CFD simulation of flow through heart: a perspective review

The heart is an organ which pumps blood around the body by contraction of muscular wall. There is a coupled system in the heart containing the motion of wall and the motion of blood fluid; both motions must be computed simultaneously, which make biological computational fluid dynamics (CFD) difficult. The wall of the heart is not rigid and hence proper boundary conditions are essential for CFD modelling. Fluid-wall interaction is very important for real CFD modelling. There are many assumptions for CFD simulation of the heart that make it far from a real model. A realistic fluid-structure interaction modelling the structure by the finite element method and the fluid flow by CFD use more realistic coupling algorithms. This type of method is very powerful to solve the complex properties of the cardiac structure and the sensitive interaction of fluid and structure. The final goal of heart modelling is to simulate the total heart function by integrating cardiac anatomy, electrical activation, mechanics, metabolism and fluid mechanics together, as in the computational framework.     

Fluid mechanics of the zebrafish embryonic heart trabeculation

Embryonic heart development is a mechanosensitive process, where specific fluid forces are needed for the correct development, and abnormal mechanical stimuli can lead to malformations. It is thus important to understand the nature of embryonic heart fluid forces. However, the fluid dynamical behaviour close to the embryonic endocardial surface is very sensitive to the geometry and motion dynamics of fine-scale cardiac trabecular surface structures. Here, we conducted image-based computational fluid dynamics (CFD) simulations to quantify the fluid mechanics associated with the zebrafish embryonic heart trabeculae. To capture trabecular geometric and motion details, we used a fish line that expresses fluorescence at the endocardial cell membrane, and high resolution 3D confocal microscopy. Our endocardial wall shear stress (WSS) results were found to exceed those reported in existing literature, which were estimated using myocardial rather than endocardial boundaries. By conducting simulations of single intra-trabecular spaces under varied scenarios, where the translational or deformational motions (caused by contraction) were removed, we found that a squeeze flow effect was responsible for most of the WSS magnitude in the intra-trabecular spaces, rather than the shear interaction with the flow in the main ventricular chamber. We found that trabecular structures were responsible for the high spatial variability of the magnitude and oscillatory nature of WSS, and for reducing the endocardial deformational burden. We further found cells attached to the endocardium within the intra-trabecular spaces, which were likely embryonic hemogenic cells, whose presence increased endocardial WSS. Overall, our results suggested that a complex multi-component consideration of both anatomic features and motion dynamics were needed to quantify the trabeculated embryonic heart fluid mechanics.     

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.     

Flow in t-bifurcations: Effect of the sharpness of the flow divider

The local geometry of a bifurcation has been hypothesized to be a potential geometrical risk factor for the development of atherosclerosis. While flow division and branch area ratios clearly affect the flow field, the importance of the flow divider shape is not as clear. A fast spectral element computational fluid mechanics (CFD) solver was used to simulate flow through 90 ° T-bifurcations with three different flow divider shapes. Other factors, such as flow partition, area ratio, and bifurcation angle, were kept constant. A Reynolds number range of 15 to 350 was studied to bracket experimental results in the literature. The variation in the sharpness of the corners had a dramatic effect on both the flow field and wall shear stress distribution in the side branch, but little effect on the flow in the main tube. The magnitude of reverse velocities and wall shear stress in the side branch increased linearly over a physiological range of Reynolds number and corner shape. This paper verifies the accuracy and usefulness of spectral element CFD in studying three-dimensional hemodynamics.     

Speckle variance optical coherence tomography of blood flow in the beating mouse embryonic heart

Efficient separation of blood and cardiac wall in the beating embryonic heart is essential and critical for experiment‐based computational modelling and analysis of early‐stage cardiac biomechanics. Although speckle variance optical coherence tomography (SV‐OCT) relying on calculation of intensity variance over consecutively acquired frames is a powerful approach for segmentation of fluid flow from static tissue, application of this method in the beating embryonic heart remains challenging because moving structures generate SV signal indistinguishable from the blood. Here, we demonstrate a modified four‐dimensional SV‐OCT approach that effectively separates the blood flow from the dynamic heart wall in the beating mouse embryonic heart. The method takes advantage of the periodic motion of the cardiac wall and is based on calculation of the SV signal over the frames corresponding to the same phase of the heartbeat cycle. Through comparison with Doppler OCT imaging, we validate this speckle‐based approach and show advantages in its insensitiveness to the flow direction and velocity as well as reduced influence from the heart wall movement. This approach has a potential in variety of applications relying on visualization and segmentation of blood flow in periodically moving structures, such as mechanical simulation studies and finite element modelling. Picture : Four‐dimensional speckle variance OCT imaging shows the blood flow inside the beating heart of an E8.5 mouse embryo.     

