Wall Shear Stress Values Research Articles

Impact of Thoracic Endografting on the Hemodynamics of the Native Aorta: Pre- and Postoperative Assessments of Wall Shear Stress and Vorticity Using Computational Fluid Dynamics

Purpose To quantify the hemodynamic consequences of thoracic endovascular aortic repair (TEVAR) by comparing the preoperative and postoperative wall shear stress (WSS) and vorticity profiles on computational fluid dynamics (CFD) simulations. Materials and Methods The pre- and postoperative computed tomography (CT) scans from 20 consecutive patients (median age 69 years, range 20–87) treated for different thoracic aortic pathologies (11 aneurysms, 5 false aneurysms, 3 penetrating ulcers, and 1 traumatic aortic rupture) were segmented to construct patient-specific CFD models using a meshless code. The simulations were run over the cardiac cycle, and the WSS and vorticity values measured at the proximal and distal landing zones were compared. Results The CFD runs provided 4-dimensional simulations of blood flow in all patients. WSS and vorticity profiles at the proximal landing zone (located in zones 0–3 in 15 patients) varied in 18 and 20 of the cases, respectively; WSS was increased in 11 cases and the vorticity in 9. Pre- and postoperative WSS median values were 4.19 and 4.90 Pa, respectively. Vorticity median values were 40.38 and 39.17 Hz, respectively. Conclusion TEVAR induces functional alterations in the native thoracic aorta, though the prognostic significance of these changes is still unknown. CFD appears to be a valuable tool to explore aortic hemodynamics, and its application in a larger series would help define a predictive role for these hemodynamic assessments.

Ultrasound Based Computational Fluid Dynamics Assessment of Brachial Artery Wall Shear Stress in Preeclamptic Pregnancy.

Preeclampsia (PE) is a pregnancy complication of abnormally elevated blood pressure and organ damage where endothelial function is impaired. Wall shear stress (WSS) strongly effects endothelial cell morphology and function but in PE the WSS values are unknown. WSS calculations from ultrasound inaccurately assume cylindrical arteries and patient specific computational fluid dynamics (CFD) typically require time-consuming 3D imaging such as CT or MRI. Two-dimensional (2D) B-mode ultrasound images were lofted together to create simplified three-dimensional (3D) geometries of the brachial artery (BA) that incorporate artery curvature and non-circular cross sections. This process was efficient and on average took 120±10 s. Patient specific CFD was then performed to quantify BA WSS for a small cohort of PE (n=5) and normotensive pregnant patients (n=5) and compared against WSS calculations assuming a cylindrical artery. For several WSS metrics (time averaged WSS (TAWSS), peak systolic WSS, oscillatory shear index (OSI), OSI/TAWSS and relative residence time) CFD on the simplified arterial geometries calculated large spatial differences in WSS that assuming a cylindrical artery cannot calculate. Bland-Altman and intra-class correlation (ICC) analyses found assuming a cylindrical artery both underestimated (p<0.05) and had poor agreement (ICC<0.5) with the maximum WSS values from CFD. WSS values that were abnormal compared to the normotensive patients (OSI=0.014±0.026) appear related to the pregnancy complications fetal growth restriction (n=2, OSI=0.14, 0.25) and gestational diabetes (n=1, OSI=0.23). Creating 3D artery geometries from 2D ultrasound images can be used for CFD simulations to calculate WSS from ultrasound without assuming cylindrical arteries. This approach requires minimal time for both medical imaging and CFD analysis.

High Wall Shear Stress Is Related to Atherosclerotic Plaque Rupture in the Aortic Arch of Patients with Cardiovascular Disease: A Study with Computational Fluid Dynamics Model and Non-Obstructive General Angioscopy.

