Computational Hemodynamics Research Articles

Near-Wall Flow in Cerebral Aneurysms

The region where the vascular lumen meets the surrounding endothelium cell layer, hence the interface region between haemodynamics and cell tissue, is of primary importance in the physiological functions of the cardiovascular system. The functions include mass transport to/from the blood and tissue, and signalling via mechanotransduction, which are primary functions of the cardiovascular system and abnormalities in these functions are known to affect disease formation and vascular remodelling. This region is denoted by the near-wall region in the present work, and we outline simple yet effective numerical recipes to analyse the near-wall flow field. Computational haemodynamics solutions are presented for six patient specific cerebral aneurysms, at three instances in the cardiac cycle: peak systole, end systole (taken as dicrotic notch) and end diastole. A sensitivity study, based on Newtonian and non-Newtonian rheological models, and different flow rate profiles, is effected for a selection of aneurysm cases. The near-wall flow field is described by the wall shear stress (WSS) and the divergence of wall shear stress (WSSdiv), as descriptors of tangential and normal velocity components, respectively, as well as the wall shear stress critical points. Relations between near-wall and free-stream flow fields are discussed.

Reaching a good agreement between computational hemodynamics results and in vitro data is not enough

Because many cardiovascular diseases are related to blood flow features, being able to predict how blood flows would open a window towards better diagnostic and treatment capabilities. To this resp...

Spatiotemporal Hemodynamic Complexity in Carotid Arteries: An Integrated Computational Hemodynamics and Complex Networks-Based Approach.

The study of the arterial hemodynamics is essential for a better understanding of the risks associated with the onset/progression of vascular disease. However, conventional quantification and visualization paradigms are not sufficient to fully capture the spatiotemporal evolution of correlated blood flow patterns and their "sphere of influence" in complex vascular geometries. In the attempt to bridge this knowledge gap, an integrated computational hemodynamics and complex networks-based approach is proposed to unveil organization principles of cardiovascular flows. The approach is applied to ten patient-specific hemodynamic models of carotid bifurcation, a vascular bed characterized by a complex hemodynamics and clinically-relevant disease. Correlation-based networks are built starting from time-histories of two fluid mechanics quantities of physiological significance, respectively (1) the blood velocity vector axial component locally aligned with the main flow direction, and (2) the kinetic helicity density. Unlike conventional hemodynamic analyses, here the spatiotemporal similarity of dynamic intravascular flow structures is encoded in a distance function. In the case of the carotid bifurcation, this study measures for the first time to what extent flow similarity is disrupted by vascular geometric features. It emerges that a larger bifurcation expansion, a hallmark of vascular disease, significantly disrupts the network topological connections between axial flow structures, reducing also their anatomical persistence length. On the contrary, connections in helical flow patterns are overall less geometry-sensitive. The integrated approach proposed here, by exploiting the connections of hemodynamic patterns undergoing similar dynamical evolution, opens avenues for further comprehension of vascular physiopathology.

Optimal B-spline Mapping of Flow Imaging Data for Imposing Patient-specific Velocity Profiles in Computational Hemodynamics.

Objective:We propose a novel method to obtainmap patient-specific blood velocity profiles (obtained from imaging data such as 2D flow MRI or 3D colour Doppler ultrasound) and map them to geometric vascular models suitable to perform CFD simulations of haemodynamics. We describe the implementation and utilisation of the method within an open-source computational hemodynamics simulation software (CRIMSON).Methods:tThe proposed method establishes point-wise correspondences between the contour of a fixed geometric model and time-varying contours containing the velocity image data, from which a continuous, smooth and cyclic deformation field is calculated. Our methodology is validated using synthetic data, and demonstrated using two different in-vivo aortic velocity datasets: a healthy subject with normal tricuspid valve and a patient with bicuspid aortic valve.Results:We compare the performance of our method with results obtained with the state-of-the-art Schwarz-Christoffel method, in terms of preservation of velocities and execution time. Our method is as accurate as the Schwarz-Christoffel method, while being over 8 times faster. The proposed method can preserve either the flow rate or the velocity field through the surface, and can cope with inconsistencies in motion and contour shape.Conclusions:Our results show that the method is as accurate as the Schwarz-Christoffel method in terms of maintaining the velocity distributions, while being more computationally efficient.Our mapping method can accurately preserve either the flow rate or the velocity field through the surface, and can cope with inconsistencies in motion and contour shape.Significance:The proposed method and its integration into the CRIMSON software enable a streamlined approach towards incorporating more patient-specific data in blood flow simulations.

