CFD simulation of flow through heart: a perspective review

The heart is an organ which pumps blood around the body by contraction of muscular wall. There is a coupled system in the heart containing the motion of wall and the motion of blood fluid; both motions must be computed simultaneously, which make biological computational fluid dynamics (CFD) difficult. The wall of the heart is not rigid and hence proper boundary conditions are essential for CFD modelling. Fluid-wall interaction is very important for real CFD modelling. There are many assumptions for CFD simulation of the heart that make it far from a real model. A realistic fluid-structure interaction modelling the structure by the finite element method and the fluid flow by CFD use more realistic coupling algorithms. This type of method is very powerful to solve the complex properties of the cardiac structure and the sensitive interaction of fluid and structure. The final goal of heart modelling is to simulate the total heart function by integrating cardiac anatomy, electrical activation, mechanics, metabolism and fluid mechanics together, as in the computational framework.     

CFD simulation of flow through heart: a perspective review

This work addresses the problem of prescribing proper boundary conditions at the artificial boundaries that separate the vascular district from the remaining part of the circulatory system. A multiscale (MS) approach is used where the Navier–Stokes equations for the district of interest are coupled to a non-linear system of ordinary differential equations which describe the circulatory system. This technique is applied to three 3D models of a carotid bifurcation with increasing stenosis resembling three phases of a plaque growth. The results of the MS simulations are compared to those obtained by two stand-alone models. The MS shows a great flexibility in numerically predicting the haemodynamic changes due to the presence of a stenosis. Nonetheless, the results are not significantly different from a stand-alone approach where flows derived by the MS without stenosis are imposed. This is a consequence of the dominant role played by the outside districts with respect to the stenosis resistance.     

CFD simulation of non-Newtonian fluid flow in anaerobic digesters

A general mathematical model that predicts the flow fields in a mixed-flow anaerobic digester was developed. In this model, the liquid manure was assumed to be a non-Newtonian fluid, and the flow governed by the continuity, momentum, and k-epsilon standard turbulence equations, and non-Newtonian power law model. The commercial computational fluid dynamics (CFD) software, Fluent, was applied to simulate the flow fields of lab-scale, scale-up, and pilot-scale anaerobic digesters. The simulation results were validated against the experimental data from literature. The flow patterns were qualitatively compared for Newtonian and non-Newtonian fluids flow in a lab-scale digester. Numerical simulations were performed to predict the flow fields in scale-up and pilot-scale anaerobic digesters with different water pump power inputs and different total solid concentration (TS) in the liquid manure. The optimal power inputs were determined for the pilot-scale anaerobic digester. Some measures for reducing dead and low velocity zones were proposed based upon the CFD simulation results.     

Reconfiguring Uyghurness in multilingualism: an internal migration perspective

This qualitative inquiry investigates how the experiences of learning and using multiple languages influenced the transformation of self-perceived ethnic identities in a group of tertiary-level Uyghur minority students in the context of internal migration in China. Data analysis showed that the majority of Uyghur participants developed a greater affinity with and attachment to their ethnic group by emphasizing the language differences between Uyghur and the dominant Han in intercultural encountering. However, they gradually probed into the meaning of “being Uyghur” in the receiving community. Participants following mother tongue and Chinese educational paradigms were found to offer contrastive answers to the question “what should be the distinguishing features of being Uyghur?”. It was further found that learning English as a third language enabled participants to develop a positive personal ethnic identity by enhancing their understanding of ethnicity and its associations with its constituent elements. We conclude with suggestions for relevant stakeholders.     

Pulsatile non-Newtonian blood flow simulation through a bifurcation with an aneurysm

Blood flow is analysed by means of computer simulation in an idealized arterial bifurcation model which is pathologically altered by a saccular aneurysm. The theoretical study of the flow pattern and the paths of fluid particles is carried out under pulsatile Newtonian and non-Newtonian flow conditions. The governing equations are solved numerically with the use of the finite element method. The results show the disturbed blood flow in the bifurcation and the relatively low intra-aneurysmal flow circulation. In addition to the study of basic flow patterns in the segment, a comparison of non-Newtonian and Newtonian results is carried out. This comparison proves that for the considered large artery model under physiological flow conditions where the yield number is relatively low there is no essential difference in the results.     

