Inertial particle dynamics in large artery flows – Implications for modeling arterial embolisms

A computational study of the connection between coronary revascularization and cardio-cerebral hemodynamics

BACKGROUND AND OBJECTIVE

Some patients experience life-threatening strokes during coronary revascularization. Despite its clinical importance, few numerical studies have investigated the impact of coronary revascularization on cardio-cerebral hemodynamics. This study aims to address this gap by evaluating the effects of eliminating coronary stenosis on both coronary and cerebral blood flow using patient-specific simulations.

METHODS

A patient-specific cardio-cerebral arterial network with a 70% stenosis in the left main coronary artery was reconstructed, and computational fluid dynamics were employed to evaluate the effects of eliminating coronary stenosis. The three-dimensional time-dependent incompressible Navier-Stokes equations were discretized using a stabilized P1-P1 Galerkin finite element method and an implicit second-order backward differentiation formula. A regional blood flow distribution model, coupled with a lumped Windkessel model, was applied at the outlet boundaries. The 3D pulsatile blood flow was solved using a parallel solver based on a scalable Newton-Krylov-Schwarz algorithm, enabling fast and efficient simulations.

RESULTS

Coronary revascularization significantly improved myocardial blood flow, increasing the coronary fractional flow reserve from 0.742 to 0.904, indicating enhanced myocardial perfusion. However, cerebral hemodynamics were negatively affected, with a 2.49% reduction in blood flow through the main cerebral artery, suggesting an elevated risk of cerebral ischemia. The proposed computational framework demonstrated good parallel scalability across thousands of processor cores.

CONCLUSIONS

This study highlights the dual impact of coronary revascularization, improving myocardial perfusion while potentially elevating the risk of cerebral ischemic complications. The efficient computational approach provides a valuable tool for evaluating cardio-cerebral hemodynamics in patient-specific settings, making it suitable for complex and time-intensive simulations.

Understanding embolus transport and source to destination mapping of thromboemboli in hemodynamics driven by left ventricular assist device

Left Ventricular Assist Devices (LVADs) are a key treatment option for patients with advanced heart failure, but they carry a significant risk of thromboembolic complications. While improved LVAD design, and systemic anticoagulation regimen, have helped mitigate thromboembolic risks, ischemic stroke due to adverse thromboembolic events remains a major concern with current LVAD therapies. Improved understanding of embolic events, and embolus movement to the brain, is critical to develop techniques to minimize risks of occlusive embolic events such as a stroke after LVAD implantation. Here, we address this need, and devise a quantitative in silico framework to characterize thromboembolus transport and distrbution in hemodynamics driven by an operating LVAD. We conduct systematic numerical experiments to establish that our framework can quantify the source-to-destination transport patterns of thromboemboli as a function of: LVAD outflow graft anastomosis, LVAD operating pulse modulation, thromboembolus sizes, and origin locations of emboli. Additionally, we demonstrate how the resulting embolus distribution patterns compare and correlate with descriptors based solely on hemodynamic patterns such as helicity, vorticity, and wall shear stress. Using the concepts of size-dependent embolus-hemodynamics interactions, and jet impingement driven flow for hemodynamics under LVAD operation as established in our prior works, we gain valuable insights on departure of thromboembolus distribution from flow distribution, and establish that our in silico model can generate deep insights into embolus dynamics which is not otherwise available from standard of care imaging and clinical data.

Computational Modeling Of Immersed Non-spherical Bodies In Viscous Flows To Study Embolus Hemodynamics Interactions For Large Vessel Occlusion Stroke

