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.     

Assessment of boundary conditions for CFD simulation in human carotid artery

Computational fluid dynamics (CFD) is an increasingly used method for investigation of hemodynamic parameters and their alterations under pathological conditions, which are important indicators for diagnosis of cardiovascular disease. In hemodynamic simulation models, the employment of appropriate boundary conditions (BCs) determines the computational accuracy of the CFD simulation in comparison with pressure and velocity measurements. In this study, we have first assessed the influence of inlet boundary conditions on hemodynamic CFD simulations. We selected two typical patients suspected of carotid artery disease, with mild stenosis and severe stenosis. Both patients underwent digital subtraction angiography (DSA), magnetic resonance angiography, and the invasive pressure guide wire measured pressure profile. We have performed computational experiments to (1) study the hemodynamic simulation outcomes of distributions of wall shear stress, pressure, pressure gradient and (2) determine the differences in hemodynamic performances caused by inlet BCs derived from DSA and Womersley analytical solution. Our study has found that the difference is related to the severity of the stenosis; the greater the stenosis, the more the difference ensues. Further, in our study, the two typical subjects with invasively measured pressure profile and thirty subjects with ultrasound Doppler velocimeter (UDV) measurement served as the criteria to evaluate the hemodynamic outcomes of wall shear stress, pressure, pressure gradient and velocity due to different outlet BCs based on the Windkessel model, structured-tree model, and fully developed flow model. According to the pressure profiles, the fully developed model appeared to have more fluctuations compared with the other two models. The Windkessel model had more singularities before convergence. The three outlet BCs models also showed good correlation with the UDV measurement, while the Windkessel model appeared to be slightly better (\( R^{2} = 0.942 \)). The structured-tree model was seen to have the best performance in terms of available computational cost and accuracy. The results of our numerical simulation and the good correlation with the computed pressure and velocity with their measurements have highlighted the effectiveness of CFD simulation in patient-specific human carotid artery with suspected stenosis.     

Effect of inlet velocity profiles on patient-specific computational fluid dynamics simulations of the carotid bifurcation

Patient-specific computational fluid dynamics (CFD) is a powerful tool for researching the role of blood flow in disease processes. Modern clinical imaging technology such as MRI and CT can provide high resolution information about vessel geometry, but in many situations, patient-specific inlet velocity information is not available. In these situations, a simplified velocity profile must be selected. We studied how idealized inlet velocity profiles (blunt, parabolic, and Womersley flow) affect patient-specific CFD results when compared to simulations employing a "reference standard" of the patient's own measured velocity profile in the carotid bifurcation. To place the magnitude of these effects in context, we also investigated the effect of geometry and the use of subject-specific flow waveform on the CFD results. We quantified these differences by examining the pointwise percent error of the mean wall shear stress (WSS) and the oscillatory shear index (OSI) and by computing the intra-class correlation coefficient (ICC) between axial profiles of the mean WSS and OSI in the internal carotid artery bulb. The parabolic inlet velocity profile produced the most similar mean WSS and OSI to simulations employing the real patient-specific inlet velocity profile. However, anatomic variation in vessel geometry and the use of a nonpatient-specific flow waveform both affected the WSS and OSI results more than did the choice of inlet velocity profile. Although careful selection of boundary conditions is essential for all CFD analysis, accurate patient-specific geometry reconstruction and measurement of vessel flow rate waveform are more important than the choice of velocity profile. A parabolic velocity profile provided results most similar to the patient-specific velocity profile.     

Validation of CFD predictions of flow in a 3D alveolated bend with experimental data

Verifying numerical predictions with experimental data is an important aspect of any modeling studies. In the case of the lung, the absence of direct in vivo flow measurements makes such verification almost impossible. We performed computational fluid dynamics (CFD) simulations in a 3D scaled-up model of an alveolated bend with rigid walls that incorporated essential geometrical characteristics of human alveolar structures and compared numerical predictions with experimental flow measurements made in the same model by particle image velocimetry (PIV). Flow in both models was representative of acinar flow during normal breathing (0.82ml/s). The experimental model was built in silicone and silicone oil was used as the carrier fluid. Flow measurements were obtained by an ensemble averaging procedure. CFD simulation was performed with STAR-CCM+ (CD-Adapco) using a polyhedral unstructured mesh. Velocity profiles in the central duct were parabolic and no bulk convection existed between the central duct and the alveoli. Velocities inside the alveoli were approximately 2 orders of magnitude smaller than the mean velocity in the central duct. CFD data agreed well with those obtained by PIV. In the central duct, data agreed within 1%. The maximum simulated velocity along the centerline of the model was 0.5% larger than measured experimentally. In the alveolar cavities, data agreed within 15% on average. This suggests that CFD techniques can satisfactorily predict acinar-type flow. Such a validation ensure a great degree of confidence in the accuracy of predictions made in more complex models of the alveolar region of the lung using similar CFD techniques.     

