Analysis of the Suitability of an Effective Viscosity to Represent Interactions Between Red Blood Cells in Shear Flow.

Many methods to computationally predict red blood cell damage have been introduced, and among these are Lagrangian methods that track the cells along their pathlines. Such methods typically do not explicitly include cell-cell interactions. Due to the high volume fraction of red blood cells (RBCs) in blood, these interactions could impact cell mechanics and thus the amount of damage caused by the flow. To investigate this question, cell-resolved simulations of red blood cells in shear flow were performed for multiple interacting cells, as well as for single cells in unbounded flow at an effective viscosity. Simulations run without adjusting the bulk viscosity produced larger errors unilaterally and were not considered further for comparison. We show that a periodic box containing at least 8 cells and a spherical harmonic of degree larger than 10 are necessary to produce converged higher-order statistics. The maximum difference between the single-cell and multiple-cell cases in terms of peak strain was 3.7%. To achieve this, one must use the whole blood viscosity and average over multiple cell orientations when adopting a single-cell simulation approach. The differences between the models in terms of average strain were slightly larger (maximum difference of 6.9%). However, given the accuracy of the single-cell approach in predicting the maximum strain, which is useful in hemolysis prediction, and its computational cost that is orders of magnitude less than the multiple-cell approach, one may use it as an affordable cell-resolved approach for hemolysis prediction.

A time-consistent stabilized finite element method for fluids with applications to hemodynamics.

Several finite element methods for simulating incompressible flows rely on the streamline upwind Petrov-Galerkin stabilization (SUPG) term, which is weighted by [Formula: see text]. The conventional formulation of [Formula: see text] includes a constant that depends on the time step size, producing an overall method that becomes exceedingly less accurate as the time step size approaches zero. In practice, such method inconsistency introduces significant error in the solution, especially in cardiovascular simulations, where small time step sizes may be required to resolve multiple scales of the blood flow. To overcome this issue, we propose a consistent method that is based on a new definition of [Formula: see text]. This method, which can be easily implemented on top of an existing streamline upwind Petrov-Galerkin and pressure stabilizing Petrov-Galerkin method, involves the replacement of the time step size in [Formula: see text] with a physical time scale. This time scale is calculated in a simple operation once every time step for the entire computational domain from the ratio of the L2-norm of the acceleration and the velocity. The proposed method is compared against the conventional method using four cases: a steady pipe flow, a blood flow through vascular anatomy, an external flow over a square obstacle, and a fluid-structure interaction case involving an oscillatory flexible beam. These numerical experiments, which are performed using linear interpolation functions, show that the proposed formulation eliminates the inconsistency issue associated with the conventional formulation in all cases. While the proposed method is slightly more costly than the conventional method, it significantly reduces the error, particularly at small time step sizes. For the pipe flow where an exact solution is available, we show the conventional method can over-predict the pressure drop by a factor of three. This large error is almost completely eliminated by the proposed formulation, dropping to approximately 1% for all time step sizes and Reynolds numbers considered.

A cell-resolved, Lagrangian solver for modeling red blood cell dynamics in macroscale flows.

When red blood cells (RBCs) experience non-physiologically high stresses, e.g., in medical devices, they can rupture in a process called hemolysis. Directly simulating this process is computationally unaffordable given that the length scales of a medical device are several orders of magnitude larger than that of a RBC. To overcome this separation of scales, the present work introduces an affordable computational framework that accurately resolves the stress and deformation of a RBC in a spatially and temporally varying macroscale flow field such as those found in a typical medical device. The underlying idea of the present framework is to treat RBCs as one-way coupled tracers in the macroscale flow by capturing the effect of the flow on their dynamics but neglecting their effect on the flow at the macroscale. As a result, the RBC dynamics are simulated after those of the flow in a postprocessing step by receiving the fluid velocity gradient tensor measured along the RBC trajectory as the input. To resolve the fluid velocity in the immediate vicinity of the RBC as well as the motion of the membrane, we employ the boundary integral method coupled to a structural solver. The governing equations are discretized in space using spherical harmonics, yielding spectral integration accuracy. The predictions produced by this formulation are in good agreement with those obtained from simulations of spherical capsules in shear flows and optical tweezers experiments. The accuracy of the present method is evaluated using unbounded shear flow as a benchmark. Its computational cost grows proportional to p 5, where p is the degree of the spherical harmonic. It also exhibits a fast convergence rate that is approximately O ( p 6 ) for p ⪅ 20.