Interactions of particles with unsteady non-linear viscous flows has widespread implications in physiological and biomedical systems. One key application where this plays a fundamental role is in the mechanism and etiology of embolic strokes. Specifically, there is a need to better understand how large occlusive emboli traverse complex vascular geometries, and block a vessel disrupting blood supply. Existing modeling approaches resort to key simplifications in terms of embolic particle shape, size, and their coupling to fluid flow. Here, we devise a novel computational model for resolving embolus-hemodynamics interactions for large non-spherical emboli approaching near occlusive regimes in anatomically real vascular segment. The formulation relies on extending an immersed finite element approach, coupled with a six degree-of-freedom particle dynamics model. The geometric complexities and their manifestation in embolus-flow and embolus-wall interactions are handles using a parametric shape representation, and projection of vessel signed distance fields on the particle boundaries. We illustrate our methodology and algorithmic details, as well as present examples of benchmark cases and convergence of our technique. Thereafter, we demonstrate a parametric study of large emboli for LVO strokes, showing that our methodology can capture the non-linear tumbling dynamics of emboli originating form their interactions with the flow and vessel walls; and resolve near-occlusive scenarios involving lubrication effects around the embolus and flow re-routing to non-occludes branches. This is a key methodological advancement in stroke modeling, as to the best of our knowledge this is the first modeling framework for LVO stroke and occlusion biofluid mechanics. Finally, even though we present our framework from the perspective of LVO strokes, the methodology as developed is broadly generalizable to two-way coupled fluid-particle interaction in unsteady viscous flows for a wide range of applications.

Optimizing distal and proximal splenic artery embolization with patient-specific computational fluid dynamics

Splenic artery embolization (SAE) has become a favored alternative to splenectomy, offering a less invasive intervention for injured spleens while preserving spleen function. However, our understanding of the role that hemodynamics plays during embolization remains limited. In this study, we utilized patient-specific computational fluid dynamics (CFD) simulations to study distal and proximal embolization strategies commonly used in SAE. Detailed 3D computer models were constructed considering the descending aorta, various major visceral arteries, and the iliac arteries. Subsequently, the blood flow and pressure associated with different coil placement locations in proximal embolization were studied considering the collateral vessels. Coil induced variations in pressure fields were quantified and compared to baseline. The coil induced flow stagnation was also quantified with particle residence time. Distal embolization was modeled with Lagrangian particle tracking and the effect of particle size, release location, and timing on embolization outcome was studied. Our findings highlight the crucial role of collateral vessels in maintaining blood supply to the spleen following proximal embolization. It was demonstrated that coil location can affect distal pressure and that strategic coil placement guided by patient-specific CFD simulations can further reduce this pressure as desired. Additionally, the results point to the critical roles that particle size, release timing, and location play in distal embolization. Our study provides an early attempt to use patient-specific computer modeling for optimizing embolization strategies and ultimately improving patient outcomes during SAE procedures.

Understanding Embolus Transport And Source To Destination Mapping Of Thromboemboli In Hemodynamics Driven By Left Ventricular Assist Device

Left Ventricular Assist Devices (LVADs) are a key treatment option for patients with advanced heart failure, but they carry a significant risk of thromboembolic complications. While improved LVAD design, and systemic anticoagulation regimen, have helped mitigate thromboembolic risks, ischemic stroke due to adverse thromboembolic events remains a major concern with current LVAD therapies. Improved understanding of embolic events, and embolus movement to the brain, is critical to develop techniques to minimize risks of occlusive embolic events such as a stroke after LVAD implantation. Here, we address this need, and devise a quantitative in silico framework to characterize thromboembolus transport and distrbution in hemodynamics driven by an operating LVAD. We conduct systematic numerical experiments to quantify the source-to-destination transport patterns of thromboemboli as a function of: LVAD outflow graft anastomosis, LVAD operating pulse modulation, thromboembolus sizes, and origin locations of emboli. Additionally, we demonstrate how the resulting embolus distribution patterns compare and correlate with descriptors based solely on hemodynamic patterns such as helicity, vorticity, and wall shear stress. Using the concepts of size-dependent embolus-hemodynamics interactions, and two jet flow model for hemodynamics under LVAD operation as established in our prior works, we gain valuable insights on departure of thromboembolus distribution from flow distribution, and establish that our in silico model can generate deep insights into embolus dynamics which is not otherwise available from standard of care imaging and clinical data.

