Multiblock High Order Large Eddy Simulation of Powered Fontan Hemodynamics: Towards Computational Surgery.

Children born with only one functional ventricle must typically undergo a series of three surgeries to obtain the so-called Fontan circulation in which the blood coming from the body passively flows from the Vena Cavae (VCs) to the Pulmonary Arteries (PAs) through the Total Cavopulmonary Connection (TCPC). The circulation is inherently inefficient due to the lack of a subpulmonary ventricle. Survivors face the risk of circulatory sequelae and eventual failure for the duration of their lives. Current efforts are focused on improving the outcomes of Fontan palliation, either passively by optimizing the TCPC, or actively by using mechanical support. We are working on a chronic implant that would be placed at the junction of the TCPC, and would provide the necessary pressure augmentation to re-establish a circulation that recapitulates a normal two-ventricle circulation. This implant is based on the Von Karman viscous pump and consists of a vaned impeller that rotates inside the TCPC. To evaluate the performance of such a device, and to study the flow features induced by the presence of the pump, Computational Fluid Dynamics (CFD) is used. CFD has become an important tool to understand hemodynamics owing to the possibility of simulating quickly a large number of designs and flow conditions without any harm for patients. The transitional and unsteady nature of the flow can make accurate simulations challenging. We developed and in-house high order Large Eddy Simulation (LES) solver coupled to a recent Immersed Boundary Method (IBM) to handle complex geometries. Multiblock capability is added to the solver to allow for efficient simulations of complex patient specific geometries. Blood simulations are performed in a complex patient specific TCPC geometry. In this study, simulations without mechanical assist are performed, as well as after virtual implantation of the temporary and chronic implants being developed. Instantaneous flow structures, hepatic factor distribution, and statistical data are presented for all three cases.

Dynamic Mode Decomposition of Fontan Hemodynamics in an Idealized Total Cavopulmonary Connection.

Univentricular heart disease is the leading cause of death from any birth defect in the first year of life. Typically, patients have to undergo three open heart surgical procedures within the first few years of their lives to eventually directly connect the superior and inferior vena cavae to the left and right pulmonary arteries forming the Total Cavopulmonary Connection or TCPC. The end result is a weak circulation where the single working ventricle pumps oxygenated blood to the body and de-oxygenated blood flows passively through the TCPC into the lungs. The fluid dynamics of the TCPC junction involve confined impinging jets resulting in a highly unstable flow, significant mechanical energy dissipation, and undesirable pressure loss. Understanding and predicting such flows is important for improving the surgical procedure and for the design of mechanical cavopulmonary assist devices. In this study, Dynamic Mode Decomposition (DMD) is used to analyze previously obtained Stereoscopic Particle Imaging Velocimetry (SPIV) data and Large Eddy Simulation (LES) results for an idealized TCPC. Analysis of the DMD modes from the SPIV and LES serve to both highlight the unsteady vortical dynamics and the qualitative agreement between measurements and simulations.

Large eddy simulation of transitional flow in an idealized stenotic blood vessel: evaluation of subgrid scale models.