Combined effects of pulsatile flow and dynamic curvature on wall shear stress in a coronary artery bifurcation model

A three-dimensional model with simplified geometry for the branched coronary artery is presented. The bifurcation is defined by an analytical intersection of two cylindrical tubes lying on a sphere that represents an idealized heart surface. The model takes into account the repetitive variation of curvature and motion to which the vessel is subject during each cardiac cycle, and also includes the phase difference between arterial motion and blood flowrate, which may be nonzero for patients with pathologies such as aortic regurgitation. An arbitrary Lagrangian Eulerian (ALE) formulation of the unsteady, incompressible, three-dimensional Navier-Stokes equations is employed to solve for the flow field, and numerical simulations are performed using the spectral/hp element method. The results indicate that the combined effect of pulsatile inflow and dynamic geometry depends strongly on the aforementioned phase difference. Specifically, the main findings of this work show that the time-variation of flowrate ratio between the two branches is minimal (less than 5%) for the simulation with phase difference angle equal to 90 degrees, and maximal (51%) for 270 degrees. In two flow pulsatile simulation cases for fixed geometry and dynamic geometry with phase angle 270 degrees, there is a local minimum of the normalized wall shear rate amplitude in the vicinity of the bifurcation, while in other simulations a local maximum is observed.     

4D subject-specific inverse modeling of the chick embryonic heart outflow tract hemodynamics

Blood flow plays a critical role in regulating embryonic cardiac growth and development, with altered flow leading to congenital heart disease. Progress in the field, however, is hindered by a lack of quantification of hemodynamic conditions in the developing heart. In this study, we present a methodology to quantify blood flow dynamics in the embryonic heart using subject-specific computational fluid dynamics (CFD) models. While the methodology is general, we focused on a model of the chick embryonic heart outflow tract (OFT), which distally connects the heart to the arterial system, and is the region of origin of many congenital cardiac defects. Using structural and Doppler velocity data collected from optical coherence tomography, we generated 4D (\(\hbox {3D}\,+\,\hbox {time}\)) embryo-specific CFD models of the heart OFT. To replicate the blood flow dynamics over time during the cardiac cycle, we developed an iterative inverse-method optimization algorithm, which determines the CFD model boundary conditions such that differences between computed velocities and measured velocities at one point within the OFT lumen are minimized. Results from our developed CFD model agree with previously measured hemodynamics in the OFT. Further, computed velocities and measured velocities differ by \(<\)15 % at locations that were not used in the optimization, validating the model. The presented methodology can be used in quantifications of embryonic cardiac hemodynamics under normal and altered blood flow conditions, enabling an in-depth quantitative study of how blood flow influences cardiac development.     

The effect of implantation orientation of a bileaflet mechanical heart valve on kinematics and hemodynamics in an anatomic aorta

We carry out three-dimensional high-resolution numerical simulations of a bileaflet mechanical heart valve under physiologic pulsatile flow conditions implanted at different orientations in an anatomic aorta obtained from magnetic resonance imaging (MRI) of a volunteer. We use the extensively validated for heart valve flow curvilinear-immersed boundary (CURVIB) fluid-structure interaction (FSI) solver in which the empty aorta is discretized with a curvilinear, aorta-conforming grid while the valve is handled as an immersed boundary. The motion of the valve leaflets are calculated through a strongly coupled FSI algorithm implemented in conjunction with the Aitken convergence acceleration technique. We perform simulations for three valve orientations, which differ from each other by 45 deg and compare the results in terms of leaflet motion and flow field. We show that the valve implanted symmetrically relative to the symmetry plane of the ascending aorta curvature exhibits the smallest overall asymmetry in the motion of its two leaflets and lowest rebound during closure. Consequently, we hypothesize that this orientation is beneficial to reduce the chance of intermittent regurgitation. Furthermore, we find that the valve orientation does not significantly affect the shear stress distribution in the aortic lumen, which is in agreement with previous studies.     

