Numerical simulation of air flow through a biofilter with heterogeneous porous media

Based on the ideal biofilter model, numerical simulation using lattice Boltzmann method is carried out to investigate the effect of Darcy number and porosity on removal efficiency of low headloss biofilter. The generalized Navier-Stokes model (Brinkman-Forchheimer-extended Darcy model) is applied making several assumptions. It is found that the Darcy number has determinant influence on the removal efficiency, and the effect of porosity on removal efficiency is very weak at lower Darcy numbers but very strong at higher Darcy numbers. It was found there was strong evidence of flow heterogeneity in the biofilter (Chitwood, D.E., Devinny, J.S., Reynolds Jr., F.E., 1999. Evaluation of a two-stage biofilter for treatment of POTW waste air. Environ. Prog. 18, 212-221). In this study we have found the biofilter performance can be improved by adjusting local Darcy number of the porous media in the biofilter.     

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.     

Numerical solution of non-steady magnetohydrodynamic flow of blood through a porous channel

Magnetohydrodynamic (MHD) principles may be used to decelerate the flow of arterial blood and hence be of potential value in the treatment of cardiovascular disorders associated with an accelerated circulation. We examine the non-steady flow of blood in a porous parallel plate channel under the influence of a transverse magnetic field and different pressure gradients.     

Numerical simulations of the blood flow through vertebral arteries

Vertebral arteries are two arteries whose structure and location in human body result in development of special flow conditions. For some of the arteries, one can observe a significant difference between flow rates in the left and the right arteries during ultrasonography diagnosis. Usually the reason of such a difference was connected with pathology of the artery in which a smaller flow rate was detected. Simulations of the flow through the selected type of the vertebral artery geometry for twenty five cases of artery diameters have been carried out. The main aim of the presented experiment was to visualize the flow in the region of vertebral arteries junction in the origin of the basilar artery. It is extremely difficult to examine this part of human circulation system, thus numerical experiments may be helpful in understanding the phenomena occurring when two relatively large arteries join together to form one vessel. The obtained results have shown that an individual configuration and diameters of particular arteries can exert an influence on the flow in them and affect a significant difference between flow rates for vertebral arteries. It has been assumed in the investigations that modelled arteries were absolutely normal, without any pathology. In the numerical experiment, the non-Newtonian model of blood was employed.     

灌草与林带搭配条件下防护效应的数值模拟

在对林带和灌草进行参数化的基础上,将有、无灌草带存在情况下绕林带流场进行了数值模拟,分析比较了两种流场中沿流相对风速、不同断面风速廓线及湍动能的变化。结果表明,灌草在防护林体系中起着重要作用,在林带迎风面和带后一定区域内,均使风速减小。最后将数值模拟结果与实验结果进行了对比,并从实验角度分析了灌草的作用。     

Numerical simulation and comparative analysis of flow field in axial blood pumps

The objective study was to estimate the rheological properties and physiological compatibility of the blood pump by simulating the internal flow field of the blood pump. In this study we use computational fluid dynamics method to simulate and analyse two models of axial blood pumps with a three-blade diffuser and a six-blade diffuser, named pump I and pump II, respectively, and to compare the flow patterns of these two kinds of blood pumps while both of them satisfy the conditions of the normal human blood differential pressure and blood flow. Results indicate that (i) the high shear force occurs between the diffuser and the rotor in which the crucial place leads to haemolysis and (ii) under the condition of 100 mmHg pressure head and 5 l/min flow rate, the difference between the two kinds of blood pumps, as far as the haemolytic performance is concerned, is notable. The haemolysis index of the two pumps is 0.32% and 0.2%. In conclusion, the performance of the blood pump is influenced by the diffusers' blade number. Pump II performed better than pump I, which can be the basic model for blood pump option.     

