A homogenized two-phase computational framework for meso- and macroscale blood flow simulations.

BACKGROUND AND OBJECTIVE: Owing to the complexity of physics linked with blood flow and its associated phenomena, appropriate modeling of the multi-constituent rheology of blood is of primary importance. To this effect, various kinds of computational fluid dynamic models have been developed, each with merits and limitations. However, when additional physics like thrombosis and embolization is included within the framework of these models, computationally efficient scalable translation becomes very difficult. Therefore, this paper presents a homogenized two-phase blood flow framework with similar characteristics to a single fluid model but retains the flow resolution of a classical two-fluid model. The presented framework is validated against four different sets of experiments. METHODS: The two-phase model of blood presented here is based on the classical diffusion-flux framework. Diffusion flux models are known to be less computationally expensive than two-fluid multiphase models since the numerical implementation resembles single-phase flow models. Diffusion flux models typically use empirical slip velocity correlations to resolve the motion between phases. However, such correlations do not exist for blood. Therefore, a modified slip velocity equation is proposed, derived rigorously from the two-fluid governing equations. An additional drag law for red blood cells (RBCs) as a function of volume fraction is evaluated using a previously published cell-resolved solver. A new hematocrit-dependent expression for lift force on RBCs is proposed. The final governing equations are discretized and solved using the open-source software OpenFOAM. RESULTS: The framework is validated against four sets of experiments: (i) flow through a rectangular microchannel to validate RBC velocity profiles against experimental measurements and compare computed hematocrit distributions against previously reported simulation results (ii) flow through a sudden expansion microchannel for comparing experimentally obtained contours of hematocrit distributions and normalized cell-free region length obtained at different flowrates and inlet hematocrits, (iii) flow through two hyperbolic channels to evaluate model predictions of cell-free layer thickness, and (iv) flow through a microchannel that mimics crevices of a left ventricular assist device to predict hematocrit distributions observed experimentally. The simulation results exhibit good agreement with the results of all four experiments. CONCLUSION: The computational framework presented in this paper has the advantage of resolving the multiscale physics of blood flow while still leveraging numerical techniques used for solving single-phase flows. Therefore, it becomes an excellent candidate for addressing more complicated problems related to blood flow, such as modeling mechanical entrapment of RBCs within blood clots, predicting thrombus composition, and visualizing clot embolization.

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 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.

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.