Impedance-based outflow boundary conditions for human carotid haemodynamics

In this study, we develop structured tree outflow boundary conditions for modelling the human carotid haemodynamics. The model geometry was reconstructed through computerised tomography scan. Unsteady-state computational fluid dynamic analyses were performed under different conditions using a commercial software package ADINA R&D, Inc., (Watertown, MA, USA) in order to assess the impact of the boundary conditions on the flow variables. In particular, the results showed that the peripheral vessels massively impact the pressure while the flow is relatively unaffected. As an example of application of these outflow conditions, an unsteady fluid-structure interaction (FSI) simulation was carried out and the dependence of the wall shear stress (WSS) on the arterial wall compliance in the carotid bifurcation was studied. In particular, a comparison between FSI and rigid-wall models was conducted. Results showed that the WSS distributions were substantially affected by the diameter variation of the arterial wall. In particular, even similar WSS distributions were found for both cases, and differences in the computed WSS values were also found.     

Does clinical data quality affect fluid-structure interaction simulations of patient-specific stenotic aortic valve models?

Numerical models are increasingly used in the cardiovascular field to reproduce, study and improve devices and clinical treatments. The recent literature involves a number of patient-specific models replicating the transcatheter aortic valve implantation procedure, a minimally invasive treatment for high-risk patients with aortic diseases. The representation of the actual patient’s condition with truthful anatomy, materials and working conditions is the first step toward the simulation of the clinical procedure.The aim of this work is to quantify how the quality of routine clinical data, from which the patient-specific models are built, affects the outputs of the numerical models representing the pathological condition of stenotic aortic valve.Seven fluid–structure interaction (FSI) simulations were performed, completed with a sensitivity analysis on patient-specific reconstructed geometries and boundary conditions. The structural parts of the models consisted of the aortic root, native tri-leaflets valve and calcifications. Ventricular and aortic pressure curves were applied to the fluid domain.The differences between clinical data and numerical results for the aortic valve area were less than 2% but reached 12% when boundary conditions and geometries were changed. The difference in the aortic stenosis jet velocity between measured and simulated values was less than 11% reaching 27% when the geometry was changed. The CT slice thickness was found to be the most sensitive parameter on the presented FSI numerical model.In conclusion, the results showed that the segmentation and reconstruction phases need to be carefully performed to obtain a truthful patient-specific domain to be used in FSI analyses.     

Numerical simulation of blood flow in the left ventricle and aortic sinus using magnetic resonance imaging and computational fluid dynamics

Understanding cardiac blood flow patterns has many applications in analysing haemodynamics and for the clinical assessment of heart function. In this study, numerical simulations of blood flow in a patient-specific anatomical model of the left ventricle (LV) and the aortic sinus are presented. The realistic 3D geometry of both LV and aortic sinus is extracted from the processing of magnetic resonance imaging (MRI). Furthermore, motion of inner walls of LV and aortic sinus is obtained from cine-MR image analysis and is used as a constraint to a numerical computational fluid dynamics (CFD) model based on the moving boundary approach. Arbitrary Lagrangian–Eulerian finite element method formulation is used for the numerical solution of the transient dynamic equations of the fluid domain. Simulation results include detailed flow characteristics such as velocity, pressure and wall shear stress for the whole domain. The aortic outflow is compared with data obtained by phase-contrast MRI. Good agreement was found between simulation results and these measurements.     

Fluid-Structure Interaction Simulation of Prosthetic Aortic Valves: Comparison between Immersed Boundary and Arbitrary Lagrangian-Eulerian Techniques for the Mesh Representation

In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary Lagrangian-Eulerian) or an Eulerian formulation. The majority of the reported 3D heart valve FSI simulations are performed with the Eulerian formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an Eulerian-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations’ outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results.     

Validation of a Fluid–Structure Interaction Model of a Heart Valve using the Dynamic Mesh Method in Fluent

Simulations of coupled problems such as fluid–structure interaction (FSI) are becoming more and more important for engineering purposes. This is particularly true when modeling the aortic valve, where the FSI between the blood and the valve determines the valve movement and the valvular hemodynamics. Nevertheless only a few studies are focusing on the opening and closing behavior during the ejection phase (systole). In this paper, we present the validation of a FSI model using the dynamic mesh method of Fluent for the two-dimensional (2D) simulation of mechanical heart valves during the ejection phase of the cardiac cycle. The FSI model is successfully validated by comparing simulation results to experimental data obtained from in vitro studies using a CCD camera.     