Quantitative comparison of CFD predicted and MRI measured velocity fields in a carotid bifurcation phantom

Steady flow of a blood mimicking fluid in a physiologically realistic model of the human carotid bifurcation was studied using both magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) modelling techniques. Quantitative comparisons of the 3D velocity field in the bifurcation phantom were made between phase contrast MRI measurements and CFD predictions. The geometry for the CFD model was reconstructed from T(1) weighted MR imaging of the test phantom. It was found that the predicted velocity fields were in fair agreement with MR measured velocities. In both the internal and external carotid arteries, the agreement between CFD predictions and MRI measurements was better along the inner-outer wall axis with a correlation factor C>0.897 (average 0.939) where the velocity profiles were skewed, than along the anterior-posterior axis (average correlation factor 0.876) where the velocity profiles were in M-shape.     

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.     

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.     

Multilaboratory particle image velocimetry analysis of the FDA benchmark nozzle model to support validation of computational fluid dynamics simulations

This study is part of a FDA-sponsored project to evaluate the use and limitations of computational fluid dynamics (CFD) in assessing blood flow parameters related to medical device safety. In an interlaboratory study, fluid velocities and pressures were measured in a nozzle model to provide experimental validation for a companion round-robin CFD study. The simple benchmark nozzle model, which mimicked the flow fields in several medical devices, consisted of a gradual flow constriction, a narrow throat region, and a sudden expansion region where a fluid jet exited the center of the nozzle with recirculation zones near the model walls. Measurements of mean velocity and turbulent flow quantities were made in the benchmark device at three independent laboratories using particle image velocimetry (PIV). Flow measurements were performed over a range of nozzle throat Reynolds numbers (Re(throat)) from 500 to 6500, covering the laminar, transitional, and turbulent flow regimes. A standard operating procedure was developed for performing experiments under controlled temperature and flow conditions and for minimizing systematic errors during PIV image acquisition and processing. For laminar (Re(throat)=500) and turbulent flow conditions (Re(throat)≥3500), the velocities measured by the three laboratories were similar with an interlaboratory uncertainty of ～10% at most of the locations. However, for the transitional flow case (Re(throat)=2000), the uncertainty in the size and the velocity of the jet at the nozzle exit increased to ～60% and was very sensitive to the flow conditions. An error analysis showed that by minimizing the variability in the experimental parameters such as flow rate and fluid viscosity to less than 5% and by matching the inlet turbulence level between the laboratories, the uncertainties in the velocities of the transitional flow case could be reduced to ～15%. The experimental procedure and flow results from this interlaboratory study (available at http://fdacfd.nci.nih.gov) will be useful in validating CFD simulations of the benchmark nozzle model and in performing PIV studies on other medical device models.     

Validation of numerical flow simulations against in vitro phantom measurements in different type B aortic dissection scenarios

An aortic dissection (AD) is a serious condition defined by the splitting of the arterial wall, thus generating a secondary lumen [the false lumen (FL)]. Its management, treatment and follow-up are clinical challenges due to the progressive aortic dilatation and potentially severe complications during follow-up. It is well known that the direction and rate of dilatation of the artery wall depend on haemodynamic parameters such as the local velocity profiles, intra-luminal pressures and resultant wall stresses. These factors act on the FL and true lumen, triggering remodelling and clinical worsening. In this study, we aimed to validate a computational fluid dynamic (CFD) tool for the haemodynamic characterisation of chronic (type B) ADs. We validated the numerical results, for several dissection geometries, with experimental data obtained from a previous in vitro study performed on idealised dissected physical models. We found a good correlation between CFD simulations and experimental measurements as long as the tear size was large enough so that the effect of the wall compliance was negligible.     