Numerical simulation of non-Newtonian blood flow dynamics in human thoracic aorta

Three non-Newtonian blood viscosity models plus the Newtonian one are analysed for a patient-specific thoracic aorta anatomical model under steady-state flow conditions via wall shear stress (WSS) distribution, non-Newtonian importance factors, blood viscosity and shear rate. All blood viscosity models yield a consistent WSS distribution pattern. The WSS magnitude, however, is influenced by the model used. WSS is found to be the lowest in the vicinity of the three arch branches and along the distal walls of the branches themselves. In this region, the local non-Newtonian importance factor and the blood viscosity are elevated, and the shear rate is low. The present study revealed that the Newtonian assumption is a good approximation at mid-and-high flow velocities, as the greater the blood flow, the higher the shear rate near the arterial wall. Furthermore, the capabilities of the applied non-Newtonian models appeared at low-flow velocities. It is concluded that, while the non-Newtonian power-law model approximates the blood viscosity and WSS calculations in a more satisfactory way than the other non-Newtonian models at low shear rates, a cautious approach is given in the use of this blood viscosity model. Finally, some preliminary transient results are presented.     

Numerical and experimental investigations of pulsatile blood flow pattern through a dysfunctional mechanical heart valve

Around 250,000 heart valve replacements are performed every year around the world. Due their higher durability, approximately 2/3 of these replacements use mechanical prosthetic heart valves (mainly bileaflet valves). Although very efficient, these valves can be subject to valve leaflet malfunctions. These malfunctions are usually the consequence of pannus ingrowth and/or thrombus formation and represent serious and potentially fatal complications. Hence, it is important to investigate the flow field downstream of a dysfunctional mechanical heart valve to better understand its impact on blood components (red blood cells, platelets and coagulation factors) and to improve the current diagnosis techniques. Therefore, the objective of this study will be to numerically and experimentally investigate the pulsatile turbulent flow downstream of a dysfunctional bileaflet mechanical heart valve in terms of velocity field, vortex formation and potential negative effect on blood components. The results show that the flow downstream of a dysfunctional valve was characterized by abnormally elevated velocities and shear stresses as well as large scale vortices. These characteristics can predispose to blood components damage. Furthermore, valve malfunction led to an underestimation of maximal transvalvular pressure gradient, using Doppler echocardiography, when compared to numerical results. This could be explained by the shifting of the maximal velocity towards the normally functioning leaflet. As a consequence, clinicians should try, when possible, to check the maximal velocity position not only at the central orifice but also through the lateral orifices. Finding the maximal velocity in the lateral orifice could be an indication of valve dysfunction.     

Numerical technique of blood flow through catheterized arteries with overlapping stenosis

This study is concerned with the surgical technique for the injection of a catheter through arteries with overlapping stenosis in the presence of externally applied magnetic field and Hall currents influences. The nature of blood is analyzed mathematically by considering it as a micropolar fluid. The analysis is carried out for an artery with a mild stenosis. The governing equations with the corresponding boundary conditions solved numerically using Crank–Nicolson implicit finite difference scheme. The numerical technique give excellent agreement for axial velocity of the fluid, the circumferential microrotation, the wall shear stress distribution and the contour plots of stream lines. The obtained results show that the value of axial velocity is higher for a Newtonian fluid than that for a micropolar fluid model, the effect of suitable moving magnetic field (Hall currents influences) accelerates the speed of blood, the size of trapped bolus for the stream lines decrease if the spinning movement of the fluid molecules have considerable value regardless of small or large size of the fluid molecules and the flow of fluid is better with increasing the Hall current effect and the size of trapping bolus increase clearly by increasing the maximum height of stenosis where the fluid moves as a bulk.     

Numerical simulation of blood pulsatile flow in a stenosed carotid artery using different rheological models

Symmetrical 30-60% stenosis in a common carotid artery under unsteady flow condition for Newtonian and six non-Newtonian viscosity models are investigated numerically. Results show power-law model produces higher deviations, in terms of velocity and wall shear stress in comparison with other models while generalized power-law and modified-Casson models are more prone to Newtonian state. Comparing separation length of recirculation region at different critical points of cardiac cycle confirms the necessity of considering blood flow in unsteady mode. Increasing stenosis intensity causes flow patterns more disturbed downstream of the stenosis and WSS appear to develop remarkably at the stenosis throat.     