In the present study, we performed large eddy simulation (LES) of axisymmetric, and 75% stenosed, eccentric arterial models with steady inflow conditions at a Reynolds number of 1000. The results obtained are compared with the direct numerical simulation (DNS) data (Varghese et al., 2007, "Direct Numerical Simulation of Stenotic Flows. Part 1. Steady Flow," J. Fluid Mech., 582, pp. 253-280). An inhouse code (WenoHemo) employing high-order numerical methods for spatial and temporal terms, along with a 2nd order accurate ghost point immersed boundary method (IBM) (Mark, and Vanwachem, 2008, "Derivation and Validation of a Novel Implicit Second-Order Accurate Immersed Boundary Method," J. Comput. Phys., 227(13), pp. 6660-6680) for enforcing boundary conditions on curved geometries is used for simulations. Three subgrid scale (SGS) models, namely, the classical Smagorinsky model (Smagorinsky, 1963, "General Circulation Experiments With the Primitive Equations," Mon. Weather Rev., 91(10), pp. 99-164), recently developed Vreman model (Vreman, 2004, "An Eddy-Viscosity Subgrid-Scale Model for Turbulent Shear Flow: Algebraic Theory and Applications," Phys. Fluids, 16(10), pp. 3670-3681), and the Sigma model (Nicoud et al., 2011, "Using Singular Values to Build a Subgrid-Scale Model for Large Eddy Simulations," Phys. Fluids, 23(8), 085106) are evaluated in the present study. Evaluation of SGS models suggests that the classical constant coefficient Smagorinsky model gives best agreement with the DNS data, whereas the Vreman and Sigma models predict an early transition to turbulence in the poststenotic region. Supplementary simulations are performed using Open source field operation and manipulation (OpenFOAM) ("OpenFOAM," http://www.openfoam.org/) solver and the results are inline with those obtained with WenoHemo.

Assessment of stretched vortex subgrid-scale models for LES of incompressible inhomogeneous turbulent flow.

The physical space version of the stretched vortex subgrid scale model [Phys. Fluids 12, 1810 (2000)] is tested in large eddy simulations (LES) of the turbulent lid driven cubic cavity flow. LES is carried out using a higher order finite-difference method [J. Comput. Phys. 229, 8802 (2010)]. The effects of different vortex orientation models and subgrid turbulence spectrums are assessed through comparisons of the LES predictions against direct numerical simulations (DNS) [Phys. Fluids 12, 1363 (2000)]. Three Reynolds numbers 12000, 18000, and 22000 are studied. Good agreement with the DNS data for the mean and fluctuating quantities is observed.

Large Eddy Simulation of FDA's Idealized Medical Device.

A hybrid large eddy simulation (LES) and immersed boundary method (IBM) computational approach is used to make quantitative predictions of flow field statistics within the Food and Drug Administration's (FDA) idealized medical device. An in-house code is used, hereafter (W enoHemo™ ), that combines high-order finite-difference schemes on structured staggered Cartesian grids with an IBM to facilitate flow over or through complex stationary or rotating geometries and employs a subgrid-scale (SGS) turbulence model that more naturally handles transitional flows [2]. Predictions of velocity and wall shear stress statistics are compared with previously published experimental measurements from Hariharan et al. [6] for the four Reynolds numbers considered.

A novel multiblock immersed boundary method for large eddy simulation of complex arterial hemodynamics.

Computational fluid dynamics (CFD) simulations are becoming a reliable tool to understand hemodynamics, disease progression in pathological blood vessels and to predict medical device performance. Immersed boundary method (IBM) emerged as an attractive methodology because of its ability to efficiently handle complex moving and rotating geometries on structured grids. However, its application to study blood flow in complex, branching, patient-specific anatomies is scarce. This is because of the dominance of grid nodes in the exterior of the fluid domain over the useful grid nodes in the interior, rendering an inevitable memory and computational overhead. In order to alleviate this problem, we propose a novel multiblock based IBM that preserves the simplicity and effectiveness of the IBM on structured Cartesian meshes and enables handling of complex, anatomical geometries at a reduced memory overhead by minimizing the grid nodes in the exterior of the fluid domain. As pathological and medical device hemodynamics often involve complex, unsteady transitional or turbulent flow fields, a scale resolving turbulence model such as large eddy simulation (LES) is used in the present work. The proposed solver (here after referred as WenoHemo), is developed by enhancing an existing in-house high order incompressible flow solver that was previously validated for its numerics and several LES models by Shetty et al. [Journal of Computational Physics 2010; 229 (23), 8802-8822]. In the present work, WenoHemo is systematically validated for additional numerics introduced, such as IBM and the multiblock approach, by simulating laminar flow over a sphere and laminar flow over a backward facing step respectively. Then, we validate the entire solver methodology by simulating laminar and transitional flow in abdominal aortic aneurysm (AAA). Finally, we perform blood flow simulations in the challenging clinically relevant thoracic aortic aneurysm (TAA), to gain insights into the type of fluid flow patterns that exist in pathological blood vessels. Results obtained from the TAA simulations reveal complex vortical and unsteady flow fields that need to be considered in designing and implanting medical devices such as stent grafts.

