Viscous flow simulation in a stenosis model using discrete particle dynamics: a comparison between DPD and CFD

Flow and stresses induced by blood flow acting on the blood cellular constituents can be represented to a certain extent by a continuum mechanics approach down to the order of the?μm level. However, the molecular effects of, e.g., adhesion/aggregation bonds of blood clotting can be on the order of nm. The coupling of the disparate length and timescales between such molecular levels and macroscopic transport represents a major computational challenge. To address this challenge, a multiscale numerical approach based on discrete particle dynamics (DPD) methodology derived from molecular dynamics (MD) principles is proposed. The feasibility of the approach was firstly tested for its ability to simulate viscous flow conditions. Simulations were conducted in low Reynolds numbers flows (Re = 25–33) through constricted tubes representing blood vessels with various degrees of stenosis. Multiple discrete particles interacting with each other were simulated, with 1.24–1.36 million particles representing the flow domain and 0.4 million particles representing the vessel wall. The computation was carried out on the massive parallel supercomputer NY BlueGene/L employing NAMD-a parallel MD package for high performance computing (HPC). Typical recirculation zones were formed distal to the stenoses. The velocity profiles and recirculation zones were in excellent agreement with computational fluid dynamics (CFD) 3D Navier–Stokes viscous fluid flow simulations and with classic numerical and experimental results by YC Fung in constricted tubes. This feasibility analysis demonstrates the potential of a methodology that widely departs from a continuum approach to simulate multiscale phenomena such as flow induced blood clotting.     

Mechanistic insight into the physiological relevance of helical blood flow in the human aorta: an in vivo study

The hemodynamics within the aorta of five healthy humans were investigated to gain insight into the complex helical flow patterns that arise from the existence of asymmetries in the aortic region. The adopted approach is aimed at (1) overcoming the relative paucity of quantitative data regarding helical blood flow dynamics in the human aorta and (2) identifying common characteristics in physiological aortic flow topology, in terms of its helical content. Four-dimensional phase-contrast magnetic resonance imaging (4D PC MRI) was combined with algorithms for the calculation of advanced fluid dynamics in this study. These algorithms allowed us to obtain a 4D representation of intra-aortic flow fields and to quantify the aortic helical flow. For our purposes, helicity was used as a measure of the alignment of the velocity and the vorticity. There were two key findings of our study: (1) intra-individual analysis revealed a statistically significant difference in the helical content at different phases of systole and (2) group analysis suggested that aortic helical blood flow dynamics is an emerging behavior that is common to normal individuals. Our results also suggest that helical flow might be caused by natural optimization of fluid transport processes in the cardiovascular system, aimed at obtaining efficient perfusion. The approach here applied to assess in vivo helical blood flow could be the starting point to elucidate the role played by helicity in the generation and decay of rotating flows in the thoracic aorta.     

A novel solution for fluid flow problems based on the lattice Boltzmann method

Recently, phase separation and fluid flow problems have represented an important development in fluid dynamics, which has many important industrial applications. Lattice Boltzmann method (LBM) is the numerical method that explains the behaviour of fluid dynamics in mesoscopic scale single-component single-phase and multi-component multiphase flows. In this paper, we study the lattice Boltzmann models (LBMs) in two dimensions (2D) with nine directions (Q9), that is the D2Q9 model was used to study the phase separation and observe that the phenomenon of fluid flow in a cylinder has obstacle and square cavity. The simulation results show that fluid flows in the square cavity and in the cylinder, present phase separation of single-component multiphase fluid flow.     

Nodal cilia dynamics and the specification of the left/right axis in early vertebrate embryo development

Nodal cilia dynamics is a key factor for left/right axis determination in mouse embryos through the induction of a leftward fluid flow. So far it has not been clearly established how such dynamics is able to induce the asymmetric leftward flow within the node. Herein we propose that an asymmetric two-phase nonplanar beating cilia dynamics that involves the bending of the ciliar axoneme is responsible for the leftward fluid flow. We support our proposal with a host of hydrodynamic arguments, in silico experiments and in vivo video microscopy data in wild-type embryos and inv mutants. Our phenomenological modeling approach underscores how the asymmetry and speed of the flow depends on different relevant parameters. In addition, we discuss how the combination of internal and external mechanisms might cause the two-phase beating cilia dynamics.     

