Characterization of coherent structures in the cardiovascular system

Impact of wall displacements on the large-scale flow coherence in ascending aorta

In the context of aortic hemodynamics, uncertainties affecting blood flow simulations hamper their translational potential as supportive technology in clinics. Computational fluid dynamics (CFD) simulations under rigid-walls assumption are largely adopted, even though the aorta contributes markedly to the systemic compliance and is characterized by a complex motion. To account for personalized wall displacements in aortic hemodynamics simulations, the moving-boundary method (MBM) has been recently proposed as a computationally convenient strategy, although its implementation requires dynamic imaging acquisitions not always available in clinics. In this study we aim to clarify the real need for introducing aortic wall displacements in CFD simulations to accurately capture the large-scale flow structures in the healthy human ascending aorta (AAo). To do that, the impact of wall displacements is analyzed using subject-specific models where two CFD simulations are performed imposing (1) rigid walls, and (2) personalized wall displacements adopting a MBM, integrating dynamic CT imaging and a mesh morphing technique based on radial basis functions. The impact of wall displacements on AAo hemodynamics is analyzed in terms of large-scale flow patterns of physiological significance, namely axial blood flow coherence (quantified applying the Complex Networks theory), secondary flows, helical flow and wall shear stress (WSS). From the comparison with rigid-wall simulations, it emerges that wall displacements have a minor impact on the AAo large-scale axial flow, but they can affect secondary flows and WSS directional changes. Overall, helical flow topology is moderately affected by aortic wall displacements, whereas helicity intensity remains almost unchanged. We conclude that CFD simulations with rigid-wall assumption can be a valid approach to study large-scale aortic flows of physiological significance.

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.

Biomechanics of Hollow Organs: Experimental Testing and Computational Modeling

Hollow organs are visceral organs that are hollow tubes or pouches (such as the intestine or the stomach, respectively) or that include a cavity (such as the heart) and which subserve a vital function [...].

On non-Kolmogorov turbulence in blood flow and its possible role in mechanobiological stimulation

The study of turbulence in physiologic blood flow is important due to its strong relevance to endothelial mechanobiology and vascular disease. Recently, Saqr et al. (Sci Rep 10, 15,492, 2020) discovered non-Kolmogorov turbulence in physiologic blood flow in vivo, traced its origins to the Navier–Stokes equation and demonstrated some of its properties using chaos and hydrodynamic-stability theories. The present work extends these findings and investigates some inherent characteristics of non-Kolmogorov turbulence in monoharmonic and multiharmonic pulsatile flow under ideal physiologic conditions. The purpose of this work is to propose a conjecture for the origins for picoNewton forces that are known to regulate endothelial cells’ functions. The new conjecture relates these forces to physiologic momentum-viscous interactions in the near-wall region of the flow. Here, we used high-resolution large eddy simulation (HRLES) to study pulsatile incompressible flow in a straight pipe of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L/D=20$$\end{document}L/D=20. The simulations presented Newtonian and Carreau–Yasuda fluid flows, at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R{e}_{m}\approx 250$$\end{document}Rem≈250, each represented by one, two and three boundary harmonics. Comparison was established based on maintaining constant time-averaged mass flow rate in all simulations. First, we report the effect of primary harmonics on the global power budget using primitive variables in phase space. Second, we describe the non-Kolmogorov turbulence in frequency domain. Third, we investigate the near-wall coherent structures in time and space domains. Finally, we propose a new conjecture for the role of turbulence in endothelial cells’ mechanobiology. The proposed conjecture correlates near-wall turbulence to a force field of picoNewton scale, suggesting possible relevance to endothelial cells mechanobiology.

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.

