Lagrangian postprocessing of computational hemodynamics

Computational study on hemodynamic effects of left superior pulmonary vein resection and associated physiological changes in the left atrium after left upper lobectomy

Left upper lobectomy (LUL) with left superior pulmonary vein (LSPV) resection alters the left atrium (LA) physiological states and LA hemodynamics associated with thrombosis, although this underlying mechanism is poorly understood. Therefore, we investigated the effects of LSPV resection and associated LA physiological changes on LA hemodynamics using four-dimensional computed tomography image-based computational simulations. Three cases were considered: the LA before and after LUL extracted from computed tomography images and artificial LSPV resection without physiological changes. Comparisons among the three cases demonstrated that physiological changes associated with LSPV resection are the possible factors that affect the LA hemodynamics after LUL.

On the nonlinear relationship between wall shear stress topology and multi-directionality in coronary atherosclerosis

BACKGROUND AND OBJECTIVE

In this paper we investigate twelve multi-directional/topological wall shear stress (WSS) derived metrics and their relationships with the formation of coronary plaques in both computational fluid dynamics (CFD) and dynamic fluid-structure interaction (FSI) frameworks. While low WSS is one of the most established biomechanical markers associated with coronary atherosclerosis progression, alone it is limited. Multi-directional and topological WSS derived metrics have been shown to be important in atherosclerosis related mechanotransduction and near-wall transport processes. However, the relationships between these twelve WSS metrics and the influence of both FSI simulations and coronary dynamics is understudied.

METHODS

We first investigate the relationships between these twelve WSS derived metrics, stenosis percentage and lesion length through a parametric, transient CFD study. Secondly, we extend the parametric study to FSI, both with and without the addition of coronary dynamics, and assess their correlations. Finally, we present the case of a patient who underwent invasive coronary angiography and optical coherence tomography imaging at two time points 18 months apart. Associations between each of the twelve WSS derived metrics in CFD, static FSI and dynamic FSI simulations were assessed against areas of positive/negative vessel remodelling, and changes in plaque morphology.

RESULTS

22-32% stenosis was the threshold beyond which adverse multi-directional/topological WSS results. Each metric produced a different relationship with changing stenoses and lesion length. Transient haemodynamics was impacted by coronary dynamics, with the topological shear variation index suppressed by up to 94%. These changes appear more critical at smaller stenosis levels, suggesting coronary dynamics could play a role in the earlier stages of atherosclerosis development. In the patient case, both dynamics and FSI vs CFD changes altered associations with measured changes in plaque morphology. An appendix of the linear fits between the various FSI- and CFD-based simulations is provided to assist in scaling CFD-based results to resemble the compliant walled characteristics of FSI more accurately.

CONCLUSIONS

These results highlight the potential for coronary dynamics to alter multi-directional/topological WSS metrics which could impact associations with changes in coronary atherosclerosis over time. These results warrant further investigation in a wider range of morphological settings and longitudinal cohort studies in the future.

Modeling the Mechanical Microenvironment of Coiled Cerebral Aneurysms

Successful occlusion of cerebral aneurysms using coil embolization is contingent upon stable thrombus formation, and the quality of the thrombus depends upon the biomechanical environment. The goal of this study was to investigate how coil embolization alters the mechanical micro-environment within the aneurysm dome. Inertialess particles were injected in three-dimensional, computational simulations of flow inside patient aneurysms using patient-specific boundary conditions. Coil embolization was simulated as a homogenous porous medium of known permeability and inertial constant. Lagrangian particle tracking was used to calculate the residence time and shear stress history for particles in the flow before and after treatment. The percentage of particles entering the aneurysm dome correlated with the neck surface area before and after treatment (pretreatment: R2 = 0.831, P < 0.001; post-treatment: R2 = 0.638, P < 0.001). There was an inverse relationship between the change in particles entering the dome and coil packing density (R2 = 0.600, P < 0.001). Following treatment, the particles with the longest residence times tended to remain within the dome even longer while accumulating lower shear stress. A significant correlation was observed between the treatment effect on residence time and the ratio of the neck surface area to porosity (R2 = 0.390, P = 0.007). The results of this study suggest that coil embolization triggers clot formation within the aneurysm dome via a low shear stress-mediated pathway. This hypothesis links independently observed findings from several benchtop and clinical studies, furthering our understanding of this treatment strategy.

Deep Learning for Computational Hemodynamics: A Brief Review of Recent Advances

Computational fluid dynamics (CFD) modeling of blood flow plays an important role in better understanding various medical conditions, designing more effective drug delivery systems, and developing novel diagnostic methods and treatments. However, despite significant advances in computational technology and resources, the expensive computational cost of these simulations still hinders their transformation from a research interest to a clinical tool. This bottleneck is even more severe for image-based, patient-specific CFD simulations with realistic boundary conditions and complex computational domains, which make such simulations excessively expensive. To address this issue, deep learning approaches have been recently explored to accelerate computational hemodynamics simulations. In this study, we review recent efforts to integrate deep learning with CFD and discuss the applications of this approach in solving hemodynamics problems, such as blood flow behavior in aorta and cerebral arteries. We also discuss potential future directions in the field. In this review, we suggest that incorporating physiologic understandings and underlying fluid mechanics laws in deep learning models will soon lead to a paradigm shift in the development novel non-invasive computational medical decisions.

Guiding the prostatic artery embolization procedure with computational uid dynamics

Benign prostatic hyperplasia (BPH) is a common disease associated with lower urinary tract symptoms and the most frequent benign tumor in men. To reduce BPH therapy complications, prostatic artery embolization (PAE) was developed to replace the surgical options. PAE is a minimally invasive technique in which emboli are injected into the prostate arteries (PA), obstructing the blood flow in the hypervascular nodules. In this work, a personalized PAE treatment strategy was proposed using patient-specific computational fluid dynamics (CFD). First, the hemodynamics environment in the iliac arterial tree considering a large network of bifurcations was studied. The results showed complex blood flow patterns in the iliac arterial network. Subsequently, the transport of embolic particulates during PAE for the standard horizontal and a hypothetical vertical patient positioning was simulated using Lagrangian particle tracking. Emboli with different sizes were released at various locations across the iliac arterial tree. The emboli entering the PA were mapped back to their initial location to create emboli release maps (ERMs). The obtained ERMs during the standard patient positioning for smaller emboli at certain release locations showed distinct regions in which if the emboli were released within these regions, all of them would reach the PA without non-target embolization. During the hypothetical vertical patient positioning, the larger emboli formed a larger coherent region in the ERMs. Our patient-specific model can be used to find the best spatial location for emboli injection and perform the embolization procedure with minimal off-target delivery.