Computer simulation of an ideal lateral inhibition function

A model for lateral inhibition is presented in the context of the auditory channel. The mechanical analyzing system of the inner ear cannot alone account for the frequency resolution of hearing. Some additional mechanism, possibly lateral inhibition located in the auditory neural network, is needed to achieve the frequency selectivity observed in electrophysiological and psychoacoustical experiments. In a computer simulation study, the shape of an ideal lateral inhibition function was obtained. Such a function is applicable to all sensory modalities. In hearing, this function permits the sharpest possible frequency resolution as it can completely remove the frequency desharpening effect of the mechanical properties of the basilar membrane. In vision, it can compensate for abberations caused by the imperfections of the optical system of the eye.An expanded version of a paper presented at the XIth Intenational Congress on Acoustics, Paris, 1983     

Probing corticular photosynthesis through in vivo chlorophyll fluorescence measurements: evidence that high internal CO levels suppress electron flow and increase the risk of photoinhibition

Twigs of many woody plants possess chlorenchyma under a well-developed periderm which lacks stomata and impedes both gas diffusion and light penetration. The so-called corticular photosynthesis, occurring in the shade and under extremely high CO(2) concentrations, was probed in this study through in vivo chlorophyll fluorescence measurements. Field comparisons between twigs and corresponding leaves in five species indicated that both the dark- and light-adapted PSII photochemical efficiencies are considerably lower in twigs at all incident photon fluence rates, in spite of the significant attenuation of solar radiation by the periderm. Light saturation curves for linear electron transport rates (corrected according to the actual light intensities reaching twig chlorenchyma) were compatible with a shade-acclimated photosynthetic machinery, showing very low maximum electron transport rates (at approximately 5% of the corresponding leaf values) and threshold irradiances for light saturation. However, removing periderms from twig segments (i.e. relieving the twig interior form the high CO(2) partial pressures) considerably improved the light-adapted (but not the dark-adapted) PSII photochemical efficiency, allowing the assumption that the high internal CO(2) levels may interfere with the smooth functioning of photosynthesis. Indeed, laboratory experiments with twig segments equilibrated under various CO(2) levels (0.036-20%), resulted in a progressive decrease of light-adapted PSII photochemical yield, with the values obtained at 20% CO(2) being similar to those obtained with intact twigs in the field. Further experiments indicated that high CO(2) combined with high light suppressed the development of a photoprotective non-photochemical quenching through a reduction of its fast relaxing component, accompanied by a higher risk of photoinhibition. It is suggested that high internal CO(2) concentrations in twigs impede photosynthesis possibly through acidification of protoplasm and impairment of the pH-dependent high energy state quenching followed by reduction in the efficiency of heat dissipation.     

CFD simulation of mass transfer and flow behaviour around a single particle in bioleaching process

The pathway to reach a certain target in many processes such as bioleaching, due to the complex and poorly understood hydrodynamics, reaction kinetics, and chemistry knowledge involved is not apparent. An investigation of the interactions between the parameters in bioleaching process can be applied to optimize the rate of metal extraction from sulphide minerals. Such investigations can be carried out with the aid of numerical simulations. In this study, a computational fluid dynamics (CFD) model was developed to better understand the mass transfer phenomenon and complex flow field around a single particle. The commercial software FLUENT 6.2 has been employed to solve the governing equations. Volume of fluid (VOF) method was used to predict the fluid volume fraction in a 3D geometry. The computational model has successfully captured the results observed in the experiments. Simulation results indicate that concentrations of species in a thin layer of liquid on the particle surface are much higher than their concentrations in the liquid bulk and significant gradients in the ion concentrations between the surface of the particle and the liquid bulk were observed.     

