Large eddy simulation of powered Fontan hemodynamics

Computational Fluid Dynamics Turbulence Model and Experimental Study for a Fontan Cavopulmonary Assist Device

Head-flow HQ curves for a Fontan cavopulmonary assist device (CPAD) were measured using a blood surrogate in a mock circulatory loop and simulated with various computational fluid dynamics (CFD) models. The tests benchmarked the CFD tools for further enhancement of the CPAD design. Recommended Reynolds-Averaged Navier-Stokes (RANS) CFD approaches for the development of conventional ventricular assist devices (VAD) were found to have shortcomings when applied to the Fontan CPAD, which is designed to neutralize off-condition obstruction risks that could contribute to a major adverse event. The no-obstruction condition is achieved with a von Karman pump, utilizing large clearances and small blade heights, which challenge conventional VAD RANS-based CFD hemodynamic simulations. High-fidelity large eddy simulation (LES) is always recommended; however, this may be cost-inhibitive for optimization studies in commercial settings, thus the reliance on RANS models. This study compares head and power predictions of various RANS turbulence models, employing experimental measurements and LES results as a basis for comparison. The models include standard k-ϵ, re-normalization group k-ϵ, realizable k-ϵ, shear stress transport (SST) k-ω, SST with transitional turbulence, and Generalized k-ω. For the pressure head predictions, it was observed that the standard k-ϵ model provided far better agreement with experiment. For the rotor torque, k-ϵ predictions were 30% lower than LES, while the SST and LES torque values were near identical. For the Fontan CPAD, the findings support using LES for the final design simulations, k-ϵ model for head and general flow simulation, and SST for power, shear stress, hemolysis, and thrombogenicity predictions.

Lumped parameter models for two-ventricle and healthy and failing extracardiac Fontan circulations

Fontan circulations are surgical strategies to treat infants born with single ventricle physiology. Clinical and mathematical definitions of Fontan failure are lacking, and understanding is needed of parameters indicative of declining physiologies. Our objective is to develop lumped parameter models of two-ventricle and single-ventricle circulations. These models, their mathematical formulations and a proof of existence of periodic solutions are presented. Sensitivity analyses are performed to identify key parameters. Systemic venous and systolic left ventricular compliances and systemic capillary and pulmonary venous resistances are identified as key parameters. Our models serve as a framework to study the differences between two-ventricle and single-ventricle physiologies and healthy and failing Fontan circulations.

In-Vitro Validation of Self-Powered Fontan Circulation for Treatment of Single Ventricle Anomaly

Around 8% of all newborns with a Congenital Heart Defect (CHD) have only a single functioning ventricle. The Fontan operation has served as palliation for this anomaly for decades, but the surgery entails multiple complications, and the survival rate is less than 50% by adulthood. A rapidly testable novel alternative is proposed by creating a bifurcating graft, or Injection Jet Shunt (IJS), used to “entrain” the pulmonary flow and thus provide assistance while reducing the caval pressure. A dynamically scaled Mock Flow Loop (MFL) has been configured to validate this hypothesis. Three IJS nozzles of varying diameters 2, 3, and 4 mm with three aortic anastomosis angles and pulmonary vascular resistance (PVR) reduction have been tested to validate the hypothesis and optimize the caval pressure reduction. The MFL is based on a Lumped-Parameter Model (LPM) of a non-fenestrated Fontan circulation. The best outcome was achieved with the experimental testing of a 3 mm IJS by producing an average caval pressure reduction of more than 5 mmHg while maintaining the clinically acceptable pulmonary flow rate (Qp) to systemic flow rate (Qs) ratio of ~1.5. Furthermore, alteration of the PVR helped in achieving higher caval pressure reduction with the 3 mm IJS at the expense of an increase in Qp/Qs ratio.

Shear stress evaluation on blood cells using computational fluid dynamics

BACKGROUND

Thrombus formation and hemolysis are important factors in developing blood pumps and mechanical heart valve prostheses. These phenomena are induced by flow properties. High shear stress induces platelet and red cell damage. Computational fluid dynamics (CFD) analysis calculates shear stress of fluid and particle pathlines of blood cells.

OBJECTIVE

We studied blood cell damage in a blood pump by using CFD analysis and proposed a method for estimating blood damage.

METHODS

We analyzed a pulsatile blood pump that was developed as a totally implantable left ventricular assist system at Tokai University. Shear stress on blood cells throughout pulsatile blood pumps were analyzed using CFD software.