Towards fast hemodynamic simulations in large-scale circulatory networks

In this work, an effective numerical method specifically conceived to simulate fluid flow in networks composed by tubular domains is presented. The present contribution addresses an extension of the so-called Transversally Enriched Pipe Element Method (TEPEM) recently developed by the authors in the computational hemodynamics realm to embrace the case of branching domains. The TEPEM approach relies on a slab-based partition of the network of vessels complemented with basis functions devised to render high-order polynomial enrichment for transversal flow phenomena, while keeping a low-order polynomial approximation for the fields along the axial direction. The main goal of such an approach is to provide a fast numerical tool to characterize flow-related quantities in large-scale networks of vessels, which are of relevance in the hemodynamics field, such as the wall shear stress. Through several numerical examples ranging from academic to patient-specific networks, it is demonstrated that the proposed strategy yields reasonably accurate qualitative and quantitative results and substantially reduced computational cost when compared with standard 3D finite element models. Hence, we conclude that this approach can be regarded as an appealing numerical technology placed halfway over-simplistic cheap 1D and computationally demanding accurate 3D models.

Reduced-Order Unscented Kalman Filter With Observations in the Frequency Domain: Application to Computational Hemodynamics.

The aim of this paper is to assess the potential of the reduced-order unscented Kalman's filter (ROUKF) in the context of computational hemodynamics, in order to estimate cardiovascular model parameters when employing real patient-specific data. The approach combines an efficient blood flow solver for one-dimensional networks (for the forward problem) with the parameter estimation problem cast in the frequency space. Namely, the ROUKF is used to correct model parameters after each cardiac cycle, depending on the discrepancies of model outputs with respect to available observations properly mapped into the frequency space. First we validate the filter in frequency domain applying it in the context of a set of experimental measurements for an in vitro model. Second, we perform different numerical experiments aiming at parameter estimation using patient-specific data. Our results demonstrate that the filter in frequency domain allows a faster and more robust parameter estimation, when compared to its time-domain counterpart. Moreover, the proposed approach allows to estimate parameters that are not directly related to the network, but are crucial for targeting inter-individual parameter variability (e.g., parameters that characterize the cardiac output). The ROUKF in frequency domain provides a robust and flexible tool for estimating parameters related to cardiovascular mathematical models using in vivo data.

Abdominal Aortic Aneurysm Endovascular Repair: Profiling Postimplantation Morphometry and Hemodynamics With Image-Based Computational Fluid Dynamics.

Endovascular aneurysm repair (EVAR) has disseminated rapidly as an alternative to open surgical repair for the treatment of abdominal aortic aneurysms (AAAs), because of its reduced invasiveness, low mortality, and morbidity rate. The effectiveness of the endovascular devices used in EVAR is always at question as postoperative adverse events can lead to re-intervention or to a possible fatal scenario for the circulatory system. Motivated by the assessment of the risks related to thrombus formation, here the impact of two different commercial endovascular grafts on local hemodynamics is explored through 20 image-based computational hemodynamic models of EVAR-treated patients (N = 10 per each endograft model). Hemodynamic features, susceptible to promote thrombus formation, such as flow separation and recirculation, are quantitatively assessed and compared with the local hemodynamics established in image-based infrarenal abdominal aortic models of healthy subjects (N = 10). Moreover, the durability of endovascular devices is investigated analyzing the displacement forces (DFs) acting on them. The hemodynamic analysis is complemented by a geometrical characterization of the EVAR-induced reshaping of the infrarenal abdominal aortic vascular region. The findings of this study indicate that (1) the clinically observed propensity to thrombus formation in devices used in EVAR strategies can be explained in terms of local hemodynamics by means of image-based computational hemodynamics approach; (2) reportedly prothrombotic hemodynamic structures are strongly associated with the geometry of the aortoiliac tract postoperatively; and (3) DFs are associated with cross-sectional area of the aortoiliac tract postoperatively. In perspective, our study suggests that future clinical followup studies could include a geometric analysis of the region of the implant, monitoring shape variations that can lead to hemodynamic disturbances of clinical significance.