Finite-horizon, energy-efficient trajectories in unsteady flows

Intelligent mobile sensors, such as uninhabited aerial or underwater vehicles, are becoming prevalent in environmental sensing and monitoring applications. These active sensing platforms operate in unsteady fluid flows, including windy urban environments, hurricanes and ocean currents. Often constrained in their actuation capabilities, the dynamics of these mobile sensors depend strongly on the background flow, making their deployment and control particularly challenging. Therefore, efficient trajectory planning with partial knowledge about the background flow is essential for teams of mobile sensors to adaptively sense and monitor their environments. In this work, we investigate the use of finite-horizon model predictive control (MPC) for the energy-efficient trajectory planning of an active mobile sensor in an unsteady fluid flow field. We uncover connections between trajectories optimized over a finite-time horizon and finite-time Lyapunov exponents of the background flow, confirming that energy-efficient trajectories exploit invariant coherent structures in the flow. We demonstrate our findings on the unsteady double gyre vector field, which is a canonical model for chaotic mixing in the ocean. We present an exhaustive search through critical MPC parameters including the prediction horizon, maximum sensor actuation, and relative penalty on the accumulated state error and actuation effort. We find that even relatively short prediction horizons can often yield energy-efficient trajectories. We also explore these connections on a three-dimensional flow and ocean flow data from the Gulf of Mexico. These results are promising for the adaptive planning of energy-efficient trajectories for swarms of mobile sensors in distributed sensing and monitoring.

Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-Bénard convection flows

We explore the transport mechanisms of heat in two- and three-dimensional turbulent convection flows by means of the long-term evolution of Lagrangian coherent sets. They are obtained from the spectral clustering of trajectories of massless fluid tracers that are advected in the flow. Coherent sets result from trajectories that stay closely together under the dynamics of the turbulent flow. For longer times, they are always destroyed by the intrinsic turbulent dispersion of material transport. Here, this constraint is overcome by the application of evolutionary clustering algorithms that add a time memory to the coherent set detection and allows individual trajectories to leak in or out of evolving clusters. Evolutionary clustering thus also opens the possibility to monitor the splits and mergers of coherent sets. These rare dynamic events leave clear footprints in the evolving eigenvalue spectrum of the Laplacian matrix of the trajectory network in both convection flows. The Lagrangian trajectories reveal the individual pathways of convective heat transfer across the fluid layer. We identify the long-term coherent sets as those fluid flow regions that contribute least to heat transfer. Thus, our evolutionary framework defines a complementary perspective on the slow dynamics of turbulent superstructure patterns in convection flows that were recently discussed in the Eulerian frame of reference. The presented framework might be well suited for studies in natural flows, which are typically based on sparse information from drifters and probes.

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.

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.

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.

Vortex dynamics and transport phenomena in stenotic aortic models using Echo-PIV

Atherosclerosis is the most fatal cardiovascular disease. As disease progresses, stenoses grow inside the arteries blocking their lumen and altering blood flow. Analysing flow dynamics can provide a deeper insight on the stenosis evolution. In this work we combined Eulerian and Lagrangian descriptors to analyze blood flow dynamics and fluid transport in stenotic aortic models with morphology, mechanical and optical properties close to those of real arteries. To this end, vorticity, particle residence time (PRT), particle's final position (FP) and finite time Lyapunov's exponents (FTLE) were computed from the experimental fluid velocity fields acquired using ultrasonic particle imaging velocimetry (Echo-PIV). For the experiments, CT-images were used to create morphological realistic models of the descending aorta with 0%, 35% and 50% occlusion degree with same mechanical properties as real arteries. Each model was connected to a circuit with a pulsatile programmable pump which mimics physiological flow and pressure conditions. The pulsatile frequency was set to ≈0.9 Hz (55 bpm) and the upstream peak Reynolds number (Re) was changed from 1100 to 2000. Flow in the post-stenotic region was composed of two main structures: a high velocity jet over the stenosis throat and a recirculation region behind the stenosis where vortex form and shed. We characterized vortex kinematics showing that vortex propagation velocity increases withRe. Moreover, from the FTLE field we identified Lagrangian coherent structures (i.e. material barriers) that dictate transport behind the stenosis. The size and strength of those barriers increased withReand the occlusion degree. Finally, from the PRT and FP maps, we showed that independently ofRe, the same amount of fluid remains on the stenosis over more than a pulsatile period.