Numerical simulation of local blood flow in the carotid and cerebral arteries under altered gravity

A computational fluid dynamics (CFD) approach was presented to model the blood flows in the carotid bifurcation and the brain arteries under altered gravity. Physical models required for CFD simulation were introduced including a model for arterial wall motion due to fluid-wall interactions, a shear thinning fluid model of blood, a vascular bed model for outflow boundary conditions, and a model for autoregulation mechanism. The three-dimensional unsteady incompressible Navier-Stokes equations coupled with these models were solved iteratively using the pseudocompressibility method and dual time stepping. Gravity source terms were added to the Navier-Stokes equations to take the effect of gravity into account. For the treatment of complex geometry, a chimera overset grid technique was adopted to obtain connectivity between arterial branches. For code validation, computed results were compared with experimental data for both steady-state and time-dependent flows. This computational approach was then applied to blood flows through a realistic carotid bifurcation and two Circle of Willis models, one using an idealized geometry and the other using an anatomical data set. A three-dimensional Circle of Willis configuration was reconstructed from subject-specific magnetic resonance images using an image segmentation method. Through the numerical simulation of blood flow in two model problems, namely, the carotid bifurcation and the brain arteries, it was observed that the altered gravity has considerable effects on arterial contraction/dilatation and consequent changes in flow conditions.     

Moving Domain Computational Fluid Dynamics to Interface with an Embryonic Model of Cardiac Morphogenesis

Peristaltic contraction of the embryonic heart tube produces time- and spatial-varying wall shear stress (WSS) and pressure gradients (∇P) across the atrioventricular (AV) canal. Zebrafish (Danio rerio) are a genetically tractable system to investigate cardiac morphogenesis. The use of Tg(fli1a:EGFP)^y1 transgenic embryos allowed for delineation and two-dimensional reconstruction of the endocardium. This time-varying wall motion was then prescribed in a two-dimensional moving domain computational fluid dynamics (CFD) model, providing new insights into spatial and temporal variations in WSS and ∇P during cardiac development. The CFD simulations were validated with particle image velocimetry (PIV) across the atrioventricular (AV) canal, revealing an increase in both velocities and heart rates, but a decrease in the duration of atrial systole from early to later stages. At 20-30 hours post fertilization (hpf), simulation results revealed bidirectional WSS across the AV canal in the heart tube in response to peristaltic motion of the wall. At 40-50 hpf, the tube structure undergoes cardiac looping, accompanied by a nearly 3-fold increase in WSS magnitude. At 110-120 hpf, distinct AV valve, atrium, ventricle, and bulbus arteriosus form, accompanied by incremental increases in both WSS magnitude and ∇P, but a decrease in bi-directional flow. Laminar flow develops across the AV canal at 20-30 hpf, and persists at 110-120 hpf. Reynolds numbers at the AV canal increase from 0.07±0.03 at 20-30 hpf to 0.23±0.07 at 110-120 hpf (p< 0.05, n=6), whereas Womersley numbers remain relatively unchanged from 0.11 to 0.13. Our moving domain simulations highlights hemodynamic changes in relation to cardiac morphogenesis; thereby, providing a 2-D quantitative approach to complement imaging analysis.     

Assessment of human left ventricle flow using statistical shape modelling and computational fluid dynamics

Blood flow patterns in the human left ventricle (LV) have shown relation to cardiac health. However, most studies in the literature are limited to a few patients and results are hard to generalize. This study aims to provide a new framework to generate more generalized insights into LV blood flow as a function of changes in anatomy and wall motion. In this framework, we studied the four-dimensional blood flow in LV via computational fluid dynamics (CFD) in conjunction with a statistical shape model (SSM), built from segmented LV shapes of 150 subjects. We validated results in an in-vitro dynamic phantom via time-resolved optical particle image velocimetry (PIV) measurements. This combination of CFD and the SSM may be useful for systematically assessing blood flow patterns in the LV as a function of varying anatomy and has the potential to provide valuable data for diagnosis of LV functionality.     

Computational fluid dynamics analysis of cyclist aerodynamics: Performance of different turbulence-modelling and boundary-layer modelling approaches

This study aims at assessing the accuracy of computational fluid dynamics (CFD) for applications in sports aerodynamics, for example for drag predictions of swimmers, cyclists or skiers, by evaluating the applied numerical modelling techniques by means of detailed validation experiments. In this study, a wind-tunnel experiment on a scale model of a cyclist (scale 1:2) is presented. Apart from three-component forces and moments, also high-resolution surface pressure measurements on the scale model’s surface, i.e. at 115 locations, are performed to provide detailed information on the flow field. These data are used to compare the performance of different turbulence-modelling techniques, such as steady Reynolds-averaged Navier–Stokes (RANS), with several k–ε and k–ω turbulence models, and unsteady large-eddy simulation (LES), and also boundary-layer modelling techniques, namely wall functions and low-Reynolds number modelling (LRNM). The commercial CFD code Fluent 6.3 is used for the simulations. The RANS shear-stress transport (SST) k–ω model shows the best overall performance, followed by the more computationally expensive LES. Furthermore, LRNM is clearly preferred over wall functions to model the boundary layer. This study showed that there are more accurate alternatives for evaluating flow around bluff bodies with CFD than the standard k–ε model combined with wall functions, which is often used in CFD studies in sports.     