Regulation of tumor invasion by interstitial fluid flow

The importance of the tumor microenvironment in cancer progression is undisputed, yet the significance of biophysical forces in the microenvironment remains poorly understood. Interstitial fluid flow is a nearly ubiquitous and physiologically relevant biophysical force that is elevated in tumors because of tumor-associated angiogenesis and lymphangiogenesis, as well as changes in the tumor stroma. Not only does it apply physical forces to cells directly, but interstitial flow also creates gradients of soluble signals in the tumor microenvironment, thus influencing cell behavior and modulating cell-cell interactions. In this paper, we highlight our current understanding of interstitial fluid flow in the context of the tumor, focusing on the physical changes that lead to elevated interstitial flow, how cells sense flow and how they respond to changes in interstitial flow. In particular, we emphasize that interstitial flow can directly promote tumor cell invasion through a mechanism known as autologous chemotaxis, and indirectly support tumor invasion via both biophysical and biochemical cues generated by stromal cells. Thus, interstitial fluid flow demonstrates how important biophysical factors are in cancer, both by modulating cell behavior and coupling biophysical and biochemical signals.     

Numerical solution of unsteady blood flow through an indented tube with atherosclerosis

The unsteady blood flow through an indented tube with atherosclerosis in the presence of mild stenosis has been studied numerically by finite difference method. The effects of hematocrit, frequency parameter, height of stenosis, parameter determining the shape of the constriction on velocity field, volumetric flow rate, pressure gradient of the fluid in stenotic region and wall shear stress at the surface of stenosis are obtained and shown graphically.     

Numerical simulation of two-phase non-Newtonian blood flow with fluid-structure interaction in aortic dissection

The behavior of blood cells and vessel compliance significantly influence hemodynamic parameters, which are closely related to the development of aortic dissection. Here the two-phase non-Newtonian model and the fluid-structure interaction (FSI) method are coupled to simulate blood flow in a patient-specific dissected aorta. Moreover, three-element Windkessel model is applied to reproduce physiological pressure waves. Important hemodynamic indicators, such as the spatial distribution of red blood cells (RBCs) and vessel wall displacement, which greatly influence the hemodynamic characteristics are analyzed. Results show that the proximal false lumen near the entry tear appears to be a vortex zone with a relatively lower volume fraction of RBCs, a low time-averaged wall shear stress (TAWSS) and a high oscillatory shear index (OSI), providing a suitable physical environment for the formation of atherosclerosis. The highest TAWSS is located in the narrow area of the distal true lumen which might cause further dilation. TAWSS distributions in the FSI model and the rigid wall model show similar trend, while there is a significant difference for the OSI distributions. We suggest that an integrated model is essential to simulate blood flow in a more realistic physiological environment with the ultimate aim of guiding clinical treatment.     

Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation

A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies by Olufsen et al. (Ann Biomed Eng 28:1281–1299, 2012) which only considered the arterial circulation. For the first three generations of vessels within the pulmonary circulation, geometry is specified from patient-specific measurements obtained using magnetic resonance imaging (MRI). Blood flow and pressure in the larger arteries and veins are predicted using a nonlinear, cross-sectional-area-averaged system of equations for a Newtonian fluid in an elastic tube. Inflow into the main pulmonary artery is obtained from MRI measurements, while pressure entering the left atrium from the main pulmonary vein is kept constant at the normal mean value of 2 mmHg. Each terminal vessel in the network of ‘large’ arteries is connected to its corresponding terminal vein via a network of vessels representing the vascular bed of smaller arteries and veins. We develop and implement an algorithm to calculate the admittance of each vascular bed, using bifurcating structured trees and recursion. The structured-tree models take into account the geometry and material properties of the ‘smaller’ arteries and veins of radii \(\ge \) 50  \(\upmu \) m. We study the effects on flow and pressure associated with three classes of pulmonary hypertension expressed via stiffening of larger and smaller vessels, and vascular rarefaction. The results of simulating these pathological conditions are in agreement with clinical observations, showing that the model has potential for assisting with diagnosis and treatment for circulatory diseases within the lung.     

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.     

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.     

Vasoactive drugs and tumor blood flow

Different observations on the reactivity of tumor vessels to vasoactive drugs have suggested a decreased, a similar or an increased reactivity to vasoactive stimuli in the vascular bed of tumors as compared to normal tissues. No adrenergic innervation of newly developed tumor vessels has been found, while preexisting normal vessels incorporated during tumor growth may retain some innervation. In transplantable rat tumors, contractile cells, including smooth muscle cells, have been seen in tumor vessels. From recent experimental studies, it was concluded that the tumor's vascular bed is probably in a state of maximal dilatation and therefore sensitive to vasoconstriction, but less sensitive to pharmacological dilatation. These observations may correspond to regional tumor hypoxia and progressive development of tumor necrosis during tumor growth. The results of experimental tumor studies might question the reliability of diagnostic and therapeutic procedures in clinical oncology, which are based on differences in the reactivity to vasoactive drugs between normal and malignant tissues.     