Abstract 360: Effective Three-element Windkessel Model based on Doppler Ultrasound Images for Noninvasive Quantification of Trans-stenotic Pressure Gradient in Aortorenal System

The research objective is to develop and validate a noninvasive method to quantify trans-stenotic pressure gradient in aortorenal system through image-based computational hemodynamics (ICH) for supporting clinical decision of stenting therapy. Renal artery stenosis (RAS) causes renovascular hypertension but the true severity of RAS is hard to be determined thus effective stenting therapy cannot be well planned. We hypothesize that the trans-stenotic pressure gradient truly reflects the severity of RAS. Recently, ICH has merged as a unique tool, using clinical CT and Doppler images as well as the 3-element WindKessel model. As schematized in Fig. 1(a), ICH noninvasively quantify the live hemodynamics, e.g. pressure in Fig. 1(b), in human vessels. One challenge in ICH is to introduce the appropriate values of proximal resistance (r), distal resistance (R), and compliance (C). We have developed a comprehensive algorithm to determine these values by comparing the computational flow-rates at the exits of aortic artery (AA), left renal (LR), and right renal (RR) arteries with the corresponding flow-rates from Doppler images. The image data of the study case consist of CT data, Doppler images at the juxtarenal AA, LR and RR arteries, and invasive pressure measurement at the corresponding arteries from pressure wire transducers. The r, R, and C values determined through the Doppler images are shown in Fig. 19(c). The three non-invasively computed pressure waves are in good agreements with the invasively measured pressure waves (Fig. 1(d)). The validated ICH is a practical tool to noninvasively measure pressure gradients so that physicians can make better decision at treatment of RAS.

Boundary control in computational haemodynamics

In this work, a data assimilation method is proposed following an optimise-then-discretise approach, and is applied in the context of computational haemodynamics. The methodology aims to make use of phase-contrast magnetic resonance imaging to perform optimal flow control in computational fluid dynamic simulations. Flow matching between observations and model predictions is performed in luminal regions, excluding near-wall areas, improving the near-wall flow reconstruction to enhance the estimation of related quantities such as wall shear stresses. The proposed approach remarkably improves the flow field at the aortic root and reveals a great potential for predicting clinically relevant haemodynamic phenomenology. This work presents model validation against an analytical solution using the standard 3-D Hagen–Poiseuille flow, and validation with real data involving the flow control problem in a glass replica of a human aorta imaged with a 3T magnetic resonance scanner.In vitroexperiments consist of both a numerically generated reference flow solution, which is considered as the ground truth, as well as real flow MRI data obtained from phase-contrast flow acquisitions. The validation against thein vitroflow MRI experiments is performed for different flow regimes and model parameters including different mesh refinements.

Efficient simulation of a low-profile visualized intraluminal support device: a novel fast virtual stenting technique

BackgroundThe low-profile visualized intraluminal support (LVIS) stent has become a promising endovascular option for treating intracranial aneurysms. To achieve better treatment of aneurysms using LVIS, we developed a fast virtual stenting technique for use with LVIS (F-LVIS) to evaluate hemodynamic changes in the aneurysm and validate its reliability.MethodsA patient-specific aneurysm was selected for making comparisons between the real LVIS (R-LVIS) and the F-LVIS. To perform R-LVIS stenting, a hollow phantom based on a patient-specific aneurysm was fabricated using a three-dimensional printer. An R-LVIS was released in the phantom according to standard procedure. F-LVIS was then applied successfully in this aneurysm model. The computational fluid dynamics (CFD) values were calculated for both the F-LVIS and R-LVIS models. Qualitative and quantitative comparisons of the two models focused on hemodynamic parameters.ResultsThe hemodynamic characteristics for R-LVIS and F-LVIS were well matched. Representative contours of velocities and wall shear stress (WSS) were consistently similar in both distribution and magnitude. The velocity vectors also showed high similarity, although the R-LVIS model showed faster and more fluid streams entering the aneurysm. Variation tendencies of the velocity in the aneurysm and the WSS on the aneurysm wall were also similar in the two models, with no statistically significant differences in either velocity or WSS.ConclusionsThe results of the computational hemodynamics indicate that F-LVIS is suitable for evaluating hemodynamic factors. This novel F-LVIS is considered efficient, practical, and effective.