How Topographic Diffusion-Weighted Imaging Patterns can Predict the Potential Embolic Source

PURPOSE

To develop an imaging prediction model for patients with embolic stroke of undetermined source (ESUS), we investigated the association of topographic diffusion-weighted imaging (DWI) patterns with potential embolic sources (PES) identified by transesophageal echocardiography.

METHODS

From a total of 992 consecutive patients with embolic stroke, 366 patients with the ESUS group were selected. ESUS was defined as no atrial fibrillation (Af) within 24h from admission and no PES after general examination. Clinical variables include age (> 80years, 70-80 years), sex, vascular risk factors and left atrial diameter > 4 cm. Age, sex and vascular risk factors adjusted odds ratio of each DWI for the different PESs were calculated. DWI was determined based on the arterial territories. Middle cerebral arteries were divided into 4 segments, i.e., M1-M4. Moreover, M2 segments were subdivided into superior and inferior branches.

RESULTS

The 366 patients consisted of 168 with paroxysmal Af (pAf), 77 with paradoxical embolism, 71 with aortic embolism and 50 with undetermined embolism after transesophageal echocardiography. The variables adjusted odds ratio (OR) of internal carotid artery (OR: 12.1, p = 0.037), M1 (4.2, p = 0.001), inferior M2 (7.5, p = 0.0041) and multiple cortical branches (12.6, p < 0.0001) were significantly higher in patients with pAf. Striatocapsular infarction (12.5, p < 0.0001) and posterior inferior cerebellar artery infarcts (3.6, p = 0.018) were significantly associated with paradoxical embolism. Clinical variables adjusted OR of multiple small scattered infarcts (8.3, p < 0.0001) were significantly higher in patients with aortic embolism.

CONCLUSION

The associations of DWI with different PES have their distinctive characteristics and DWI along with clinical variables may help predict PES in patients with ESUS.

Modelling large scale artery haemodynamics from the heart to the eye in response to simulated microgravity

We investigated variations in haemodynamics in response to simulated microgravity across a semi-subject-specific three-dimensional (3D) continuous arterial network connecting the heart to the eye using computational fluid dynamics (CFD) simulations. Using this model we simulated pulsatile blood flow in an upright Earth gravity case and a simulated microgravity case. Under simulated microgravity, regional time-averaged wall shear stress (TAWSS) increased and oscillatory shear index (OSI) decreased in upper body arteries, whilst the opposite was observed in the lower body. Between cases, uniform changes in TAWSS and OSI were found in the retina across diameters. This work demonstrates that 3D CFD simulations can be performed across continuously connected networks of small and large arteries. Simulated results exhibited similarities to low dimensional spaceflight simulations and measured data-specifically that blood flow and shear stress decrease towards the lower limbs and increase towards the cerebrovasculature and eyes in response to simulated microgravity, relative to an upright position in Earth gravity.

Evidence and Mechanisms for Embolic Stroke in Contralateral Hemispheres From Carotid Artery Sources

BACKGROUND

Disambiguation of embolus pathogenesis in embolic strokes is often a clinical challenge. One common source of embolic stroke is the carotid arteries, with emboli originating due to plaque buildup or perioperatively during revascularization procedures. Although it is commonly thought that thromboemboli from carotid sources travel to cerebral arteries ipsilaterally, there are existing reports of contralateral embolic events that complicate embolus source destination relationship for carotid sources. Here, we hypothesize that emboli from carotid sources can travel to contralateral hemispheres and that embolus interactions with collateral hemodynamics in the circle of Willis influence this process.

METHODS AND RESULTS

We use a patient-specific computational embolus-hemodynamics interaction model developed in prior works to conduct an in silico experiment spanning 4 patient vascular models, 6 circle of Willis anastomosis variants, and 3 different thromboembolus sizes released from left and right carotid artery sites. This led to a total of 144 different experiments, estimating trajectories and distribution of approximately 1.728 million embolus samples. Across all cases considered, emboli from left and right carotid sources showed nonzero contralateral transport (P value <-0.05). Contralateral movement revealed a size dependence, with smaller emboli traveling more contralaterally. Detailed analysis of embolus dynamics revealed that collateral flow routes in the circle of Willis played a role in routing emboli, and transhemispheric movement occurred through the anterior and posterior communicating arteries in the circle of Willis.