Aims: Wall shear stress (WSS) has been considered a major determinant of aortic atherosclerosis. Recently, non-obstructive general angioscopy (NOGA) was developed to visualize various atherosclerotic pathologies, including in vivo ruptured plaque (RP) in the aorta. However, the relationship between aortic RP and WSS distribution within the aortic wall is unclear. This study aimed to investigate the relationship between aortic NOGA-derived RP and the stereographic distribution of WSS by computational fluid dynamics (CFD) modeling using three-dimensional computed tomography (3D-CT) angiography. Methods: We investigated 45 consecutive patients who underwent 3D-CT before coronary angiography and NOGA during coronary angiography. WSS in the aortic arch was measured by CFD analysis based on the finite element method using uniform inlet and outlet flow conditions. Aortic RP was detected by NOGA. Results: Patients with a distinct RP showed a significantly higher maximum WSS value in the aortic arch than those without aortic RP (56.2±30.6 Pa vs 36.2±19.8 Pa, p =0.017), no significant difference was noted in the mean WSS between those with and without aortic RP. In a multivariate logistic regression analysis, the presence of a maximum WSS value more than a specific value was a significant predictor of aortic RP (odds ratio 7.21, 95% confidence interval 1.78-37.1, p =0.005). Conclusions: Aortic RP detected by NOGA was strongly associated with a higher maximum WSS in the aortic arch derived by CFD using 3D-CT. The maximum WSS value may have an important role in the underlying mechanism of not only aortic atherosclerosis, but also aortic RP.

Spatial Configuration of Abdominal Aortic Aneurysm Analysis as a Useful Tool for the Estimation of Stent-Graft Migration.

The aim of this study was to prepare a self-made mathematical algorithm for the estimation of risk of stent-graft migration with the use of data on abdominal aortic aneurysm (AAA) size and geometry of blood flow through aneurysm sac before or after stent-graft implantation. AngioCT data from 20 patients aged 50–60 years, before and after stent-graft placement in the AAA was analyzed. In order to estimate the risk of stent-graft migration for each patient we prepared an opposite spatial configuration of virtually reconstructed stent-graft with long body or short body. Thus, three groups of 3D geometries were analyzed: 20 geometries representing 3D models of aneurysm, 20 geometries representing 3D models of long body stent-grafts, and 20 geometries representing 3D models of short body stent-graft. The proposed self-made algorithm demonstrated its efficiency and usefulness in estimating wall shear stress (WSS) values. Comparison of the long or short type of stent-graft with AAA geometries allowed to analyze the implants’ spatial configuration. Our study indicated that short stent-graft, after placement in the AAA sac, generated lower drug forces compare to the long stent-graft. Each time shape factor was higher for short stent-graft compare to long stent-graft.

Can the Wall Shear Stress Values of Left Internal Mammary Artery Grafts during the Perioperative Period Reflect the One-Year Patency?

The left internal mammary artery (LIMA) is the preferred graft for coronary artery bypass grafting, but the reasoning for LIMA occlusion is unclear. We sought to examine whether the wall shear stress (WSS) values of LIMA grafts during the perioperative period reflected the 1-year patency by using combining computational fluid dynamics (CFD) and coronary computed tomography angiography (CCTA) images. CCTA was performed in 233 patients with LIMA graft perioperatively and 1 year later from October 2014 to May 2017. LIMA occlusion was detected in six patients at the 1-year follow-up CCTA. Two patients were excluded due to poor imaging quality. The remaining four patients were enrolled as occlusive (OCC) group, and eight patients with patent LIMA were recruited as patent (PAT) group. The WSS values of LIMA during perioperative period were calculated. LIMA graft was artificially divided into three even segments, proximal (pLIMA), middle (mLIMA) and distal (dLIMA) segments. The independent samples t-test and the Student-Newman-Keuls test were used. The WSS values of dLIMA were significantly higher in the PAT group than in the OCC group (4.43 vs. 2.56, p < 0.05). The WSS values of dLIMA in the PAT group were significantly higher than pLIMA, which was absent in the OCC group. A higher WSS value of the distal segment of LIMA and a higher WSS value of the distal segment compared with the proximal segment of LIMA in the PAT were observed; this tendency might be helpful in predicting the 1-year patency of LIMA.

Wall shear stress analysis using 17.6 Tesla MRI: A longitudinal study in ApoE-/- mice with histological analysis.

