Comparison of patient-specific inlet boundary conditions in the numerical modelling of blood flow in abdominal aortic aneurysm disease

The Effect of Blood Rheology and Inlet Boundary Conditions on Realistic Abdominal Aortic Aneurysms under Pulsatile Flow Conditions

BACKGROUND

The effects of non-Newtonian rheology and boundary conditions on various pathophysiologies have been studied quite extensively in the literature. The majority of results present qualitative and/or quantitative conclusions that are not thoroughly assessed from a statistical perspective.

METHODS

The finite volume method was employed for the numerical simulation of seven patient-specific abdominal aortic aneurysms. For each case, five rheological models and three inlet velocity boundary conditions were considered. Outlier- and heteroscedasticity-robust ANOVA tests assessed the simultaneous effect of rheological specifications and boundary conditions on fourteen variables that capture important characteristics of vascular flows.

RESULTS

The selection of inlet velocity profiles appears as a more critical factor relative to rheological specifications, especially regarding differences in the oscillatory characteristics of computed flows. Response variables that relate to the average tangential force on the wall over the entire cycle do not differ significantly across alternative factor levels, as long as one focuses on non-Newtonian specifications.

CONCLUSIONS

The two factors, namely blood rheological models and inlet velocity boundary condition, exert additive effects on variables that characterize vascular flows, with negligible interaction effects. Regarding thrombus-prone conditions, the Plug inlet profile offers an advantageous hemodynamic configuration with respect to the other two profiles.

Efficient parallel simulation of hemodynamics in patient-specific abdominal aorta with aneurysm

Surgical planning for aortic aneurysm repair is a difficult task. In addition to the morphological features obtained from medical imaging, alternative features obtained with computational modeling may provide additional useful information. Though numerical studies are noninvasive, they are often time-consuming, especially when we need to study and compare multiple repair scenarios, because of the high computational complexity. In this paper, we present a highly parallel algorithm for the numerical simulation of unsteady blood flows in the patient-specific abdominal aorta before and after the aneurysmic repair. We model the blood flow with the unsteady incompressible Navier-Stokes equations with different outlet boundary conditions, and solve the discretized system with a highly scalable domain decomposition method. With this approach, a high resolution simulation of a full-size adult aorta can be obtained in less than an hour, instead of days with older methods and software. In addition, we show that the parallel efficiency of the proposed method is near 70% on a parallel computer with 2, 880 processor cores.

Haemodynamic assessment of bicuspid aortic valve aortopathy: a systematic review of the current literature

Both genetic and haemodynamic theories explain the aetiology, progression and optimal management of bicuspid aortic valve aortopathy. In recent years, the haemodynamic theory has been explored with the help of magnetic resonance imaging and computational fluid dynamics. The objective of this review was to summarize the findings of these investigations with focus on the blood flow pattern and associated variables, including flow eccentricity, helicity, flow displacement, cusp opening angle, systolic flow angle, wall shear stress (WSS) and oscillatory shear index. A structured literature review was performed from January 1990 to January 2018 and revealed the following 3 main findings: (i) the bicuspid aortic valve is associated with flow eccentricity and helicity in the ascending aorta compared to healthy and diseased tricuspid aortic valve, (ii) flow displacement is easier to obtain than WSS and has been shown to correlate with valve morphology and type of aortopathy and (iii) the stenotic bicuspid aortic valve is associated with elevated WSS along the greater curvature of the ascending aorta, where aortic dilatation and aortic wall thinning are commonly found. We conclude that new haemodynamic variables should complement ascending aorta diameter as an indicator for disease progression and the type and timing of intervention. WSS describes the force that blood flow exerts on the vessel wall as a function of viscosity and geometry of the vessel, making it a potentially more reliable marker of disease progression.

