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Simulation of the dynamic behavior of mitral valve closure could improve clinical treatment by predicting surgical procedures outcome. We propose here a method to achieve this goal by using the immersed boundary method. In order to go towards patient-based simulation, we tailor our method to be adapted to a valve extracted from medical image data. It includes investigating segmentation process, smoothness of geometry, case setup and the shape of the left ventricle. We also study the influence of leaflet tissue anisotropy on the quality of the valve closure by comparing with an isotropic model. As part of the anisotropy analysis, we study the influence of the principal material direction by comparing methods to obtain them without dissection. Results show that our method can be scaled to various image-based data. We evaluate the mitral valve closure quality based on measuring bulging area, contact map, and flow rate. The results show also that the anisotropic material model more precisely represents the physiological characteristics of the valve tissue. Furthermore, results indicate that the orientation of the principal material direction plays a role in the effectiveness of the valve seal., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier B.V. All rights reserved.)

In this work, we employed the Immersed Boundary-Lattice Boltzmann Method (IB-LBM) to simulate the motion of a microparticle in a microchannel under the influence of a standing surface acoustic wave (SSAW). To capture the response of the target microparticle in a straight channel under the effect of the SSAW, in-house code was built in C language. The SSAW creates pressure nodes and anti-nodes inside the microchannel. Here, the target particle was forced to traverse toward the pressure node. A mapping mechanism was developed to accurately apply the physical acoustic force field in the numerical simulation. First, benchmarking studies were conducted to compare the numerical results in the IB-LBM with the available analytical, numerical, and experimental results. Next, several parametric studies were carried out in which the particle types, sizes, compressibility coefficients, and densities were varied. When the SSAW is applied, the microparticles (with a positive acoustic contrast factor) move toward the pressure node locations during their motion in the microchannel. Hence, their steady-state locations are controlled by adjusting the pressure nodes to the desired locations, such as the centerline or near the microchannel sidewalls. Moreover, the geometric parameters, such as radius, density, and compressibility of the particles affect their transient response, and the particles ultimately settle at the pressure nodes. To validate the numerical work, a microfluidic device was fabricated in-house in the cleanroom using lithographic techniques. Experiments were performed, and the target particle was moved either to the centerline or sidewalls of the channel, depending on the location of the pressure node. The steady-state placements obtained in the computational model and experiments exhibit excellent agreement and are reported.

The ability to track simulated cancer cells through the circulatory system, important for developing a mechanistic understanding of metastatic spread, pushes the limits of today's supercomputers by requiring the simulation of large fluid volumes at cellular-scale resolution. To overcome this challenge, we introduce a new adaptive physics refinement (APR) method that captures cellular-scale interaction across large domains and leverages a hybrid CPU-GPU approach to maximize performance. Through algorithmic advances that integrate multi-physics and multi-resolution models, we establish a finely resolved window with explicitly modeled cells coupled to a coarsely resolved bulk fluid domain. In this work we present multiple validations of the APR framework by comparing against fully resolved fluid-structure interaction methods and employ techniques, such as latency hiding and maximizing memory bandwidth, to effectively utilize heterogeneous node architectures. Collectively, these computational developments and performance optimizations provide a robust and scalable framework to enable system-level simulations of cancer cell transport.

This paper describes a novel 2 nd order direct forcing immersed boundary method designed for simulation of 2D and 3D incompressible flow problems with complex immersed boundaries. In this formulation, each cell cut by the immersed boundary (IB) is reshaped to conform to the shape of the IB. IBs are modeled as a series of 2D planes in 3D space that connect seamlessly at the edges of the cut cells, in a way that mimics conformal grid. IBs are represented in a continuous and consistent fashion from one cell to another, thus eliminating spatial pressure oscillations originating from inconsistent description of the IB as well as the traditional stair-step problem, leading to a more accurate resolution of the boundary layer. Boundary conditions are enforced at the exact location of the IB devoid of interpolation, which guarantees sound simulations even on grids with high aspect ratio, and enables simulations of flow packed with multiple IBs in close proximity. Boundary conditions for each phase across the IB are enforced independently, yielding a unique capability to solve flows with zero-thickness IBs. Simulations of a large number of 2D and 3D test cases confirm the prowess of the devised immersed boundary method in solving flows over multiple loosely/closely-packed IBs; stationary, moving and highly morphing IBs; as well as IBs with zero-thickness. Results show that predictions from the proposed scheme agree remarkably well with theoretical models and experimental data for both integral variables and local flow fields and they are often with less than 1% deviation from solutions obtained by conformal grid of similar resolution., Competing Interests: Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