This longitudinal study was performed to evaluate the feasibility of detecting the interaction between wall shear stress (WSS) and plaque development. 20 ApoE-/- mice were separated in 12 mice with Western Diet and 8 mice with Chow Diet. Magnetic resonance (MR) scans at 17.6 Tesla and histological analysis were performed after one week, eight and twelve weeks. All in vivo MR measurements were acquired using a flow sensitive phase contrast method for determining vectorial flow. Histological sections were stained with Hematoxylin and Eosin, Elastica van Gieson and CD68 staining. Data analysis was performed using Ensight and a Matlab-based “Flow Tool”. The body weight of ApoE-/- mice increased significantly over 12 weeks. WSS values increased in the Western Diet group over the time period; in contrast, in the Chow Diet group the values decreased from the first to the second measurement point. Western Diet mice showed small plaque formations with elastin fragmentations after 8 weeks and big plaque formations after 12 weeks; Chow Diet mice showed a few elastin fragmentations after 8 weeks and small plaque formations after 12 weeks. Favored by high-fat diet, plaque formation results in higher values of WSS. With wall shear stress being a known predictor for atherosclerotic plaque development, ultra highfield MRI can serve as a tool for studying the causes and beginnings of atherosclerosis.

A Flush-Mounted Dual-Axis Wall Shear Stress Sensor

This paper presents the fabrication, packaging, and calibration of a flush-mounted, dual-axis, differential capacitive wall shear stress sensor. The two-mask fabrication process produces a 7-mm die with a 2-mm by 2-mm floating element supported by eight, compliant crab-leg tethers. Taking advantage of backside wire bonds, the hydraulically smooth package is suitable for wind tunnel testing and is designed to have a resonant frequency of 3.7 kHz. Initial dynamic calibration data are presented using both single-ended and fully-differential electronics, with sensitivities as high as 80 mV/Pa and minimum detectable wall shear stress values as low as $10~\mu $ Pa/Hz1/2, resulting in dynamic ranges near 135 dB. [2020-0175]

Mechanism of pulsatile flushing technique for saline injection via a peripheral intravenous catheter

BackgroundThe underlying mechanism of pulsatile flushing technique has not been fully elucidated, and the partial understanding of the mechanism has been confined to hydrodynamic simulation, ignoring the dynamic interaction among the catheter, blood vessel, blood stream, and saline. MethodsThe peripheral intravenous catheter and vein models and their internal flow fields were assessed using a commercial software. The parameters of both fluid and structural mechanics were calculated and compared in the push and pause phase. The effect of different flushing volumes per bolus before each pause (0.5, 1.0, 1.5, and 2.0 mL) were compared, respectively corresponding to group (A, B, C and D). FindingsIn groups C and D, the wall shear stress value (≥2 Pa) and enhanced shear rates (peaks up to 10,000 s−1) were higher in the vessel wall near the catheter tip, which may be at risk of vascular endothelial injury. Furthermore, extraluminal flushing might be attributed to the recirculation of jet from the catheter outlet. The vortices of all groups faded away in an extremely short period (≤0.1 s) if the push was suddenly discontinued. Finally, overlarge displacement of the catheter tip in groups C and D (0.91 and 1.1 mm, respectively) caused the peripheral intravenous catheters to angle with the venous wall. InterpretationThe pulsatile flushing technique can facilitate intra- and extraluminal flushing of peripheral intravenous catheters. Furthermore, an insufficient volume per bolus can lead to inefficient flushing, and an overdose of single push may cause mechanical endothelial injury.

Enhanced wall shear stress prevents obstruction by astrocytes in ventricular catheters.

The treatment of hydrocephalus often involves the placement of a shunt catheter into the cerebrospinal ventricular space, though such ventricular catheters often fail by tissue obstruction. While diverse cell types contribute to the obstruction, astrocytes are believed to contribute to late catheter failure that can occur months after shunt insertion. Using in vitro microfluidic cultures of astrocytes, we show that applied fluid shear stress leads to a decrease of cell confluency and the loss of their typical stellate cell morphology. Furthermore, we show that astrocytes exposed to moderate shear stress for an extended period of time are detached more easily upon suddenly imposed high fluid shear stress. In light of these findings and examining the range of values of wall shear stress in a typical ventricular catheter through computational fluid dynamics (CFD) simulation, we find that the typical geometry of ventricular catheters has low wall shear stress zones that can favour the growth and adhesion of astrocytes, thus promoting obstruction. Using high-precision direct flow visualization and CFD simulations, we discover that the catheter flow can be formulated as a network of Poiseuille flows. Based on this observation, we leverage a Poiseuille network model to optimize ventricular catheter design such that the distribution of wall shear stress is above a critical threshold to minimize astrocyte adhesion and growth. Using this approach, we also suggest a novel design principle that not only optimizes the wall shear stress distribution but also eliminates a stagnation zone with low wall shear stress, which is common to current ventricular catheters.