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.

Computational investigation of blood flow and flow-mediated transport in arterial thrombus neighborhood

A pathologically formed blood clot or thrombus is central to major cardiovascular diseases like heart attack and stroke. Detailed quantitative evaluation of flow and flow-mediated transport processes in the thrombus neighborhood within large artery hemodynamics is crucial for understanding disease progression and assessing treatment efficacy. This, however, remains a challenging task owing to the complexity of pulsatile viscous flow interactions with arbitrary shape and heterogeneous microstructure of realistic thrombi. Here, we address this challenge by conducting a systematic parametric simulation-based study on characterizing unsteady hemodynamics and flow-mediated transport in the neighborhood of an arterial thrombus. We use a hybrid particle-continuum-based finite element approach to handle arbitrary thrombus shape and microstructural variations. Results from a cohort of 50 different unsteady flow scenarios are presented, including unsteady vortical structures, pressure gradient across the thrombus boundary, finite time Lyapunov exponents, and dynamic coherent structures that organize advective transport. We clearly illustrate the combined influence of three key parameters-thrombus shape, microstructure, and extent of wall disease-in terms of: (a) determining hemodynamic features in the thrombus neighborhood and (b) governing the balance between advection, permeation, and diffusion to regulate transport processes in the thrombus neighborhood.

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.

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.

Fluid dynamics of thoracic cavity venous flow in multiple sclerosis

This paper hypothesizes, based on fluid dynamics principles, that in multiple sclerosis (MS) non-laminar, vortex blood flow occurs in the superior vena cava (SVC) and brachiocephalic veins (BVs), particularly at junctions with their tributary veins. The physics-based analysis demonstrates that the morphology and physical attributes of the major thoracic veins, and their tributary confluent veins, together with the attributes of the flowing blood, predict transition from laminar to non-laminar flow, primarily vortex flow, at select vein curvatures and junctions. Non-laminar, vortex flow results in the development of immobile stenotic valves and intraluminal flow obstructions, particularly in the internal jugular veins (IJVs) and in the azygos vein (AV) at their confluences with the SVC or BVs. Clinical trials' observations of vascular flow show that regions of low and reversing flow are associated with endothelial malformation. The physics-based analysis predicts the growth of intraluminal flaps and septa at segments of vein curvature and flow confluences. The analysis demonstrates positive correlations between predicted and clinically observed elongation of valve leaflets and between the predicted and observed prevalence of immobile valves at various venous flow confluences. The analysis predicts the formation of sclerotic plaques at venous junctions and curvatures, in locations that are analogous to plaques in atherosclerosis. The analysis predicts that increasing venous compliance increases the laminarity of venous flow and reduces the prevalence and severity of vein malformations and plaques, a potentially significant clinical result. An over-arching observation is that the correlations between predicted phenomena and clinically observed phenomena are sufficiently positive that the physics-based approach represents a new means for understanding the relationships between venous flow in MS and clinically observed venous malformations.

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.

Modeling the odor-landscape resulting from the pumping behavior of bivalve clams in the presence of predators

Motivated by experimental findings, a computational fluid dynamics (CFD) model was used to investigate whether the clam Mercenaria mercenaria may alter its cue downstream variability by an exhalant random pumping behavior. This behavior was hypothesized to occur in the presence of predator chemical signals in order to prevent successful tracking by the predator. Simulated downstream flow and mixing conditions derived from the random nature of the clam exhalant jet in a crossflow were analyzed by computing an intermittency factor, determining the field of finite-time Lyapunov exponents (FTLEs) and identifying the resulting Lagrangian coherent structures (LCSs). Numerical simulations illustrate that the effectiveness of a fluctuating exhalant jet to prevent downstream tracking by a crab, depends on the ratio of the exhalant jet to the crossflow. Specifically, the clam could effectively enhance the downstream dispersion to prevent tracking, but only in the range of parameters where LCSs are generated (jet-to-crossflow ratio ≥ 1). Then, the probability of detection is reduced with respect to the case of a less fluctuating exhalant jet.