Performance evaluation of a pediatric viscous impeller pump for Fontan cavopulmonary assist.

OBJECTIVE: The anatomic and physiologic constraints for pediatric cavopulmonary assist differ markedly from adult Fontan circulations owing to smaller vessel sizes and risk of elevated pulmonary resistance. In this study, hemodynamic and hemolysis performance of a catheter-based viscous impeller pump (VIP) to power the Fontan circulation is assessed at a pediatric scale (∼15 kg) and performance range (0-30 mm Hg). METHODS: Computer simulation and mock circulation studies were conducted to assess the hydraulic performance, acute hemodynamic response to different levels VIP support, and the potential for vena caval collapse. Computational fluid dynamics simulations were used to estimate VIP hydraulic performance, shear rates, and potential for hemolysis. Hemolysis was quantified in a mock loop with fresh bovine blood. RESULTS: A VIP augmented 4-way total cavopulmonary connection flow at pediatric scales and restored systemic pressures and flows to biventricular values, without causing flow obstruction or suction. VIP generated flows up to 4.1 L/min and pressure heads of up to 38 mm Hg at 11,000 rpm. Maximal shear rate was 160 Pa, predicting low hemolysis risk. Observed hemolysis was low with plasma free hemoglobin of 11.4 mg · dL(-1) · h(-1). CONCLUSIONS: A VIP will augment Fontan cavopulmonary flow in the proper pressure and flow ranges, with low hemolysis risk under more stringent pediatric scale and physiology compared with adult scale. This technology may be developed to simultaneously reduce systemic venous pressure and improve cardiac output after stage 2 or 3 Fontan repair. It may serve to compress surgical staging, lessening the pathophysiologic burden of repair.

Cavopulmonary assist: (em)powering the univentricular fontan circulation.

Since the Fontan/Kreutzer procedure was introduced, evolutionary clinical advances via a staged surgical reconstructive approach have markedly improved outcomes for patients with functional single ventricle. However, significant challenges remain. Early stage mortality risk seems impenetrable. Serious morbidities - construed as immutable consequences of palliation - have hardly been addressed. Late functional status is increasingly linked to pathophysiologic consequences of prior staged procedures. As more single-ventricle patients survive into adulthood, Fontan failure is emerging as an intractable problem for which there is no targeted therapy. Incremental solutions to address these ongoing problems have not had a measurable impact. Therefore, a fundamental reconsideration of the overall approach is reasonable and warranted. The ability to provide a modest pressure boost (2 to 6 mmHg) to existing blood flow at the total cavopulmonary connection can effectively restore more stable biventricular status. This would impact not only treatment of late Fontan failure, but also facilitate early surgical repair. A realistic means to provide such a pressure boost has never been apparent. Recent advances are beginning to unravel the unique challenges that must be addressed to realize this goal, with promise to open single-ventricle palliation to new therapeutic vistas.

Cavopulmonary assist for the univentricular Fontan circulation: von Kármán viscous impeller pump.