A SOX17-PDGFB signaling axis regulates aortic root development.

Developmental etiologies causing complex congenital aortic root abnormalities are unknown. Here we show that deletion of Sox17 in aortic root endothelium in mice causes underdeveloped aortic root leading to a bicuspid aortic valve due to the absence of non-coronary leaflet and mispositioned left coronary ostium. The respective defects are associated with reduced proliferation of non-coronary leaflet mesenchyme and aortic root smooth muscle derived from the second heart field cardiomyocytes. Mechanistically, SOX17 occupies a Pdgfb transcriptional enhancer to promote its transcription and Sox17 deletion inhibits the endothelial Pdgfb transcription and PDGFB growth signaling to the non-coronary leaflet mesenchyme. Restoration of PDGFB in aortic root endothelium rescues the non-coronary leaflet and left coronary ostium defects in Sox17 nulls. These data support a SOX17-PDGFB axis underlying aortic root development that is critical for aortic valve and coronary ostium patterning, thereby informing a potential shared disease mechanism for concurrent anomalous aortic valve and coronary arteries.

Simulation of a vacuum helmet to contain pathogen-bearing droplets in dental and otolaryngologic outpatient interventions.

Clinic encounters of dentists and otolaryngologists inherently expose these specialists to an enhanced risk of severe acute respiratory syndrome coronavirus 2 infection, thus threatening them, their patients, and their practices. In this study, we propose and simulate a helmet design that could be used by patients to minimize the transmission risk by retaining droplets created through coughing. The helmet has a port for accessing the mouth and nose and another port connected to a vacuum source to prevent droplets from exiting through the access port and contaminating the environment or clinical practitioners. We used computational fluid dynamics in conjunction with Lagrangian point-particle tracking to simulate droplet trajectories when a patient coughs while using this device. A range of droplet diameters and different operating conditions were simulated. The results show that 100% of the airborne droplets and 99.6% of all cough droplets are retained by the helmet.

An Efficient Assisted Bidirectional Glenn Design With Lowered Superior Vena Cava Pressure for Stage-One Single Ventricle Patients.

Recently, the assisted bidirectional Glenn (ABG) procedure has been proposed as an alternative to the modified Blalock-Taussig shunt (mBTS) operation for neonates with single-ventricle physiology. Despite success in reducing heart workload and maintaining sufficient pulmonary flow, the ABG also raised the superior vena cava (SVC) pressure to a level that may not be tolerated by infants. To lower the SVC pressure, we propose a modified version of the ABG (mABG), in which a shunt with a slit-shaped nozzle exit is inserted at the junction of the right and left brachiocephalic veins. The proposed operation is compared against the ABG, the mBTS, and the bidirectional Glenn (BDG) operations using closed-loop multiscale simulations. Both normal (2.3 Wood units-m2) and high (7 Wood units-m2) pulmonary vascular resistance (PVR) values are simulated. The mABG provides the highest oxygen saturation, oxygen delivery, and pulmonary flow rate in comparison to the BDG and the ABG. At normal PVR, the SVC pressure is significantly reduced below that of the ABG and the BDG (mABG: 4; ABG: 8; BDG: 6; mBTS: 3 mmHg). However, the SVC pressure remains high at high PVR (mABG: 15; ABG: 16; BDG: 12; mBTS: 3 mmHg), motivating an optimization study to improve the ABG hemodynamics efficiency for a broader range of conditions in the future. Overall, the mABG preserves all advantages of the original ABG procedure while reducing the SVC pressure at normal PVR.

An optimal 𝒪(N) scheme for simulations of colliding, particle-laden flows on unstructured grids.

The cost of tracking Lagrangian particles in a domain discretized on an unstructured grid can become prohibitively expensive as the number of particles or elements grows. A major part of the cost in these calculations is spent on locating the element that hosts a particle and detecting binary collisions, with the latter traditionally requiring 𝒪(N2) operations, N being the number of particles. This paper introduces an optimal search box strategy to significantly reduce the cost of these two operations, ensuring a nearly 𝒪(N) scaling of the cost of collision detection for large-scale simulations. The particle localization strategy is constructed by obtaining an a priori estimate for the optimal number of search boxes as a function of the number of elements, particles, and time steps. The introduced method is generic, as it must be tuned only once for a given implementation and element type. The optimal number of search boxes for collision detection, although complex in form, can be reasonably approximated as the number of particles. The optimality of our method is shown using three drastically varying geometries.