The effect of the degree and location of coronary stenosis on the hemodynamic status of a coronary vessel.

The ongoing advances in the field of cardiovascular modelling during the past years have allowed for the creation of accurate three-dimensional models of the major coronary arteries. The aforementioned 3D models can accurately mimic the human coronary vasculature if they are combined with sophisticated computational fluid dynamics algorithms and shed light to non-trivial issues that concern the clinicians. One of these issues is to define whether a coronary lesion is more dangerous to present with ischemia if it is at a proximal or a distal part of the vessel. In this work, we aim to investigate the aforementioned issue by reconstructing in 3D a coronary arterial model from a healthy subject using Computed Tomography Coronary Angiography images and by editing it to create eight diseased arterial models that contain one or two lesions of different severities. After carrying out the appropriate blood flow simulations using the finite element method, we observed that the distal lesions are more dangerous than the proximal ones in terms of hemodynamic significance. Moreover, the distal severe stenosis (i.e. 70% diameter reduction) present with the highest peak Wall Shear Stress (WSS) values in comparison to the proximal ones.

Flow dynamics of vitreous humour during saccadic eye movements

In this work, we reveal the flow dynamics of Vitreous Humour (VH) gel and liquid phases during saccadic movements of the eye, considering the biofluids viscoelastic character as well as realistic eye chamber geometry and taking into account the saccade profile. We quantify the differences in the flow dynamics of VH gel and liquid phases using viscoelastic rheological models that are able to model the VH shear rheology, considering different amplitudes of saccadic movements (10∘, 20∘, 30∘ and 40∘). For this purpose, the computational fluid dynamics (CFD) open source software OpenFOAM® was used. The results portray a distinct flow behaviour for the VH gel and liquid phases, with inertial effects being more significant for the VH liquid phase. Moreover, the Wall Shear Stress (WSS) values produced by the VH gel phase are more than twice of those generated by the VH liquid phase. Results also show that for different amplitudes of eye movement both the velocity magnitude in the vitreous cavity and the shear stresses on the cavity walls rise with increasing saccadic movement displacement.

A pilot study using a machine-learning approach of morphological and hemodynamic parameters for predicting aneurysms enhancement.

The development of straightforward classification methods is needed to identify unstable aneurysms and rupture risk for clinical use. In this study, we aim to investigate the relative importance of geometrical, hemodynamic and clinical risk factors represented by the PHASES score for predicting aneurysm wall enhancement using several machine-learning (ML) models. Nine different ML models were applied to 65 aneurysm cases with 24 predictor variables. ML models were optimized with the training set using tenfold cross-validation with five repeats with the area under the curve (AUC) as cost parameter. Models were validated using the test set. Accuracy being significantly higher (p < 0.05) than the non-information rate (NIR) was used as measure of performance. The relative importance of the predictor variables was determined from a subset of five ML models in which this information was available. Best-performing ML model was based on gradient boosting (AUC = 0.98). Second best-performing model was based on generalized linear modeling (AUC = 0.80). The size ratio was determined as the dominant predictor for wall enhancement followed by the PHASES score and mean wall shear stress value at the aneurysm wall. Four ML models exhibited a statistically significant higher accuracy (0.79) than the NIR (0.58): random forests, generalized linear modeling, gradient boosting and linear discriminant analysis. ML models are capable of predicting the relative importance of geometrical, hemodynamic and clinical parameters for aneurysm wall enhancement. Size ratio, PHASES score and mean wall shear stress value at the aneurysm wall are of highest importance when predicting wall enhancement in cerebral aneurysms.