Combined experimental and numerical analysis of the flow structure into the left ventricle

Fluid dynamics is used for diagnosis in cardiology only to a partial extent. Indeed several aspects of cardiac flows and their relation with pathophysiology are unknown. The flow that develops into the left ventricle is here studied by using a combination of numerical and experimental models. The former allows a detailed three-dimensional analysis, the latter can be used in conditions, like in presence of turbulence, that are out of reach of the current computational power. The three-dimensional flow dynamics is analyzed in terms of its vortical structure. The study, within its limitations, provides further physical understanding about the intraventricular flow structure. This could eventually support the development of cardiac diagnostic indicators based on fluid dynamics.     

The Shape of the Urine Stream — From Biophysics to Diagnostics

We develop a new computational model of capillary-waves in free-jet flows, and apply this to the problem of urological diagnosis in this first ever study of the biophysics behind the characteristic shape of the urine stream as it exits the urethral meatus. The computational fluid dynamics model is used to determine the shape of a liquid jet issuing from a non-axisymmetric orifice as it deforms under the action of surface tension. The computational results are verified with experimental modelling of the urine stream. We find that the shape of the stream can be used as an indicator of both the flow rate and orifice geometry. We performed volunteer trials which showed these fundamental correlations are also observed in vivo for male healthy volunteers and patients undergoing treatment for low flow rate. For healthy volunteers, self estimation of the flow shape provided an accurate estimation of peak flow rate (). However for the patients, the relationship between shape and flow rate suggested poor meatal opening during voiding. The results show that self measurement of the shape of the urine stream can be a useful diagnostic tool for medical practitioners since it provides a non-invasive method of measuring urine flow rate and urethral dilation.     

Macro-scale topology optimization for controlling internal shear stress in a porous scaffold bioreactor

Shear stress is an important physical factor that regulates proliferation, migration, and morphogenesis. In particular, the homeostasis of blood vessels is dependent on shear stress. To mimic this process ex vivo, efforts have been made to seed scaffolds with vascular and other cell types in the presence of growth factors and under pulsatile flow conditions. However, the resulting bioreactors lack information on shear stress and flow distributions within the scaffold. Consequently, it is difficult to interpret the effects of shear stress on cell function. Such knowledge would enable researchers to improve upon cell culture protocols. Recent work has focused on optimizing the microstructural parameters of the scaffold to fine tune the shear stress. In this study, we have adopted a different approach whereby flows are redirected throughout the bioreactor along channels patterned in the porous scaffold to yield shear stress distributions that are optimized for uniformity centered on a target value. A topology optimization algorithm coupled to computational fluid dynamics simulations was devised to this end. The channel topology in the porous scaffold was varied using a combination of genetic algorithm and fuzzy logic. The method is validated by experiments using magnetic resonance imaging readouts of the flow field.     

Numerical simulation of local blood flow in the carotid and cerebral arteries under altered gravity

A computational fluid dynamics (CFD) approach was presented to model the blood flows in the carotid bifurcation and the brain arteries under altered gravity. Physical models required for CFD simulation were introduced including a model for arterial wall motion due to fluid-wall interactions, a shear thinning fluid model of blood, a vascular bed model for outflow boundary conditions, and a model for autoregulation mechanism. The three-dimensional unsteady incompressible Navier-Stokes equations coupled with these models were solved iteratively using the pseudocompressibility method and dual time stepping. Gravity source terms were added to the Navier-Stokes equations to take the effect of gravity into account. For the treatment of complex geometry, a chimera overset grid technique was adopted to obtain connectivity between arterial branches. For code validation, computed results were compared with experimental data for both steady-state and time-dependent flows. This computational approach was then applied to blood flows through a realistic carotid bifurcation and two Circle of Willis models, one using an idealized geometry and the other using an anatomical data set. A three-dimensional Circle of Willis configuration was reconstructed from subject-specific magnetic resonance images using an image segmentation method. Through the numerical simulation of blood flow in two model problems, namely, the carotid bifurcation and the brain arteries, it was observed that the altered gravity has considerable effects on arterial contraction/dilatation and consequent changes in flow conditions.     