On the Impact of Left Upper Lobectomy on the Left Atrial Hemodynamics

The left atrium (LA) functions to transport oxygenated blood from the pulmonary veins (PVs) to the left ventricle (LV). LA hemodynamics has received much attention because thrombosis in the LA in pathological states, such as atrial fibrillation, is a major factor leading to thromboembolic stroke. In the last 5 years, multiple cohort studies have revealed that left upper lobectomy (LUL) with PV resection risks thrombus formation in the PV stump even in the normal LA without a history of cardiac disease; the causal mechanism is, however, an open question. The present study investigated the potential effect of an LUL on LA hemodynamics associated with thrombus formation through computational simulation using four-dimensional computed tomography (4D-CT) images. Time series of patient-specific LA geometries before and after LUL were extracted from the 4D-CT images and these motions were estimated through non-rigid registration. Adopting the LA geometries and prescribed moving wall boundary conditions, the LA blood flow was determined using a Cartesian-grid computational fluid dynamics solver. The obtained results show that the LUL resulted in blood flow impingement from the left and right PV inflows into the LA upper region throughout most of the cardiac cycle. This characteristic alteration of the LA hemodynamics generated fine-scale vortices with viscous energy dissipations, enhancing the flow stasis associated with thrombus formation in the PV stump. These findings show that an LUL affects the hemodynamics not only in the PV stump but also throughout the LA region. They also highlight the importance of computational analysis of LA hemodynamics in understanding the underlying mechanism of LUL-induced thrombus formation.

Investigation of the effect of anticoagulant usage in the flow diverter stent treatment of the patient-specific cerebral aneurysm using the Lagrangian coherent structures

Anticoagulants are prescribed to the flow diverter treated patients to diminish the risk of embolism in the arteries. In the present study, digital subtraction angiography images of a 49-year-old female patient with a left paraophthalmic aneurysm were used to build a numerical model to investigate the effect of an anticoagulant on hemodynamics at the aneurysm site. The Carreau-Yasuda viscosity model was utilized to define blood viscosity, and the coefficients of the viscosity model were updated based on the usage of warfarin. The five-cardiac cycle-long numerical simulations were performed, and Lagrangian coherent structures, hyperbolic time, and fluid particle analyses were also employed in the numerical models. These analyses allowed us to evaluate the formation of stagnated regions, recirculation zones, and the number of jailed particles inside the aneurysm sac following a flow diverter placement. It is realized that anticoagulant use caused blood to be less viscous, yielding a substantial amount of incoming blood flow to enter the aneurysm sac. Only 12% of the nearly 25,000 fluid particles seeded from the artery inlet have stayed inside the sac. Furthermore, the deviation between warfarin added blood and normal blood flow becomes more extensive, with every heartbeat undermining the effectiveness of patient-specific CFD models when the use of anticoagulants is overlooked in the viscosity models.

Spectral-Clustering of Lagrangian Trajectory Graphs: Application to Abdominal Aortic Aneurysms

PURPOSE

Identification of coherent structures in cardiovascular flows is crucial to describe the transport and mixing of blood. Coherent structures can highlight locations where minimal blood mixing takes place, thus, potential thrombus formation can be expected thither. Graph-based approaches have recently been introduced in order to describe fluid transport and mixing between multiple Lagrangian trajectories, where each trajectory serves as a node that can be connected to another trajectory based on their relative distance during the course of time.

METHODS

In this study, we compute the Lagrangian trajectories from in vitro planar instantaneous velocity fields in two models of abdominal aortic aneurysms, (AAA) namely single bulge and bi-lobed. Then, we construct unweighted and undirected graphs based on the pairwise distance of Lagrangian trajectories. We report local measures of the graph namely the degree and the clustering coefficient. We also perform spectral clustering of the graph Laplacian to extract the flow coherent sets.

RESULTS

Local graph measures reveal fluid regions of high mixing such as vortex boundaries. Through spectral clustering, the fluid is partitioned into a reduced number of coherent sets where within each set, inner mixing of fluid is maximized while the fluid mixing between different coherent sets is minimized. The approach reveals multiple coherent sets adjacent to the AAA bulge that have sustained this adjacency to the wall through their coherent motion during one cardiac cycle.

CONCLUSION

Identifying coherent sets enables tracking their transport during the cardiac cycle and identify their role in the flow dynamics. Moreover, the size and the transport of the long residing coherent sets inside the AAA bulges can be deduced which may aid in predicting thrombus formation at such location.

In Silico Hemodynamics and Filtering Evaluation of a Commercial Embolic Protection Device

During the last years, several kinds of Embolic Protection Devices (EPD) have been developed, with the aim of minimizing complication caused by thrombi generated during Carotid Artery Stenting (CAS). These devices are capable of capturing small particles generated during the intervention, avoiding cerebral stroke and improving the outcomes of the surgery. However, they have associated complications, like the increase on flow resistance associated by their use or the lack of knowledge on their actual filtration efficiency for thrombi of low size. Current work proposes a validated computational methodology in order to predict the hemodynamic features and filtering efficiency of a commercial EPD. It will be observed how Computational Fluid Dynamics predicts pressure drop with fair agreement with the experimental measurements. Finally, this work analyzes the filtration efficiency and the influence of the distribution of injected particles on this parameter. The capabilities of the filter for retaining particles of diameter below the pore size is, additionally, discussed.

