A Computational Fluid Dynamics (CFD) analysis to optimize size and shape pattern for endothelial cell growth

Competitive flow from native coronary vessels is considered a major factor in the failure of coronary bypass grafts. However, the pathophysiological effects are not fully understood. Low and oscillatory wall shear stress (WSS) is known to induce endothelial dysfunction and vascular disease, like atherosclerosis and intimal hyperplasia. The aim was to investigate the impact of competitive flow on WSS in mammary artery bypass grafts. Using computational fluid dynamics, WSS was calculated in a left internal mammary artery (LIMA) graft to the left anterior descending artery in a three-dimensional in vivo porcine coronary artery bypass graft model. The following conditions were investigated: high competitive flow (non-significant coronary lesion), partial competitive flow (significant coronary lesion), and no competitive flow (totally occluded coronary vessel). Time-averaged WSS of LIMA at high, partial, and no competitive flow were 0.3-0.6, 0.6-3.0, and 0.9-3.0 Pa, respectively. Further, oscillatory WSS quantified as the oscillatory shear index (OSI) ranged from (maximum OSI = 0.5 equals zero net WSS) 0.15 to 0.35, <0.05, and <0.05, respectively. Thus, high competitive flow resulted in substantial oscillatory and low WSS. Moderate competitive flow resulted in WSS and OSI similar to the no competitive flow condition. Graft flow is highly dependent on the degree of competitive flow. High competitive flow was found to produce unfavourable WSS consistent with endothelial dysfunction and subsequent graft narrowing and failure. Partial competitive flow, however, may be better tolerated as it was found to be similar to the ideal condition of no competitive flow.

Background: Intracranial aneurysms (IAs) result from abnormal enlargement of the arterial lumen. IAs are mostly quiescent and asymptomatic, but their rupture leads to severe brain damage or death. As the evolution of IAs is hard to predict and intricates medical decision, it is essential to improve our understanding of their pathophysiology. Wall shear stress (WSS) is proposed to influence IA growth and rupture. In this study, we investigated the effects of low and supra-high aneurysmal WSS on endothelial cells (ECs).Methods: Porcine arterial ECs were exposed for 48 h to defined levels of shear stress (2, 30, or 80 dyne/cm2) using an Ibidi flow apparatus. Immunostaining for CD31 or γ-cytoplasmic actin was performed to outline cell borders or to determine cell architecture. Geometry measurements (cell orientation, area, circularity and aspect ratio) were performed on confocal microscopy images. mRNA was extracted for RNAseq analysis.Results: ECs exposed to low or supra-high aneurysmal WSS were more circular and had a lower aspect ratio than cells exposed to physiological flow. Furthermore, they lost the alignment in the direction of flow observed under physiological conditions. The effects of low WSS on differential gene expression were stronger than those of supra-high WSS. Gene set enrichment analysis highlighted that extracellular matrix proteins, cytoskeletal proteins and more particularly the actin protein family were among the protein classes the most affected by shear stress. Interestingly, most genes showed an opposite regulation under both types of aneurysmal WSS. Immunostainings for γ-cytoplasmic actin suggested a different organization of this cytoskeletal protein between ECs exposed to physiological and both types of aneurysmal WSS.Conclusion: Under both aneurysmal low and supra-high WSS the typical arterial EC morphology molds to a more spherical shape. Whereas low WSS down-regulates the expression of cytoskeletal-related proteins and up-regulates extracellular matrix proteins, supra-high WSS induces opposite changes in gene expression of these protein classes. The differential regulation in EC gene expression observed under various WSS translate into a different organization of the ECs’ architecture. This adaptation of ECs to different aneurysmal WSS conditions may affect vascular remodeling in IAs.

Atherosclerosis involves an inflammatory response due to plaque formation within the arteries, which can lead to ischemic stroke and heart disease. It is one of the leading causes of death worldwide, with various contributing factors such as hyperlipidemia, hypertension, obesity, diabetes, and smoking. Wall shear stress (WSS) is also known as a contributing factor of the formation of atherosclerotic plaques. Since the causes of atherosclerosis cannot be attributed to a single factor, clearly understanding the mechanisms and causes of its occurrence is crucial for preventing the disease and developing effective treatment strategies. To better understand atherosclerosis and define the correlation between various contributing factors, computational fluid dynamics (CFD) analysis is primarily used. CFD simulates WSS, the frictional force caused by blood flow on the vessel wall with various hemodynamic changes. Using apolipoprotein E knockout (ApoE-KO) mice subjected to partial ligation and a high-fat diet at 1-week, 2-week, and 4-week intervals as an atherosclerosis model, CFD analysis was conducted along with the reconstruction of carotid artery blood flow via magnetic resonance imaging (MRI) and compared to the inflammatory factors and pathological staining. In this experiment, a comparative analysis of the effects of high WSS and low WSS was conducted by comparing the standard deviation of time-averaged wall shear stress (TAWSS) at each point within the vessel wall. As a novel approach, the standard deviation of TAWSS within the vessel was analyzed with the staining results and pathological features. Since the onset of atherosclerosis cannot be explained by a single factor, the aim was to find the correlation between the thickness of atherosclerotic plaques and inflammatory factors through standard deviation analysis. As a result, the gap between low WSS and high WSS widened as the interval between weeks in the atherosclerosis mouse model increased. This finding not only linked the occurrence of atherosclerosis to WSS differences but also provided a connection to the causes of vulnerable plaques.