Numerical simulation of a single cell passing through a narrow slit

The narrow slit between endothelial cells that line the microvessel wall is the principal pathway for tumor cell extravasation to the surrounding tissue. To understand this crucial step for tumor hematogenous metastasis, we used dissipative particle dynamics method to investigate an individual cell passing through a narrow slit numerically. The cell membrane was simulated by a spring-based network model which can separate the internal cytoplasm and surrounding fluid. The effects of the cell elasticity, cell shape, nucleus and slit size on the cell transmigration through the slit were investigated. Under a fixed driving force, the cell with higher elasticity can be elongated more and pass faster through the slit. When the slit width decreases to 2/3 of the cell diameter, the spherical cell becomes jammed despite reducing its elasticity modulus by 10 times. However, transforming the cell from a spherical to ellipsoidal shape and increasing the cell surface area by merely 9.3 % can enable the cell to pass through the narrow slit. Therefore, the cell shape and surface area increase play a more important role than the cell elasticity in cell passing through the narrow slit. In addition, the simulation results indicate that the cell migration velocity decreases during entrance but increases during exit of the slit, which is qualitatively in agreement with the experimental observation.     

Numerical simulation of the urine flow in a stented ureter

When a stent is implanted in a blocked ureter, the urine passing from the kidney to the bladder must traverse a very complicated flow path. That path consists of two parallel passages, one of which is the bore of the stent and the other is the annular space between the external surface of the stent and the inner wall of the ureter. The flow path is further complicated by the presence of numerous pass-through holes that are deployed along the length of the stent. These holes allow urine to pass between the annulus and the bore. Further complexity in the pattern of the urine flow occurs because the coiled "pig tails," which hold the stent in place, contain multiple ports for fluid ingress and egress. The fluid flow in a stented ureter has been quantitatively analyzed here for the first time using numerical simulation. The numerical solutions obtained here fully reveal the details of the urine flow throughout the entire stented ureter. It was found that in the absence of blockages, most of the pass-through holes are inactive. Furthermore, only the port in each coiled pig tail that is nearest the stent proper is actively involved in the urine flow. Only in the presence of blockages, which may occur due to encrustation or biofouling, are the numerous pass-through holes activated. The numerical simulations are able to track the urine flow through the pass-through holes as well as adjacent to the blockages. The simulations are also able to provide highly accurate results for the kidney-to-bladder urine flow rate. The simulation method presented here constitutes a powerful new tool for rational design of ureteral stents in the future.     

Numerical modeling of fluid flow in solid tumors

A mathematical model of interstitial fluid flow is developed, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for a predefined tumor geometry. The interstitial fluid pressure and velocity are calculated using a numerical method, element based finite volume. Simulations of interstitial fluid transport in a homogeneous solid tumor demonstrate that, in a uniformly perfused tumor, i.e., one with no necrotic region, because of the interstitial pressure distribution, the distribution of drug particles is non-uniform. Pressure distribution for different values of necrotic radii is examined and two new parameters, the critical tumor radius and critical necrotic radius, are defined. Simulation results show that: 1) tumor radii have a critical size. Below this size, the maximum interstitial fluid pressure is less than what is generally considered to be effective pressure (a parameter determined by vascular pressure, plasma osmotic pressure, and interstitial osmotic pressure). Above this size, the maximum interstitial fluid pressure is equal to effective pressure. As a consequence, drugs transport to the center of smaller tumors is much easier than transport to the center of a tumor whose radius is greater than the critical tumor radius; 2) there is a critical necrotic radius, below which the interstitial fluid pressure at the tumor center is at its maximum value. If the tumor radius is greater than the critical tumor radius, this maximum pressure is equal to effective pressure. Above this critical necrotic radius, the interstitial fluid pressure at the tumor center is below effective pressure. In specific ranges of these critical sizes, drug amount and therefore therapeutic effects are higher because the opposing force, interstitial fluid pressure, is low in these ranges.