Hemodynamics-driven deposition of intraluminal thrombus in abdominal aortic aneurysms

Accumulating evidence suggests that intraluminal thrombus plays many roles in the natural history of abdominal aortic aneurysms. There is, therefore, a pressing need for computational models that can describe and predict the initiation and progression of thrombus in aneurysms. In this paper, we introduce a phenomenological metric for thrombus deposition potential and use hemodynamic simulations based on medical images from 6 patients to identify best-fit values of the 2 key model parameters. We then introduce a shape optimization method to predict the associated radial growth of the thrombus into the lumen based on the expectation that thrombus initiation will create a thrombogenic surface, which in turn will promote growth until increasing hemodynamically induced frictional forces prevent any further cell or protein deposition. Comparisons between predicted and actual intraluminal thrombus in the 6 patient-specific aneurysms suggest that this phenomenological description provides a good first estimate of thrombus deposition. We submit further that, because the biologically active region of the thrombus appears to be confined to a thin luminal layer, predictions of morphology alone may be sufficient to inform fluid-solid-growth models of aneurysmal growth and remodeling.

SimVascular: An Open Source Pipeline for Cardiovascular Simulation

Patient-specific cardiovascular simulation has become a paradigm in cardiovascular research and is emerging as a powerful tool in basic, translational and clinical research. In this paper we discuss the recent development of a fully open-source SimVascular software package, which provides a complete pipeline from medical image data segmentation to patient-specific blood flow simulation and analysis. This package serves as a research tool for cardiovascular modeling and simulation, and has contributed to numerous advances in personalized medicine, surgical planning and medical device design. The SimVascular software has recently been refactored and expanded to enhance functionality, usability, efficiency and accuracy of image-based patient-specific modeling tools. Moreover, SimVascular previously required several licensed components that hindered new user adoption and code management and our recent developments have replaced these commercial components to create a fully open source pipeline. These developments foster advances in cardiovascular modeling research, increased collaboration, standardization of methods, and a growing developer community.

Fast Coherent Particle Advection through Time-Varying Unstructured Flow Datasets

Tracing the paths of collections of particles through a flow field is a key step for many flow visualization and analysis methods. When a flow field is interpolated from the nodes of an unstructured mesh, the process of advecting a particle must first find which cell in the unstructured mesh contains the particle. Since the paths of nearby particles often diverge, the parallelization of particle advection quickly leads to incoherent memory accesses of the unstructured mesh. We have developed a new block advection GPU approach that reorganizes particles into spatially coherent bundles as they follow their advection paths, which greatly improves memory coherence and thus shared-memory GPU performance. This approach works best for flows that meet the CFL criterion on unstructured meshes of uniformly sized elements, small enough to fit at least two timesteps in GPU memory.

Numerical analysis of blood flow through an elliptic stenosis using large eddy simulation

The presence of a stenosis caused by the abnormal narrowing of the lumen in the artery tree can cause significant variations in flow parameters of blood. The original flow, which is believed to be laminar in most situations, may turn out to turbulent by the geometric perturbation created by the stenosis. Flow may evolve to fully turbulent or it may relaminarise back according to the intensity of the perturbation. This article reports the numerical simulation of flow through an eccentrically located asymmetric stenosis having elliptical cross section using computational fluid dynamics. Large eddy simulation technique using dynamic Smagorinsky sub-grid scale model is applied to capture the turbulent features of flow. Analysis is carried out for two situations: steady inflow as ideal condition and pulsatile inflow corresponding to the actual physiological condition in common carotid artery. The spatially varying pulsatile inflow waveforms are mathematically derived from instantaneous mass flow measurements available in the literature. Carreau viscosity model is used to estimate the effect of non-Newtonian nature of blood. The present simulations for steady and pulsatile conditions show that post-stenotic flow field undergoes transition to turbulence in all cases. The characteristics of mean and turbulent flow fields have been presented and discussed in detail.