Simulation of upper airway occlusion without and with mandibular advancement in obstructive sleep apnea using fluid-structure interaction

Obstructive Sleep Apnea (OSA) is a common sleep disorder characterized by repetitive collapse of the upper airway (UA). One treatment option is a mandibular advancement splint (MAS) which protrudes the lower jaw, stabilizing the airway. However not all patients respond to MAS therapy and individual effects are not well understood. Simulations of airway behavior may represent a non-invasive means to understand OSA and individual treatment responses. Our aims were (1) to analyze UA occlusion and flow dynamics in OSA using the fluid structure interaction (FSI) method, and (2) to observe changes with MAS. Magnetic resonance imaging (MRI) scans were obtained at baseline and with MAS in a known treatment responder. Computational models of the patients' UA geometry were reconstructed for both conditions. The FSI model demonstrated full collapse of the UA (maximum 5.83 mm) pre-treatment (without MAS). The UA collapse was located at the oropharynx with low oropharyngeal pressure (−51.18 Pa to −39.08 Pa) induced by velopharyngeal jet flow (maximum 10.0 m/s). By comparison, simulation results from the UA with MAS, showed smaller deformation (maximum 2.03 mm), matching the known clinical response. Our FSI modeling method was validated by physical experiment on a 1:1 flexible UA model fabricated using 3D steriolithography. This is the first study of airflow dynamics in a deformable UA structure and inspiratory flow. These results expand on previous UA models using computational fluid dynamics (CFD), and lay a platform for application of computational models to study biomechanical properties of the UA in the pathogenesis and treatment of OSA.     

Validation of a fluid-structure interaction model of a heart valve using the dynamic mesh method in fluent

Simulations of coupled problems such as fluid-structure interaction (FSI) are becoming more and more important for engineering purposes. This is particularly true when modeling the aortic valve, where the FSI between the blood and the valve determines the valve movement and the valvular hemodynamics. Nevertheless only a few studies are focusing on the opening and closing behavior during the ejection phase (systole). In this paper, we present the validation of a FSI model using the dynamic mesh method of Fluent for the two-dimensional (2D) simulation of mechanical heart valves during the ejection phase of the cardiac cycle. The FSI model is successfully validated by comparing simulation results to experimental data obtained from in vitro studies using a CCD camera.     

The influence of computational strategy on prediction of mechanical stress in carotid atherosclerotic plaques: Comparison of 2D structure-only, 3D structure-only,one-way and fully coupled fluid-structure interaction analyses

Background

Compositional and morphological features of carotid atherosclerotic plaques provide complementary information to luminal stenosis in predicting clinical presentations. However, they alone cannot predict cerebrovascular risk. Mechanical stress within the plaque induced by cyclical changes in blood pressure has potential to assess plaque vulnerability. Various modeling strategies have been employed to predict stress, including 2D and 3D structure-only, 3D one-way and fully coupled fluid-structure interaction (FSI) simulations. However, differences in stress predictions using different strategies have not been assessed.

Methods

Maximum principal stress (Stress-P1) within 8 human carotid atherosclerotic plaques was calculated based on geometry reconstructed from in vivo computerized tomography and high resolution, multi-sequence magnetic resonance images. Stress-P1 within the diseased region predicted by 2D and 3D structure-only, and 3D one-way FSI simulations were compared to 3D fully coupled FSI analysis.

Results

Compared to 3D fully coupled FSI, 2D structure-only simulation significantly overestimated stress level (94.1 kPa [65.2, 117.3] vs. 85.5 kPa [64.4, 113.6]; median [inter-quartile range], p=0.0004). However, when slices around the bifurcation region were excluded, stresses predicted by 2D structure-only simulations showed a good correlation (R²=0.69) with values obtained from 3D fully coupled FSI analysis. 3D structure-only model produced a small yet statistically significant stress overestimation compared to 3D fully coupled FSI (86.8 kPa [66.3, 115.8] vs. 85.5 kPa [64.4, 113.6]; p<0.0001). In contrast, one-way FSI underestimated stress compared to 3D fully coupled FSI (78.8 kPa [61.1, 100.4] vs. 85.5 kPa [64.4, 113.7]; p<0.0001).