OBJECTIVE: In a univentricular Fontan circulation, modest augmentation of existing cavopulmonary pressure head (2-5 mm Hg) would reduce systemic venous pressure, increase ventricular filling, and thus substantially improve circulatory status. An ideal means of providing mechanical cavopulmonary support does not exist. We hypothesized that a viscous impeller pump, based on the von Kármán viscous pump principle, is optimal for this role. METHODS: A 3-dimensional computational model of the total cavopulmonary connection was created. The impeller was represented as a smooth 2-sided conical actuator disk with rotation in the vena caval axis. Flow was modeled under 3 conditions: (1) passive flow with no disc; (2) passive flow with a nonrotating disk, and (3) induced flow with disc rotation (0-5K rpm). Flow patterns and hydraulic performance were examined for each case. Hydraulic performance for a vaned impeller was assessed by measuring pressure increase and induced flow over 0 to 7K rpm in a laboratory mock loop. RESULTS: A nonrotating actuator disc stabilized cavopulmonary flow, reducing power loss by 88%. Disk rotation (from baseline dynamic flow of 4.4 L/min) resulted in a pressure increase of 0.03 mm Hg. A further increase in pressure of 5 to 20 mm Hg and 0 to 5 L/min flow was obtained with a vaned impeller at 0 to 7K rpm in a laboratory mock loop. CONCLUSIONS: A single viscous impeller pump stabilizes and augments cavopulmonary flow in 4 directions, in the desired pressure range, without venous pathway obstruction. A viscous impeller pump applies to the existing staged protocol as a temporary bridge-to-recovery or -transplant in established univentricular Fontan circulations and may enable compressed palliation of single ventricle without the need for intermediary surgical staging or use of a systemic-to-pulmonary arterial shunt.

Performance of a 3-bladed propeller pump to provide cavopulmonary assist in the failing Fontan circulation.

PURPOSE: We hypothesized that a propeller pump design would function optimally to provide cavopulmonary assist in a univentricular Fontan circulation. DESCRIPTION: The hydraulic and hemolysis performance of a rigid three-bladed propeller prototype (similar to a folding propeller design) was characterized. Pressure and flow measurements were taken for flow rates of 0.5 to 3 liters per minute (LPM) for 5,000 to 7,000 revolutions per minute (RPM) using a blood analog fluid. Hemolysis testing was performed using fresh bovine blood for 2 LPM at 6,000 RPM for a 6-hour duration. EVALUATION: The prototype performed well over the design operating range by producing a pressure rise of 5 to 50 mm Hg. Plasma free hemoglobin concentration remained less than 15 mg/dL. The normalized index of hemolysis peaked during the first hour, and then remained less than 10 mg/dL thereafter. CONCLUSIONS: A propeller pump has the pressure-flow characteristics and minimal risk of hemolysis and venous pathway obstruction which make it ideal for temporary cavopulmonary assist. This type of device has the potential to provide a new therapeutic option for patients with failing univentricular Fontan physiology as a bridge-to-recovery or transplantation.

Comparing turbulence models for flow through a rigid glottal model.

Flow through a rigid model of the human vocal tract featuring a divergent glottis was numerically modeled using the Reynolds-averaged Navier-Stokes approach. A number of different turbulence models, available in a widely used commercial computational fluid dynamics code, were tested to determine their ability to capture various flow features recently observed in laboratory experiments and large eddy simulation studies. The study reveals that results from unsteady simulations employing the k-omega shear stress transport model were in much better agreement with previous measurements and predictions with regard to the ability to predict glottal jet skewing due to the Coanda effect and the intraglottal pressure distribution or related skin friction coefficient, than either steady or unsteady simulations using the Spalart-Allmaras model or any other two-equation turbulence model investigated in this study.

Modeling transition to turbulence in eccentric stenotic flows.

Mean flow predictions obtained from a host of turbulence models were found to be in poor agreement with recent direct numerical simulation results for turbulent flow distal to an idealized eccentric stenosis. Many of the widely used turbulence models, including a large eddy simulation model, were unable to accurately capture the poststenotic transition to turbulence. The results suggest that efforts toward developing more accurate turbulence models for low-Reynolds number, separated transitional flows are necessary before such models can be used confidently under hemodynamic conditions where turbulence may develop.

Mechanical cavopulmonary assist for the univentricular Fontan circulation using a novel folding propeller blood pump.