Hierarchical model reduction for incompressible fluids in pipes

SummaryHierarchical model reduction is intended to solve efficiently partial differential equations in domains with a geometrically dominant direction. In many engineering applications, these problems are often reduced to 1‐dimensional differential systems. This guarantees computational efficiency yet dumps local accuracy as nonaxial dynamics are dropped. Hierarchical model reduction recovers the secondary components of the dynamics of interest with a combination of different discretization techniques, following up a natural separation of variables. The dominant direction is generally solved by the finite element method or isogeometric analysis to guarantee flexibility, while the transverse components are solved by spectral methods, to guarantee a small number of degrees of freedom. By judiciously selecting the number of transverse modes, the method has been proven to improve significantly the accuracy of purely 1‐dimensional solvers, with great computational efficiency. A Cartesian framework has been used so far both in slab domains and cylindrical pipes (including arteries) mapped to Cartesian reference domains. In this paper, we investigate the alternative use of a polar coordinates system for the transverse dynamics in circular or elliptical pipes. This seems a natural choice for applications like computational hemodynamics. In spite of this, the selection of a basis function set for the transverse dynamics is troublesome. As pointed out in the literature—even for simple elliptical problems—there is no “best” basis available. In this paper, we perform an extensive investigation of hierarchical model reduction in polar coordinates to discuss different possible choices for the transverse basis, pointing out pros and cons of the polar coordinate system.

Computational Hemodynamics of Aneurismal Model in the Circle of Willis Virtually Treated with Closed Cell and Open Cell Stent

To investigate the difference of the hemodynamics of aneurismal model in the circle of Willis virtually treated with closed cell and open cell stent, two kinds of stents were constructed. One is Enterprise stent (Closed-cell), and the other is Neuroform stent (open-cell). Five treatment strategies based on the combination of two kinds of stents were used. The computational fluid dynamics of these five different treatment strategies was calculated and the corresponding hemodynamic characteristics of aneurismal model were analyzed. In particular, the effects of different structural stents and their combinations on the blood flow characteristics (streamline, wall shear stress) of the aneurysm cavity were discussed.

A Computational Hemodynamics Analysis on the Correlation Between Energy Loss and Clinical Outcomes for Flow Diverters Treatment of Intracranial Aneurysm

The rupture of intracranial aneurysms might lead to permanent disability or even death. One possible endovascular treatment is the deployment of flow diverters (FDs), which reduces flow into the sac and promotes thrombosis. Computational fluid dynamics simulations were used to assess the flow patterns and dynamics. The concept of energy loss, as a measure of necessary work done to overcome flow resistance, was utilized to correlate with clinical outcome. If a surgical operation is successful, the flow would be diverted to a shorter path and energy loss should be reduced. Conversely, persistent flow in the sac, associated with treatment failure, would display an increased energy loss as blood is then squeezed through the stent pores. Four illustrative clinical cases, involving both bifurcation and sidewall aneurysms, were selected. To reduce the numerical complexity, earlier works in the literature had used a porous medium approximation for the FDs. Here, the FD was simulated explicitly as a virtual (or computer-generated) stent, which would likely provide a more accurate description. Furthermore, quantitative comparisons between the approaches of virtual stenting and a porous medium with typical parameters were conducted by examining the effective flow influx into the aneurysm.