Three-dimensional convective alveolar flow induced by rhythmic breathing motion of the pulmonary acinus

Low Reynolds number flows (Re<1) in the human pulmonary acinus are often difficult to assess due to the submillimeter dimensions and accessibility of the region. In the present computational study, we simulated three-dimensional alveolar flows in an alveolated duct at each generation of the pulmonary acinar tree using recent morphometric data. Rhythmic lung expansion and contraction motion was modeled using moving wall boundary conditions to simulate realistic sedentary tidal breathing. The resulting alveolar flow patterns are largely time independent and governed by the ratio of the alveolar to ductal flow rates, Qa/Qd. This ratio depends uniquely on geometrical configuration such that alveolar flow patterns may be entirely determined by the location of the alveoli along the acinar tree. Although flows within alveoli travel very slowly relative to those in acinar ducts, 0.021%相似文献   

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.

     

Computational modeling of the mechanical behavior of the cerebrospinal fluid system

A computational fluid dynamics (CFD) model of the cerebrospinal fluid system was constructed based on a simplified geometry of the brain ventricles and their connecting pathways. The flow is driven by a prescribed sinusoidal motion of the third ventricle lateral walls, with all other boundaries being rigid. The pressure propagation between the third and lateral ventricles was examined and compared to data obtained from a similar geometry with a stenosed aqueduct. It could be shown that the pressure amplitude in the lateral ventricles increases in the presence of aqueduct stenosis. No difference in phase shift between the motion of the third ventricle walls and the pressure in the lateral ventricles because of the aqueduct stenosis could be observed. It is deduced that CFD can be used to analyze the pressure propagation and its phase shift relative to the ventricle wall motion. It is further deduced that only models that take into account the coupling between ventricles, which feature a representation of the original geometry that is as accurate as possible and which represent the ventricle boundary motion realistically, should be used to make quantitative statements on flow and pressure in the ventricular space.     

Laser assessment of leaflet closing motion in prosthetic heart valves

The dynamics of leaflet motion in heart valve prostheses (HVP), and in particular the closing velocity, is believed to be related to the valve sound and possibly to the phenomenon of valve cavitation. This paper describes a non-intrusive laser sweeping technique enabling the study of leaflet motion. The principle of measurement and the equipment involved are presented, together with the results of two commerially available, 29 mm bileaflet mitral valves, a St. Jude Medical, and an Edwards Duromedic valve. Experiments were carried out in a pulsatile mock flow testing loop designed to mimic physiological pressure waveforms and ventricular contraction. Measurements of heart rate were made in the range 70–120 beats min⁻¹, with a ventricular pressure slope range of 1800–5600 mm Hgs⁻¹ and a cardiac output range of 5.0–7.5 litres min⁻¹. Motion analysis of the measured data focuses on the velocity of the leaflet immediately before closure.     

Validation of CFD simulations of cerebral aneurysms with implication of geometric variations

BACKGROUND: Computational fluid dynamics (CFD) simulations using medical-image-based anatomical vascular geometry are now gaining clinical relevance. This study aimed at validating the CFD methodology for studying cerebral aneurysms by using particle image velocimetry (PIV) measurements, with a focus on the effects of small geometric variations in aneurysm models on the flow dynamics obtained with CFD. METHOD OF APPROACH: An experimental phantom was fabricated out of silicone elastomer to best mimic a spherical aneurysm model. PIV measurements were obtained from the phantom and compared with the CFD results from an ideal spherical aneurysm model (S1). These measurements were also compared with CFD results, based on the geometry reconstructed from three-dimensional images of the experimental phantom. We further performed CFD analysis on two geometric variations, S2 and S3, of the phantom to investigate the effects of small geometric variations on the aneurysmal flow field. Results. We found poor agreement between the CFD results from the ideal spherical aneurysm model and the PIV measurements from the phantom, including inconsistent secondary flow patterns. The CFD results based on the actual phantom geometry, however, matched well with the PIV measurements. CFD of models S2 and S3 produced qualitatively similar flow fields to that of the phantom but quantitatively significant changes in key hemodynamic parameters such as vorticity, positive circulation, and wall shear stress. CONCLUSION: CFD simulation results can closely match experimental measurements as long as both are performed on the same model geometry. Small geometric variations on the aneurysm model can significantly alter the flow-field and key hemodynamic parameters. Since medical images are subjected to geometric uncertainties, image-based patient-specific CFD results must be carefully scrutinized before providing clinical feedback.     