Analysis of Inlet Velocity Profiles in Numerical Assessment of Fontan Hemodynamics

Computational fluid dynamic (CFD) simulations are widely utilized to assess Fontan hemodynamics that are related to long-term complications. No previous studies have systemically investigated the effects of using different inlet velocity profiles in Fontan simulations. This study implements real, patient-specific velocity profiles for numerical assessment of Fontan hemodynamics using CFD simulations. Four additional, artificial velocity profiles were used for comparison: (1) flat, (2) parabolic, (3) Womersley, and (4) parabolic with inlet extensions [to develop flow before entering the total cavopulmonary connection (TCPC)]. The differences arising from the five velocity profiles, as well as discrepancies between the real and each of the artificial velocity profiles, were quantified by examining clinically important metrics in TCPC hemodynamics: power loss (PL), viscous dissipation rate (VDR), hepatic flow distribution, and regions of low wall shear stress. Statistically significant differences were observed in PL and VDR between simulations using real and flat velocity profiles, but differences between those using real velocity profiles and the other three artificial profiles did not reach statistical significance. These conclusions suggest that the artificial velocity profiles (2)-(4) are acceptable surrogates for real velocity profiles in Fontan simulations, but parabolic profiles are recommended because of their low computational demands and prevalent applicability.

Suitability of lattice Boltzmann inlet and outlet boundary conditions for simulating flow in image-derived vasculature

The lattice Boltzmann method (LBM) is a popular alternative to solving the Navier-Stokes equations for modeling blood flow. When simulating flow using the LBM, several choices for inlet and outlet boundary conditions exist. While boundary conditions in the LBM have been evaluated in idealized geometries, there have been no extensive comparisons in image-derived vasculature, where the geometries are highly complex. In this study, the Zou-He (ZH) and finite difference (FD) boundary conditions were evaluated in image-derived vascular geometries by comparing their stability, accuracy, and run times. The boundary conditions were compared in four arteries: a coarctation of the aorta, dissected aorta, femoral artery, and left coronary artery. The FD boundary condition was more stable than ZH in all four geometries. In general, simulations using the ZH and FD method showed similar convergence rates within each geometry. However, the ZH method proved to be slightly more accurate compared with experimental flow using three-dimensional printed vasculature. The total run times necessary for simulations using the ZH boundary condition were significantly higher as the ZH method required a larger relaxation time, grid resolution, and number of time steps for a simulation representing the same physiological time. Finally, a new inlet velocity profile algorithm is presented for complex inlet geometries. Overall, results indicated that the FD method should generally be used for large-scale blood flow simulations in image-derived vasculature geometries. This study can serve as a guide to researchers interested in using the LBM to simulate blood flow.

Computational modeling of bicuspid aortopathy: Towards personalized risk strategies

This paper describes current advances on the application of in-silico for the understanding of bicuspid aortopathy and future perspectives of this technology on routine clinical care. This includes the impact that artificial intelligence can provide to develop computer-based clinical decision support system and that wearable sensors can offer to remotely monitor high-risk bicuspid aortic valve (BAV) patients. First, we discussed the benefit of computational modeling by providing tangible examples of in-silico software products based on computational fluid-dynamic (CFD) and finite-element method (FEM) that are currently transforming the way we diagnose and treat cardiovascular diseases. Then, we presented recent findings on computational hemodynamic and structural mechanics of BAV to highlight the potentiality of patient-specific metrics (not-based on aortic size) to support the clinical-decision making process of BAV-associated aneurysms. Examples of BAV-related personalized healthcare solutions are illustrated.

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

OBJECTIVE

We propose a novel method to map patient-specific blood velocity profiles obtained from imaging data such as 2D flow MRI or 3D colour Doppler ultrasound) 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

The 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 our method 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.

CONCLUSIONS

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.

Investigation of the hemodynamics of a juxtarenal aortic aneurysm with intervention by dual-stents strategy

OBJECTIVE

To study the feasibility of using two stents (a combination of multilayer stent [MS] and stent graft [SG]) in the treatment of a juxtarenal aortic aneurysm that involves a significant branch artery and to determine the advantages and disadvantages of using SGs upstream and downstream from the aneurysm so as to provide some theoretical guidance for preoperative clinical decision-making in the future.

METHODS

Four ideal geometric models were established for numerical computation: case 1 refers to an aneurysm without the use of stents, case 2 represents the implantation of two MSs in an aneurysm, and case 3 (SG + MS) and case 4 (MS + SG) both involve the treatment of an aneurysm by using a combination of SG and MG.