Go with the FLOW: visualizing spatiotemporal dynamics in optical widefield calcium imaging

Widefield calcium imaging has recently emerged as a powerful experimental technique to record coordinated large-scale brain activity. These measurements present a unique opportunity to characterize spatiotemporally coherent structures that underlie neural activity across many regions of the brain. In this work, we leverage analytic techniques from fluid dynamics to develop a visualization framework that highlights features of flow across the cortex, mapping wavefronts that may be correlated with behavioural events. First, we transform the time series of widefield calcium images into time-varying vector fields using optic flow. Next, we extract concise diagrams summarizing the dynamics, which we refer to as FLOW (flow lines in optical widefield imaging) portraits. These FLOW portraits provide an intuitive map of dynamic calcium activity, including regions of initiation and termination, as well as the direction and extent of activity spread. To extract these structures, we use the finite-time Lyapunov exponent technique developed to analyse time-varying manifolds in unsteady fluids. Importantly, our approach captures coherent structures that are poorly represented by traditional modal decomposition techniques. We demonstrate the application of FLOW portraits on three simple synthetic datasets and two widefield calcium imaging datasets, including cortical waves in the developing mouse and spontaneous cortical activity in an adult mouse.

Engineering Perspective on Cardiovascular Simulations of Fontan Hemodynamics: Where Do We Stand with a Look Towards Clinical Application

BACKGROUND

Cardiovascular simulations for patients with single ventricles undergoing the Fontan procedure can assess patient-specific hemodynamics, explore surgical advances, and develop personalized strategies for surgery and patient care. These simulations have not yet been broadly accepted as a routine clinical tool owing to a number of limitations. Numerous approaches have been explored to seek innovative solutions for improving methodologies and eliminating these limitations.

PURPOSE

This article first reviews the current state of cardiovascular simulations of Fontan hemodynamics. Then, it will discuss the technical progress of Fontan simulations with the emphasis of its clinical impact, noting that substantial improvements have been made in the considerations of patient-specific anatomy, flow, and blood rheology. The article concludes with insights into potential future directions involving clinical validation, uncertainty quantification, and computational efficiency. The advancements in these aspects could promote the clinical usage of Fontan simulations, facilitating its integration into routine clinical practice.

Fluid Flow Characteristics of Healthy and Calcified Aortic Valves Using Three-Dimensional Lagrangian Coherent Structures Analysis

Aortic valve calcification is an important cardiovascular disorder that deteriorates the accurate functioning of the valve leaflets. The increasing stiffness due to the calcification prevents the complete closure of the valve and therefore leads to significant hemodynamic alterations. Computational fluid dynamics (CFD) modeling enables the investigation of the entire flow domain by processing medical images from aortic valve patients. In this study, we computationally modeled and simulated a 3D aortic valve using patient-specific dimensions of the aortic root and aortic sinus. Leaflet stiffness is deteriorated in aortic valve disease due to calcification. In order to investigate the influence of leaflet calcification on flow dynamics, three different leaflet-stiffness values were considered for healthy, mildly calcified, and severely calcified leaflets. Time-dependent CFD results were used for applying the Lagrangian coherent structures (LCS) technique by performing finite-time Lyapunov exponent (FTLE) computations along with Lagrangian particle residence time (PRT) analysis to identify unique vortex structures at the front and backside of the leaflets. Obtained results indicated that the peak flow velocity at the valve orifice increased with the calcification rate. For the healthy aortic valve, a low-pressure field was observed at the leaflet tips. This low-pressure field gradually expanded through the entire aortic sinus as the calcification level increased. FTLE field plots of the healthy and calcified valves showed a variety of differences in terms of flow structures. When the number of fluid particles in the healthy valve model was taken as reference, 1.59 and 1.74 times more particles accumulated in the mildly and severely calcified valves, respectively, indicating that the calcified valves were not sufficiently opened to allow normal mass flow rates.

The association between hemodynamics and wall characteristics in human intracranial aneurysms: a review

Hemodynamics plays a key role in the natural history of intracranial aneurysms (IAs). However, studies exploring the association between aneurysmal hemodynamics and the biological and mechanical characteristics of the IA wall in humans are sparse. In this review, we survey the current body of literature, summarize the studies' methodologies and findings, and assess the degree of consensus among them. We used PubMed to perform a systematic review of studies that explored the association between hemodynamics and human IA wall features using different sources. We identified 28 publications characterizing aneurysmal flow and the IA wall: 4 using resected tissues, 17 using intraoperative images, and 7 using vessel wall magnetic resonance imaging (MRI). Based on correlation to IA tissue, higher flow conditions, such as high wall shear stress (WSS) with complex pattern and elevated pressure, were associated with degenerated walls and collagens with unphysiological orientation and faster synthesis. MRI studies strongly supported that low flow, characterized by low WSS and high blood residence time, was associated with thicker walls and post-contrast enhancement. While significant discrepancies were found among those utilized intraoperative images, they generally supported that thicker walls coexist at regions with prolonged residence time and that thinner regions are mainly exposed to higher pressure with complex WSS patterns. The current body of literature supports a theory of two general hemodynamic-biologic mechanisms for IA development. One, where low flow conditions are associated with thickening and atherosclerotic-like remodeling, and the other where high and impinging flow conditions are related to wall degeneration, thinning, and collagen remodeling.

Wall Shear Stress Topological Skeleton Analysis in Cardiovascular Flows: Methods and Applications

A marked interest has recently emerged regarding the analysis of the wall shear stress (WSS) vector field topological skeleton in cardiovascular flows. Based on dynamical system theory, the WSS topological skeleton is composed of fixed points, i.e., focal points where WSS locally vanishes, and unstable/stable manifolds, consisting of contraction/expansion regions linking fixed points. Such an interest arises from its ability to reflect the presence of near-wall hemodynamic features associated with the onset and progression of vascular diseases. Over the years, Lagrangian-based and Eulerian-based post-processing techniques have been proposed aiming at identifying the topological skeleton features of the WSS. Here, the theoretical and methodological bases supporting the Lagrangian- and Eulerian-based methods currently used in the literature are reported and discussed, highlighting their application to cardiovascular flows. The final aim is to promote the use of WSS topological skeleton analysis in hemodynamic applications and to encourage its application in future mechanobiology studies in order to increase the chance of elucidating the mechanistic links between blood flow disturbances, vascular disease, and clinical observations.