Brownian dynamics simulation of ion flow through porin channels

Bacterial porins, which allow the passage of solutes across the outer bacterial membrane, are structurally well characterized. They therefore lend themselves to detailed studies of the determinants of ion flow through transmembraneous channels. In a comparative study, we have performed Brownian dynamics simulations to obtain statistically significant transfer efficiencies for cations and anions through matrix porin OmpF, osmoporin OmpK36, phosphoporin PhoE and two OmpF charge mutants.The simulations show that the electrostatic potential at the highly charged channel constriction serves to enhance ion permeability of either cations or anions, dependent on the type of porin. At the same time translocation of counterions is not severely impeded. At the constriction, cations and anions follow distinct trajectories, due to the segregation of basic and acidic protein residues.Simulated ion selectivity and relative conductance agree well with experimental values, and are dependent crucially on the charge constellation at the pore constriction. The experimentally observed decrease in ion selectivity and single channel conductance with increasing ionic strength is well reproduced and can be attributed to electrostatic shielding of the pore lining.     

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.     

Analysis of the distribution and molecular heterogeneity of the ospD gene among the Lyme disease spirochetes: evidence for lateral gene exchange.

Analysis of the ospD gene has revealed that this gene is not universal among Lyme disease spirochete isolates. The gene was found to be carried by 90, 50, and 24% of the Borrelia garinii, B. afzelii, and B. burgdorferi isolates tested. Size variability in the ospD-encoding plasmid was also observed. Sequence analysis has demonstrated the presence of various numbers of a 17-bp repeated sequence in the upstream control (promoter) region of the gene. In addition, a region within the coding sequence where various insertions, deletions, and direct repeats occur was identified. ospD gene sequences from 31 different isolates were determined and utilized in pairwise sequence comparisons and construction of a gene tree. These analyses suggest that the ospD gene was the target of several recombinational events and that the gene was recently acquired by Lyme disease spirochetes and laterally transferred between species.     

Numerical simulation of blood and interstitial flow through a solid tumor

A theoretical framework is presented for describing blood flow through the irregular vasculature of a solid tumor. The tumor capillary bed is modeled as a capillary tree of bifurcating segments whose geometrical construction involves deterministic and random parameters. Blood flow along the individual capillaries accounts for plasma leakage through the capillary walls due to the transmural pressure according to Sterling’s law. The extravasation flow into the interstitium is described by Darcy’s law for a biological porous medium. The pressure field developing in the interstitium is computed by solving Laplace’s equation subject to derived boundary conditions at the capillary vessel walls. Given the arterial, venous, and tumor surface pressures, the problem is formulated as a coupled system of integral and differential equations arising from the interstitium and capillary flow transport equations. Numerical discretization yields a system of linear algebraic equations for the interstitial and capillary segment pressures whose solution is found by iterative methods. Results of numerical computations document the effect of the interstitial hydraulic and vascular permeability on the fractional plasma leakage. Given the material properties, the fractional leakage reaches a maximum at a particular grade of the bifurcating vascular tree.     

CFD transient simulation of the cough clearance process using an Eulerian wall film model

In this study, a cough cycle is reproduced using a computational methodology. The Eulerian wall film approach is proposed to simulate airway mucus flow during a cough. The reproduced airway domain is based on realistic geometry from the literature and captures the deformation of flexible tissue. To quantify the overall performance of this complex phenomenon, cough efficiency (CE) was calculated, which provided an easily reproducible measurement parameter for the cough clearance process. Moreover, the effect of mucus layer thickness was examined. The relationship between the CE and the mucus viscosity was quantified using reductions from 20 to 80%. Finally, predictions of CE values based on healthy person inputs were compared with values obtained from patients with different respiratory diseases, including chronic obstructive pulmonary disease (COPD) and respiratory muscle weakness (RMW). It was observed that CE was reduced by 50% in patients with COPD compared with that of a healthy person. On average, CE was reduced in patients with RMW to 10% of the average value of a healthy person.     