RESULTS

The aneurysm pressure is slightly lower and there are more vortices when the SG is implanted (case 3 and case 4). In particular, for case 4, additional vortices appear in the sac and the area of the low-wall shear stress is larger on the aneurysm compared with those of the other three cases. However, the pressure becomes uneven, and a peak pressure region is observed on the wall of the aneurysm, and therefore, the aneurysmal wall will become buckled. In addition, the flux of the renal artery in the four cases is greater than that in the normal case.

CONCLUSION

The arrangements in cases 3 and 4 can effectively isolate the aneurysm from circulation, but clinically, it is necessary to avoid such a high-risk situation wherein the SG is positioned downstream of the aneurysm (case 4), even though this leads to improved isolation.

Hemodynamics and Oxygen Transport through Pararenal Aortic Aneurysm Treated with Multilayer Stent: A Numerical Study

BACKGROUND

As opposed to an endoluminal stent graft, a multilayer stent (MS) consists of a porous mesh, which allows for the possibility of treating pararenal aortic aneurysms (PRAAs) that involve a significant branch vessel. However, the choice of the density of the MS plays a vital role in isolating the aneurysm and allowing unobstructed blood flow in the branch vessel.

METHOD

In the present study, we examined 3 cases (without a stent and with single-layer and double-layer stents) via numerical simulations to explore the feasibility of the MSs used in the treatment of such aneurysms and estimate whether there is a more appropriate or optimal stent density.

RESULTS

With stent intervention, the velocity of blood flow in the sac decreased, but the pressure on the surface of the aneurysm did not decrease although it became more uniform. In addition, the "region of double low" (with low wall shear stress and a low Sherwood number) enlarged after stent implantation. Even with the double-layer stent, however, the flux of the branch vessel was still above normal, and we could predict that the optimal stent porosity was approximately 49.9%.

CONCLUSIONS

Unlike in previous studies, an MS could not be feasibly applied to high-risk PRAAs. However, an MS can induce sac thrombosis in the later stages while maintaining visceral vessel patency, and our results suggest that the optimal stent may be a 4-layer stent.

Impact of Patient-Specific Inflow Velocity Profile on Hemodynamics of the Thoracic Aorta

Computational fluid dynamics (CFD) provides a noninvasive method to functionally assess aortic hemodynamics. The thoracic aorta has an anatomically complex inlet comprising of the aortic valve and root, which is highly prone to different morphologies and pathologies. We investigated the effect of using patient-specific (PS) inflow velocity profiles compared to idealized profiles based on the patient's flow waveform. A healthy 31 yo with a normally functioning tricuspid aortic valve (subject A), and a 52 yo with a bicuspid aortic valve (BAV), aortic valvular stenosis, and dilated ascending aorta (subject B) were studied. Subjects underwent MR angiography to image and reconstruct three-dimensional (3D) geometric models of the thoracic aorta. Flow-magnetic resonance imaging (MRI) was acquired above the aortic valve and used to extract the patient-specific velocity profiles. Subject B's eccentric asymmetrical inflow profile led to highly complex velocity patterns, which were not replicated by the idealized velocity profiles. Despite having identical flow rates, the idealized inflow profiles displayed significantly different peak and radial velocities. Subject A's results showed some similarity between PS and parabolic inflow profiles; however, other parameters such as Flowasymmetry were significantly different. Idealized inflow velocity profiles significantly alter velocity patterns and produce inaccurate hemodynamic assessments in the thoracic aorta. The complex structure of the aortic valve and its predisposition to pathological change means the inflow into the thoracic aorta can be highly variable. CFD analysis of the thoracic aorta needs to utilize fully PS inflow boundary conditions in order to produce truly meaningful results.

Patient-Specific Cardiovascular Computational Modeling: Diversity of Personalization and Challenges

Patient-specific computer models have been developed representing a variety of aspects of the cardiovascular system spanning the disciplines of electrophysiology, electromechanics, solid mechanics, and fluid dynamics. These physiological mechanistic models predict macroscopic phenomena such as electrical impulse propagation and contraction throughout the entire heart as well as flow and pressure dynamics occurring in the ventricular chambers, aorta, and coronary arteries during each heartbeat. Such models have been used to study a variety of clinical scenarios including aortic aneurysms, coronary stenosis, cardiac valvular disease, left ventricular assist devices, cardiac resynchronization therapy, ablation therapy, and risk stratification. After decades of research, these models are beginning to be incorporated into clinical practice directly via marketed devices and indirectly by improving our understanding of the underlying mechanisms of health and disease within a clinical context.