Fluid flows and forces in development: functions, features and biophysical principles

Throughout morphogenesis, cells experience intracellular tensile and contractile forces on microscopic scales. Cells also experience extracellular forces, such as static forces mediated by the extracellular matrix and forces resulting from microscopic fluid flow. Although the biological ramifications of static forces have received much attention, little is known about the roles of fluid flows and forces during embryogenesis. Here, we focus on the microfluidic forces generated by cilia-driven fluid flow and heart-driven hemodynamics, as well as on the signaling pathways involved in flow sensing. We discuss recent studies that describe the functions and the biomechanical features of these fluid flows. These insights suggest that biological flow determines many aspects of cell behavior and identity through a specific set of physical stimuli and signaling pathways.     

Interrogating the role of liposome size in mediating the dynamics of a chromophore in the acyl chain region of a phospholipid bilayer

We have examined the temperature-dependent reorientation dynamics of perylene imbedded in bilayers of 1,2-dimyristoyl-sn-phosphatidylcholine (DMPC), where the bilayers exist in the form of unilamellar vesicles. Previous work using 100-nm diameter DMPC vesicles has shown that the phase transition from the gel phase to the fluid phase can be detected using the reorientation dynamics of perylene. In this work we explore the vesicle size dependence of the perylene reorientation dynamics in DMPC vesicles. The size of the vesicles is determined by extrusion and the reorientation dynamics of perylene are measured as a function of vesicle size between 100-nm and 5-microm diameter. We find that, while the phase transition for DMPC is seen in smaller vesicles, perylene becomes insensitive to the phase transition for vesicles larger than ca. 800-nm diameter. We also find a discontinuous change in perylene reorientation dynamics with increasing vesicle size, and we consider this result in the context of the location of perylene within the bilayer.     

Computational fluid dynamics as a tool for testing functional and ecological hypotheses in fossil taxa

Computational fluid dynamics is a method for simulating fluid flows that has been widely used in engineering for decades, and which also has applications for studying function and ecology in fossil taxa. However, despite the possible benefits of this approach, computational fluid dynamics has been used only rarely in palaeontology to date. The theoretical basis underlying the technique is outlined and the main steps involved in carrying out computer simulations of fluid flows are detailed. I also describe previous studies that have applied the method to fossils and discuss their potential for informing future research directions in palaeontology. Computational fluid dynamics can enable large‐scale comparative analyses, as well as exacting tests of hypotheses related to the function and ecology of ancient organisms. In this way, it could transform our understanding of many extinct fossil groups.     

Speckle variance optical coherence tomography of blood flow in the beating mouse embryonic heart

Efficient separation of blood and cardiac wall in the beating embryonic heart is essential and critical for experiment‐based computational modelling and analysis of early‐stage cardiac biomechanics. Although speckle variance optical coherence tomography (SV‐OCT) relying on calculation of intensity variance over consecutively acquired frames is a powerful approach for segmentation of fluid flow from static tissue, application of this method in the beating embryonic heart remains challenging because moving structures generate SV signal indistinguishable from the blood. Here, we demonstrate a modified four‐dimensional SV‐OCT approach that effectively separates the blood flow from the dynamic heart wall in the beating mouse embryonic heart. The method takes advantage of the periodic motion of the cardiac wall and is based on calculation of the SV signal over the frames corresponding to the same phase of the heartbeat cycle. Through comparison with Doppler OCT imaging, we validate this speckle‐based approach and show advantages in its insensitiveness to the flow direction and velocity as well as reduced influence from the heart wall movement. This approach has a potential in variety of applications relying on visualization and segmentation of blood flow in periodically moving structures, such as mechanical simulation studies and finite element modelling. Picture : Four‐dimensional speckle variance OCT imaging shows the blood flow inside the beating heart of an E8.5 mouse embryo.     