Proposition of an outflow boundary approach for carotid artery stenosis CFD simulation

The purpose of this study was to propose an innovative approach of setting outlet boundary conditions for the computational fluid dynamics (CFD) simulation of human common carotid arteries (CCAs) bifurcation based on the concept of energy loss minimisation at flow bifurcation. Comparisons between this new approach and previously reported boundary conditions were also made. The results showed that CFD simulation based on the proposed boundary conditions gave an accurate prediction of the critical stenosis ratio of carotid arteries (at around 65%). Other boundary conditions, such as the constant external pressure (P = 0) and constant outflow ratio, either overestimated or underestimated the critical stenosis ratio of carotid arteries. The patient-specific simulation results furthermore indicated that the calculated internal carotid artery flow ratio at CCA bifurcation (61%) coincided with the result obtained by clinical measurements through the use of Colour Doppler ultrasound.     

Finite element simulation of pulsatile flow through arterial stenosis.

The problem of blood flow through a stenosis is solved using the incompressible Navier-Stokes equations in a rigid circular tube presenting a partial occlusion. Calculations are based on a Galerkin finite element method. The time marching scheme employs a predictor-corrector technique using a variable time step. Results are obtained for steady and physiological pulsatile flows. Computational experiments analyse the effect of varying the degree of stenosis, the stricture length, the Reynolds number and Womersley number. The method gives results which agree well with previous computations for steady flows and experimental findings for steady and pulsatile flows.     

Computer simulation of cellular movements: cell-sorting, cellular migration through a mass of cells and contact inhibition

The motility rules for cellular movement proposed earlier by Goel &; Rogers for engulfment of two or more intact embryonic tissues have been used to simulate on a computer the phenomena of cell-sorting, migration of individual cells through a mass of cells and contact inhibition of overlapping. These simulations in the most part are found to be consistent with the observations with real cells.     

Cell migration: neurons go with the flow

Cilia lining the surfaces of the brain ventricles may be responsible for the graded distribution of chemorepellents that drive the directed migration of neurons.     

3-D numerical simulation of blood flow through models of the human aorta

A Spiral Computerized Tomography (CT) scan of the aorta were obtained from a single subject and three model variations were examined. Computational fluid dynamics modeling of all three models showed variations in the velocity contours along the aortic arch with differences in the boundary layer growth and recirculation regions. Further down-stream, all three models showed very similar velocity profiles during maximum velocity with differences occurring in the decelerating part of the pulse. Flow patterns obtained from transient 3-D computational fluid dynamics are influenced by different reconstruction methods and the pulsatility of the flow. Caution is required when analyzing models based on CT scans.     

FRAP analysis of membrane-associated proteins: lateral diffusion and membrane-cytoplasmic exchange

Obtaining quantitative kinetic parameters from fluorescence recovery after photobleaching (FRAP) experiments generally requires a theoretical analysis of protein mobility and appropriate solutions for FRAP recovery derived for a given geometry. Here we provide a treatment of FRAP recovery for a molecule undergoing a combined process of reversible membrane association and lateral diffusion on the plasma membrane for two commonly used bleach geometries: stripes, and boxes. Such analysis is complicated by the fact that diffusion of a molecule during photobleaching can lead to broadening of the bleach area, resulting in significant deviations of the actual bleach shape from the desired bleach geometry, which creates difficulty in accurately measuring kinetic parameters. Here we overcome the problem of deviations between actual and idealized bleach geometries by parameterizing, more accurately, the initial postbleach state. This allows for reconstruction of an accurate and analytically tractable approximation of the actual fluorescence distribution. Through simulated FRAP experiments, we demonstrate that this method can be used to accurately measure a broad range of combinations of diffusion constants and exchange rates. Use of this method to analyze the plextrin homology domain of PLC-δ1 in Caenorhabditis elegans results in quantitative agreement with prior analysis of this domain in other cells using other methods. Because of the flexibility, relative ease of implementation, and its use of standard, easily obtainable bleach geometries, this method should be broadly applicable to investigation of protein dynamics at the plasma membrane.