Flow topology and targeted drug delivery in cardiovascular disease

Targeted drug delivery is a promising technique to direct the drug to the specific diseased region. Nanoparticles have provided an attractive approach for this purpose. In practice, the major focus of targeted delivery has been on targeting cell receptors. However, the complex fluid mechanics in diseased biomedical flows questions if a sufficient number of nanoparticles can reach the desired region. In this paper, we propose that hidden topological structures in cardiovascular flows identified with Lagrangian coherent structures (LCS) control drug transport and provide valuable information for optimizing targeted drug delivery efficiency. We couple image-based computational fluid dynamics (CFD) with continuum transport models to study nanoparticle transport in coronary artery disease. We simulate nanoparticle transport as well as the recently proposed shear targeted drug delivery system that couples micro-carriers with nanoparticle drugs. The role of the LCS formed near the stenosed artery in controlling drug transport is discussed. Our results motivate the design of smart micro-needles guided by flow topology, which could achieve optimal drug delivery efficiency.

Impact of BASILICA on the thrombogenicity potential of valve-in-valve implantations

Subclinical leaflet thrombosis is becoming a major concern in valve-in-valve procedures, whereby a transcatheter aortic valve device is deployed inside a failed bioprosthetic surgical valve. Blood flow stagnation and prolonged residence times in the neo-sinuses have been suggested as possible explanations for leaflet thrombosis. The BASILICA technique, which was originally developed to treat coronary flow obstruction, has also been proposed as an alternative to reduce the risk of thrombus formation. The aim of this study is to understand the impact of BASILICA on the valve-in-valve thrombogenicity using computational fluid dynamics simulations. To this end, two Eulerian and two Lagrangian approaches were employed to estimate near-wall stagnation measures in eight valve-in-valve models. The models included an intact or lacerated Sorin Mitroflow surgical valve, and either a SAPIEN or Evolut transcatheter aortic valve device. The Lagrangian approaches predicted a high number of particles and vortices concentration in the proximal areas of the neo-sinuses, while the Eulerian approaches did so in the distal areas. As a consequence, this study demonstrated that Lagrangian approaches are better predictors of subclinical leaflet thrombosis, since they match experimental and clinical findings. Additionally, the SAPIEN valve possess a higher risk for developing leaflet thrombosis, and two lacerations are shown to provide the best results in terms of development of vortices and accumulation of particles within the neo-sinuses. This study highlights the potential of computational modeling in aiding clinicians in their decision-making in valve-in-valve and BASILICA procedures.

A Distributed Lumped Parameter Model of Blood Flow

We propose a distributed lumped parameter (DLP) modeling framework to efficiently compute blood flow and pressure in vascular domains. This is achieved by developing analytical expressions describing expected energy losses along vascular segments, including from viscous dissipation, unsteadiness, flow separation, vessel curvature and vessel bifurcations. We apply this methodology to solve for unsteady blood flow and pressure in a variety of complex 3D image-based vascular geometries, which are typically approached using computational fluid dynamics (CFD) simulations. The proposed DLP framework demonstrated consistent agreement with CFD simulations in terms of flow rate and pressure distribution, with mean errors less than 7% over a broad range of hemodynamic conditions and vascular geometries. The computational cost of the DLP framework is orders of magnitude lower than the computational cost of CFD, which opens new possibilities for hemodynamics modeling in timely decision support scenarios, and a multitude of applications of imaged-based modeling that require ensembles of numerical simulations.

Numerical models for assessing the risk of leaflet thrombosis post-transcatheter aortic valve-in-valve implantation

Leaflet thrombosis has been suggested as the reason for the reduced leaflet motion in cases of hypoattenuated leaflet thickening of bioprosthetic aortic valves. This work aimed to estimate the risk of leaflet thrombosis in two post-valve-in-valve (ViV) configurations, using five different numerical approaches. Realistic ViV configurations were calculated by modelling the deployments of the latest version of transcatheter aortic valve devices (Medtronic Evolut PRO, Edwards SAPIEN 3) in the surgical Sorin Mitroflow. Computational fluid dynamics simulations of blood flow followed the dry models. Lagrangian and Eulerian measures of near-wall stagnation were implemented by particle and concentration tracking, respectively, to estimate the thrombogenicity and to predict the risk locations. Most of the numerical approaches indicate a higher leaflet thrombosis risk in the Edwards SAPIEN 3 device because of its intra-annular implantation. The Eulerian approaches estimated high-risk locations in agreement with the wall sheer stress (WSS) separation points. On the other hand, the Lagrangian approaches predicted high-risk locations at the proximal regions of the leaflets matching the low WSS magnitude regions of both transcatheter aortic valve implantation models and reported clinical and experimental data. The proposed methods can help optimizing future designs of transcatheter aortic valves with minimal thrombotic risks.

Fluid-Structure Interaction Simulation of an Intra-Atrial Fontan Connection

Simple Summary

A fluid-structure interaction (FSI) simulation of an intra-atrial Fontan connection was performed. Power loss and pressure drop results fluctuated less during the FSI simulation than during the simulation run with rigid walls, but there were no observable differences in time-averaged pressure drop, connection power loss or hepatic flow distribution. These results suggested that employing a rigid wall is a reasonable assumption when evaluating time-averaged hemodynamic quantities of the Fontan connection under resting breath-held flow conditions.