CONCLUSIONS

We generated quantitative data demonstrating the complex dynamics of finite size thromboembolus particles as they interact with pulsatile arterial hemodynamics and traverse the vascular network of the circle of Willis. This leads to a nonintuitive source-destination relationship for emboli originating from carotid artery sites, and emboli from carotid sources can potentially travel to cerebral arteries on contralateral hemispheres.

Evidence And Mechanisms For Embolic Stroke In Contralateral Hemispheres From Carotid Artery Sources

Disambiguation of embolus etiology in embolic strokes is often a clinical challenge. One common source of embolic stroke is the carotid arteries, with emboli originating due to plaque build up, or perioperatively during revascularization procedures. While it is commonly thought that thromboemboli from carotid sources travel to cerebral arteries ipsilaterally, there are existing reports of contralateral embolic events which complicate embolus source destination relationship for carotid sources. Here, we hypothesize that emboli from carotid sources can travel to contralateral hemispheres, and that embolus interactions with collateral hemodynamics in the Circle of Willis influences this process. We use a patient-specific computational embolus-hemodynamics interaction model developed in prior works to conduct an in silico experiment spanning 4 patient vascular models, 6 Circle of Willis anastomosis variants, and 3 different thromboembolus sizes released from left and right carotid artery sites. This led to a total of 144 different experiments, estimating trajectories and distribution of approximately 1.728 million embolus samples. Across all cases considered, emboli from left and right carotid sources showed non-zero contralateral transport (p value < 0.05). Contralateral movement revealed a size-dependence, with smaller emboli traveling more contralaterally. Detailed analysis of embolus dynamics revealed that collateral flow routes in Circle of Willis played a role in routing emboli, and transhemispheric movement occurred through the anterior and posterior communicating arteries in the Circle of Willis. We generated quantitative data demonstrating the complex dynamics of finite size thromboembolus particles as they interact with pulsatile arterial hemodynamics, and traverse the vascular network of the Circle of Willis. This leads to a non-intuitive source-destination relationship for emboli originating from carotid artery sites, and emboli from carotid sources can potentially travel to cerebral arteries on contralateral hemispheres.

The Relation Between Viscous Energy Dissipation and Pulsation for Aortic Hemodynamics Driven by a Left Ventricular Assist Device

Left ventricular assist device (LVAD) provides mechanical circulatory support for patients with advanced heart failure. Treatment using LVAD is commonly associated with complications such as stroke and gastro-intestinal bleeding. These complications are intimately related to the state of hemodynamics in the aorta, driven by a jet flow from the LVAD outflow graft that impinges into the aorta wall. Here we conduct a systematic analyses of hemodynamics driven by an LVAD with a specific focus on viscous energy transport and dissipation. We conduct a complementary set of analysis using idealized cylindrical tubes with diameter equivalent to common carotid artery and aorta, and a patient-specific model of 27 different LVAD configurations. Results from our analysis demonstrate how energy dissipation is governed by key parameters such as frequency and pulsation, wall elasticity, and LVAD outflow graft surgical anastomosis. We find that frequency, pulsation, and surgical angles have a dominant effect, while wall elasticity has a weaker effect, in determining the state of energy dissipation. For the patient-specific scenario, we also find that energy dissipation is higher in the aortic arch and lower in the abdominal aorta, when compared to the baseline flow without an LVAD. This further illustrates the key hemodynamic role played by the LVAD outflow jet impingement, and subsequent aortic hemodynamics during LVAD operation.

A Fluid-Structure Interaction Analysis of Blood Clot Motion in a Branch of Pulmonary Arteries

INTRODUCTION

Pulmonary embolism (PE) is one of the most prevalent diseases amid hospitalized patients taking many people's lives annually. This phenomenon, however, has not been investigated via numerical simulations.