Patient-Specific Multiscale Modeling of the Assisted Bidirectional Glenn.

BACKGROUND: First-stage palliation of neonates with single-ventricle physiology is associated with poor outcomes and challenging clinical management. Prior computational modeling and in vitro experiments introduced the assisted bidirectional Glenn (ABG), which increased pulmonary flow and oxygenation over the bidirectional Glenn (BDG) and the systemic-to-pulmonary shunt in idealized models. In this study, we demonstrate that the ABG achieves similar performance in patient-specific models and assess the influence of varying shunt geometry. METHODS: In a small cohort of single-ventricle prestage 2 patients, we constructed three-dimensional in silico models and tuned lumped parameter networks to match clinical measurements. Each model was modified to produce virtual BDG and ABG surgeries. We simulated the hemodynamics of the stage 1 procedure, BDG, and ABG by using multiscale computational modeling, coupling a finite-element flow solver to the lumped parameter network. Two levels of pulmonary vascular resistances (PVRs) were investigated: baseline (low) PVR of the patients and doubled (high) PVR. The shunt nozzle diameter, anastomosis location, and shape were also manipulated. RESULTS: The ABG increased the pulmonary flow rate and pressure by 15% to 20%, which was accompanied by a rise in superior vena caval pressure (2 to 3 mm Hg) at both PVR values. Pulmonary flow rate and superior vena caval pressures were most sensitive to the shunt nozzle diameter. CONCLUSIONS: Patient-specific ABG performance was similar to prior idealized simulations and experiments, with good performance at lower PVR values in the range of measured clinical data. Larger shunt outlet diameters and lower PVR led to improved ABG performance.

Optimization of the Assisted Bidirectional Glenn Procedure for First Stage Single Ventricle Repair.

BACKGROUND: First-stage single-ventricle palliation is challenging to manage, and significant interstage morbidity and mortality remain. Prior computational and in vitro studies of the assisted bidirectional Glenn (ABG), a novel first-stage procedure that has shown potential for early conversion to a more stable augmented Glenn physiology, demonstrated increased pulmonary flow and oxygen delivery while decreasing cardiac work, as compared to conventional stage-1 alternatives. This study aims to identify optimal shunt designs for the ABG to improve pulmonary flow while maintaining or decreasing superior vena caval (SVC) pressure. METHODS: A representative three-dimensional model of a neonatal bidirectional Glenn (BDG) was created, with a shunt connecting the innominate artery to the SVC. The shunt design was studied as a six-parameter constrained shape optimization problem. We simulated hemodynamics for each candidate designs using a multiscale finite element flow solver and compared performance against designs with taper-less shunts, the standalone BDG, and a simplified control volume model. Three values of pulmonary vascular resistance (PVR) of 2.3, 4.3, and 7.1 WUm2 were studied. RESULTS: Increases in pulmonary flow were generally accompanied by increases in SVC pressure, except at low PVR (2.3 WUm2), where the optimal shunt geometry achieved a 13% increase in pulmonary flow without incurring any increase in SVC pressure. Shunt outlet area was the most influential design parameter, while others had minimal effect. CONCLUSION: Assisted bidirectional Glenn performance is sensitive to PVR and shunt outlet diameter. An increase in pulmonary flow without a corresponding increase in SVC pressure is possible only when PVR is low.

Benchmark problems for numerical treatment of backflow at open boundaries.

In computational fluid dynamics, incoming velocity at open boundaries, or backflow, often yields unphysical instabilities already for moderate Reynolds numbers. Several treatments to overcome these backflow instabilities have been proposed in the literature. However, these approaches have not yet been compared in detail in terms of accuracy in different physiological regimes, in particular because of the difficulty to generate stable reference solutions apart from analytical forms. In this work, we present a set of benchmark problems in order to compare different methods in different backflow regimes (with a full reversal flow and with propagating vortices after a stenosis). The examples are implemented in FreeFem++, and the source code is openly available, making them a solid basis for future method developments.