Estimation of valvular resistance of segmented aortic valves using computational fluid dynamics

Aortic valve stenosis is associated with an elevated left ventricular pressure and transaortic pressure drop. Clinicians routinely use Doppler ultrasound to quantify aortic valve stenosis severity by estimating this pressure drop from blood velocity. However, this method approximates the peak pressure drop, and is unable to quantify the partial pressure recovery distal to the valve. As pressure drops are flow dependent, it remains difficult to assess the true significance of a stenosis for low-flow low-gradient patients. Recent advances in segmentation techniques enable patient-specific Computational Fluid Dynamics (CFD) simulations of flow through the aortic valve. In this work a simulation framework is presented and used to analyze data of 18 patients. The ventricle and valve are reconstructed from 4D Computed Tomography imaging data. Ventricular motion is extracted from the medical images and used to model ventricular contraction and corresponding blood flow through the valve. Simplifications of the framework are assessed by introducing two simplified CFD models: a truncated time-dependent and a steady-state model. Model simplifications are justified for cases where the simulated pressure drop is above 10 mmHg. Furthermore, we propose a valve resistance index to quantify stenosis severity from simulation results. This index is compared to established metrics for clinical decision making, i.e. blood velocity and valve area. It is found that velocity measurements alone do not adequately reflect stenosis severity. This work demonstrates that combining 4D imaging data and CFD has the potential to provide a physiologically relevant diagnostic metric to quantify aortic valve stenosis severity.     

Three-dimensional surface geometries of the rabbit soleus muscle during contraction: input for biomechanical modelling and its validation

There exists several numerical approaches to describe the active contractile behaviour of skeletal muscles. These models range from simple one-dimensional to more advanced three-dimensional ones; especially, three-dimensional models take up the cause of describing complex contraction modes in a realistic way. However, the validation of such concepts is challenging, as the combination of geometry, material and force characteristics is so far not available from the same muscle. To this end, we present in this study a comprehensive data set of the rabbit soleus muscle consisting of the muscles’ characteristic force responses (active and passive), its three-dimensional shape during isometric, isotonic and isokinetic contraction experiments including the spatial arrangement of muscle tissue and aponeurosis–tendon complex, and the fascicle orientation throughout the whole muscle at its optimal length. In this way, an extensive data set is available giving insight into the three-dimensional geometry of the rabbit soleus muscle and, further, allowing to validate three-dimensional numerical models.     

Comparison of 4D Phase-Contrast MRI Flow Measurements to Computational Fluid Dynamics Simulations of Cerebrospinal Fluid Motion in the Cervical Spine

Cerebrospinal fluid (CSF) dynamics in the cervical spinal subarachnoid space (SSS) have been thought to be important to help diagnose and assess craniospinal disorders such as Chiari I malformation (CM). In this study we obtained time-resolved three directional velocity encoded phase-contrast MRI (4D PC MRI) in three healthy volunteers and four CM patients and compared the 4D PC MRI measurements to subject-specific 3D computational fluid dynamics (CFD) simulations. The CFD simulations considered the geometry to be rigid-walled and did not include small anatomical structures such as nerve roots, denticulate ligaments and arachnoid trabeculae. Results were compared at nine axial planes along the cervical SSS in terms of peak CSF velocities in both the cranial and caudal direction and visual interpretation of thru-plane velocity profiles. 4D PC MRI peak CSF velocities were consistently greater than the CFD peak velocities and these differences were more pronounced in CM patients than in healthy subjects. In the upper cervical SSS of CM patients the 4D PC MRI quantified stronger fluid jets than the CFD. Visual interpretation of the 4D PC MRI thru-plane velocity profiles showed greater pulsatile movement of CSF in the anterior SSS in comparison to the posterior and reduction in local CSF velocities near nerve roots. CFD velocity profiles were relatively uniform around the spinal cord for all subjects. This study represents the first comparison of 4D PC MRI measurements to CFD of CSF flow in the cervical SSS. The results highlight the utility of 4D PC MRI for evaluation of complex CSF dynamics and the need for improvement of CFD methodology. Future studies are needed to investigate whether integration of fine anatomical structures and gross motion of the brain and/or spinal cord into the computational model will lead to a better agreement between the two techniques.     