METHODS

In this study, an image-based model of pulmonary arteries has been constructed from a 44-year-old man's computed tomography images. The fluid-structure interaction method was used to simulate the motion of the blood clot. In this regard, Navier-Stokes equations, as the governing equations, have been solved in an arbitrary Lagrangian-Eulerian (ALE) formulation.

RESULTS

According to our results, the velocity of visco-hyperelastic model of the emboli was relatively higher than the emboli with hyperelastic model, despite their similar behavioral pattern. The stresses on the clot were also investigated and showed that the blood clot continuously sustained stresses greater than 165 Pa over an about 0.01 s period, which can cause platelets to leak and make the clot grow or tear apart.

CONCLUSIONS

It could be concluded that in silico analysis of the cardiovascular diseases initiated from clot motion in blood flow is a valuable tool for a better understanding of these phenomena.

Quantitative Assessment of Aortic Hemodynamics for Varying Left Ventricular Assist Device Outflow Graft Angles and Flow Pulsation

Left ventricular assist devices (LVADs) comprise a primary treatment choice for advanced heart failure patients. Treatment with LVAD is commonly associated with complications like stroke and gastro-intestinal (GI) bleeding, which adversely impacts treatment outcomes, and causes fatalities. The etiology and mechanisms of these complications can be linked to the fact that LVAD outflow jet leads to an altered state of hemodynamics in the aorta as compared to baseline flow driven by aortic jet during ventricular systole. Here, we present a framework for quantitative assessment of aortic hemodynamics in LVAD flows realistic human vasculature, with a focus on quantifying the differences between flow driven by LVAD jet and the physiological aortic jet when no LVAD is present. We model hemodynamics in the aortic arch proximal to the LVAD outflow graft, as well as in the abdominal aorta away from the LVAD region. We characterize hemodynamics using quantitative descriptors of flow velocity, stasis, helicity, vorticity and mixing, and wall shear stress. These are used on a set of 27 LVAD scenarios obtained by parametrically varying LVAD outflow graft anastomosis angles, and LVAD flow pulse modulation. Computed descriptors for each of these scenarios are compared against the baseline flow, and a detailed quantitative characterization of the altered state of hemodynamics due to LVAD operation (when compared to baseline aortic flow) is compiled. These are interpreted using a conceptual model for LVAD flow that distinguishes between flow originating from the LVAD outflow jet (and its impingement on the aorta wall), and flow originating from aortic jet during aortic valve opening in normal physiological state.

Micromechanical Force Measurement of Clotted Blood Particle Cohesion: Understanding Thromboembolic Aggregation Mechanisms

PURPOSE

Arterial shear forces may promote the embolization of clotted blood from the surface of thrombi, displacing particles that may occlude vasculature, with increased risk of physiological complications and mortality. Thromboemboli may also collide in vivo to form metastable aggregates that increase vessel occlusion likelihood.

METHODS

A micromechanical force (MMF) apparatus was modified for aqueous applications to study clot-liquid interfacial phenomena between clotted porcine blood particles suspended in modified continuous phases. The MMF measurement is based on visual observation of particle-particle separation, where Hooke's Law is applied to calculate separation force. This technique has previously been deployed to study solid-fluid interfacial phenomena in oil and gas pipelines, providing fundamental insight to cohesive and adhesive properties between solids in multiphase flow systems.

RESULTS

This manuscript introduces distributed inter-particle separation force properties as a function of governing physio-chemical parameters; pre-load (contact) force, contact time, and bulk phase chemical modification. In each experimental campaign, the hysteresis and distributed force properties were analysed, to derive insight as to the governing mechanism of cohesion between particles. Porcine serum, porcine albumin and pharmaceutical agents (alteplase, tranexamic acid and hydrolysed aspirin) reduced the measurement by an order of magnitude from the baseline measurement-the apparatus provides a platform to study how surface-active chemistries impact the solid-fluid interface.

CONCLUSION

These results provide new insight to potential mechanisms of macroscopic thromboembolic aggregation via particles cohering in the vascular system-data that can be directly applied to computational simulations to predict particle fate, better informing the mechanistic developments of embolic occlusion.