Computational study of aortic hemodynamics for patients with an abnormal aortic valve: The importance of secondary flow at the ascending aorta inlet

Blood flow in the aorta is helical, but most computational studies ignore the presence of secondary flow components at the ascending aorta (AAo) inlet. The aim of this study is to ascertain the importance of inlet boundary conditions (BCs) in computational analysis of flow patterns in the thoracic aorta based on patient-specific images, with a particular focus on patients with an abnormal aortic valve. Two cases were studied: one presenting a severe aortic valve stenosis and the other with a mechanical valve. For both aorta models, three inlet BCs were compared; these included the flat profile and 1D through-plane velocity and 3D phase-contrast magnetic resonance imaging derived velocity profiles, with the latter being used for benchmarking. Our results showed that peak and mean velocities at the proximal end of the ascending aorta were underestimated by up to 41% when the secondary flow components were neglected. The results for helical flow descriptors highlighted the strong influence of secondary velocities on the helical flow structure in the AAo. Differences in all wall shear stress (WSS)-derived indices were much more pronounced in the AAo and aortic arch (AA) than in the descending aorta (DAo). Overall, this study demonstrates that using 3D velocity profiles as inlet BC is essential for patient-specific analysis of hemodynamics and WSS in the AAo and AA in the presence of an abnormal aortic valve. However, predicted flow in the DAo is less sensitive to the secondary velocities imposed at the inlet; hence, the 1D through-plane profile could be a sufficient inlet BC for studies focusing on distal regions of the thoracic aorta.

Large eddy simulations of blood dynamics in abdominal aortic aneurysms

We study the effects of transition to turbulence in abdominal aortic aneurysms (AAA). The presence of transitional effects in such districts is related to the heart pulsatility and the sudden change of diameter of the vessels, and has been recorded by means of clinical measures as well as of computational studies. Here we propose, for the first time, the use of a large eddy simulation (LES) model to accurately describe transition to turbulence in realistic scenarios of AAA obtained from radiological images. To this aim, we post-process the obtained numerical solutions to assess significant quantities, such as the ensemble-averaged velocity and wall shear stress, the standard deviation of the fluctuating velocity field, and vortical structures educed via the so-called Q-criterion. The results demonstrate the suitability of the considered LES model and show the presence of significant transitional effects around the impingement region during the mid-deceleration phase.

Patient specific modeling of palpation-based prostate cancer diagnosis: effects of pelvic cavity anatomy and intrabladder pressure

Computational modeling has become a successful tool for scientific advances including understanding the behavior of biological and biomedical systems as well as improving clinical practice. In most cases, only general models are used without taking into account patient-specific features. However, patient specificity has proven to be crucial in guiding clinical practice because of disastrous consequences that can arise should the model be inaccurate. This paper proposes a framework for the computational modeling applied to the example of the male pelvic cavity for the purpose of prostate cancer diagnostics using palpation. The effects of patient specific structural features on palpation response are studied in three selected patients with very different pathophysiological conditions whose pelvic cavities are reconstructed from MRI scans. In particular, the role of intrabladder pressure in the outcome of digital rectal examination is investigated with the objective of providing guidelines to practitioners to enhance the effectiveness of diagnosis. Furthermore, the presence of the pelvic bone in the model is assessed to determine the pathophysiological conditions in which it has to be modeled. The conclusions and suggestions of this work have potential use not only in clinical practice and also for biomechanical modeling where structural patient-specificity needs to be considered. © 2015 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons Ltd.

A Review of Computational Methods to Predict the Risk of Rupture of Abdominal Aortic Aneurysms

Computational methods have played an important role in health care in recent years, as determining parameters that affect a certain medical condition is not possible in experimental conditions in many cases. Computational fluid dynamics (CFD) methods have been used to accurately determine the nature of blood flow in the cardiovascular and nervous systems and air flow in the respiratory system, thereby giving the surgeon a diagnostic tool to plan treatment accordingly. Machine learning or data mining (MLD) methods are currently used to develop models that learn from retrospective data to make a prediction regarding factors affecting the progression of a disease. These models have also been successful in incorporating factors such as patient history and occupation. MLD models can be used as a predictive tool to determine rupture potential in patients with abdominal aortic aneurysms (AAA) along with CFD-based prediction of parameters like wall shear stress and pressure distributions. A combination of these computer methods can be pivotal in bridging the gap between translational and outcomes research in medicine. This paper reviews the use of computational methods in the diagnosis and treatment of AAA.