We use computational fluid dynamics (CFD) to simulate blood flow in intracranial aneurysms (IAs). Despite ongoing improvements in the accuracy and efficiency of body-fitted CFD solvers, generation of a high quality mesh appears as the bottleneck of the flow simulation and strongly affects the accuracy of the numerical solution. To overcome this drawback, we use an immersed boundary method. The proposed approach solves the incompressible Navier-Stokes equations on a rectangular (box) domain discretized using uniform Cartesian grid using the finite element method. The immersed object is represented by a set of points (Lagrangian points) located on the surface of the object. Grid local refinement is applied using an automated algorithm. We verify and validate the proposed method by comparing our numerical findings with published experimental results and analytical solutions. We demonstrate the applicability of the proposed scheme on patient-specific blood flow simulations in IAs., (© 2021 John Wiley & Sons Ltd.)

This paper presents a new stabilized form of incompressible Navier-Stokes equations for weak enforcement of Dirichlet boundary conditions at immersed boundaries. The boundary terms are derived via the Variational Multiscale (VMS) method which involves solving the fine-scale variational problem locally within a narrow band along the boundary. The fine-scale model is then variationally embedded into the coarse-scale form that yields a stabilized method which is free of user defined parameters. The derived boundary terms weakly enforce the Dirichlet boundary conditions along the immersed boundaries that may not align with the inter-element edges in the mesh. A unique feature of this rigorous derivation is that the structure of the stabilization tensor which emerges is naturally endowed with the mathematical attributes of area-averaging and stress-averaging. The method is implemented using 4-node quadrilateral and 8-node hexahedral elements. A set of 2D and 3D benchmark problems is presented that investigate the mathematical attributes of the method. These test cases show that the proposed method is mathematically robust as well as computationally stable and accurate for modeling boundary layers around immersed objects in the fluid domain., Competing Interests: Conflict of interest The authors declare that they have no conflict of interest.

In this work a Lattice Boltzmann-Immersed Boundary method is used for predicting the dynamics of rigid and deformable adhesive micro-carriers (1 μm) navigating a capillary by the size of 10 μm with 20% hematocrit. Red cells and particles are modeled as a collection of mass-spring elements responding to a bending potential, an elastic potential and total enclosed area conservation constraint. Furthermore, particle surfaces are uniformly decorated with adhesive molecules (ligands) interacting with receptors disposed on the walls. Particle adhesion is modeled as a short-range ligad-receptor interaction and in term of formation and destruction probability functions that discriminate whether a chemical bond can be formed or destroyed. If a bond is established an attractive elastic force is activated. Particle transport and adhesion are characterized in terms of their ability to reach the capillary peripheries (margination rate) and firmly adhere the vasculature. This analysis is carried out systematically by varying particles' and cells' releasing positions and stiffness (Ca = 0 and 10 -2 ). Moreover, three rigid and soft representative particles are transported on a finer mesh (Δx = 15 nm) and the chemical strength of their adhesive coating is varied (σ = 0.5, 1.0, and 2.0) to precisely analyze the resulting adhesion mechanics. Stiffness is found to weakly influence the margination rate while significantly affect the ability of such constructs to efficiently interact with the endothelium by forming stable chemical bonds., Competing Interests: Declaration of competing interest The author declares no competing interests., (Copyright © 2020 Elsevier Inc. All rights reserved.)