Endovascular stent has been employed to treat patients with intravascular diseases. Research on stent optimization is currently performed in order to find the best design in increasing the treatment efficacy. In this research, stent optimization is performed based on a finite element analysis method via Kriging surrogate model to observe the wall shear stress (WSS) conditions on the strut vicinity. Two configurations, rectangle and triangle are adopted as the cross section of a stent strut and compared to see the effects of the cross section on WSS condition. Strut gap in the range from 1 mm to 3 mm and the strut size length from 0.05 mm to 0.45 mm are considered as the design variables for each cross section. Structure contact simulation between stent and vessel wall is carried out to obtain the 5% vessel expansion. Afterward, computational fluid dynamics simulation is performed to analyze the hemodynamic effect of stent design along with wall deformation. Minimizing the percentage of low WSS area (WSS < 1 Pa) relative to the length of stent deployment area is set as the objective function of this optimization since low WSS is believed to promote some problems such as atherosclerosis. In total, 45 and 42 simulation iterations are conducted respectively for both cross sections to develop the Kriging surrogate models for efficient global optimization. Besides the prediction of the optimized configuration, broader observation on its behavior within the design range is also well predicted. The optimized configuration has 2.99 mm gap and 0.1 mm width for the rectangular strut, and 2.00 mm gap and 0.99 mm width for the triangular strut. The triangular strut has better performance in reducing the low WSS area with 14.6% of low WSS area on its optimized design, compared to 18.3% of the rectangular strut. Moreover, the triangular shape strut produces more stable performance; most design configuration with the strut width of less than 0.35 mm can keep low WSS area at the minimum value.

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

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.

Magnetohydrodynamic blood flow in patients with coronary artery disease

This study aims to evaluate the hemodynamic effect of tilting after implantation of a bioprosthetic heart valve in an enlarged aortic annulus using computational fluid dynamics (CFD). The objective is to define the cost of excessive enlargement in transprosthetical flow and identify the optimal prosthesis size and implantation angle to reduce thrombosis and early degeneration. Virtual implantation of a 23-mm bioprosthetic model was conducted in a prespecified virtual aortic annulus of 23mm. CFD simulations were conducted to analyze the hemodynamic parameters, including wall shear stress and turbulent kinetic energy, for bioprosthetic heart valves of the 23mm (perpendicular implantation), 25mm, and 27mm (tilted implantation at different angles) after virtual annular enlargement. The simulations utilized transient flow models and mesh convergence studies, to ensure numerical accuracy and clinical relevance. The 23-mm valve implanted without annular enlargement and in an aligned fashion to the annulus exhibited higher wall shear stress (WSS) and shear stress (SS) values than the 25-mm valve implanted at 12° tilted position and better hemodynamics than the 27-mm valve at 25° tilted position. The 25-mm valve after annular enlargement and implantation at 12° tilted position achieved the best hemodynamic performance together with a 23% and 7% reduction of WSS and SS as compared to the 23-mm valve. Slight oversizing and tilting after annular enlargement yields the best performance of an aortic bioprosthetic valve with lowest WSS and balanced turbulence.

Despite significant progress, malapposed or overlapped stents are a complication that affects daily percutaneous coronary intervention (PCI) procedures. These malapposed stents affect blood flow and create a micro re-circulatory environment. These disturbances are often associated with a change in Wall Shear Stress (WSS), Time-averaged WSS (TAWSS), relative residence time (RRT) and oscillatory character of WSS and disrupt the delicate balance of vascular biology, providing a possible source of thrombosis and restenosis. In this study, 2D axisymmetric parametric computational fluid dynamics (CFD) simulations were performed to systematically analyze the hemodynamic effects of malapposition and stent overlap for two types of stents (drug-eluting stent and a bioresorbable stent). The results of the modeling are mainly analyzed using streamlines, TAWSS, oscillatory shear index (OSI) and RRT. The risks of restenosis and thrombus are evaluated according to commonly accepted thresholds for TAWSS and OSI. The small malapposition distances (MD) cause both low TAWSS and high OSI, which are potential adverse outcomes. The region of low OSI decrease with MD. Overlap configurations produce areas with low WSS and high OSI. The affected lengths are relatively insensitive to the overlap distance. The effects of strut size are even more sensitive and adverse for overlap configurations compared to a well-applied stent.