Abstract

Total cavopulmonary connection (TCPC) hemodynamics has been hypothesized to be associated with long-term complications in single ventricle heart defect patients. Rigid wall assumption has been commonly used when evaluating TCPC hemodynamics using computational fluid dynamics (CFD) simulation. Previous study has evaluated impact of wall compliance on extra-cardiac TCPC hemodynamics using fluid-structure interaction (FSI) simulation. However, the impact of ignoring wall compliance on the presumably more compliant intra-atrial TCPC hemodynamics is not fully understood. To narrow this knowledge gap, this study aims to investigate impact of wall compliance on an intra-atrial TCPC hemodynamics. A patient-specific model of an intra-atrial TCPC is simulated with an FSI model. Patient-specific 3D TCPC anatomies were reconstructed from transverse cardiovascular magnetic resonance images. Patient-specific vessel flow rate from phase-contrast magnetic resonance imaging (MRI) at the Fontan pathway and the superior vena cava under resting condition were prescribed at the inlets. From the FSI simulation, the degree of wall deformation was compared with in vivo wall deformation from phase-contrast MRI data as validation of the FSI model. Then, TCPC flow structure, power loss and hepatic flow distribution (HFD) were compared between rigid wall and FSI simulation. There were differences in instantaneous pressure drop, power loss and HFD between rigid wall and FSI simulations, but no difference in the time-averaged quantities. The findings of this study support the use of a rigid wall assumption on evaluation of time-averaged intra-atrial TCPC hemodynamic metric under resting breath-held condition.

A Mixture Theory Model for Blood Combined With Low-Density Lipoprotein Transport to Predict Early Atherosclerosis Regions in Idealized and Patient-Derived Abdominal Aorta

Genesis and onset of atherosclerosis are greatly influenced by hemodynamic forces. Two-phase transient computational fluid dynamic (CFD) simulations are performed using a mixture theory model for blood, and a transport equation for low-density lipoprotein (LDL), in idealized and patient-derived abdominal aorta to predict the sites at risk for atherosclerosis. Flow patterns at different time instants and relevant hemodynamic indicators-wall shear stress (WSS)-based (time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), and relative residence time (RRT)), and LDL concentration-are used concurrently to predict the susceptible sites of atherosclerosis. In the case of idealized geometry, flow recirculations are observed on the posterior wall opposite the superior mesenteric artery and below the renal bifurcations. Low TAWSS, high OSI, high RRT and high concentration of LDL are observed in these regions. This suggests that in idealized abdominal aorta, the posterior wall proximal to the renal artery junction is more prone to atherosclerosis. This matches qualitatively with the experimental and simulation data in the literature. In the case of patient-derived geometry, flow reversal, low TAWSS, high OSI and high RRT are observed infrarenal on the anterior wall. Further, high concentration of LDL is observed at the same location on the anterior wall suggesting anterior wall distal to the renal artery junction is more prone to atherosclerosis. These findings demonstrate the use of a novel method to predict the sites at risk for atherosclerosis in geometries where complexities like junctions and curvature play a major role.

Transport of blood particles: Chaotic advection even in a healthy scenario

We study the advection of blood particles in the carotid bifurcation, a site that is prone to plaque development. Previously, it has been shown that chaotic advection can take place in blood flows with diseases. Here, we show that even in a healthy scenario, chaotic advection can take place. To understand how the particle dynamics is affected by the emergence and growth of a plaque, we study the carotid bifurcation in three cases: a healthy bifurcation, a bifurcation with a mild stenosis, and the another with a severe stenosis. The result is non-intuitive: there is less chaos for the mild stenosis case even when compared to the healthy, non-stenosed, bifurcation. This happens because the partial obstruction of the mild stenosis generates a symmetry in the flow that does not exist for the healthy condition. For the severe stenosis, there is more irregular motion and more particle trapping as expected.

Understanding the effect of effective metal surface area of flow diverter stent's on the patient-specific intracranial aneurysm numerical model using Lagrangian coherent structures

The effective metal surface area (EMSA) of flow diversions plays an essential role in the occlusion mechanism inside the aneurysm since the value of EMSA determines the amount of blood flow into the aneurysm sac. In the present study, three different models of a flow diverter stent, namely FRED 4017, FRED 4038, and FRED 4539, were virtually placed at the aneurysm neck of a 52-years-old female patient to identify the effect of EMSA on stagnation region formation inside the aneurysm sac. Lagrangian coherent structures (LCSs), hyperbolic time, and particle tracking analysis were employed to the velocity vectors obtained from computational fluid dynamics (CFD). It is noticed that use of FRED 4017 stent with 0.42 EMSA value caused nearly 40% of the weightless blood flow particles (more than FRED 4038 and FRED 4539) to stay inside the aneurysm while only 0.35% of the blood flow was remaining inside the aneurysm sac when no stent was placed into the aneurysm site. Furthermore, hyperbolic time computations illustrated the formation of stagnation fluid flow zones that can be associated with the residence time of the blood flow particles. Lastly, the results of hyperbolic time analysis are in good agreement with digital subtraction angiography (DSA) images taken in the clinic a few minutes after a FRED 4017 implantation.

Platelet activation via dynamic conformational changes of von Willebrand factor under shear

Shear-induced conformational changes of von Willebrand factor (VWF) play an important role in platelet activation. A novel approach describing VWF unfolding on the platelet surface under dynamic shear stress is proposed. Cumulative effect of dynamic shear on platelet activation via conformational changes of VWF is analysed. The critical condition of shear-induced platelet activation is formulated. The explicit expression for the threshold value of cumulative shear stress as a function of VWF multimer size is derived. The results open novel prospects for pharmacological regulation of shear-induced platelet activation through control of VWF multimers size distribution.

Computational prediction of hemodynamical and biomechanical alterations induced by aneurysm dilatation in patient-specific ascending thoracic aortas

The aim of the present work is to propose a robust computational framework combining computational fluid dynamics (CFD) and 4D flow MRI to predict the progressive changes in hemodynamics and wall rupture index (RPI) induced by aortic morphological evolutions in patients harboring ascending thoracic aortic aneurysms (ATAAs). An analytical equation has been proposed to predict the aneurysm progression based on age, sex, and body surface area. Parameters such as helicity, wall shear stress (WSS), time-averaged WSS, oscillatory shear index, relative residence time, and viscosity were evaluated for two patients at different stages of aneurysm growth, and compared with age-sex-matched healthy subjects. The study shows that evolution of hemodynamics and RPI, despite being very slow in ATAAs, is strongly affected by morphological alterations and, in turn could impact biomechanical factors and aortic mechanobiology. An aspect of the current work is that the patient-specific 4D MRI data sets were obtained with a follow-up of 1 year and the measured time-averaged velocity maps and flow eccentricity were compared with the CFD simulation for validation. The computational framework presented here is capable of capturing the blood flow patterns and the hemodynamic descriptors during the various stages of aneurysm growth. Further investigations will be conducted in order to verify these results on a larger cohort of patients and with long follow-up times to finally elucidate the link between deranged hemodynamics, AA geometry, and wall mechanical properties in ATAAs.