RESULTS

Based on the assumption that the effect of shear stress on platelets is accumulated along the trace, we proposed a method for estimating blood damage using the damage parameter D. Platelet damage parameter is calculated regardless of the division time 𝛥t which is dependent on the calculation time step. The results of the simulations are in good agreement with Giersiepen's equation obtained from the experiments.

CONCLUSION

The history of shear stress on a particle was calculated using CFD analysis. The new damage parameter D yields a value close to that of Giersiepen's equation with small errors.

Computational fluid dynamic simulations of a cavopulmonary assist device for failing Fontan circulation

OBJECTIVES

Adult patients who have undergone the Fontan procedure are highly vulnerable to gradual, progressive circulatory failure, and options to reverse this situation are few. A cavopulmonary assist device could decongest the venous and lymphatic systems, overcome elevated pulmonary vascular resistance, increase cardiac output, and support some of these patients to heart transplant. This study characterizes the performance and challenges of a novel multilumen cannula coupled to an external blood pump proposed as a potential Fontan cavopulmonary assist strategy.

METHODS

Computational fluid dynamic simulations were conducted for 3 extracardiac Fontan geometries consisting of 1 idealized model and 2 patient-specific models. A range of physiologic flow rates and pump assist levels were simulated to calculate the pressure gain provided by the multilumen cannula. Hemolysis index was estimated for the idealized model with Lagrangian particle tracking and 2 variations of the power-law. Wall shear stresses were also examined.

RESULTS

Pressure gains up to 4 and 9 mm Hg were achieved for the idealized and patient-specific models, respectively. Pressure gains increased with both higher cardiac output and larger pump intake through the external pump. Flow-weighted hemolysis show hemoglobin damage levels to be several times lower than the 2% threshold at the highest pump intake flow cases. Wall shear stress predictions depict elevated areas in the pulmonary vessels and regions of the cannula device.

CONCLUSIONS

The cannula tested in this study shows promise as a percutaneous option to bridge support in some patients with a failing extracardiac Fontan. Limitations identified will be addressed in future design iterations and in ongoing experimental tests.

HEMODYNAMIC EFFECT OF OBSTRUCTION TO RENAL ARTERIES CAUSED BY STENT GRAFTS IN PATIENTS WITH ABDOMINAL AORTIC ANEURYSMS

To investigate the hemodynamic effects of partial obstruction to the renal orifice caused by inappropriate stent-graft location. Pre-operative and deployment models of a stent graft with various degrees of obstruction to the renal orifice are constructed based on medical images of abdominal aortic aneurysm. Hemodynamics, including flow pattern, time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), as well as relative residence time (RRT) are analyzed using numerical simulations. Flow rate distributions are assessed and verified by in vitro experiments. Results show that partial blockage to the renal branch orifice leads to flow recirculation and vortices with low wall shear stress around the renal ostia, whereas OSI and RRT on the renal arteries increase with the degree of obstruction. While the in vitro experiment indicates a decreasing flow rate to the bilateral renal arteries as renal artery ostia are obstructed. In conclusion, obstruction to the renal arteries induced by an inappropriate stent graft location causes stenosis in the renal artery in the long term. This study reveals a possible pathological mechanism of renal complications due to the implantation of a stent graft.

Computational Investigation of a Self-Powered Fontan Circulation

Children born with anatomic or functional "single ventricle" must progress through two or more major operations to sustain life. This management sequence culminates in the total cavopulmonary connection, or "Fontan" operation. A consequence of the "Fontan circulation", however, is elevated central venous pressure and inadequate ventricular preload, which contribute to continued morbidity. We propose a solution to these problems by increasing pulmonary blood flow using an "injection jet" (IJS) in which the source of blood flow and energy is the ventricle itself. The IJS has the unique property of lowering venous pressure while enhancing pulmonary blood flow and ventricular preload. We report preliminary results of an analysis of this circulation using a tightly-coupled, multi-scale computational fluid dynamics model. Our calculations show that, constraining the excess volume load to the ventricle at 50% (pulmonary to systemic flow ratio of 1.5), an optimally configured IJS can lower venous pressure by 3 mmHg while increasing systemic oxygen delivery. Even this small decrease in venous pressure may have substantial clinical impact on the Fontan patient. These findings support the potential for a straightforward surgical modification to decrease venous pressure, and perhaps improve clinical outcome in selected patients.