Conclusions

A 3D structure-only model seems to be a computationally inexpensive yet reasonably accurate approximation for stress within carotid atherosclerotic plaques with mild to moderate luminal stenosis as compared to fully coupled FSI analysis.     

Effect of exercise on blood flow through the aortic valve: a combined clinical and numerical study

The aim of this study was to measure the cardiac output and stroke volume for a healthy subject by coupling an echocardiogram Doppler (echo-Doppler) method with a fluid–structure interaction (FSI) simulation at rest and during exercise. Blood flow through aortic valve was measured by Doppler flow echocardiography. Aortic valve geometry was calculated by echocardiographic imaging. An FSI simulation was performed, using an arbitrary Lagrangian–Eulerian mesh. Boundary conditions were defined by pressure loads on ventricular and aortic sides. Pressure loads applied brachial pressures with (stage 1) and without (stage 2) differences between brachial, central and left ventricular pressures. FSI results for cardiac output were 15.4% lower than Doppler results for stage 1 (r = 0.999). This difference increased to 22.3% for stage 2. FSI results for stroke volume were undervalued by 15.3% when compared to Doppler results at stage 1 and 26.2% at stage 2 (r = 0.94). The predicted mean backflow of blood was 4.6%. Our results show that numerical methods can be combined with clinical measurements to provide good estimates of patient-specific cardiac output and stroke volume at different heart rates.     

An integrated fluid–structure interaction and thrombosis model for type B aortic dissection

False lumen thrombosis (FLT) in type B aortic dissection has been associated with the progression of dissection and treatment outcome. Existing computational models mostly assume rigid wall behavior which ignores the effect of flap motion on flow and thrombus formation within the FL. In this study, we have combined a fully coupled fluid–structure interaction (FSI) approach with a shear-driven thrombosis model described by a series of convection–diffusion reaction equations. The integrated FSI-thrombosis model has been applied to an idealized dissection geometry to investigate the interaction between vessel wall motion and growing thrombus. Our simulation results show that wall compliance and flap motion can influence the progression of FLT. The main difference between the rigid and FSI models is the continuous development of vortices near the tears caused by drastic flap motion up to 4.45 mm. Flap-induced high shear stress and shear rates around tears help to transport activated platelets further to the neighboring region, thus speeding up thrombus formation during the accelerated phase in the FSI models. Reducing flap mobility by increasing the Young’s modulus of the flap slows down the thrombus growth. Compared to the rigid model, the predicted thrombus volume is 25% larger using the FSI-thrombosis model with a relatively mobile flap. Furthermore, our FSI-thrombosis model can capture the gradual effect of thrombus growth on the flow field, leading to flow obstruction in the FL, increased blood viscosity and reduced flap motion. This model is a step closer toward simulating realistic thrombus growth in aortic dissection, by taking into account the effect of intimal flap and vessel wall motion.

     

An innovative numerical approach to resolve the pulse wave velocity in a healthy thoracic aorta model

Aortic dissection and atherosclerosis are highly fatal diseases. The development of both diseases is closely associated with highly complex haemodynamics. Thus, in predicting the onset of cardiac disease, it is desirable to obtain a detailed understanding of the flowfield characteristics in the human cardiovascular circulatory system. Accordingly, in this study, a numerical model of a normal human thoracic aorta is constructed using the geometry information obtained from a phase-contrast magnetic resonance imaging (PC-MRI) technique. The interaction between the blood flow and the vessel wall dynamics is then investigated using a coupled fluid–structure interaction (FSI) analysis. The simulations focus specifically on the flowfield characteristics and pulse wave velocity (PWV) of the blood flow. Instead of using a conventional PC-MRI method to measure PWV, we present an innovative application of using the FSI approach to numerically resolve PWV for the assessment of wall compliance in a thoracic aorta model. The estimated PWV for a normal thoracic aorta agrees well with the results obtained via PC-MRI measurement. In addition, simulations which consider the FSI effect yield a lower predicted value of the wall shear stress at certain locations in the cardiac cycle than models which assume a rigid vessel wall. Consequently, the model provides a suitable basis for the future development of more sophisticated methods capable of performing the computer-aided analysis of aortic blood flows.     