Locomotion with flexible propulsors: II. Computational modeling of pectoral fin swimming in sunfish

This paper describes a computational fluid dynamics (CFD) based investigation of the pectoral fin hydrodynamics of a bluegill sunfish. The pectoral fin of this fish undergoes significant shape-change during its abduction-adduction cycle and the effect of this deformation on the thrust performance remains far from understood. The current study is part of a combined experimental-numerical approach wherein the numerical simulations are being used to examine features and issues that are not easily amenable to the experiments. These numerical simulations are highly challenging and we briefly describe the computational methodology that has been developed to handle such flows. Finally, we describe some of the key computational results including wake vortex topologies and hydrodynamics forces.     

Computational modeling and validation of human nasal airflow under various breathing conditions

The human nose serves vital physiological functions, including warming, filtration, humidification, and olfaction. These functions are based on transport phenomena that depend on nasal airflow patterns and turbulence. Accurate prediction of these airflow properties requires careful selection of computational fluid dynamics models and rigorous validation. The validation studies in the past have been limited by poor representations of the complex nasal geometry, lack of detailed airflow comparisons, and restricted ranges of flow rate. The objective of this study is to validate various numerical methods based on an anatomically accurate nasal model against published experimentally measured data under breathing flow rates from 180 to 1100 ml/s. The numerical results of velocity profiles and turbulence intensities were obtained using the laminar model, four widely used Reynolds-averaged Navier-Stokes (RANS) turbulence models (i.e., k-ε, standard k-ω, Shear Stress Transport k-ω, and Reynolds Stress Model), large eddy simulation (LES) model, and direct numerical simulation (DNS). It was found that, despite certain irregularity in the flow field, the laminar model achieved good agreement with experimental results under restful breathing condition (180 ml/s) and performed better than the RANS models. As the breathing flow rate increased, the RANS models achieved more accurate predictions but still performed worse than LES and DNS. As expected, LES and DNS can provide accurate predictions of the nasal airflow under all flow conditions but have an approximately 100-fold higher computational cost. Among all the RANS models tested, the standard k-ω model agrees most closely with the experimental values in terms of velocity profile and turbulence intensity.     

Synchrony between parasite development and host behaviour change

Teleost fish are commonly used as model species in laboratory studies of behaviour and ecology. In comparison to other groups of vertebrates used routinely in such studies, however, relatively little attention has been paid to their environmental requirements from a welfare perspective. Fish naturally inhabit a wide variety of aquatic habitats that differ enormously in the range of light environments they provide, and light regime has enormous potential to affect behaviour. Yet the level and quality of illumination (in terms of intensity and wavelength spectrum) provided in experimental studies of fish behaviour is generally designed to maximize ease of recording by the observer. In addition, display or home aquaria provide illumination that maximizes the 'viewing pleasure' of the observer, and specialist lighting tubes are available to stimulate rapid plant growth and to 'show off' the colours of fish, rather than to provide 'natural' light environments. Here we present the results of three studies designed to examine the effects of light intensity, wavelength spectrum and their interactions on the behaviour of a model species commonly used in behavioural studies, the three‐spined stickleback Gasterosteus aculeatus . Our aims are to determine whether unnatural light environments, generated by manipulating light intensity and wavelength spectrum, affect behaviour in ways that may lead to concern for the welfare of fish as research animals or pets.     

Human cochlear hydrodynamics: A high-resolution μCT-based finite element study

Measurements of perilymph hydrodynamics in the human cochlea are scarce, being mostly limited to the fluid pressure at the basal or apical turn of the scalae vestibuli and tympani. Indeed, measurements of fluid pressure or volumetric flow rate have only been reported in animal models. In this study we imaged the human ear at 6.7 and 3-µm resolution using µCT scanning to produce highly accurate 3D models of the entire ear and particularly the cochlea scalae. We used a contrast agent to better distinguish soft from hard tissues, including the auditory canal, tympanic membrane, malleus, incus, stapes, ligaments, oval and round window, scalae vestibule and tympani. Using a Computational Fluid Dynamics (CFD) approach and this anatomically correct 3D model of the human cochlea, we examined the pressure and perilymph flow velocity as a function of location, time and frequency within the auditory range. Perimeter, surface, hydraulic diameter, Womersley and Reynolds numbers were computed every 45° of rotation around the central axis of the cochlear spiral. CFD results showed both spatial and temporal pressure gradients along the cochlea. Small Reynolds number and large Womersley values indicate that the perilymph fluid flow at auditory frequencies is laminar and its velocity profile is plug-like. The pressure was found 102–106° out of phase with the fluid flow velocity at the scalae vestibule and tympani, respectively. The average flow velocity was found in the sub-µm/s to nm/s range at 20–100 Hz, and below the nm/s range at 1–20 kHz.     