Breaking symmetry in non-planar bifurcations: distribution of flow and wall shear stress

Non-planarity in blood vessels is known to influence arterial flows and wall shear stress. To gain insight, computational fluid dynamics (CFD) has been used to investigate effects of curvature and out-of-plane geometry on the distribution of fluid flows and wall shear stresses in a hypothetical non-planar bifurcation. Three-dimensional Navier-Stokes equations for a steady state Newtonian fluid were solved numerically using a finite element method. Non-planarity in one of the two daughter vessels is found to deflect flow from the inner wall of the vessel to the outer wall and to cause changes in the distribution of wall shear stresses. Results from this study agree to experimental observations and CFD simulations in the literature, and support the view that non-planarity in blood vessels is a factor with important haemodynamic significance and may play a key role in vascular biology and pathophysiology.     

Fluid mechanics of the zebrafish embryonic heart trabeculation

Embryonic heart development is a mechanosensitive process, where specific fluid forces are needed for the correct development, and abnormal mechanical stimuli can lead to malformations. It is thus important to understand the nature of embryonic heart fluid forces. However, the fluid dynamical behaviour close to the embryonic endocardial surface is very sensitive to the geometry and motion dynamics of fine-scale cardiac trabecular surface structures. Here, we conducted image-based computational fluid dynamics (CFD) simulations to quantify the fluid mechanics associated with the zebrafish embryonic heart trabeculae. To capture trabecular geometric and motion details, we used a fish line that expresses fluorescence at the endocardial cell membrane, and high resolution 3D confocal microscopy. Our endocardial wall shear stress (WSS) results were found to exceed those reported in existing literature, which were estimated using myocardial rather than endocardial boundaries. By conducting simulations of single intra-trabecular spaces under varied scenarios, where the translational or deformational motions (caused by contraction) were removed, we found that a squeeze flow effect was responsible for most of the WSS magnitude in the intra-trabecular spaces, rather than the shear interaction with the flow in the main ventricular chamber. We found that trabecular structures were responsible for the high spatial variability of the magnitude and oscillatory nature of WSS, and for reducing the endocardial deformational burden. We further found cells attached to the endocardium within the intra-trabecular spaces, which were likely embryonic hemogenic cells, whose presence increased endocardial WSS. Overall, our results suggested that a complex multi-component consideration of both anatomic features and motion dynamics were needed to quantify the trabeculated embryonic heart fluid mechanics.     

Acinus-on-a-chip: A microfluidic platform for pulmonary acinar flows

Convective respiratory flows in the pulmonary acinus and their influence on the fate of inhaled particles are typically studied using computational fluid dynamics (CFD) or scaled-up experimental models. However, experiments that replicate several generations of the acinar tree while featuring cyclic wall motion have not yet been realized. Moreover, current experiments generally capture only flow dynamics, without inhaled particle dynamics, due to difficulties in simultaneously matching flow and particle dynamics. In an effort to overcome these limitations, we introduce a novel microfluidic device mimicking acinar flow characteristics directly at the alveolar scale. The model features an anatomically-inspired geometry that expands and contracts periodically with five dichotomously branching airway generations lined with alveolar-like cavities. We use micro-particle image velocimetry with a glycerol solution as the carrying fluid to quantitatively characterize detailed flow patterns within the device and reveal experimentally for the first time a gradual transition of alveolar flow patterns along the acinar tree from recirculating to radial streamlines, in support of hypothesized predictions from past CFD simulations. The current measurements show that our microfluidic system captures the underlying characteristics of the acinar flow environment, including Reynolds and Womersley numbers as well as cyclic wall displacements and alveolar flow patterns at a realistic length scale. With the use of air as the carrying fluid, our miniaturized platform is anticipated to capture both particle and flow dynamics and serve in the near future as a promising in vitro tool for investigating the mechanisms of particle deposition deep in the lung.     

