Assumptions in modelling of large artery hemodynamics

Mathematical modeling in assessing the risk of restenosis after carotid endarterectomy

Carotid endarterectomy is the main way to combat atherosclerosis of the carotid arteries, which disrupts cerebral circulation. The generally accepted marker of atherogenesis risk are hemodynamic indices associated with near-wall shear stress. The purpose of the work is to conduct a comparative analysis of hemodynamic indices in various carotid bifurcation models. The influence of a virtual change in the geometric shape of the model in order to optimize hemodynamic indices is also being studied. On the basis of computed angiography data, carotid bifurcation models are constructed, in which critical zones of hemodynamic indices are built using computational fluid dynamics. A comparative analysis of the critical zones for different classes of models is carried out. Comparison of averaged indices for critical zones between 'normal' and post-operative groups gave more than 5-x worse results for the latter. The same results for the near-bifurcation parts of the zones give a 25% better result for postoperative models. Virtual 'removal' of insignificant plaques leads to a deterioration of the indices of up to 40% in the places of the plaque's former location. The described method makes it possible to build the indices critical zones and compare them for various types of models. A technique for virtual changing the shape of a vessel (virtual surgery) is proposed. The novelty of the approach lies in the use for comparative analysis both real vessel models and hypothetical 'improved' virtual ones, as well in the proposed division of post-operative model's critical zones into subzones of different genesis.

Numerical investigation of different viscosity models on pulsatile blood flow of thoracic aortic aneurysm (TAA) in a patient-specific model

Aortic aneurysm is one of the most common aortic diseases that can lead to unfortunate consequences. Numerical simulations have an important role in the prediction of the aftereffects of vascular diseases including aneurysm. In this research, numerical simulation of pulsatile blood flow is performed for a 3-dimensional patient-specific model of a thoracic aortic aneurysm (TAA). Since the choice of blood viscosity model may have a significant impact on the simulation results, the effects of four non-Newtonian models of blood viscosity namely Carreau, Casson, Herschel-Bulkley, power low, and the Newtonian model on the wall shear stress (WSS) distribution, shear rate, and oscillatory shear index (OSI) have been analyzed. Simulation results showed that all the non-Newtonian and Newtonian models generally, predict similar patterns for blood flow and shear rate. At high flow rates in the cardiac cycle, the WSS value for all the models are similar to each other except for the power-law model due to the shear thinning behavior. All models predict high values of OSI on the inner wall of the ascending aorta and broad areas of the inner wall of the aneurysm sac. However, the Newtonian model predicts the OSI less than the non-Newtonian models in some areas of the aneurysm sac. Results indicated that the Newtonian model generally can predict the hemodynamic parameters of the blood flow similar to the non-Newtonian but for more precise analysis and to predict the regions prone to rupture and atherosclerosis, choosing a proper non-Newtonian model is recommended.

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

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

Sensitivity of flow patterns in aneurysms on the anterior communicating artery to anatomic variations of the cerebral arterial network

Recent studies raised increasing concern about the reliability of computer models in reproducing in vivo hemodynamics in cerebral aneurysms. Boundary condition problem is among the most frequently addressed issues since three-dimensional (3-D) modeling is usually restricted to local arterial segments. The present study focused on aneurysms on the anterior communicating artery (ACoA) which represent a large subgroup of detected cerebral aneurysms and, in particular, have a relatively high risk of rupture compared to aneurysms located in other regions. The sensitivity of blood flows in three ACoA aneurysms to boundary conditions was investigated using 3-D hemodynamic models. The boundary conditions of the 3-D models were predicted by a one-dimensional (1-D) model of the cerebral arterial network. The parameters of the 1-D model were assigned based respectively on population-averaged data and patient-specific data derived from medical images, yielding a population-generic model and a patient-specific model. In addition, particle image velocimetry (PIV) experiments were performed to validate the code used to simulate intra-aneurysmal blood flows. Obtained results showed that switching the boundary conditions of the aneurysm models from population-generic ones to patient-specific ones led to pronounced changes in simulated intra-aneurysmal flow patterns in terms of vortex structure, impingement region and the magnitude and spatial distribution of wall shear stress and oscillatory shear index. In particular, the way and the degree in which hemodynamic quantities are influenced by boundary conditions exhibited pronounced inter-patient variability. In summary, our study underlines the importance of patient-specific treatment of boundary conditions in model studies focusing on ACoA aneurysms.

Computational fluid dynamic simulation of human carotid artery bifurcation based on anatomy and volumetric blood flow rate measured with magnetic resonance imaging

Blood flow patterns and local hemodynamic parameters have been widely associated with the onset and progression of atherosclerosis in the carotid artery. Assessment of these parameters can be performed noninvasively using cine phase-contrast (PC) magnetic resonance imaging (MRI). In addition, in the last two decades, computational fluid dynamics (CFD) simulation in three dimensional models derived from anatomic medical images has been employed to investigate the blood flow in the carotid artery. This study developed a workflow of a subject-specific CFD analysis using MRI to enhance estimating hemodynamics of the carotid artery. Time-of-flight (TOF) MRI scans were used to construct three-dimensional computational models. PC-MRI measurements were utilized to impose the boundary condition at the inlet and a 0-dimensional lumped parameter model was employed for the outflow boundary condition. The choice of different viscosity models of blood flow as a source of uncertainty was studied, by means of the axial velocity, wall shear stress, and oscillatory shear index. The sequence of workflow in CFD analysis was optimized for a healthy subject using PC-MRI. Then, a patient with carotid artery stenosis and its hemodynamic parameters were examined. The simulations indicated that the lumped parameter model used at the outlet gives physiologically reasonable values of hemodynamic parameters. Moreover, the dependence of hemodynamics parameters on the viscosity models was observed to vary for different geometries. Other factors, however, may be required for a more accurate CFD analysis, such as the segmentation and smoothness of the geometrical model, mechanical properties of the artery's wall, and the prescribed velocity profile at the inlet.