Comparison of hemodynamic endpoints between normal subject and tetralogy patient using Womersley velocity profile and MR based flow measurements

Right ventricular (RV) enlargement and pulmonary valve insufficiency (PI) are well-known, unavoidable long term sequelae encountered by patients who undergo tetralogy of Fallot (TOF) surgery. Despite their lifelong need for cardiac surveillance and occasional re-intervention, there is a paucity of numerical data characterizing blood flows in their pulmonary arteries (PA). Specifically, although PA regurgitation is well-known to be ubiquitously present in adult repaired TOF (rTOF) patients yet, there have been only limited numerical studies to fully characterize this process. The few studies available have utilized idealized, simplistic geometric models or overly simplistic boundary conditions that fail to account for flow reversals near the arterial walls as observed in in-vitro and MRI based in-vivo studies. The objective of this study was to establish and validate a numerical methodology of PA blood flow using actual patient specific geometry and flow measurements obtained using phase-contrast MRI, employing Womersley type velocity profiles that model flow reversals near walls. The results from computation were validated with measurements. For the normal subject, the time averaged right PA pressure from computation (13.8 mmHg) and experiment (14.6 mmHg) differed by 6%. The time-averaged main PA pressure from computation (16.5 mmHg) and experiment (16.3 mmHg) differed by 1%. The numerically computed left PA regurgitant fraction was 89% compared to measured 77.5%, while the same for the rTOF was 43% (computation), compared to 39.6% (measured). We conclude that the use of numerical computations using the Womersley boundary condition allows reliable modeling of the pathophysiology of PA flow in rTOF.     

Numerical modeling of pulsatile turbulent flow in stenotic vessels

Pulsatile turbulent flow in stenotic vessels has been numerically modeled using the Reynolds-averaged Navier-Stokes equation approach. The commercially available computational fluid dynamics code (CFD), FLUENT, has been used for these studies. Two different experiments were modeled involving pulsatile flow through axisymmetric stenoses. Four different turbulence models were employed to study their influence on the results. It was found that the low Reynolds number k-omega turbulence model was in much better agreement with previous experimental measurements than both the low and high Reynolds number versions of the RNG (renormalization-group theory) k-epsilon turbulence model and the standard k-epsilon model, with regard to predicting the mean flow distal to the stenosis including aspects of the vortex shedding process and the turbulent flow field. All models predicted a wall shear stress peak at the throat of the stenosis with minimum values observed distal to the stenosis where flow separation occurred.     

Quantitatively measuring in situ flows using a self-contained underwater velocimetry apparatus (SCUVA)

The ability to directly measure velocity fields in a fluid environment is necessary to provide empirical data for studies in fields as diverse as oceanography, ecology, biology, and fluid mechanics. Field measurements introduce practical challenges such as environmental conditions, animal availability, and the need for field-compatible measurement techniques. To avoid these challenges, scientists typically use controlled laboratory environments to study animal-fluid interactions. However, it is reasonable to question whether one can extrapolate natural behavior (i.e., that which occurs in the field) from laboratory measurements. Therefore, in situ quantitative flow measurements are needed to accurately describe animal swimming in their natural environment. We designed a self-contained, portable device that operates independent of any connection to the surface, and can provide quantitative measurements of the flow field surrounding an animal. This apparatus, a self-contained underwater velocimetry apparatus (SCUVA), can be operated by a single scuba diver in depths up to 40 m. Due to the added complexity inherent of field conditions, additional considerations and preparation are required when compared to laboratory measurements. These considerations include, but are not limited to, operator motion, predicting position of swimming targets, available natural suspended particulate, and orientation of SCUVA relative to the flow of interest. The following protocol is intended to address these common field challenges and to maximize measurement success.