Comparison of vortical structures induced by arteriovenous grafts using vector Doppler ultrasound

Arteriovenous prosthetic grafts are used in hemodialysis. Stenosis in the venous anastomosis is the main cause of occlusion and the role of local hemodynamics in this is considered significant. A new spiral graft design has been proposed to stabilize the flow phenomena in the host vein. Cross-flow vortical structures in the outflow of this graft were compared with those from a control device. Both grafts were integrated in identical in-house ultrasound-compatible flow phantoms with realistic surgical configurations. Constant flow rates were applied. In-plane 2-D velocity and vorticity mapping was developed using a vector Doppler technique. One or two vortices were detected for the spiral graft and two to four for the control, along with reduced stagnation points for the former. The in-plane peak velocity and circulation were calculated and found to be greater for the spiral device, implying increased in-plane mixing, which is believed to inhibit thrombosis and neo-intimal hyperplasia.

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.

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.

Secondary flow in peripheral vascular prosthetic grafts using vector Doppler imaging

Prosthetic grafts are used for the treatment of peripheral arterial disease. Re-stenosis in the distal anastomosis of these grafts is a common reason for graft occlusion. The role of local hemodynamics in development of neo-intimal hyperplasia is well known. A new graft design has been proposed for the induction of optimized spiral flow in the host vessel. The secondary flow motions induced by this graft were compared with those of a control device. Both types of grafts were connected with vessel mimic and positioned in ultrasound flow phantoms with identical geometry. Constant flow rates were applied. Data collected in the cross-sectional view distal from the graft outflow and dual-beam vector Doppler was applied to create 2-D velocity maps. A single-spiral flow pattern was found for the flow-modified graft, and double or triple spirals for the control graft. In-plane maximum velocity was greater for the flow-modified graft than for the control device.

Flow-induced ATP release in patient-specific arterial geometries--a comparative study of computational models

The importance of the endothelium in the local regulation of blood flow is reflected by its influence on vascular tone by means of vasodilatory responses to many physiological stimuli. Regulatory pathways are affected by mass transport and wall shear stress (WSS), via mechanotransduction mechanisms. In the present work, we review the most relevant computational models that have been proposed to date, and introduce a general framework for modelling the responses of the endothelium to alteration in the flow, with a view to understanding the biomechanical processes involved in the pathways to endothelial dysfunction. Simulations are performed on two different patient-specific stenosed carotid artery geometries to investigate the influence of WSS and mass transport phenomena upon the agonist coupling response at the endothelium. In particular, results presented for two different models of WSS-dependent adenosine-5'-triphosphate (ATP) release reveal that existing paradigms may not account for the conditions encountered in vivo and may therefore not be adequate to model the kinetics of ATP at the endothelium.

Accurate determination of patient-specific boundary conditions in computational vascular hemodynamics using 3D cine phase-contrast MRI

In the patient-specific vascular CFD, determination of the inlet and outlet boundary conditions (BCs) is an important issue for a valid diagnosis. The 3D cine phase-contrast MRI (4D Flow) velocimetry is promising for this issue; yet, its measured velocities contain relatively large error and are not admissible as the BCs without any correction. This paper proposes a novel correction method for determining the BCs accurately using the 4D Flow velocimetry. First, we reveal that the error of the velocity measured by the 4D Flow at each measurement voxel is large but is distributed symmetrically. Secondly, our method pays attention to the incompressibility of the blood and the fact that the volume flow rate (VFR) in each vessel is constant on any cross sections. We reveal that the average of the cross-sectional VFRs integrated from many measurement voxel in each vessel is accurate despite the large error. Finally, we propose the novel correction method, which applies a smoothing to the measured velocities on each inlet or outlet boundary with a low-pass filter and then corrects them with the VFR. The results of the several phantom studies are presented to validate the accuracy of our method. A demonstrative analysis for an actual aneurysm is also presented to show the feasibility and effectiveness of our method.