An anatomy-based lumped parameter model of cerebrospinal venous circulation: can an extracranial anatomical change impact intracranial hemodynamics?

BACKGROUND

The relationship between extracranial venous system abnormalities and central nervous system disorders has been recently theorized. In this paper we delve into this hypothesis by modeling the venous drainage in brain and spinal column areas and simulating the intracranial flow changes due to extracranial morphological stenoses.

METHODS

A lumped parameter model of the cerebro-spinal venous drainage was created based on anatomical knowledge and vessels diameters and lengths taken from literature. Each vein was modeled as a hydraulic resistance, calculated through Poiseuille's law. The inputs of the model were arterial flow rates of the intracranial, vertebral and lumbar districts. The effects of the obstruction of the main venous outflows were simulated. A database comprising 112 Multiple Sclerosis patients (Male/Female = 42/70; median age ± standard deviation = 43.7 ± 10.5 years) was retrospectively analyzed.

RESULTS

The flow rate of the main veins estimated with the model was similar to the measures of 21 healthy controls (Male/Female = 10/11; mean age ± standard deviation = 31 ± 11 years), obtained with a 1.5 T Magnetic Resonance scanner. The intracranial reflux topography predicted with the model in cases of internal jugular vein diameter reduction was similar to those observed in the patients with internal jugular vein obstacles.

CONCLUSIONS

The proposed model can predict physiological and pathological behaviors with good fidelity. Despite the simplifications introduced in cerebrospinal venous circulation modeling, the key anatomical feature of the lumped parameter model allowed for a detailed analysis of the consequences of extracranial venous impairments on intracranial pressure and hemodynamics.

Mechanical platelet activation potential in abdominal aortic aneurysms

Intraluminal thrombus (ILT) in abdominal aortic aneurysms (AAA) has potential implications to aneurysm growth and rupture risk; yet, the mechanisms underlying its development remain poorly understood. Some researchers have proposed that ILT development may be driven by biomechanical platelet activation within the AAA, followed by adhesion in regions of low wall shear stress. Studies have investigated wall shear stress levels within AAA, but platelet activation potential (AP) has not been quantified. In this study, patient-specific computational fluid dynamic (CFD) models were used to analyze stress-induced AP within AAA under rest and exercise flow conditions. The analysis was conducted using Lagrangian particle-based and Eulerian continuum-based approaches, and the results were compared. Results indicated that biomechanical platelet activation is unlikely to play a significant role for the conditions considered. No consistent trend was observed in comparing rest and exercise conditions, but the functional dependence of AP on stress magnitude and exposure time can have a large impact on absolute levels of anticipated platelet AP. The Lagrangian method obtained higher peak AP values, although this difference was limited to a small percentage of particles that falls below reported levels of physiologic background platelet activation.

A haemodynamic predictor of intraluminal thrombus formation in abdominal aortic aneurysms

Intraluminal thrombus (ILT) is present in over 75% of all abdominal aortic aneurysms (AAAs) and probably contributes to the complex biomechanics and pathobiology of these lesions. A reliable predictor of thrombus formation in enlarging lesions could thereby aid clinicians in treatment planning. The primary goal of this work was to identify a new phenomenological metric having clinical utility that is motivated by the hypothesis that two basic haemodynamic features must coincide spatially and temporally to promote the formation of a thrombus on an intact endothelium—platelets must be activated within a shear flow and then be presented to a susceptible endothelium. Towards this end, we propose a new thrombus formation potential (TFP) that combines information on the flow-induced shear history experienced by blood-borne particles that come in close proximity to the endothelium with information on both the time-averaged wall shear stress (WSS) and the oscillatory shear index (OSI) that locally affect the endothelial mechanobiology. To illustrate the possible utility of this new metric, we show computational results for 10 carotid arteries from five patients where regions of low WSS and high OSI tend not to be presented with activated platelets (i.e. they have a low TFP), consistent with the thrombo-resistance of the healthy carotid despite its complex haemodynamics. Conversely, we show results for three patients that high TFP co-localizes with regions of observed thin thrombus in AAAs, which contrasts with findings of low TFP for the abdominal aorta of three healthy subjects. We submit that these promising results suggest the need for further consideration of the TFP, or a similar combined metric, as a potentially useful clinical predictor of the possible formation of ILT in AAAs.