What is needed to make low-density lipoprotein transport in human aorta computational models suitable to explore links to atherosclerosis? Impact of initial and inflow boundary conditions

Personalized computational hemodynamics (CH) is a promising tool to clarify/predict the link between low density lipoproteins (LDL) transport in aorta, disturbed shear and atherogenesis. However, CH uses simplifying assumptions that represent sources of uncertainty. In particular, modelling blood-side to wall LDL transfer is challenged by the cumbersomeness of protocols needed to obtain reliable LDL concentration profile estimations. This paucity of data is limiting the establishment of rigorous CH protocols able to balance the trade-offs among the variety of in vivo data to be acquired, and the accuracy required by biological/clinical applications.In this study, we analyze the impact of LDL concentration initialization (initial conditions, ICs) and inflow boundary conditions (BCs) on CH models of LDL blood-to-wall transfer in aorta. Technically, in an image-based model of human aorta, two different inflow BCs are generated imposing subject-specific inflow 3D PC-MRI measured or idealized (flat) velocity profiles. For each simulated BC, four different ICs for LDL concentration are applied, imposing as IC the LDL distribution resulting from steady-state simulations with average conditions, or constant LDL concentration values.Based on CH results, we conclude that: (1) the imposition of realistic 3D velocity profiles as inflow BC reduces the uncertainty affecting the representation of LDL transfer; (2) different LDL concentration ICs lead to markedly different patterns of LDL transfer.Given that it is not possible to verify in vivo the proper LDL concentration initialization to be applied, we suggest to carefully set and unambiguously declare the imposed BCs and LDL concentration IC when modelling LDL transfer in aorta, in order to obtain reproducible and ultimately comparable results among different laboratories.

Numerical methods for polyline-to-point-cloud registration with applications to patient-specific stent reconstruction.

We present novel numerical methods for polyline-to-point-cloud registration and their application to patient-specific modeling of deployed coronary artery stents from image data. Patient-specific coronary stent reconstruction is an important challenge in computational hemodynamics and relevant to the design and improvement of the prostheses. It is an invaluable tool in large-scale clinical trials that computationally investigate the effect of new generations of stents on hemodynamics and eventually tissue remodeling. Given a point cloud of strut positions, which can be extracted from images, our stent reconstruction method aims at finding a geometrical transformation that aligns a model of the undeployed stent to the point cloud. Mathematically, we describe the undeployed stent as a polyline, which is a piecewise linear object defined by its vertices and edges. We formulate the nonlinear registration as an optimization problem whose objective function consists of a similarity measure, quantifying the distance between the polyline and the point cloud, and a regularization functional, penalizing undesired transformations. Using projections of points onto the polyline structure, we derive novel distance measures. Our formulation supports most commonly used transformation models including very flexible nonlinear deformations. We also propose 2 regularization approaches ensuring the smoothness of the estimated nonlinear transformation. We demonstrate the potential of our methods using an academic 2D example and a real-life 3D bioabsorbable stent reconstruction problem. Our results show that the registration problem can be solved to sufficient accuracy within seconds using only a few number of Gauss-Newton iterations.

Uncertainty propagation of phase contrast-MRI derived inlet boundary conditions in computational hemodynamics models of thoracic aorta

This study investigates the impact that uncertainty in phase contrast-MRI derived inlet boundary conditions has on patient-specific computational hemodynamics models of the healthy human thoracic aorta. By means of Monte Carlo simulations, we provide advice on where, when and how, it is important to account for this source of uncertainty. The study shows that the uncertainty propagates not only to the intravascular flow, but also to the shear stress distribution at the vessel wall. More specifically, the results show an increase in the uncertainty of the predicted output variables, with respect to the input uncertainty, more marked for blood pressure and wall shear stress. The methodological approach proposed here can be easily extended to study uncertainty propagation in both healthy and pathological computational hemodynamic models.

Boundary conditions involving pressure for the Stokes problem and applications in computational hemodynamics

Pressure driven flows typically occur in hydraulic networks, e.g. oil ducts, water supply, biological flows, microfluidic channels etc. However, Stokes and Navier–Stokes problems are most often studied in a framework where Dirichlet type boundary conditions on the velocity field are imposed, thanks to the simpler settings from the theoretical and numerical points of view. In this work, we propose a novel formulation of the Stokes system with pressure boundary condition, together with no tangential flow, on a part of the boundary in a standard Stokes functional framework using Lagrange multipliers to enforce the latter constraint on velocity. More precisely, we carry out (i) a complete analysis of the formulation from the continuous to discrete level in two and three dimensions (ii) the description of our solution strategy, (iii) a verification of the convergence properties with an analytic solution and finally (iv) three-dimensional simulations of blood flow in the cerebral venous network that are in line with in-vivo measurements and the presentation of some performance metrics with respect to our solution strategy.