Magnetic Resonance Imaging Based Flow Field and Lagrangian Particle Tracking From a Left Ventricular Assist Device

This study explores the optimal left ventricular assist device (LVAD) cannula outflow configuration in a patient-specific replica of the aorta. The volumetric velocity field is measured using phase-contrast magnetic resonance imaging (PC-MRI) under a physiologically relevant steady flow. The effect of the LVAD outflow graft insertion site and anastomosis angle on the transport of embolic particles to cranial vessels is studied by solving the particle equation of motion for spheres in the range of 0.1-1.0 mm using the measured three-dimensional (3D) velocity field. Results show that for a given aorta anatomy, it is possible to design the cannula graft location and terminal curvature so that the probability of embolic transport to the cranial vessels is significantly minimized. This is particularly important since the complex flow pattern in each cannula case affects the embolic trajectories differently, and hence the common assumption that particles distribute by the volumetric flow division does not hold.

Quantifying hemodynamics within an aneurysm exposed to prolonged exercise levels

BACKGROUND AND OBJECTIVE

Non-invasive treatment of unruptured Abdominal Aortic Aneurysm involves subjecting the patients to certain physiological levels of the heart. Flow topology (Re_peak = 200-1200, frequency: f = 1.18-2.41 Hz) within an aneurysm geometry (2-D) under resting and exercise (mild and moderate) conditions are explored in the present study. Blood is assumed to be Newtonian in nature. Spatio-temporal evolution of the flow patterns and vorticity are established. Hemodynamic indicators (TAWSS and OSI), movement of vortex cores and Particle Residence Index (PRI) are quantified to select an optimum exercise level in attenuating the disease.

METHODS

The finite volume method is employed for numerical solutions using ANSYS-Fluent^Ⓡ software. The SIMPLE scheme has been used for the pressure-velocity coupling. Least Square cell-based method is used for the spatial discretization of the gradients. Second order upwind scheme is considered for discretization of the pressure term. Third order upwind (QUICK) scheme is used to discretize the momentum equation. First order Implicit Scheme was used for the discretization of the temporal terms. Discrete Phase Material (DPM) technique is employed throughout, to visualize the signature of particle deposits within the aneurysm.

RESULTS

Vortex impingement induces a pressure peak within the aneurysm (moderate) while the peaks are anchored at the proximal and distal ends under resting and mild conditions. Along the averaged flow separation zone, exercise increases the maximum TAWSS from 1.21 N/m² (mild) to 9.3 N/m² (moderate). The distal site is exposed to oscillatory loading (OSI = 0.5) under mild activity whereas the loading becomes distributed almost over the entire wall, when subjected to moderate conditions. This in turn, reduces the time involved in 50 percent clearance of particles (PRI = 0.5) from 10.56 s (resting) to 3.98 s (mild) and 0.87 s (moderate), respectively.

CONCLUSIONS

Resting conditions manifests the aneurysmal wall to recirculating fluid for most of cycle time. Moderate exercise exhibits the least particle clearance time, but it exposes the aneurysmal wall and the distal end to high pressure, which otherwise has low intensity under mild activity. This in turn establishes that mild exercise for prolonged duration can be an optimum level for non-invasive aneurysmal treatment.

A Eulerian method to analyze wall shear stress fixed points and manifolds in cardiovascular flows

Based upon dynamical systems theory, a fixed point of a vector field such as the wall shear stress (WSS) at the luminal surface of a vessel is a point where the vector field vanishes. Unstable/stable manifolds identify contraction/expansion regions linking fixed points. The significance of such WSS topological features lies in their strong link with "disturbed" flow features like flow stagnation, separation and reversal, deemed responsible for vascular dysfunction initiation and progression. Here, we present a Eulerian method to analyze WSS topological skeleton through the identification and classification of WSS fixed points and manifolds in complex vascular geometries. The method rests on the volume contraction theory and analyzes the WSS topological skeleton through the WSS vector field divergence and Poincar[Formula: see text] index. The method is here applied to computational hemodynamics models of carotid bifurcation and intracranial aneurysm. An in-depth analysis of the time dependence of the WSS topological skeleton along the cardiac cycle is provided, enriching the information obtained from cycle-average WSS. Among the main findings, it emerges that on the carotid bifurcation, instantaneous WSS fixed points co-localize with cycle-average WSS fixed points for a fraction of the cardiac cycle ranging from 0 to [Formula: see text]; a persistent instantaneous WSS fixed point confined on the aneurysm dome does not co-localize with the cycle-average low-WSS region. In conclusion, the here presented approach shows the potential to speed up studies on the physiological significance of WSS topological skeleton in cardiovascular flows, ultimately increasing the chance of finding mechanistic explanations to clinical observations.

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).

In Vitro Study of Particle Transport in Successively Bifurcating Vessels

To reach a predictive understanding of how particles travel through bifurcating vessels is of paramount importance in many biomedical settings, including embolization, thromboembolism, and drug delivery. Here we utilize an in vitro model in which solid particles are injected through a rigid vessel that symmetrically bifurcates in successive branching generations. The geometric proportion and fluid dynamics parameters are relevant to the liver embolization. The volumetric flow field is reconstructed via phase-contrast magnetic resonance imaging, from which the particle trajectories are calculated for a range of size and density using the particle equation of motion. The method is validated by directly tracking the injected particles via optical imaging. The results indicate that, opposite to the common assumption, the particles distribution is fundamentally different from the volumetric flow partition. In fact, the amount of delivered particles vary substantially between adjacent branches even when the flow is uniformly distributed. This is not due to the inertia of the particles, nor to gravity. The particle distribution is rather rooted in their different pathways, which in turn are linked to their release origin along the main vessel cross-section. Therefore, the tree geometry and the associated flow streamlines are the prime determinant of the particle fate, while local changes of volumetric flow rate to selected branches do not generally produce proportional changes of particle delivery.