A longitudinal comparison of hemodynamics and intraluminal thrombus deposition in abdominal aortic aneurysms

Abdominal aortic aneurysm (AAA) is often accompanied by in traluminal thrombus (ILT), which complicates AAA progression and risk of rupture. Patient-specific computational fluid dynamics modeling of 10 small human AAA was performed to investigate relations between hemodynamics and ILT progression. The patients were imaged using magnetic resonance twice in a 2- to 3-yr interval. Wall content data were obtained by a planar T1-weighted fast spin echo black-blood scan, which enabled quantification of thrombus thickness at midaneurysm location during baseline and followup. Computational simulations with patient-specific geometry and boundary conditions were performed to quantify the hemodynamic parameters of time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), and mean exposure time at baseline. Spatially resolved quantifications of the change in ILT thickness were compared with the different hemodynamic parameters. Regions of low OSI had the strongest correlation with ILT growth and demonstrated a statistically significant correlation coefficient. Prominent regions of high OSI (>0.4) and low TAWSS (<1 dyn/cm(2)) did not appear to coincide with locations of thrombus deposition.

Lagrangian postprocessing of computational hemodynamics

Recent advances in imaging, modeling, and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries, and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform Lagrangian particle tracking, and other Lagrangian-based postprocessing. As described herein, Lagrangian methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review Lagrangian methods that have been used in post-processing velocity data of cardiovascular flows.

Thrombotic risk stratification using computational modeling in patients with coronary artery aneurysms following Kawasaki disease

Kawasaki disease (KD) is the leading cause of acquired heart disease in children and can result in life-threatening coronary artery aneurysms in up to 25 % of patients. These aneurysms put patients at risk of thrombus formation, myocardial infarction, and sudden death. Clinicians must therefore decide which patients should be treated with anticoagulant medication, and/or surgical or percutaneous intervention. Current recommendations regarding initiation of anticoagulant therapy are based on anatomy alone with historical data suggesting that patients with aneurysms [Formula: see text]8 mm are at greatest risk of thrombosis. Given the multitude of variables that influence thrombus formation, we postulated that hemodynamic data derived from patient-specific simulations would more accurately predict risk of thrombosis than maximum diameter alone. Patient-specific blood flow simulations were performed on five KD patients with aneurysms and one KD patient with normal coronary arteries. Key hemodynamic and geometric parameters, including wall shear stress, particle residence time, and shape indices, were extracted from the models and simulations and compared with clinical outcomes. Preliminary fluid structure interaction simulations with radial expansion were performed, revealing modest differences in wall shear stress compared to the rigid wall case. Simulations provide compelling evidence that hemodynamic parameters may be a more accurate predictor of thrombotic risk than aneurysm diameter alone and motivate the need for follow-up studies with a larger cohort. These results suggest that a clinical index incorporating hemodynamic information be used in the future to select patients for anticoagulant therapy.