4D subject-specific inverse modeling of the chick embryonic heart outflow tract hemodynamics

Blood flow plays a critical role in regulating embryonic cardiac growth and development, with altered flow leading to congenital heart disease. Progress in the field, however, is hindered by a lack of quantification of hemodynamic conditions in the developing heart. In this study, we present a methodology to quantify blood flow dynamics in the embryonic heart using subject-specific computational fluid dynamics (CFD) models. While the methodology is general, we focused on a model of the chick embryonic heart outflow tract (OFT), which distally connects the heart to the arterial system, and is the region of origin of many congenital cardiac defects. Using structural and Doppler velocity data collected from optical coherence tomography, we generated 4D (\(\hbox {3D}\,+\,\hbox {time}\)) embryo-specific CFD models of the heart OFT. To replicate the blood flow dynamics over time during the cardiac cycle, we developed an iterative inverse-method optimization algorithm, which determines the CFD model boundary conditions such that differences between computed velocities and measured velocities at one point within the OFT lumen are minimized. Results from our developed CFD model agree with previously measured hemodynamics in the OFT. Further, computed velocities and measured velocities differ by \(<\)15 % at locations that were not used in the optimization, validating the model. The presented methodology can be used in quantifications of embryonic cardiac hemodynamics under normal and altered blood flow conditions, enabling an in-depth quantitative study of how blood flow influences cardiac development.     

Porohyperviscoelastic model simultaneously predicts parenchymal fluid pressure and reaction force in perfused liver

Porohyperviscoelastic (PHVE) modeling gives a simplified continuum approximation of pore fluid behavior within the parenchyma of liver tissue. This modeling approach is particularly applicable to tissue engineering of artificial livers, where the inherent complexity of the engineered scaffolds prevents the use of computational fluid dynamics. The objectives of this study were to simultaneously predict the experimental parenchymal fluid pressure (PFP) and compression response in a PHVE liver model. The model PFP matched the experimental measurements (318?Pa) to within 1.5%. Linear regression of both phases of compression, ramp, and hold, demonstrated a strong correlation between the model and the experimental reaction force (p<0.5). The ability of this PVE model to accurately predict both fluid and solid behavior is important due to the highly vascularized nature of liver tissue and the mechanosensitivity of liver cells to solid matrix and fluid flow properties.     

Pulsatile flow in an end-to-side vascular graft model: comparison of computations with experimental data

Various hemodynamic factors have been implicated in vascular graft intimal hyperplasia, the major mechanism contributing to chronic failure of small-diameter grafts. However, a thorough knowledge of the graft flow field is needed in order to determine the role of hemodynamics and how these factors affect the underlying biological processes. Computational fluid dynamics offers much more versatility and resolution than in vitro or in vivo methods, yet computations must be validated by careful comparison with experimental data. Whereas numerous numerical and in vitro simulations of arterial geometries have been reported, direct point-by-point comparisons of the two techniques are rare in the literature. We have conducted finite element computational analyses for a model of an end-to-side vascular graft and compared the results with experimental data obtained using laser-Doppler velocimetry. Agreement for velocity profiles is found to be good, with some clear differences near the recirculation zones during the deceleration and reverse-flow segments of the flow waveform. Wall shear stresses are determined from velocity gradients, whether by computational or experimental methods, and hence the agreement for this quantity, while still good, is less consistent than for velocity itself from the wall shear stress numerical results, we computed four variables that have been cited in the development of intiimal hyperplasia-the time-averaged wall shear stress, an oscillating shear index, and spatial and temporal wall shear stress gradients in order to illustrate the versatility of numerical methods. We conclude that the computational approach is a valid alternative to the experimental approach for quantitative hemodynamic studies. Where differences in velocity were found by the two methods, it was generally attributed to the inability of the numerical method to model the fluid dynamics when flow conditions are destabilizing. Differences in wall shear, in the absence of destabilizing phenomena, were more likely to be caused by difficulties in calculating wall shear from relatively low resolution in vitro data.