V Flow technology in measurement of wall shear stress of common carotid arteries in healthy adults: Feasibility and normal values.

To evaluate the feasibility of vector flow imaging technique (V Flow) in measurement of wall shear stress (WSS) of common carotid arteries (CCA) in healthy adults and to provide the normal WSS values assessed by V Flow. This prospective study was approved by the Ethics Committee of our University. Eighty healthy adult volunteers were included (mean age 43.3 y, 47 females, 33 males). The volunteers were classified into three groups according to their age: group I (age 20 - 39 y), group II (age 40 - 59 y) and group III (age 60 - 80 y). Mindray Resona 8 ultrasound machine and a linear array transducer (3-9 MHz) was used, equipped with the updated V Flow function. Common carotid arteries of both sides were evaluated in three segments (initial segment, middle segment and near bifurcation segment). The WSS values of CCA were measured by two independent radiologists. The intraclass correlation coefficient (ICC) of observer reliability in WSS measurement was calculated. Inter-observer reproducibility was also evaluated with the 95% Bland-Altman limits of agreement (LOA). V Flow measurements were performed successfully in 79 volunteers (98.8 %, 79/80). The mean value of WSS in right CCA was (0.66±0.24) Pa, in left CCA was (0.66±0.18) Pa (P > 0.05). Mean WSS value had a moderately negative correlation with age group (P < 0.05). The mean WSS value of group I(mean±SD, 0.75±0.25 Pa) is larger than group II (mean±SD, 0.62±0.13 Pa) and group III (mean±SD, 0.49±0.11 Pa) (P < 0.05). The ICC of observer reliability of group I, II and III was 0.96 (95% confidence interval (95% CI) 0.92-0.98), 0.94 (95% CI 0.88-0.97), 0.93 (95% CI 0.76-0.98) respectively. The Bland-Altman plots showed that the 95% LOA were -0.17-0.12 (Pa) for group I, -0.09-0.13 (Pa) for group II and -0.08-0.10 (Pa) for group III. V Flow measurement is a simple, rapid and feasible imaging method for the WSS assessment of CCA in healthy volunteers, which will probably be an important tool for assessing CCA function.

Hemodynamic effects of blood clots trapped by an inferior vena cava filter.

The alteration of blood flow around an OPTEASE inferior vena cava filter with one or two blood clots attached was investigated by means of computational fluid dynamics. We used a patient-specific vein wall geometry, and we generated different clot models with shapes adapted to the filter and vein wall geometries. A total of eight geometries, with one or two clots and a total clot volume of 0.5 or 1 cm3 , were considered. A non-Newtonian model for blood viscosity was adopted and the possible development of turbulence was accounted for by means of a three-equation model. Two blood flow rates were considered for each case, representative for rest and exercise conditions. In exercise conditions, flow unsteadiness and even turbulence was detected in some cases. Pressure and wall shear stress (WSS) distributions were modified in all cases. Clots attached to the filter downstream basket considerably increased averaged WSS values by up to almost 50%. In all the cases a flow recirculation region appeared downstream of the clot. The degree of flow stagnation in these regions, an indicator of propensity to thrombogenesis, was estimated in terms of mean residence times and mean blood viscosity. High levels of flow stagnation were detected in rest conditions in the wake of those clots that were placed upstream from the filter. Our results suggest that one downstream placed big clot, showing a higher tendency to induce flow instabilities and turbulence, might be more harmful than two small clots placed in tandem.

Computational fluid dynamics simulations of cerebral aneurysm using Newtonian, power-law and quasi-mechanistic blood viscosity models.