Evaluation of 4D flow MRI-based non-invasive pressure assessment in aortic coarctations

Severity of aortic coarctation (CoA) is currently assessed by estimating trans-coarctation pressure drops through cardiac catheterization or echocardiography. In principle, more detailed information could be obtained non-invasively based on space- and time-resolved magnetic resonance imaging (4D flow) data. Yet the limitations of this imaging technique require testing the accuracy of 4D flow-derived hemodynamic quantities against other methodologies.With the objective of assessing the feasibility and accuracy of this non-invasive method to support the clinical diagnosis of CoA, we developed an algorithm (4DF-FEPPE) to obtain relative pressure distributions from 4D flow data by solving the Poisson pressure equation. 4DF-FEPPE was tested against results from a patient-specific fluid-structure interaction (FSI) simulation, whose patient-specific boundary conditions were prescribed based on 4D flow data. Since numerical simulations provide noise-free pressure fields on fine spatial and temporal scales, our analysis allowed to assess the uncertainties related to 4D flow noise and limited resolution.4DF-FEPPE and FSI results were compared on a series of cross-sections along the aorta. Bland-Altman analysis revealed very good agreement between the two methodologies in terms of instantaneous data at peak systole, end-diastole and time-averaged values: biases (means of differences) were +0.4 mmHg, −1.1 mmHg and +0.6 mmHg, respectively. Limits of agreement (2 SD) were ±0.978 mmHg, ±1.06 mmHg and ±1.97 mmHg, respectively. Peak-to-peak and maximum trans-coarctation pressure drops obtained with 4DF-FEPPE differed from FSI results by 0.75 mmHg and −1.34 mmHg respectively. The present study considers important validation aspects of non-invasive pressure difference estimation based on 4D flow MRI, showing the potential of this technology to be more broadly applied to the clinical practice.     

Multi-patient study for coronary vulnerable plaque model comparisons: 2D/3D and fluid–structure interaction simulations

Several image-based computational models have been used to perform mechanical analysis for atherosclerotic plaque progression and vulnerability investigations. However, differences of computational predictions from those models have not been quantified at multi-patient level. In vivo intravascular ultrasound (IVUS) coronary plaque data were acquired from seven patients. Seven 2D/3D models with/without circumferential shrink, cyclic bending and fluid–structure interactions (FSI) were constructed for the seven patients to perform model comparisons and quantify impact of 2D simplification, circumferential shrink, FSI and cyclic bending plaque wall stress/strain (PWS/PWSn) and flow shear stress (FSS) calculations. PWS/PWSn and FSS averages from seven patients (388 slices for 2D and 3D thin-layer models) were used for comparison. Compared to 2D models with shrink process, 2D models without shrink process overestimated PWS by 17.26%. PWS change at location with greatest curvature change from 3D FSI models with/without cyclic bending varied from 15.07% to 49.52% for the seven patients (average = 30.13%). Mean Max-FSS, Min-FSS and Ave-FSS from the flow-only models under maximum pressure condition were 4.02%, 11.29% and 5.45% higher than those from full FSI models with cycle bending, respectively. Mean PWS and PWSn differences between FSI and structure-only models were only 4.38% and 1.78%. Model differences had noticeable patient variations. FSI and flow-only model differences were greater for minimum FSS predictions, notable since low FSS is known to be related to plaque progression. Structure-only models could provide PWS/PWSn calculations as good approximations to FSI models for simplicity and time savings in calculation.

     

A decoupled fluid structure approach for estimating wall stress in abdominal aortic aneurysms

Abdominal aortic aneurysm (AAA) is a localized dilatation of the aortic wall. The lack of an accurate AAA rupture risk index remains an important problem in the clinical management of the disease. To accurately estimate AAA rupture risk, detailed information on patient-specific wall stress distribution and aortic wall tissue yield stress is required. A complete fluid structure interaction (FSI) study is currently impractical and thus of limited clinical value. On the other hand, isolated static structural stress analysis based on a uniform wall loading is a widely used approach for AAA rupture risk estimation that, however, neglects the flow-induced wall stress variation. The aim of this study was to assess the merit of a decoupled fluid structure analysis of AAA wall stress. Anatomically correct, patient specific AAA wall models were created by 3D reconstruction of computed tomography images. Flow simulations were carried out with inflow and outflow boundary conditions obtained from patient extracted data. Static structural stress analysis was performed applying both a uniform pressure wall loading and a flow induced non-uniform pressure distribution obtained during early systolic deceleration. For the structural analysis, a hyperelastic arterial wall model and an elastic intraluminal thrombus model were assumed. The results of this study demonstrate that although the isolated static structural stress analysis approach captures the gross features of the stress distribution it underestimates the magnitude of the peak wall stress by as much as 12.5% compared to the proposed decoupled fluid structure approach. Furthermore, the decoupled approach provides potentially useful information on the nature of the aneurysmal sac flow.     