Biomechanical Investigation of Disturbed Hemodynamics-Induced Tissue Degeneration in Abdominal Aortic Aneurysms Using Computational and Experimental Techniques

Abdominal aortic aneurysm (AAA) is the dilatation of the aorta beyond 50% of the normal vessel diameter. It is reported that 4-8% of men and 0.5-1% of women above 50 years of age bear an AAA and it accounts for ~15,000 deaths per year in the United States alone. If left untreated, AAA might gradually expand until rupture; the most catastrophic complication of the aneurysmal disease that is accompanied by a striking overall mortality of 80%. The precise mechanisms leading to AAA rupture remains unclear. Therefore, characterization of disturbed hemodynamics within AAAs will help to understand the mechanobiological development of the condition which will contribute to novel therapies for the condition. Due to geometrical complexities, it is challenging to directly quantify disturbed flows for AAAs clinically. Two other approaches for this investigation are computational modeling and experimental flow measurement. In computational modeling, the problem is first defined mathematically, and the solution is approximated with numerical techniques to get characteristics of flow. In experimental flow measurement, once the setup providing physiological flow pattern in a phantom geometry is constructed, velocity measurement system such as particle image velocimetry (PIV) enables characterization of the flow. We witness increasing number of applications of these complimentary approaches for AAA investigations in recent years. In this paper, we outline the details of computational modeling procedures and experimental settings and summarize important findings from recent studies, which will help researchers for AAA investigations and rupture mechanics.

Two closely-spaced Aneurysms of the Supraclinoid Internal Carotid Artery: How Does One Influence the Other?

The objective of this study was to use image-based CFD simulation techniques to analyze the impact that multiple closely spaced IAs of the supra-clinioid segment of the ICA have on each other's hemodynamic characteristics. The vascular geometry of fifteen (15) subjects with 2 IAs were gathered using a 3D clinical system. Two groups of computer models were created for each subject's vascular geometry: both IAs present (Model A) and after removal of one IA (Model B). Models were separated into two groups based on IA separation: tandem (one proximal and one distal) and tandem (aneurysms directly opposite on a vessel). Simulations using a pulsatile velocity waveform were solved by a commercial CFD solver. Proximal IAs altered flow into distal IAs (5 of 7), increasing flow energy and spatial-temporally averaged wall shear stress (STA-WSS: 3-50\% comparing Model A to B) while decreasing flow stability within distal IAs. Thus, proximal IAs may ``protect" a distal aneurysm from destructive remodeling due to flow stagnation. Among adjacent IAs, the presence of both IAs decreased each other's flow characteristics, lowering WSS (Model A to B) and increasing flow stability: all changes statistically significant (t-test p < 0.05). A negative relationship exists between the mean percent change in flow stability in relation to adjacent IA volume and ostium area. Closely spaced IAs impact hemodynamic alterations onto each other concerning flow energy, stressors and stability. Understanding these alterations may improve clinical management of closely-spaced IAs.

Impact of Intracranial Aneurysm Morphology and Rupture Status on the Particle Residence Time

BACKGROUND AND PURPOSE

Aneurysm hemodynamics play an important role in aneurysm growth and subsequent rupture. Within the available hemodynamic characteristics, particle residence time (PRT) is relatively unexplored. However, some studies have shown that PRT is related to thrombus formation and inflammation. The goal of this study is to evaluate the association between PRT and aneurysm rupture and morphology.

METHODS

We determined the PRT for 113 aneurysms (61 unruptured, 53 ruptured) based on computational fluid dynamic models. Virtual particles were injected into the parent vessel and followed during multiple cardiac cycles. PRT was defined as the time needed for 99% of the particles that entered an aneurysm to leave the aneurysm. Subsequently, we evaluated the association between PRT, rupture, and morphology (aneurysm type, presence of blebs, or multiple lobulations).

RESULTS

PRT showed no significant difference between unruptured (1.1 seconds interquartile range [IQR .39-2.0 seconds]) and ruptured aneurysms (1.2 seconds [IQR .47-2.3 seconds]). PRT was influenced by aneurysm morphology. Longer PRTs were seen in bifurcation aneurysms (1.3 seconds [IQR .54-2.4 seconds], P = .01) and aneurysms with blebs or multiple lobulations (1.92 seconds [IQR .94-2.8 seconds], P < .001). Four of five partially thrombosed aneurysms had a long residence time (>1.9 seconds).

CONCLUSIONS

Our study shows an influence of aneurysm morphology on PRT. Nevertheless, it suggests that PRT cannot be used to differentiate unruptured and ruptured aneurysms.

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.

Accounting for residence-time in blood rheology models: do we really need non-Newtonian blood flow modelling in large arteries?

Patient-specific computational fluid dynamics (CFD) is a promising tool that provides highly resolved haemodynamics information. The choice of blood rheology is an assumption in CFD models that has been subject to extensive debate. Blood is known to exhibit shear-thinning behaviour, and non-Newtonian modelling has been recommended for aneurysmal flows. Current non-Newtonian models ignore rouleaux formation, which is the key player in blood's shear-thinning behaviour. Experimental data suggest that red blood cell aggregation and rouleaux formation require notable red blood cell residence-time (RT) in a low shear rate regime. This study proposes a novel hybrid Newtonian and non-Newtonian rheology model where the shear-thinning behaviour is activated in high RT regions based on experimental data. Image-based abdominal aortic and cerebral aneurysm models are considered and highly resolved CFD simulations are performed using a minimally dissipative solver. Lagrangian particle tracking is used to define a backward particle RT measure and detect stagnant regions with increased rouleaux formation likelihood. Our novel RT-based non-Newtonian model shows a significant reduction in shear-thinning effects and provides haemodynamic results qualitatively identical and quantitatively close to the Newtonian model. Our results have important implications in patient-specific CFD modelling and suggest that non-Newtonian models should be revisited in large artery flows.