Cerebral aneurysm is a fatal neurovascular disorder. Computational fluid dynamics simulation of aneurysm haemodynamics is one of the most important research tools which provide increasing potential for clinical applications. However, computational fluid dynamics modelling of such delicate neurovascular disorder involves physical complexities that cannot be easily simplified. Recently, it was shown that the Newtonian simplification used to close the shear stress tensor of the Navier-Stokes equation is not sufficient to explore aneurysm haemodynamics. This article explores the differences between the latter simplification, non-Newtonian power-law model and a newly proposed quasi-mechanistic model. The modified Krieger model, which treats blood as a suspension of plasma and particles, was implemented in computational fluid dynamics context here for the first time and is made available to the readers in a C# code in the supplementary material of this article. Two middle-cerebral artery and two anterior-communicating artery aneurysms, all ruptured, were utilized here as case studies. It was shown that the modified Krieger model had higher sensitivity for wall shear stress calculations in comparison with the other two models. The modified Krieger model yielded lower wall shear stress values consistently in comparison with the other two models. Moreover, the modified Krieger model has generally predicted higher pressure in the aneurysm models. Based on published aneurysm rupture studies, it is believed that ruptured aneurysms are usually correlated with lower wall shear stress values than unruptured ones. Therefore, this work concludes that the modified Krieger model is a potential candidate for providing better clinical relevance to aneurysm computational fluid dynamics simulations.

Ultrasound Deep Learning for Wall Segmentation and Near-Wall Blood Flow Measurement

Studies of medical flow imaging have technical limitations for accurate analysis of blood flow dynamics and vessel wall interaction at arteries. We propose a new deep learning-based boundary detection and compensation (DL-BDC) technique in ultrasound (US) imaging. It can segment vessel boundaries by harnessing the convolutional neural network and wall motion compensation in the analysis of near-wall flow dynamics. The network enables training from real and synthetic US images together. The performance of the technique is validated through synthetic US images and tissue-mimicking phantom experiments. The neural network performs well with high Dice coefficients of over 0.94 and 0.9 for lumens and walls, outperforming previous segmentation techniques. Then, the performance of the wall motion compensation is examined for compliant phantoms. When DL-BDC is applied to flow influenced by wall motion, root-mean-square errors are less than 0.07%. The technique is utilized to analyze flow dynamics and wall interaction with varying elastic moduli of the phantoms. The results show that the flow dynamics and wall shear stress values are consistent with the expected values of the compliant phantoms, and their wall motion behavior is observed with pulse wave propagation. This strategy makes US imaging capable of simultaneous measurement of blood flow and vessel dynamics in human arteries for their accurate interaction analysis. DL-BDC can segment vessel walls fast, accurately, and robustly. It enables to measure the near-wall flow precisely by determining the vessel boundary dynamics. This approach can be beneficial in flow dynamics and wall interaction analyses in various biomedical applications.

Microfluidic Biofabrication of 3D Multicellular Spheroids by Modulation of Non-geometrical Parameters.

Three-dimensional (3D) cell spheroids are being increasingly applied in many research fields due to their enhanced biological functions as compared to conventional two-dimensional (2D) cultures. 3D cell spheroids can replicate tissue functions, which enables their use both as in vitro models and as building blocks in tissue biofabrication approaches. In this study, we developed a perfusable microfluidic platform suitable for robust and reproducible 3D cell spheroid formation and tissue maturation. The geometry of the device was optimized through computational fluid dynamic (CFD) simulations to improve cell trapping. Experimental data were used in turn to generate a model able to predict the number of trapped cells as a function of cell concentration, flow rate, and seeding time. We demonstrated that tuning non-geometrical parameters it is possible to control the size and shape of 3D cell spheroids generated using articular chondrocytes (ACs) as cellular model. After seeding, cells were cultured under perfusion at different flow rates (20, 100, and 500 μl/min), which induced the formation of conical and spherical spheroids. Wall shear stress values on cell spheroids, computed by CFD simulations, increased accordingly to the flow rate while remaining under the chondroprotective threshold in all configurations. The effect of flow rate on cell number, metabolic activity, and tissue-specific matrix deposition was evaluated and correlated with fluid velocity and shear stress distribution. The obtained results demonstrated that our device represents a helpful tool to generate stable 3D cell spheroids which can find application both to develop advanced in vitro models for the study of physio-pathological tissue maturation mechanisms and to obtain building blocks for the biofabrication of macrotissues.