Statistical Shape Modeling for Cavopulmonary Assist Device Development: Variability of Vascular Graft Geometry and Implications for Hemodynamics

Patients born with a single functional ventricle typically undergo three-staged surgical palliation in the first years of life, with the last stage realizing a cross-like total cavopulmonary connection (TCPC) of superior and inferior vena cavas (SVC and IVC) with both left and right pulmonary arteries, allowing all deoxygenated blood to flow passively back to the lungs (Fontan circulation). Even though within the past decades more patients survive into adulthood, the connection comes at the prize of deficiencies such as chronic systemic venous hypertension and low cardiac output, which ultimately may lead to Fontan failure. Many studies have suggested that the TCPC's inherent insufficiencies might be addressed by adding a cavopulmonary assist device (CPAD) to provide the necessary pressure boost. While many device concepts are being explored, few take into account the complex cardiac anatomy typically associated with TCPCs. In this study, we focus on the extra cardiac conduit vascular graft connecting IVC and pulmonary arteries as one possible landing zone for a CPAD and describe its geometric variability in a cohort of 18 patients that had their TCPC realized with a 20mm vascular graft. We report traditional morphometric parameters and apply statistical shape modeling to determine the main contributors of graft shape variability. Such information may prove useful when designing CPADs that are adapted to the challenging anatomical boundaries in Fontan patients. We further compute the anatomical mean 3D graft shape (template graft) as a representative of key shape features of our cohort and prove this template graft to be a significantly better approximation of population and individual patient's hemodynamics than a commonly used simplified tube geometry. We therefore conclude that statistical shape modeling results can provide better models of geometric and hemodynamic boundary conditions associated with complex cardiac anatomy, which in turn may impact on improved cardiac device development.

Improvement of hemodynamic performance using novel helical flow vena cava filter design

We propose a vena cava filter in which helical flow is created in the filter’s working zone to minimize filter blockage by trapped clots and facilitate the lysis of trapped clots. To validate this new design, we compared five helical flow inducers with different thread pitches in terms of blood flow patterns in the filter. The vena cava was reconstructed based on computed tomography images. Both the numerical simulation and in vitro experiment revealed that the helical flow inducer can effectively create a helical flow in the vessel, thereby subduing the filter structure’s adverse disruption to blood flow, and increasing flow-induced shear stress in the filter center. In addition, the smaller thread pitch helical flow inducer reduced the oscillating shear index and relative residence time on the vessel wall. Moreover, we observed that the helical flow inducer in the vena cava could induce flow rotation both in clockwise and counterclockwise directions. In conclusion, the new design of the filter with the smaller thread pitch inducer is advantageous over the traditional filter in terms of improving local hemodynamics, which may reduce thrombosis build-up after deployment.

Computational modeling and engineering in pediatric and congenital heart disease

PURPOSE OF REVIEW

Recent methodological advances in computational simulations are enabling increasingly realistic simulations of hemodynamics and physiology, driving increased clinical utility. We review recent developments in the use of computational simulations in pediatric and congenital heart disease, describe the clinical impact in modeling in single-ventricle patients, and provide an overview of emerging areas.

RECENT FINDINGS

Multiscale modeling combining patient-specific hemodynamics with reduced order (i.e., mathematically and computationally simplified) circulatory models has become the de-facto standard for modeling local hemodynamics and 'global' circulatory physiology. We review recent advances that have enabled faster solutions, discuss new methods (e.g., fluid structure interaction and uncertainty quantification), which lend realism both computationally and clinically to results, highlight novel computationally derived surgical methods for single-ventricle patients, and discuss areas in which modeling has begun to exert its influence including Kawasaki disease, fetal circulation, tetralogy of Fallot (and pulmonary tree), and circulatory support.

SUMMARY

Computational modeling is emerging as a crucial tool for clinical decision-making and evaluation of novel surgical methods and interventions in pediatric cardiology and beyond. Continued development of modeling methods, with an eye towards clinical needs, will enable clinical adoption in a wide range of pediatric and congenital heart diseases.

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.

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.

A paired membrane umbrella double-lumen cannula ensures consistent cavopulmonary assistance in a Fontan sheep model

OBJECTIVES

The Avalon Elite (Macquet, Rastatt, Germany) double-lumen cannula can provide effective cavopulmonary assistance in a Fontan (total cavopulmonary connection) sheep model, but it requires strict alignment. The objective was to fabricate and test a newly designed paired umbrella double-lumen cannula without alignment requirement.

METHODS

The paired membrane umbrellas were designed on the double-lumen cannula to bracket infusion blood flow toward the pulmonary artery. Two umbrellas were attached, one 4 cm above and one 4 cm below the infusion opening. Umbrellas were temporarily wrapped and glued to the double-lumen cannula body to facilitate insertion. A total cavopulmonary connection mock loop was used to test cavopulmonary assistance performance and reliability with double-lumen cannula rotation and displacement. The paired umbrella double-lumen cannula also was tested in a total cavopulmonary connection adult sheep model (n = 6).