Wall stress and flow dynamics in abdominal aortic aneurysms: finite element analysis vs. fluid–structure interaction

Abdominal aortic aneurysm (AAA) rupture is the clinical manifestation of an induced force exceeding the resistance provided by the strength of the arterial wall. This force is most frequently assumed to be the product of a uniform luminal pressure acting along the diseased wall. However fluid dynamics is a known contributor to the pathogenesis of AAAs, and the dynamic interaction of blood flow and the arterial wall represents the in vivo environment at the macro-scale. The primary objective of this investigation is to assess the significance of assuming an arbitrary estimated peak fluid pressure inside the aneurysm sac for the evaluation of AAA wall mechanics, as compared with the non-uniform pressure resulting from a coupled fluid–structure interaction (FSI) analysis. In addition, a finite element approach is utilised to estimate the effects of asymmetry and wall thickness on the wall stress and fluid dynamics of ten idealised AAA models and one non-aneurysmal control. Five degrees of asymmetry with uniform and variable wall thickness are used. Each was modelled under a static pressure-deformation analysis, as well as a transient FSI. The results show that the inclusion of fluid flow yields a maximum AAA wall stress up to 20% higher compared to that obtained with a static wall stress analysis with an assumed peak luminal pressure of 117 mmHg. The variable wall models have a maximum wall stress nearly four times that of a uniform wall thickness, and also increasing with asymmetry in both instances. The inclusion of an axial stretch and external pressure to the computational domain decreases the wall stress by 17%.     

Wall stress and flow dynamics in abdominal aortic aneurysms: finite element analysis vs. fluid-structure interaction

Abdominal aortic aneurysm (AAA) rupture is the clinical manifestation of an induced force exceeding the resistance provided by the strength of the arterial wall. This force is most frequently assumed to be the product of a uniform luminal pressure acting along the diseased wall. However fluid dynamics is a known contributor to the pathogenesis of AAAs, and the dynamic interaction of blood flow and the arterial wall represents the in vivo environment at the macro-scale. The primary objective of this investigation is to assess the significance of assuming an arbitrary estimated peak fluid pressure inside the aneurysm sac for the evaluation of AAA wall mechanics, as compared with the non-uniform pressure resulting from a coupled fluid-structure interaction (FSI) analysis. In addition, a finite element approach is utilised to estimate the effects of asymmetry and wall thickness on the wall stress and fluid dynamics of ten idealised AAA models and one non-aneurysmal control. Five degrees of asymmetry with uniform and variable wall thickness are used. Each was modelled under a static pressure-deformation analysis, as well as a transient FSI. The results show that the inclusion of fluid flow yields a maximum AAA wall stress up to 20% higher compared to that obtained with a static wall stress analysis with an assumed peak luminal pressure of 117 mmHg. The variable wall models have a maximum wall stress nearly four times that of a uniform wall thickness, and also increasing with asymmetry in both instances. The inclusion of an axial stretch and external pressure to the computational domain decreases the wall stress by 17%.     

A patient-specific aortic valve model based on moving resistive immersed implicit surfaces

In this paper, we propose a full computational framework to simulate the hemodynamics in the aorta including the valve. Closed and open valve surfaces, as well as the lumen aorta, are reconstructed directly from medical images using new ad hoc algorithms, allowing a patient-specific simulation. The fluid dynamics problem that accounts from the movement of the valve is solved by a new 3D–0D fluid–structure interaction model in which the valve surface is implicitly represented through level set functions, yielding, in the Navier–Stokes equations, a resistive penalization term enforcing the blood to adhere to the valve leaflets. The dynamics of the valve between its closed and open position is modeled using a reduced geometric 0D model. At the discrete level, a finite element formulation is used and the SUPG stabilization is extended to include the resistive term in the Navier–Stokes equations. Then, after time discretization, the 3D fluid and 0D valve models are coupled through a staggered approach. This computational framework, applied to a patient-specific geometry and data, allows to simulate the movement of the valve, the sharp pressure jump occurring across the leaflets, and the blood flow pattern inside the aorta.     