A blood pump specifically designed to operate in the unique anatomic and physiologic conditions of a cavopulmonary connection has never been developed. Mechanical augmentation of cavopulmonary blood flow in a univentricular circulation would reduce systemic venous pressure, increase preload to the single ventricle, and temporarily reproduce a scenario analogous to the normal two-ventricle circulation. We hypothesize that a folding propeller blood pump would function optimally in this cavopulmonary circulation. The hydraulic performance of a two-bladed propeller prototype was characterized in an experimental flow loop using a blood analog fluid for 0.5-3.5 lpm at rotational speeds of 3,600-4,000 rpm. We also created five distinctive blood pump designs and evaluated their hydraulic performance using computational fluid dynamics (CFD). The two-bladed prototype performed well over the design range of 0.5-3.5 lpm, producing physiologic pressure rises of 5-18 mm Hg. Building upon this proof-of-concept testing, the CFD analysis of the five numerical models predicted a physiologic pressure range of 5-40 mm Hg over 0.5-4 lpm for rotational speeds of 3,000-7,000 rpm. These preliminary propeller designs and the two-bladed prototype achieved the expected hydraulic performance. Optimization of these configurations will reduce fluid stress levels, remove regions of recirculation, and improve the hydraulic performance of the folding propeller. This propeller design produces the physiologic pressures and flows that are in the ideal range to mechanically support the cavopulmonary circulation and represents an exciting new therapeutic option for the support of a univentricular Fontan circulation.

Numerical simulation of turbulence transition and sound radiation for flow through a rigid glottal model.

Large eddy simulation (LES)-based computational aeroacoustics techniques were applied to a static model of the human glottis, idealized here as a planar channel with an orifice, to study flow-acoustic interactions related to speech. Rigid models of both converging and diverging glottal passages, each featuring a 20 deg included angle and a minimal glottal diameter of 0.04 cm, with an imposed transglottal pressure of 15 cm H2O, were studied. The Favre-filtered compressible Navier-Stokes equations were integrated for this low-Mach-number flow using an additive semi-implicit Runge-Kutta method and a high-order compact finite-difference scheme with characteristic-based nonreflecting boundary conditions and a multiblock approach. Flow asymmetries related to the Coanda effect and transition to turbulence, as well as the far-field sound, were captured. Acoustic-analogy-based far-field sound predictions were compared with direct simulations and showed that dipole sources, arising from unsteady flow forces exerted on the glottal walls, are primarily responsible for the tonal sound observed in the divergent glottis case.

Flow over a membrane-covered, fluid-filled cavity.

The flow-induced response of a membrane covering a fluid-filled cavity located in a section of a rigid-walled channel was explored using finite element analysis. The membrane was initially aligned with the channel wall and separated the channel fluid from the cavity fluid. As fluid flowed over the membrane-covered cavity, a streamwise-dependent transmural pressure gradient caused membrane deformation. This model has application to synthetic models of the vocal fold cover layer used in voice production research. In this paper, the model is introduced and responses of the channel flow, the membrane, and the cavity flow are summarized for a range of flow and membrane parameters. It is shown that for high values of cavity fluid viscosity, the intracavity pressure and the beam deflection both reached steady values. For combinations of low cavity viscosity and sufficiently large upstream pressures, large-amplitude membrane vibrations resulted. Asymmetric conditions were introduced by creating cavities on opposing sides of the channel and assigning different stiffness values to the two membranes. The asymmetry resulted in reduction in or cessation of vibration amplitude, depending on the degree of asymmetry, and in significant skewing of the downstream flow field.

Aerodynamic transfer of energy to the vocal folds.