Effect of exercise on patient specific abdominal aortic aneurysm flow topology and mixing

Computational fluid dynamics modeling was used to investigate changes in blood transport topology between rest and exercise conditions in five patient-specific abdominal aortic aneurysm models. MRI was used to provide the vascular anatomy and necessary boundary conditions for simulating blood velocity and pressure fields inside each model. Finite-time Lyapunov exponent fields and associated Lagrangian coherent structures were computed from blood velocity data and were used to compare features of the transport topology between rest and exercise both mechanistically and qualitatively. A mix-norm and mix-variance measure based on fresh blood distribution throughout the aneurysm over time were implemented to quantitatively compare mixing between rest and exercise. Exercise conditions resulted in higher and more uniform mixing and reduced the overall residence time in all aneurysms. Separated regions of recirculating flow were commonly observed in rest, and these regions were either reduced or removed by attached and unidirectional flow during exercise, or replaced with regional chaotic and transiently turbulent mixing, or persisted and even extended during exercise. The main factor that dictated the change in flow topology from rest to exercise was the behavior of the jet of blood penetrating into the aneurysm during systole.

A novel multiblock immersed boundary method for large eddy simulation of complex arterial hemodynamics

Computational fluid dynamics (CFD) simulations are becoming a reliable tool to understand hemodynamics, disease progression in pathological blood vessels and to predict medical device performance. Immersed boundary method (IBM) emerged as an attractive methodology because of its ability to efficiently handle complex moving and rotating geometries on structured grids. However, its application to study blood flow in complex, branching, patient-specific anatomies is scarce. This is because of the dominance of grid nodes in the exterior of the fluid domain over the useful grid nodes in the interior, rendering an inevitable memory and computational overhead. In order to alleviate this problem, we propose a novel multiblock based IBM that preserves the simplicity and effectiveness of the IBM on structured Cartesian meshes and enables handling of complex, anatomical geometries at a reduced memory overhead by minimizing the grid nodes in the exterior of the fluid domain. As pathological and medical device hemodynamics often involve complex, unsteady transitional or turbulent flow fields, a scale resolving turbulence model such as large eddy simulation (LES) is used in the present work. The proposed solver (here after referred as WenoHemo), is developed by enhancing an existing in-house high order incompressible flow solver that was previously validated for its numerics and several LES models by Shetty et al. [Journal of Computational Physics 2010; 229 (23), 8802-8822]. In the present work, WenoHemo is systematically validated for additional numerics introduced, such as IBM and the multiblock approach, by simulating laminar flow over a sphere and laminar flow over a backward facing step respectively. Then, we validate the entire solver methodology by simulating laminar and transitional flow in abdominal aortic aneurysm (AAA). Finally, we perform blood flow simulations in the challenging clinically relevant thoracic aortic aneurysm (TAA), to gain insights into the type of fluid flow patterns that exist in pathological blood vessels. Results obtained from the TAA simulations reveal complex vortical and unsteady flow fields that need to be considered in designing and implanting medical devices such as stent grafts.

Simulation based planning of surgical interventions in pediatric cardiology

Hemodynamics plays an essential role in the progression and treatment of cardiovascular disease. However, while medical imaging provides increasingly detailed anatomical information, clinicians often have limited access to hemodynamic data that may be crucial to patient risk assessment and treatment planning. Computational simulations can now provide detailed hemodynamic data to augment clinical knowledge in both adult and pediatric applications. There is a particular need for simulation tools in pediatric cardiology, due to the wide variation in anatomy and physiology in congenital heart disease patients, necessitating individualized treatment plans. Despite great strides in medical imaging, enabling extraction of flow information from magnetic resonance and ultrasound imaging, simulations offer predictive capabilities that imaging alone cannot provide. Patient specific simulations can be used for in silico testing of new surgical designs, treatment planning, device testing, and patient risk stratification. Furthermore, simulations can be performed at no direct risk to the patient. In this paper, we outline the current state of the art in methods for cardiovascular blood flow simulation and virtual surgery. We then step through pressing challenges in the field, including multiscale modeling, boundary condition selection, optimization, and uncertainty quantification. Finally, we summarize simulation results of two representative examples from pediatric cardiology: single ventricle physiology, and coronary aneurysms caused by Kawasaki disease. These examples illustrate the potential impact of computational modeling tools in the clinical setting.

