperplasia.     

Experimental study of laminar blood flow through an artery treated by a stent implantation: characterisation of intra-stent wall shear stress

The stimulation of endothelial cells by arterial wall shear stress (WSS) plays a central role in restenosis. The fluid-structure interaction between stent wire and blood flow alters the WSS, particularly between stent struts. We have designed an in vitro model of struts of an intra-vascular prosthesis to study blood flow through a 'stented' section. The experimental artery consisted of a transparent square section test vein, which reproduced the strut design (100x magnifying power). A programmable pump was used to maintain a steady blood flow. Particle image velocimetry method was used to measure the flow between and over the stent branches, and to quantify WSS. Several prosthesis patterns that were representative of the total stent strut geometry were studied in a greater detail. We obtained WSS values of between -1.5 and 1.5Pa in a weak SS area which provided a source of endothelial stimulation propitious to restenosis. We also compared two similar patterns located in two different flow areas (one at the entry of the stent and one further downstream). We only detected a slight difference between the weakest SS levels at these two sites. As the endothelial proliferation is greatly influenced by the SS, knowledge of the SS modification induced by the stent implantation could be of importance for intra-vascular prostheses design optimisation and thus can help to reduce the restenosis incidence rate.     

Design and analysis of flow velocity distribution inside a raceway pond using computational fluid dynamics

Bioprocess and Biosystems Engineering - Open raceway ponds are widely adopted for cultivating microalgae on a large scale. Working depth of the raceway pond is the major component to be analysed...     

Accurate prediction of wall shear stress in a stented artery: newtonian versus non-newtonian models

A significant amount of evidence linking wall shear stress to neointimal hyperplasia has been reported in the literature. As a result, numerical and experimental models have been created to study the influence of stent design on wall shear stress. Traditionally, blood has been assumed to behave as a Newtonian fluid, but recently that assumption has been challenged. The use of a linear model; however, can reduce computational cost, and allow the use of Newtonian fluids (e.g., glycerine and water) instead of a blood analog fluid in an experimental setup. Therefore, it is of interest whether a linear model can be used to accurately predict the wall shear stress caused by a non-Newtonian fluid such as blood within a stented arterial segment. The present work compares the resulting wall shear stress obtained using two linear and one nonlinear model under the same flow waveform. All numerical models are fully three-dimensional, transient, and incorporate a realistic stent geometry. It is shown that traditional linear models (based on blood's lowest viscosity limit, 3.5 Pa s) underestimate the wall shear stress within a stented arterial segment, which can lead to an overestimation of the risk of restenosis. The second linear model, which uses a characteristic viscosity (based on an average strain rate, 4.7 Pa s), results in higher wall shear stress levels, but which are still substantially below those of the nonlinear model. It is therefore shown that nonlinear models result in more accurate predictions of wall shear stress within a stented arterial segment.     

On the choice of outlet boundary conditions for patient-specific analysis of aortic flow using computational fluid dynamics

Boundary conditions (BCs) are an essential part in computational fluid dynamics (CFD) simulations of blood flow in large arteries. Although several studies have investigated the influence of BCs on predicted flow patterns and hemodynamic wall parameters in various arterial models, there is a lack of comprehensive assessment of outlet BCs for patient-specific analysis of aortic flow. In this study, five different sets of outlet BCs were tested and compared using a subject-specific model of a normal aorta. Phase-contrast magnetic resonance imaging (PC-MRI) was performed on the same subject and velocity profiles extracted from the in vivo measurements were used as the inlet boundary condition. Computational results obtained with different outlet BCs were assessed in terms of their agreement with the PC-MRI velocity data and key hemodynamic parameters, such as pressure and flow waveforms and wall shear stress related indices. Our results showed that the best overall performance was achieved by using a well-tuned three-element Windkessel model at all model outlets, which not only gave a good agreement with in vivo flow data, but also produced physiological pressure waveforms and values. On the other hand, opening outlet BCs with zero pressure at multiple outlets failed to reproduce any physiologically relevant flow and pressure features.     