NUMERICAL SIMULATION OF TRANSIENT BLOOD FLOW THROUGH THE LEFT CORONARY ARTERY WITH VARYING DEGREES OF BIFURCATION ANGLES

Atherosclerosis is a cardiovascular condition that can occur in any part of the vascular system. Especially, it can exist in bifurcated arteries such as the left and right coronary arteries, abdominal aortic bifurcation or carotid artery bifurcation. In our study, we examine the left coronary artery as an exemplification using wall shear stress (WSS) and wall pressure gradient (WPG). Then, we attempt to find the relationship between bifurcated arterial geometry and hemodynamics. Computational fluid dynamics (CFD) is a common technique applied to characterize blood flow accurately and assist us to gain an insight of atherosclerosis. In this paper, we used CFD as the computational hemodynamics analysis technique to examine flow through the left coronary artery that has variable angular bifurcation. Our results demonstrated that the region of low WSS area and magnitudes of maximum WPG increases with the angles of bifurcation. Such hemodynamic condition resulting from the large bifurcation angles has an effect on atherogenesis and is worthy of investigation for better understanding of atherosclerosis.

A seepage outlet boundary condition in hemodynamics modeling.

In computational fluid dynamics (CFD) models for hemodynamics applications, boundary conditions remain one of the major issues in obtaining accurate fluid flow predictions. As an important part of the arterial circulation, microcirculation plays important roles in many aspects, such as substance exchange, interstitial fluid generation and inverse flow. It is necessary to consider microcirculation in hemodynamics modeling. This is a methodological paper to test and validate a new type of boundary condition never applied to microcirculation before. In order to address this issue, we introduce microcirculation as a seepage outlet boundary condition in computational hemodynamics. Microcirculation is treated as a porous medium in this paper. Numerical comparisons of the seepage and traditional boundary conditions are made. The results show that the seepage boundary condition has significant impacts on numerical simulation. Under the seepage boundary condition, the fluctuation range of the pressures progressively rises in the artery zone. The results obtained from the traditional boundary condition show that the pressure fluctuation range gradually falls. In addition, the wall shear stresses under the traditional outlet boundary condition are much higher than those under the seepage outlet boundary condition. The proposed boundary condition is more suitable in hemodynamics modeling.

Phantom-based experimental validation of fast virtual deployment of self-expandable stents for cerebral aneurysms.

BackgroundEndovascular intervention using a stent is a mainstream treatment for cerebral aneurysms. To assess the effect of intervention strategies on aneurysm hemodynamics, we have developed a fast virtual stenting (FVS) technique to simulate stent deployment in patient-specific aneurysms. However, quantitative validation of the FVS against experimental data has not been fully addressed. In this study, we performed in vitro analysis of a patient-specific model to illustrate the realism and usability of this novel FVS technique.MethodsWe selected a patient-specific aneurysm and reproduced it in a manufactured realistic aneurismal phantom. Three numerical simulation models of the aneurysm with an Enterprise stent were constructed. Three models were constructed to obtain the stented aneurysms: a physical phantom scanned by micro-CT, fast virtual stenting technique and finite element method. The flow in the three models was simulated using a computational fluid dynamics software package, and the hemodynamics parameters for the three models were calculated and analyzed.ResultsThe computational hemodynamics in the patient-specific aneurysm of the three models resembled the very well. A qualitative comparison revealed high similarity in the wall shear stress, streamline, and velocity plane among the three different methods. Quantitative comparisons revealed that the difference ratios of the hemodynamic parameters were less than 10%, with the difference ratios for area average of wall shear stress in the aneurysm being very low.ConclusionsIn conclusion, the results of the computational hemodynamics indicate that FVS is suitable for evaluation of the hemodynamic factors that affect treatment outcomes.