Transitional flow in aneurysms and the computation of haemodynamic parameters

Haemodynamic forces appear to play an influential role in the evolution of aneurysms. This has led to numerous studies, usually based on computational fluid dynamics. Their focus is predominantly on the wall shear stress (WSS) and associated derived parameters, attempting to find correlations between particular patterns of haemodynamic indices and regions subjected to disease formation and progression. The indices are generally determined by integration of flow properties over a single cardiac cycle. In this study, we illustrate that in some cases the transitional flow in aneurysms can lead to significantly different WSS distributions in consecutive cardiac cycles. Accurate determination of time-averaged haemodynamic indices may thus require simulation of a large number of cycles, which contrasts with the common approach to determine parameters using data from a single cycle. To demonstrate the role of transitional flow, two exemplary cases are considered: flow in an abdominal aortic aneurysm and in an intracranial aneurysm. The key differences that are observed between these cases are explained in terms of the integral timescale of the transitional flows in comparison with the cardiac cycle duration: for relatively small geometries, transients will decay before the next cardiac cycle. In larger geometries, transients are still present when the systolic phase produces new instabilities. These residual fluctuations serve as random initial conditions and thus seed different flow patterns in each cycle. To judge whether statistics are converged, the derived indices from at least two successive cardiac cycles should be compared.

Computational fluid dynamics evaluation of flow reversal treatment of giant basilar tip aneurysm

Therapeutic parent artery flow reversal is a treatment option for giant, partially thrombosed basilar tip aneurysms. The effectiveness of this treatment has been variable and not yet studied by applying computational fluid dynamics. Computed tomography images and blood flow velocities acquired with transcranial Doppler ultrasonography were obtained prior to and after bilateral endovascular vertebral artery occlusion for a giant basilar tip aneurysm. Patient-specific geometries and velocity waveforms were used in computational fluid dynamics simulations in order to determine the velocity and wall shear stress changes induced by treatment. Therapeutic parent artery flow reversal lead to a dramatic increase in aneurysm inflow and wall shear stress (30 to 170 Pa) resulting in an increase in intra-aneurysmal circulation. The enlargement of the circulated area within the aneurysm led to a re-normalization of the wall shear stress and the aneurysm remained stable for more than 8 years thereafter. Therapeutic parent artery flow reversal can lead to unintended, potentially harmful changes in aneurysm inflow which can be quantified and possibly predicted by applying computational fluid dynamics.

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.

A study of wall shear stress in 12 aneurysms with respect to different viscosity models and flow conditions

Recent computational fluid dynamics (CFD) studies relate abnormal blood flow to rupture of cerebral aneurysms. However, it is still debated how to model blood flow with sufficient accuracy. Common assumptions made include Newtonian behaviour of blood, traction free outlet boundary conditions and inlet boundary conditions based on available literature. These assumptions are often required since the available patient specific data is usually restricted to the geometry of the aneurysm and the surrounding vasculature. However, the consequences of these assumptions have so far been inadequately addressed. This study investigates the effects of 4 different viscosity models, 2 different inflow conditions and 2 different outflow conditions in 12 middle cerebral artery aneurysms. The differences are quantified in terms of 3 different wall shear stress (WSS) metrics, involving maximal WSS, average WSS, and proportion of aneurysm sac area with low WSS. The results were compared with common geometrical metrics such as volume, aspect ratio, size ratio and parent vessel diameter and classifications in terms of sex and aneurysm type. The results demonstrate strong correlations between the different viscosity models and boundary conditions. The correlation between the different WSS metrics range from weak to medium. No strong correlations were found between the different WSS metrics and the geometrical metrics or classifications.

Physical factors effecting cerebral aneurysm pathophysiology

Many factors that are either blood-, wall-, or hemodynamics-borne have been associated with the initiation, growth, and rupture of intracranial aneurysms. The distribution of cerebral aneurysms around the bifurcations of the circle of Willis has provided the impetus for numerous studies trying to link hemodynamic factors (flow impingement, pressure, and/or wall shear stress) to aneurysm pathophysiology. The focus of this review is to provide a broad overview of such hemodynamic associations as well as the subsumed aspects of vascular anatomy and wall structure. Hemodynamic factors seem to be correlated to the distribution of aneurysms on the intracranial arterial tree and complex, slow flow patterns seem to be associated with aneurysm growth and rupture. However, both the prevalence of aneurysms in the general population and the incidence of ruptures in the aneurysm population are extremely low. This suggests that hemodynamic factors and purely mechanical explanations by themselves may serve as necessary, but never as necessary and sufficient conditions of this disease's causation. The ultimate cause is not yet known, but it is likely an additive or multiplicative effect of a handful of biochemical and biomechanical factors.