An explicit immersed boundary-lattice Boltzmann method is applied to numerically investigate the dynamics of primary cilium in pulsatile blood flows with two-way fluid-structure interaction considered. To well characterize the effect of cilium basal body on cilium dynamics, the cilium base is modeled as a nonlinear rotational spring attached to the cilium's basal end as proposed by Resnick (Biophys J 109:18-25, 2015. https://doi.org/10.1016/j.bpj.2015.05.031). After several careful validations, the fluid-cilium interaction system is investigated in detail at various pulsatile flow conditions that are characterized by peak Reynolds numbers ([Formula: see text]) and Womersley numbers ([Formula: see text]). The periodic flapping of primary cilium observed in our simulations is very similar to the in vivo ciliary oscillation captured by O'Connor et al. (Cilia 2:8, 2013. https://doi.org/10.1186/2046-2530-2-8). The cilium's dynamics is found to be closely related to the [Formula: see text] and [Formula: see text]. Increase the [Formula: see text] or decrease the [Formula: see text] bring to an increase in the cilium's flapping amplitude, tip angular speed, basal rotation, and maximum tensile stress. It is also demonstrated that by reducing the [Formula: see text] or enhancing the [Formula: see text] to a certain level, one can shift the flapping pattern of cilium from its original two-side one to a one-side one, making the stretch only happen on one particular side. During the flapping process, the location of the maximum tensile stress is not always found at the basal region; instead, it is able to propagate from time to time within a certain distance to the base. Due to the obstruction of the primary cilium, the distribution of wall shear stress no longer remains uniform as in the absence of cilia. It oscillates in space with the minimum magnitude which is always found near where the cilium is located. The presence of cilium also reduces the overall level of wall shear stress, especially at the region near the cilium's anchor point.

The fluid transport and mixing induced by beating cilia, present in the bronchial airways, are studied using a coupled lattice Boltzmann-Immersed Boundary solver. This solver allows the simulation of both single and multi-component fluid flows around moving solid boundaries. The cilia are modeled by a set of Lagrangian points, and Immersed Boundary forces are computed onto these points in order to ensure the no-slip velocity conditions between the cilia and the fluids. The cilia are immersed in a two-layer environment: the periciliary layer (PCL) and the mucus above it. The motion of the cilia is prescribed, as well as the phase lag between two cilia in order to obtain a typical collective motion of cilia, known as metachronal waves. The results obtained from a parametric study show that antiplectic metachronal waves are the most efficient regarding the fluid transport. A specific value of phase lag, which generates the larger mucus transport, is identified. The mixing is studied using several populations of tracers initially seeded into the pericilary liquid, in the mucus just above the PCL-mucus interface, and in the mucus far away from the interface. We observe that each zone exhibits different chaotic mixing properties. The larger mixing is obtained in the PCL layer where only a few beating cycles of the cilia are required to obtain a full mixing, while above the interface, the mixing is weaker and takes more time. Almost no mixing is observed within the mucus, and almost all the tracers do not penetrate the PCL layer. Lyapunov exponents are also computed for specific locations to assess how the mixing is performed locally. Two time scales are introduced to allow a comparison between mixing induced by fluid advection and by molecular diffusion. These results are relevant in the context of respiratory flows to investigate the transport of drugs for patients suffering from chronic respiratory diseases.

In the present article, hybrid lattice Boltzmann-immersed boundary method is utilized to simulate two-dimensional incompressible viscous flow involving flexible immersed red blood cell (RBC) in a microchannel. The main focus of the present research is to study motion and deformation of both healthy and sick RBCs in a vessel with different sizes of stenosis. The presented computational results consent reasonably well with the available data in the literature. Two different channels i.e. a simple and a constricted channel are investigated in the present manuscript. The results show that the RBC transfer and deform without any lift force and rotation induced when it is located on the symmetry axis of the microchannel. However, when the RBC is located off the symmetry axis, the pressure difference produced in the flow around the RBC would apply lift forces on them and expel them towards the center of the channel. The healthy RBC always shows more deformation related to the sick one along the channel. Another important result of the present research is that for the ratio of [Formula: see text] a sick RBC cannot pass the stenosis, and it reasons serious difficulties for body. The present results have been compared with the available experimental and numerical results which show good agreements.