On the reversibility of deposit formation in low temperature milk microfiltration with ceramic membranes depending on mode of adjustment of transmembrane pressure and wall shear stress

During the microfiltration of skim milk, flux and protein permeation decrease due to the formation of a deposit layer. For a better understanding of the deposit formation during the microfiltration of skim milk at 10 °C, flux and protein permeation were studied with a ceramic multichannel membrane (nominal pore size (nps) = 0.1 µm) at wall shear stress (τw) values from 45 to 341 Pa. When the limiting transmembrane pressure was applied, the flux showed a nearly linear increase with increasing wall shear stress and peaked at a critical τw. A further increase of τw resulted in a reduction of the flux until it levelled off. Thus, we could define a limiting τw additionally to the critical τw, at which no further changes in flux were observable. The limiting flux indicates that no structural changes in the deposit layer occur beyond the limiting τw. This conclusion is reassured by the development of the protein permeation. Beyond the limiting τw, no changes in the protein permeation could be observed. The critical and limiting τw are useful values for the design of fractionation processes by means of ceramic microfiltration.

ESTIMATION OF WALL SHEAR STRESS OF COMPLIANT THORACIC AORTA WITH ANEURYSM

In this paper, a numerical estimation of wall shear stress (WSS) in a compliant Thoracic Aorta (TA) with aneurysm is modeled and the hemodynamic pattern is studied using Computational Fluid Dynamics (CFD). Thoracic Aortic Aneurysm (TAA) is an excessively localized enlargement of TA caused by weakness in the arterial wall and it can rupture the inner wall intima and continue on to the outer wall adventitia. WSS is a tangential force exerted by blood flow on the vessel wall, and its estimation is clinically very important because any change in WSS is considered as a vital cue in the onset of aneurysm. In this work, a three-dimensional (3D) model of a TAA reconstructed from computed tomography (CT) images comprising of 600 slices with 1-mm resolution from neck to hip is considered and patient-specific simulations have been carried out in compliant TA under rest and exercise conditions. The findings show that the change in wall geometry was marginal due to variation in pressure forces inside and is not the primary source for expansion of an aneurysm. It was inferred that expansion was rather due to thinning of the wall, owing to damage caused to the inner lining of the tissues, at regions of high WSS. It was found that the geometry extraction is important as any change in length causes a corresponding variation in mass flow through it. Although mass conservation is maintained irrespective of the length, it does affect the rate of flow due to shifting in the pressure boundary conditions with the length as it varies the pressure inside the system. Modeling of the geometry is very important as the change in mass flow will affect the outlet velocity and strength of vortices. Surprisingly, the split-up of flow is consistent but the geometric change in the model has no effect on WSS values and flow pattern. The results of this study provide important information such as blood flow pattern and pressure drops in the compliant TA on WSS estimations with TAA diseases.

The impact of non-linear viscoelastic property of blood in right coronary arteries hemodynamics — A numerical implementation

The numerical implementation of the complex rheology of blood, namely the viscoelastic property, in hemodynamic simulations is still a challenge. A more accurate numerical tool is essential for diagnosis, prevention and treatment of atherosclerotic disease in arteries. In particular, in small vessels or vessels with stenosis and aneurysms, the elastic effects of blood should not be neglected. Since these are regions with high velocity gradients, the storage and release of elastic energy from red blood cells and the constant changes in shear rate have a demarked impact on the flow. Although the importance of the viscoelastic property is well emphasized in the literature, only a restrict set of authors have considered this property in their hemodynamic simulations. Thus, the aim of the present work is to go further and implement several viscoelastic models for blood in user-defined-functions of ANSYS software, in order to conclude which model is the most accurate for further applications. The Generalized Oldroyd-B (GOB) model, a quasi-linear model, and two non-linear models, the Multi-mode Giesekus and Simplified Phan-Thien/ Tanner (sPTT) models, were implemented. For right coronary arteries, velocity and wall shear stress were compared, considering a purely shear-thinning model, Carreau model, and the implemented viscoelastic models. An overall reduction of the velocity in regions of higher velocity gradients was observed, considering the non-linear viscoelastic multi-mode models (Giesekus and sPTT). Moreover, the difference in peak wall shear stress values considering these multi-mode viscoelastic models is close to half the magnitude (51%) of Carreau model solutions. Despite different arteries and hemodynamic conditions, the present results are in accordance with those found in the literature. The sPTT model should be the preferential option for further applications, since Giesekus model introduces the second normal stress difference, which so far has not been reported for blood.