Effects of vessel compliance on flow pattern in porcine epicardial right coronary arterial tree

The compliance of the vessel wall affects hemodynamic parameters which may alter the permeability of the vessel wall. Based on experimental measurements, the present study established a finite element (FE) model in the proximal elastic vessel segments of epicardial right coronary arterial (RCA) tree obtained from computed tomography. The motion of elastic vessel wall was measured by an impedance catheter and the inlet boundary condition was measured by an ultrasound flow probe. The Galerkin FE method was used to solve the Navier–Stokes and Continuity equations, where the convective term in the Navier–Stokes equation was changed in the arbitrary Lagrangian–Eulerian (ALE) framework to incorporate the motion due to vessel compliance. Various hemodynamic parameters (e.g., wall shear stress—WSS, WSS spatial gradient—WSSG, oscillatory shear index—OSI) were analyzed in the model. The motion due to vessel compliance affects the time-averaged WSSG more strongly than WSS at bifurcations. The decrease of WSSG at flow divider in elastic bifurcations, as compared to rigid bifurcations, implies that the vessel compliance decreases the permeability of vessel wall and may be atheroprotective. The model can be used to predict coronary flow pattern in subject-specific anatomy as determined by noninvasive imaging.     

A porous-medium approach for modeling heart mechanics. I. theory

A method is developed for evaluating the distribution of the blood pressure, stresses and strains of the muscle fibers, and motion of the cardiac wall due to the cyclic contractions of the heart. The cardiac system is subdivided into two media: the chambers and the wall; the latter is enclosed by two impermeable surfaces (with one interface separating the two media and the other confining the wall). The momentum balance equation for the blood in the (two) cardiac ventricles is averaged, yielding a modification of Forchheimer's law, namely inclusion of the time derivative of the flux. The contracting muscle provides the driving force for the blood flow, and the endocardial velocity is thus taken as identical to that of the blood in the cavity next to the wall. Translation of the endocardium is governed by the blood pressure gradients in the ventricles. The blood pressure and stress-strain pattern in the myocardium are analyzed by applying concepts of the theory of mixtures to the blood and to the saturated solid matrix. With the blood pressure simulated by a modified Darcy law with relative fluid-solid velocity, fiber stresses and strains can be assessed with the aid of appropriate constitutive and compatibility laws.     

Effect of left atrial ligation-driven altered inflow hemodynamics on embryonic heart development: clues for prenatal progression of hypoplastic left heart syndrome

Congenital heart defects (CHDs) are abnormalities in the heart structure present at birth. One important condition is hypoplastic left heart syndrome (HLHS) where severely underdeveloped left ventricle (LV) cannot support systemic circulation. HLHS usually initiates as localized tissue malformations with no underlying genetic cause, suggesting that disturbed hemodynamics contribute to the embryonic development of these defects. Left atrial ligation (LAL) is a surgical procedure on embryonic chick resulting in a phenotype resembling clinical HLHS. In this study, we investigated disturbed hemodynamics and deteriorated cardiac growth following LAL to investigate possible mechanobiological mechanisms for the embryonic development of HLHS. We integrated techniques such as echocardiography, micro-CT and computational fluid dynamics (CFD) for these analyses. Specifically, LAL procedure causes an immediate flow disturbance over atrioventricular (AV) cushions. At later stages after the heart septation, it causes hemodynamic disturbances in LV. As a consequence of the LAL procedure, the left-AV canal and LV volume decrease in size, and in the opposite way, the right-AV canal and right ventricle volume increase. According to our CFD analysis, LAL results in an immediate decrease in the left AV canal WSS levels for 3.5-day (HH21) pre-septated hearts. For 7-day post-septated hearts (HH30), LAL leads to further reduction in WSS levels in the left AV canal, and relatively increased WSS levels in the right AV canal. This study demonstrates the critical importance of the disturbed hemodynamics during the heart valve and ventricle development.