Biomechanical forces may play a key role in saphenous vein graft (SVG) disease after coronary artery bypass graft (CABG) surgery. Computed tomography angiography (CTA) of 430 post-CABG patients were evaluated and 15 patients were identified with both stenosed and healthy SVGs for paired analysis. The stenosis was virtually removed, and detailed 3D models were reconstructed to perform patient-specific computational fluid dynamic (CFD) simulations. Models were processed to compute anatomic parameters, and hemodynamic parameters such as local and vessel-averaged wall shear stress (WSS), normalized WSS (WSS*), low shear area (LSA), oscillatory shear index (OSI), and flow rate. WSS* was significantly lower in pre-diseased SVG segments compared to corresponding control segments without disease (1.22 vs. 1.73, p = 0.012) and the area under the ROC curve was 0.71. No differences were observed in vessel-averaged anatomic or hemodynamic parameters between pre-stenosed and control whole SVGs. There are currently no clinically available tools to predict SVG failure post-CABG. CFD modeling has the potential to identify high-risk CABG patients who may benefit from more aggressive medical therapy and closer surveillance. Graphical Abstract.

Four commercially available stent designs (two balloon expandable-Bx Velocity and NIR, and two self-expanding-Wallstent and Aurora) were modeled to compare the near-wall flow characteristics of stented arteries using computational fluid dynamics simulations under pulsatile flow conditions. A flat rectangular stented vessel model was constructed and simulations were carried out using rigid walls and sinusoidal velocity input (nominal wall shear stress of 10+/-5 dyn/cm2). Mesh independence was determined from convergence (<10%) of the axial wall shear stress (WSS) along the length of the stented model. The flow disturbance was characterized and quantified by the distributions of axial and transverse WSS, WSS gradients, and flow separation parameters. Normalized time-averaged effective WSS during the flow cycle was the smallest for the Wallstent (2.9 dyn/cm2) compared with the others (5.8 dyn/cm2 for the Bx Velocity stent, 5.0 dyn/cm2 for the Aurora stent, and 5.3 dyn/cm2 for the NIR stent). Regions of low mean WSS (<5 dyn/cm2) and elevated WSS gradients (>20 dyn/cm3) were also the largest for the Wallstent compared with the others. WSS gradients were the largest near the struts and remained distinctly nonzero for most of the region between the struts for all stent designs. Fully recirculating regions (as determined by separation parameter) were the largest for the Bx Velocity stent compared with the others. The most hemodynamically favorable stents from our computational analysis were the Bx Velocity and NIR stents, which were slotted-tube balloon-expandable designs. Since clinical data indicate lower restenosis rates for the Bx Velocity and NIR stents compared with the Wallstent, our data suggest that near-wall hemodynamics may predict some aspects of in vivo performance. Further consideration of biomechanics, including solid mechanics, in stent design is warranted.

The significant progress in computer innovation technique, computational fluid dynamics (CFD) has been applied for real applications on patient-specific hemodynamics and extensively used to study cerebral aneurysm rupture. In addition, the computational study with representative blood vessel configuration has become a great tool in providing comprehensive information on geometry, the flow field of blood and wall shear stress (WSS). Generally, the numerical simulations have an expected problem on the specification of the exact boundary conditions which leads to unphysical numerical solutions. Therefore, this paper tends to find out whether CFD simulation manages to obtain precise and better predictions of hemodynamics patterns at present time especially for phase-contrast magnetic resonance imaging (PC-MRI) in terms of the velocity flow field and WSS distribution. Several research articles are included and their qualitative and quantitative results on hemodynamics have been compared. Both MRI measurement and CFD simulation have reasonably good agreement on velocity flow fields and a detailed spiral recirculating flow pattern can be observed in CFD simulation as compared to MRI measurement instead. However, CFD simulation has overestimated the WSS, especially at the maximum WSS location. The CFD simulation is capable to achieve good agreement on velocity flow fields with MRI measurement, yet the result for WSS distribution has to be further improved and justified with consistent assumptions and techniques.

Uncertainty quantification of wall shear stress in intracranial aneurysms using a data-driven statistical model of systemic blood flow variability

In previous studies, the radial and tangential leakage flow velocities in the gap between the rotating impeller and the pump casing of a biocentrifugal ventricular assist device (VAD) model were obtained by hot wire. Based on the velocities obtained, the leakage flow rate through the clearance gap between the impeller and the stationary casing, as well as the wall shear stress distributions on the inner surface of the stationary casing, can be determined. By integrating the radial velocities numerically, the leakage flow rate through the clearance gap was found to be 6.43 x 10(-4) m3/s under operating conditions, which is 25.7% of the inlet flow. This is equivalent to approximately 1.7 L/min in the prototype. The leakage flow rate was found to be 5.22 x 10(-4) m3/s and 3.66 x 10(-4) m3/s under fully opened and fully closed conditions, respectively. The double volute design significantly affected wall shear stress distributions, with the high wall shear stress region concentrated at the beginning of the splitter plate under all three flow conditions. In contrast, the high wall shear stress region could only be observed at the cutwater in the fully closed condition. The highest wall shear stress was found to be 44.1 Pa, which is much lower than the threshold values that cause hemolysis. On the other hand, the lowest wall shear stress was found to be 21.31 Pa. This wall shear stress level is much higher than the shear stress required to disrupt aggregates of blood cells and platelets. These findings explain why hemolysis and thrombosis are at the low level in the clearance gap of this VAD.

CFD simulations of turbulent flow in baffle-filled membrane tubes