Organotypic 3D cell culture models: using the rotating wall vessel to study host-pathogen interactions

Appropriately simulating the three-dimensional (3D) environment in which tissues normally develop and function is crucial for engineering in vitro models that can be used for the meaningful dissection of host-pathogen interactions. This Review highlights how the rotating wall vessel bioreactor has been used to establish 3D hierarchical models that range in complexity from a single cell type to multicellular co-culture models that recapitulate the 3D architecture of tissues observed in vivo. The application of these models to the study of infectious diseases is discussed.     

Computational evaluation of oxygen and shear stress distributions in 3D perfusion culture systems: macro-scale and micro-structured models

We present a combined macro-scale/micro-scale computational approach to quantify oxygen transport and flow-mediated shear stress to human chondrocytes cultured in three-dimensional scaffolds in a perfusion bioreactor system. A macro-scale model was developed to assess the influence of the bioreactor design and to identify the proper boundary conditions for the micro-scale model. The micro-scale model based on a micro-computed tomography (microCT) reconstruction of a poly(ethylene glycol terephthalate)/poly(butylene terephthalate) (PEGT/PBT) foam scaffold, was developed to assess the influence of the scaffold micro-architecture on local shear stress and oxygen levels within the scaffold pores. Experiments were performed to derive specific oxygen consumption rates for constructs perfused under flow rates of 0.3 and 0.03 ml min(-1). While macro-scale and micro-scale models predicted similar average oxygen levels at different depths within the scaffold, microCT models revealed small local oxygen variations within the scaffold micro-architecture. The combined macro-scale/micro-scale approach indicated that 0.3 ml min(-1), which subjected 95% of the cells to less than 6.3 mPa shear, would maintain the oxygen supply throughout the scaffold above anoxic levels (>1%), with 99.5% of the scaffold supplied with 8-2% O(2). Alternatively, at 0.03 ml min(-1), the macro-scale model predicted 6% of the cells would be supplied with 0.5-1% O(2), although this region of cells was confined to the periphery of the scaffold. Together with local variations predicted by the micro-scale model, the simulations underline that in the current model system, reducing the flow below 0.03 ml min(-1) would likely have dire consequences on cell viability to pronounced regions within the engineered construct. The presented approach provides a sensitive tool to aid efficient bioreactor optimization and scaffold design.     

Computational models for wall shear stress estimation in scaffolds: a comparative study of two complete geometries

Fluid mechanical stimuli are known to upregulate cell differentiation and matrix formation. Since wall shear stress plays an important role various studies tried to estimate the scaffold fluid dynamic environment. However, because of the geometrical complexity, nearly all studies created their CFD model based on a submodel of the entire scaffold assuming that the model covers heterogeneity sufficiently. However to the authors' knowledge no study exist providing guidelines in this matter. In a previous study we demonstrated that submodels are influenced by the boundary conditions, inevitable when flow channels are chopped off. For the current study we therefore developed μCT based models of two complete scaffold geometries (one titanium and one hydroxyapatite). Imposing a 0.04 ml/min flow rate resulted in a surface area averaged wall shear stress of 1.41 mPa for titanium and 1.09 mPa for hydroxyapatite. In order to get insight in required model size we subdivided the domain in regions of different size. From our results we propose a model size between 6 and 10 times the average pore size. The wall shears stress should be calculated on a region at least one pore size away from the boundaries. These guidelines could be of use for computationally more costly simulations where it is not possible to simulate the complete scaffold domain.     

Experimental and numerical study of pulsatile flows through stenosis: wall shear stress analysis.

Different shapes of pulsatile flows through a model of stenosis are experimentally and numerically modeled to validate both methods and to determine the wall shear stress temporal evolution downstream from the stenosis. Two-dimensional velocity measurements are performed in a 75% severity stenosis using a pulsed Doppler ultrasonic velocimeter. Finite element package is employed for the transient numerical simulations. Polynomial method, based on the experimental velocity values, is proposed to determine the wall shear stress temporal evolution. There is a good agreement between the numerical and experimental results. The wall shear stress temporal analysis shows oscillating wall shear stress values during the cycle with high wall shear stress values at the throat of about 120 dyn/cm2, and low values downstream from the stenosis of about - 2.5 dyn/cm2. The key result of the study is that the presence of the stenosis leads the artery to work in a direction which is opposite to the direction of a healthy artery.