Fluid-solid interaction in arteries incorporating the autoregulation concept in boundary conditions

In pre-surgery decisions in hospital emergency cases, fast and reliable results of the solid and fluid mechanics problems are of great interest to clinicians. In the current investigation, an iterative process based on a pressure-type boundary condition is proposed in order to reduce the computational costs of blood flow simulations in arteries, without losing control of the important clinical parameters. The incorporation of cardiovascular autoregulation, together with the well-known impedance boundary condition, forms the basis of the proposed methodology. With autoregulation, the instabilities associated with conventional pressure-type or impedance boundary conditions are avoided without an excessive increase in computational costs. The general behaviour of pulsatile blood flow in arteries, which is important from the clinical point of view, is well reproduced through this new methodology. In addition, the interaction between the blood and the arterial walls occurs via a modified weak coupling, which makes the simulation more stable and computationally efficient. Based on in vitro experiments, the hyperelastic behaviour of the wall is characterised and modelled. The applications and benefits of the proposed pressure-type boundary condition are shown in a model of an idealised aortic arch with and without an ascending aorta dissection, which is a common cardiovascular disorder.     

Influence of inlet boundary conditions on the local haemodynamics of intracranial aneurysms

Haemodynamics is believed to play an important role in the initiation, growth and rupture of intracranial aneurysms. In this context, computational haemodynamics has been extensively used in an effort to establish correlations between flow variables and clinical outcome. It is common practice in the application of Dirichlet boundary conditions at domain inlets to specify transient velocities as either a flat (plug) profile or a spatially developed profile based on Womersley's analytical solution. This paper provides comparative haemodynamics measures for three typical cerebral aneurysms.

Three dimentional rotational angiography images of aneurysms at three common locations, viz. basilar artery tip, internal carotid artery and middle cerebral artery were obtained. The computational tools being developed in the European project @neurIST were used to reconstruct the fluid domains and solve the unsteady Navier–Stokes equations, using in turn Womersley and plug-flow inlet velocity profiles. The effects of these assumptions were analysed and compared in terms of relevant haemodynamic variables within the aneurismal sac. For the aneurysm at the basilar tip geometries with different extensions of the afferent vasculature were considered to study the plausibility of a fully-developed axial flow at the inlet boundaries.

The study shows that assumptions made on the velocity profile while specifying inlet boundary conditions have little influence on the local haemodynamics in the aneurysm, provided that a sufficient extension of the afferent vasculature is considered and that geometry is the primary determinant of the flow field within the aneurismal sac. For real geometries the Womersley profile is at best an unnecessary over-complication, and may even be worse than the plug profile in some anatomical locations (e.g. basilar confluence).     

Numerical simulation of flow in mechanical heart valves: grid resolution and the assumption of flow symmetry

A numerical method is developed for simulating unsteady, 3-D, laminar flow through a bileaflet mechanical heart valve with the leaflets fixed. The method employs a dual-time-stepping artificial-compressibility approach together with overset (Chimera) grids and is second-order accurate in space and time. Calculations are carried out for the full 3-D valve geometry under steady inflow conditions on meshes with a total number of nodes ranging from 4 x 10(5) to 1.6 x 10(6). The computed results show that downstream of the leaflets the flow is dominated by two pairs of counter-rotating vortices, which originate on either side of the central orifice in the aortic sinus and rotate such that the common flow of each pair is directed away from the aortic wall. These vortices intensify with Reynolds number, and at a Reynolds number of approximately 1200 their complex interaction leads to the onset of unsteady flow and the break of symmetry with respect to both geometric planes of symmetry. Our results show the highly 3-D structure of the flow; question the validity of computationally expedient assumptions of flow symmetry; and demonstrate the need for highly resolved, fully 3-D simulations if computational fluid dynamics is to accurately predict the flow in prosthetic mechanical heart valves.