Topology of blood transport in the human left ventricle by novel processing of Doppler echocardiography

Novel processing of Doppler-echocardiography data was used to study blood transport in the left ventricle (LV) of six patients with dilated cardiomyopathy and six healthy volunteers. Bi-directional velocity field maps in the apical long axis of the LV were reconstructed from color-Doppler echocardiography. Resulting velocity field data were used to perform trajectory-based computation of Lagrangian coherent structures (LCS). LCS were shown to reveal the boundaries of blood injected and ejected from the heart over multiple beats. This enabled qualitative and quantitative assessments of blood transport patterns and residence times in the LV. Quantitative assessments of stasis in the LV are reported, as well as characterization of LV vortex formations from E-wave and A-wave filling.

Lagrangian analysis of hemodynamics data from FSI simulation

We present the computation of lagrangian-based flow characterization measures for time-dependent, deformable-wall, finite-element blood flow simulations. Applicability of the algorithm is demonstrated in a fluid-structure interaction simulation of blood flow through a total cavopulmonary connection (Fontan procedure), and results are compared with a rigid-vessel simulation. Specifically, we report on several important lagrangian-based measures including flow distributions, finite-time Lyapunov exponent fields, particle residence time, and exposure time calculations. Overall, strong similarity in lagrangian measures of the flow between deformable and rigid-vessel models was observed.

Optimization of a Y-Graft Design for Improved Hepatic Flow Distribution in the Fontan Circulation

Single ventricle heart defects are among the most serious congenital heart diseases, and are uniformly fatal if left untreated. Typically, a three-staged surgical course, consisting of the Norwood, Glenn, and Fontan surgeries is performed, after which the superior vena cava (SVC) and inferior vena cava (IVC) are directly connected to the pulmonary arteries (PA). In an attempt to improve hemodynamic performance and hepatic flow distribution (HFD) of Fontan patients, a novel Y-shaped graft has recently been proposed to replace the traditional tube-shaped extracardiac grafts. Previous studies have demonstrated that the Y-graft is a promising design with the potential to reduce energy loss and improve HFD. However these studies also found suboptimal Y-graft performance in some patient models. The goal of this work is to determine whether performance can be improved in these models through further design optimization. Geometric and hemodynamic factors that influence the HFD have not been sufficiently investigated in previous work, particularly for the Y-graft. In this work, we couple Lagrangian particle tracking to an optimal design framework to study the effects of boundary conditions and geometry on HFD. Specifically, we investigate the potential of using a Y-graft design with unequal branch diameters to improve hepatic distribution under a highly uneven RPA/LPA flow split. As expected, the resulting optimal Y-graft geometry largely depends on the pulmonary flow split for a particular patient. The unequal branch design is demonstrated to be unnecessary under most conditions, as it is possible to achieve the same or better performance with equal-sized branches. Two patient-specific examples show that optimization-derived Y-grafts effectively improve the HFD, compared to initial nonoptimized designs using equal branch diameters. An instance of constrained optimization shows that energy efficiency slightly increases with increasing branch size for the Y-graft, but that a smaller branch size is preferred when a proximal anastomosis is needed to achieve optimal HFD.

A robust and efficient valve model based on resistive immersed surfaces

A procedure for modeling the heart valves is presented. Instead of modeling complete leaflet motion, leaflets are modeled in open and closed configurations. The geometry of each configuration can be defined, for example, from in vivo image data. This method enables significant computational savings compared with complete fluid-structure interaction and contact modeling, while maintaining realistic three-dimensional velocity and pressure distributions near the valve, which is not possible from lumped parameter modeling. Leaflets are modeled as immersed, fixed surfaces over which a resistance to flow is assigned. On the basis of local flow conditions, the resistance values assigned for each configuration are changed to switch the valve between open and closed states. This formulation allows for the pressure to be discontinuous across the valve. To illustrate the versatility of the model, realistic and patient-specific simulations are presented, as well as comparison with complete fluid-structure interaction simulation.