Embolus Analog Trajectory Paths Under Physiological Flowrates Through Patient-Specific Aortic Arch Models

Atrial fibrillation (AF) is the most common irregular heartbeat among the world's population and is a major contributor to cardiogenic embolisms and acute ischemic stroke (AIS). However, the role AF flow plays in the trajectory paths of cardiogenic emboli has not been experimentally investigated. A physiological simulation system was designed to analyze the trajectory patterns of bovine embolus analogs (EAs) (n = 720) through four patient-specific models, under three flow conditions: steady flow, normal pulsatile flow, and AF pulsatile flow. It was seen that EA trajectory paths were proportional to the percentage flowrate split of 25–31% along the branching vessels. Overall, AF flow conditions increased trajectories through the left- (LCCA) and right (RCCA)-common carotid artery by 25% with respect to normal pulsatile flow. There was no statistical difference in the distribution of clot trajectories when the clot was released from the right, left, or anterior positions. Significantly, more EAs traveled through the brachiocephalic trunk (BCT) than through the LCCA or the left subclavian. Yet of the EAs that traveled through the common carotid arteries, there was a greater affiliation toward the LCCA compared to the RCCA (p < 0.05).

A Re-Engineered Software Interface and Workflow for the Open-Source SimVascular Cardiovascular Modeling Package

Patient-specific simulation plays an important role in cardiovascular disease research, diagnosis, surgical planning and medical device design, as well as education in cardiovascular biomechanics. simvascular is an open-source software package encompassing an entire cardiovascular modeling and simulation pipeline from image segmentation, three-dimensional (3D) solid modeling, and mesh generation, to patient-specific simulation and analysis. SimVascular is widely used for cardiovascular basic science and clinical research as well as education, following increased adoption by users and development of a GATEWAY web portal to facilitate educational access. Initial efforts of the project focused on replacing commercial packages with open-source alternatives and adding increased functionality for multiscale modeling, fluid-structure interaction (FSI), and solid modeling operations. In this paper, we introduce a major SimVascular (SV) release that includes a new graphical user interface (GUI) designed to improve user experience. Additional improvements include enhanced data/project management, interactive tools to facilitate user interaction, new boundary condition (BC) functionality, plug-in mechanism to increase modularity, a new 3D segmentation tool, and new computer-aided design (CAD)-based solid modeling capabilities. Here, we focus on major changes to the software platform and outline features added in this new release. We also briefly describe our recent experiences using SimVascular in the classroom for bioengineering education.

Dilution and microfiltration of particulate corticosteroids for spinal epidural injections: impact on drug concentration and agglomerate formation

Particulate corticosteroids have been described to lead to greater pain improvement compared with their non-particulate counterparts when used in epidural injections. It is hypothesised that filtering may significantly impact their concentration and long-term efficacy. We investigated if passing particulate suspensions through different commonly-used filters affects drug dosage. Two particulate corticosteroid formulations, triamcinolone acetonide and methylprednisolone acetate, were mixed at different concentrations with either bupivacaine hydrochloride or 0.9% sodium chloride. Solutions were passed through a 5-μm and a 0.2-μm filter. Mass spectroscopy results indicated a complete loss of corticosteroid from the solutions using both filters, and light microscopy imaging demonstrated agglomerate formation, suggesting that filtering interferes with drug dosage. The choice of diluents must also be considered to reduce large agglomerate formation. Clinicians should be aware of the consequences of filtering particulate suspensions and carefully consider the selection of diluent when considering treatment plans.

Reversed Auxiliary Flow to Reduce Embolism Risk During TAVI: A Computational Simulation and Experimental Study

INTRODUCTION

Endovascular treatments, such as transcatheter aortic valve implantation (TAVI), carry a risk of embolization due to debris dislodgement during various procedural steps. Although embolic filters are already available and marketed, mechanisms underlying cerebral embolism still need to be elucidated in order to further reduce cerebrovascular events.