Quantification of near-wall hemodynamic risk factors in large-scale cerebral arterial trees

Detailed hemodynamic analysis of blood flow in pathological segments close to aneurysm and stenosis has provided physicians with invaluable information about the local flow patterns leading to vascular disease. However, these diseases have both local and global effects on the circulation of the blood within the cerebral tree. The aim of this paper is to demonstrate the importance of extending subject-specific hemodynamic simulations to the entire cerebral arterial tree with hundreds of bifurcations and vessels, as well as evaluate hemodynamic risk factors and waveform shape characteristics throughout the cerebral arterial trees. Angioarchitecture and in vivo blood flow measurement were acquired from healthy subjects and in cases with symptomatic intracranial aneurysm and stenosis. A global map of cerebral arterial blood flow distribution revealed regions of low to high hemodynamic risk that may significantly contribute to the development of intracranial aneurysms or atherosclerosis. Comparison of pre-intervention and post-intervention of pathological cases further shows large angular phase shift (~33.8°), and an augmentation of the peak-diastolic velocity. Hemodynamic indexes of waveform analysis revealed on average a 16.35% reduction in the pulsatility index after treatment from lesion site to downstream distal vessels. The lesion regions not only affect blood flow streamlines of the proximal sites but also generate pulse wave shift and disturbed flow in downstream vessels. This network effect necessitates the use of large-scale simulation to visualize both local and global effects of pathological lesions.

A parallel fluid-solid coupling model using LAMMPS and Palabos based on the immersed boundary method

The study of viscous fluid flow coupled with rigid or deformable solids has many applications in biological and engineering problems, e.g., blood cell transport, drug delivery, and particulate flow. We developed a partitioned approach to solve this coupled Multiphysics problem. The fluid motion was solved by Palabos (Parallel Lattice Boltzmann Solver), while the solid displacement and deformation was simulated by LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The coupling was achieved through the immersed boundary method (IBM). The code modeled both rigid and deformable solids exposed to flow. The code was validated with the Jeffery orbits of an ellipsoid particle in shear flow, red blood cell stretching test, and effective blood viscosity flowing in tubes. It demonstrated essentially linear scaling from 512 to 8192 cores for both strong and weak scaling cases. The computing time for the coupling increased with the solid fraction. An example of the fluid-solid coupling was given for flexible filaments (drug carriers) transport in a flowing blood cell suspensions, highlighting the advantages and capabilities of the developed code.

Hemodynamics in a giant intracranial aneurysm characterized by in vitro 4D flow MRI

Experimental and computational data suggest that hemodynamics play a critical role in the development, growth, and rupture of cerebral aneurysms. The flow structure, especially in aneurysms with a large sac, is highly complex and three-dimensional. Therefore, volumetric and time-resolved measurements of the flow properties are crucial to fully characterize the hemodynamics. In this study, phase-contrast Magnetic Resonance Imaging is used to assess the fluid dynamics inside a 3D-printed replica of a giant intracranial aneurysm, whose hemodynamics was previously simulated by multiple research groups. The physiological inflow waveform is imposed in a flow circuit with realistic cardiovascular impedance. Measurements are acquired with sub-millimeter spatial resolution for 16 time steps over a cardiac cycle, allowing for the detailed reconstruction of the flow evolution. Moreover, the three-dimensional and time-resolved pressure distribution is calculated from the velocity field by integrating the fluid dynamics equations, and is validated against differential pressure measurements using precision transducers. The flow structure is characterized by vortical motions that persist within the aneurysm sac for most of the cardiac cycle. All the main flow statistics including velocity, vorticity, pressure, and wall shear stress suggest that the flow pattern is dictated by the aneurysm morphology and is largely independent of the pulsatility of the inflow, at least for the flow regimes investigated here. Comparisons are carried out with previous computational simulations that used the same geometry and inflow conditions, both in terms of cycle-averaged and systolic quantities.

A comparison of hemodynamic metrics and intraluminal thrombus burden in a common iliac artery aneurysm

Aneurysms of the common iliac artery (CIAA) are typically found in association with an abdominal aortic aneurysm (AAA). Isolated CIAAs, in the absence of an AAA, are uncommon. Similar to AAAs, CIAA may develop intraluminal thrombus (ILT). As isolated CIAAs have a contralateral common iliac artery for comparison, they provide an opportunity to study the hemodynamic mechanisms behind ILT formation. In this study, we compared a large isolated CIAA and the contralateral iliac artery using computational fluid dynamics to determine if hemodynamic metrics correlate with the location of ILT. We performed a comprehensive computational fluid dynamics study and investigated the residence time of platelets and monocytes, velocity fields, time-averaged wall shear stress, oscillatory shear index, and endothelial cell activation potential. We then correlated these data to ILT burden determined with computed tomography. We found that high cell residence times, low time-averaged wall shear stress, high oscillatory shear index, and high endothelial cell activation potential all correlate with regions of ILT development. Our results show agreement with previous hypotheses of thrombus formation in AAA and provide insights into the computational hemodynamics of iliac artery aneurysms.

Extending the Power-Law Hemolysis Model to Complex Flows

Hemolysis (damage to red blood cells) is a long-standing problem in blood contacting devices, and its prediction has been the goal of considerable research. The most popular model relating hemolysis to fluid stresses is the power-law model, which was developed from experiments in pure shear only. In the absence of better data, this model has been extended to more complex flows by replacing the shear stress in the power-law equation with a von Mises-like scalar stress. While the validity of the scalar stress also remains to be confirmed, inconsistencies exist in its application, in particular, two forms that vary by a factor of 2 have been used. This article will clarify the proper extension of the power law to complex flows in a way that maintains correct results in the limit of pure shear.