A fundamental step in the rational design of vascular targeted particles is the firm adhesion at the blood vessel walls. Here, a combined lattice Boltzmann-immersed boundary model is presented for predicting the near-wall dynamics of circulating particles. A moving least squares algorithm is used to reconstruct the forcing term accounting for the immersed particle, whereas ligand-receptor binding at the particle-wall interface is described via forward and reverse probability distributions. First, it is demonstrated that the model predicts with good accuracy the rolling velocity of tumor cells over an endothelial layer in a microfluidic channel. Then, particle-wall interactions are systematically analyzed in terms of particle geometries (circular, elliptical with aspect ratios 2 and 3), surface ligand densities (0.3, 0.5, 0.7 and 0.9), ligand-receptor bond strengths (1 and 2) and Reynolds numbers ( Re  = 0.01, 0.1 and 1.0). Depending on these conditions, four different particle-wall interaction regimens are identified, namely not adhering, rolling, sliding and firmly adhering particles. The proposed computational strategy can be efficiently used for predicting the near-wall dynamics of particles with arbitrary geometries and surface properties and represents a fundamental tool in the rational design of particles for the specific delivery of therapeutic and imaging agents., Competing Interests: Conflict of interestThe authors have no competing interests., (© The Author(s) 2017.)

Complex fluid-structure interactions between elastic filaments, or cilia, immersed in viscous flows are commonplace in nature and bear important roles. Some biological systems have evolved to interpret flow-induced motion into signals for the purpose of feedback response. Given the challenges associated with extracting meaningful experimental data at this scale, there has been particular focus on the numerical study of these effects. Porous models have proven useful where cilia arrangements are relatively dense, but for more sparse configurations the dynamic interactions of individual structures play a greater role and direct modelling becomes increasingly necessary. The present study reports efforts towards explicit modelling of regularly spaced wall-mounted cilia using a lattice Boltzmann-immersed boundary method. Both steady and forced unsteady 2D channel flows at different Reynolds numbers are investigated, with and without the presence of a periodic array of elastic inextensible filaments. It is demonstrated that the structure response depends significantly on Reynolds number. For low Reynolds flow, the recirculation vortex aft of successive filaments is small relative to the cilia spacing and does not fully bridge the gap, in which case the structure lags the flow. At higher Reynolds number, when this gap is fully bridged the structure and flow move in phase. The trapping of vortices between cilia is associated with relatively lower wall shear stress. At low to intermediate Reynolds, vortex bridging is incomplete and large deflection is still possible, which is reflected in the tip dynamics and wall shear stress profiles., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

A size-based blood cell sorting model with a micro-fence structure is proposed in the frame of immersed boundary and lattice Boltzmann method (IB-LBM). The fluid dynamics is obtained by solving the discrete lattice Boltzmann equation, and the cells motion and deformation are handled by the immersed boundary method. A micro-fence consists of two parallel slope post rows which are adopted to separate red blood cells (RBCs) from white blood cells (WBCs), in which the cells to be separated are transported one after another by the flow into the passageway between the two post rows. Effected by the cross flow, RBCs are schemed to get through the pores of the nether post row since they are smaller and more deformable compared with WBCs. WBCs are required to move along the nether post row till they get out the micro-fence. Simulation results indicate that for a fix width of pores, the slope angle of the post row plays an important role in cell sorting. The cells mixture can not be separated properly in a small slope angle, while obvious blockages by WBCs will take place to disturb the continuous cell sorting in a big slope angle. As an optimal result, an adaptive slope angle is found to sort RBCs form WBCs correctly and continuously.