METHODS

We propose an experimental framework with an in silico duplicate allowing release of particles at the level of the aortic valve and their subsequent capture in the supra-aortic branches, simulating embolization under constant inflow and controlled hemodynamic conditions. The effect of a simple flow modulation, consisting of an auxiliary constant flow via the right subclavian artery (RSA), on the amount of particle entering the brachiocephalic trunk was investigated. Preliminary computational fluid dynamics (CFD) simulations were performed in order to assess the minimum retrograde flow-rate from RSA required to deviate particles.

RESULTS

Our results show that a constant reversed auxiliary flow of 0.5 L/min from the RSA under a constant inflow of 4 L/min from the ascending aorta is able to protect the brachiocephalic trunk from particle embolisms. Both computational and experimental results also demonstrate that the distribution of the bulk flow dictates the distribution of the particles along the aortic branches. This effect has also shown to be independent of release location and flow rate.

CONCLUSIONS

The present study confirms that the integration of in vitro experiments and in silico analyses allows designing and benchmarking novel solutions for cerebral embolic protection during TAVI such as the proposed embo-deviation technique based on an auxiliary retrograde flow from the right subclavian artery.

The effect of inlet and outlet boundary conditions in image-based CFD modeling of aortic flow

Background

Computational modeling of cardiovascular flow is a growing and useful field, but such simulations usually require the researcher to guess the flow’s inlet and outlet conditions since they are difficult and expensive to measure. It is critical to determine the amount of uncertainty introduced by these assumptions in order to evaluate the degree to which cardiovascular flow simulations are accurate. Our work begins to address this question by examining the sensitivity of flow to several different assumed velocity inlet and outlet conditions in a patient-specific aorta model.

Methods

We examined the differences between plug flow, parabolic flow, linear shear flows, skewed cubic flow profiles, and Womersley flow at the inlet. Only the shape of the inlet velocity profile was varied—all other parameters were identical among these simulations. Secondary flow in the form of a counter-rotating pair of vortices was also added to parabolic axial flow to study its effect on the solution. In addition, we examined the differences between two-element Windkessel, three element Windkessel and the outflow boundary conditions. In these simulations, only the outlet boundary condition was varied.

Results

The results show axial and in-plane velocities are considerably different close to the inlet for the cases with different inlet velocity profile shapes. However, the solutions are qualitatively similar beyond 1.75D, where D is the inlet diameter. This trend is also observed in other quantities such as pressure and wall shear stress. Normalized root-mean-square deviation, a measure of axial velocity magnitude differences between the different cases, generally decreases along the streamwise coordinate. The linear shear inlet velocity boundary condition and plug velocity boundary condition solution exhibit the highest time-averaged wall shear stress, approximately \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$8\%$$\end{document}8% higher than the parabolic inlet velocity boundary condition. Upstream of 1D from the inlet, adding secondary flow has a significant impact on temporal wall shear stress distributions. This is especially observable during diastole, when integrated wall shear stress magnitude varies about \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$26\%$$\end{document}26% between simulations with and without secondary flow. The results from the outlet boundary condition study show the Windkessel models differ from the outflow boundary condition by as much as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$18\%$$\end{document}18% in terms of time-averaged wall shear stress. Furthermore, normalized root-mean-square deviation of axial velocity magnitude, a measure of deviation between Windkessel and the outflow boundary condition, increases along the streamwise coordinate indicating larger variations near outlets.

Conclusion

It was found that the selection of inlet velocity conditions significantly affects only the flow region close to the inlet of the aorta. Beyond two diameters distal to the inlet, differences in flow solution are small. Although additional studies must be performed to verify this result, the data suggest that it is important to use patient-specific inlet conditions primarily if the researcher is concerned with the details of the flow very close to the inlet. Similarly, the selection of outlet conditions significantly affects the flow in the vicinity of the outlets. Upstream of five diameters proximal to the outlet, deviations between the outlet boundary conditions examined are insignificant. Although the inlet and outlet conditions only affect the flow significantly in their respective neighborhoods, our study indicates that outlet conditions influence a larger percentage of the solution domain.