The aerodynamic transfer of energy from glottal airflow to vocal fold tissue during phonation was explored using complementary synthetic and numerical vocal fold models. The synthetic model was fabricated using a flexible polyurethane rubber compound. The model size, shape, and material properties were generally similar to corresponding human vocal fold characteristics. Regular, self-sustained oscillations were achieved at a frequency of approximately 120 Hz. The onset pressure was approximately 1.2 kPa. A corresponding two-dimensional finite element model was developed using geometry definitions and material properties based on the synthetic model. The finite element model upstream and downstream pressure boundary conditions were based on experimental values acquired using the synthetic model. An analysis of the fully coupled fluid and solid numerical domains included flow separation and unsteady effects. The numerical results provided detailed flow data that was used to investigate aerodynamic energy transfer mechanisms. The results support the hypothesis that a cyclic variation of the orifice profile from a convergent to a divergent shape leads to a temporal asymmetry in the average wall pressure, which is the key factor for the achievement of self-sustained vocal fold oscillations. me rica.

Sound generation by steady flow through glottis-shaped orifices.

Although the signature of human voice is mostly tonal, it also includes a significant broadband component. Quadrupolelike sources due to turbulence in the region downstream of the glottis, and dipolelike sources due to the force applied by the vocal folds onto the surrounding fluid are the two primary broadband sound generating mechanisms. In this study, experiments were conducted to characterize the broadband sound emissions of confined stationary jets through rubber orifices formed to imitate the approximate shape of the human glottis at different stages during one cycle of vocal fold vibrations. The radiated sound pressure spectra downstream of the orifices were measured for varying flow rates, orifice shapes, and gas mixtures. The nondimensional sound pressure spectra were decomposed into the product of three functions: a source function F, a radiation efficiency function M, and an acoustic response function G. The results show that, as for circular jets, the quadrupole source contributions dominated for straight and convergent orifices. For divergent jets, whistling tonal sounds were emitted at low flow rates. At high flow rates for the same geometry, dipole contributions dominated the sound radiated by free jets. However, possible source-load acoustic feedback may have hampered accurate source identification in confined flows.

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.

Computational aeroacoustics of phonation, part I: Computational methods and sound generation mechanisms.

The aerodynamic generation of sound during phonation was studied using direct numerical simulations of the airflow and the sound field in a rigid pipe with a modulated orifice. Forced oscillations with an imposed wall motion were considered, neglecting fluid-structure interactions. The compressible, two-dimensional, axisymmetric form of the Navier-Stokes equations were numerically integrated using highly accurate finite difference methods. A moving grid was used to model the effects of the moving walls. The geometry and flow conditions were selected to approximate the flow within an idealized human glottis and vocal tract during phonation. Direct simulations of the flow and farfield sound were performed for several wall motion programs, and flow conditions. An acoustic analogy based on the Ffowcs Williams-Hawkings equation was then used to decompose the acoustic source into its monopole, dipole, and quadrupole contributions for analysis. The predictions of the farfield acoustic pressure using the acoustic analogy were in excellent agreement with results from the direct numerical simulations. It was found that the dominant sound production mechanism was a dipole induced by the net force exerted by the surfaces of the glottis walls on the fluid along the direction of sound wave propagation. A monopole mechanism, specifically sound from the volume of fluid displaced by the wall motion, was found to be comparatively weak at the frequency considered (125 Hz). The orifice geometry was found to have only a weak influence on the amplitude of the radiated sound.

Computational aeroacoustics of phonation, part II: Effects of flow parameters and ventricular folds.

The results are described of the second part of an ongoing study aimed at performing direct numerical simulations of translaryngeal flows during phonation. The use of accurate numerical schemes allows the radiated sound to be calculated directly, without the need for acoustic analogy models. The goal is to develop a better understanding of this class of flow, and of the basic sound generation mechanisms involved in phonation. In the present study, the effects of subglottal pressure and of glottal oscillation frequency on the near-field flow and farfield sound were investigated. The effects of the presence of the ventricular folds downstream of the oscillating glottal region were also examined. The results highlighted the effects of subglottal pressure and oscillation frequency on the jet vortical structure, wall pressure and shear stress, and sound radiation. Jet impingement on the ventricular folds introduced additional dipole sources similar to those observed in problems involving grazing flows over cavities.