RESULTS

The bench test showed up to 4.5 L/min pumping flow and approximately 90% pumping flow efficiency at 360° rotation and 8-cm displacement of double-lumen cannula. The total cavopulmonary connection model with compromised hemodynamics was successfully created in all 6 sheep. The cavopulmonary assistance double-lumen cannula with paired umbrellas was smoothly inserted into the superior vena cava and extracardiac conduit in all sheep. At 3.5 to 4.0 L/min pump flow, the systolic arterial blood pressure and central venous pressure returned to normal baseline and remained stable throughout the 90-minute experiment, demonstrating effective cavopulmonary assistance support. Double-lumen cannula rotation and displacement did not affect performance. Autopsy revealed well-opened and positioned paired umbrellas, and double-lumen cannulas were easily removed from the right jugular vein.

CONCLUSIONS

Our double-lumen cannula with paired umbrellas is easy to insert and remove. The paired umbrellas eliminated the strict alignment requirement and ensured consistent cavopulmonary assistance performance.

In Vitro Ultrasound Measurements of Powered and Unpowered Total Cavopulmonary Connection

Three-staged Fontan palliation is performed on children suffering from single ventricle congenital heart disease. The series of surgical procedures reroutes blood from the vena cavae directly to the pulmonary arteries, creating a total cavopulmonary connection (TCPC). A viscous impeller pump (VIP) is currently being developed as a cavopulmonary assist device that can modestly augment cavopulmonary flow, reduce systemic venous pressure, and improve ventricular preload. This study used ultrasound to visualize complex flow patterns in powered and unpowered in vitro mock Fontan circulations. The idealized TCPC was modeled with a silicone mold and blood analog made of water and glycerol that was seeded with 10-μm glass beads. B-mode, color Doppler, and pulsed-wave Doppler images were used to visualize complex flow patterns in the idealized TCPC with (1) no VIP, (2) static VIP, and powered VIP rotation rates of (3) 500 and (4) 2,000 rotations per minute (RPM). Pulsed-wave Doppler data showed higher mean velocities and greater variance in the outlets relative to the larger inlets. The maximum inlet velocity ± SD increased from 10.9 ± 3.53 cm/s with no VIP to 15.9 ± 1.03 when the VIP was rotating at 2,000 RPM. Likewise, the maximum outlet velocity increased from 14.9 ± 11.2 cm/s to 18.9 ± 7.25 cm/s at 2,000 RPM. The faster mean velocities with the VIP rotating suggest that the pump augments cavopulmonary flow. The results of this study suggest that measuring complex flow patterns with ultrasound in vivo could be used clinically to optimize VIP positioning and rotation rate during and after implantation.

Reflections on five decades of the fontan kreutzer procedure

The first successful total right heart bypass via atriopulmonary anastomosis (APA) were reported in 1971 for patients with tricuspid atresia. At the Children's Hospital of Buenos Aires, the cohort of such procedures started in July, when the first fenestrated right heart by pass was performed, with the interposition of a homograft between the right atrial appendage and the main pulmonary artery. In the second patient, instead of placing a homograft, the APA was achieved with the patient's own pulmonary root harvested from the outflow tract of the right ventricle. These techniques were soon replaced in 1978 with the development of the direct valveless posterior APA. Since the very beginning the principle was that the right atrium only functions as a pathway rather than a pump (reason why no inferior vena cava valves were ever used), and the diastolic properties of the systemic ventricle regulate the only real "pump" of this system. The late hemodynamic problems inherent of the APA diminished with modern surgical techniques like the lateral tunnel (LT) or the extracardiac conduit (EC). In spite of the improvement in prognosis and quality of life that the modern techniques have brought for univentricular hearts (UH), with the passing of time, deterioration of this system is frequently seen, due to chronic low cardiac output, elevated central venous pressure making heart transplantation the final stage of treatment. Progressive increase in pulmonary vascular resistances and ventricular dysfunction result in a decline in quality of life and survival. However, the timing of this occurrence is variable, and many survivors enjoy today a satisfactory clinical status. The challenge is to develop a better solution for UH, but in the mean time the Fontan Kreutzer palliation represents the best and only surgical option. It is undoubtedly one of the triumphs of cardiac surgery in congenital heart disease.

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.

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.