Biofilm development and the dynamics of preferential flow paths in porous media

A two-dimensional pore-scale numerical model was developed to evaluate the dynamics of preferential flow paths in porous media caused by bioclogging. The liquid flow and solute transport through the pore network were coupled with a biofilm model including biomass attachment, growth, decay, lysis, and detachment. Blocking of all but one flow path was obtained under constant liquid inlet flow rate and biomass detachment caused by shear forces only. The stable flow path formed when biofilm detachment balances growth, even with biomass weakened by decay. However, shear forces combined with biomass lysis upon starvation could produce an intermittently shifting location of flow channels. Dynamic flow pathways may also occur when combined liquid shear and pressure forces act on the biofilm. In spite of repeated clogging and unclogging of interconnected pore spaces, the average permeability reached a quasi-constant value. Oscillations in the medium permeability were more pronounced for weaker biofilms.     

Flow through a Collapsible Tube: Experimental Analysis and Mathematical Model

Flow through thin-wall axisymmetric tubes has long been of interest to physiologists. Analysis is complicated by the fact that such tubes will collapse when the transmural pressure (internal minus external pressure) is near zero. Because of the absence of any body of related knowledge in other sciences or engineering, previous workers have directed their efforts towards experimental studies of flow in collapsible tubes. More recently, some attention has been given towards analytical studies. Results of an extensive series of experiments show that the significant system parameter is transmural pressure. The cross-sectional area of the tube depends upon the transmural pressure, and changes in cross-section in turn affect the flow geometry. Based on experimental studies, a lumped parameter system model is proposed for the collapsible tube. The mathematical model is simulated on a hybrid computer. Experimental data were used to define the functional relationship between cross-sectional area and transmural pressure as well as the relation between the energy loss coefficient and cross-sectional area. Computer results confirm the validity of the model for both steady and transient flow conditions.     

Non-Newtonian Blood Flow in Left Coronary Arteries with Varying Stenosis: A Comparative Study

This paper presents Computational fluid dynamic (CFD) analysis of blood flow in three different 3-D models of left coronary artery (LCA). A comparative study of flow parameters (pressure distribution, velocity distribution and wall shear stress) in each of the models is done for a non-Newtonian (Carreau) as well as the Newtonian nature of blood viscosity over a complete cardiac cycle. The difference between these two types of behavior of blood is studied for both transient and steady states of flow. Additionally, flow parameters are compared for steady and transient boundary conditions considering blood as non-Newtonian fluid. The study shows that the highest wall shear stress (WSS), velocity and pressure are found in artery having stenosis in all the three branches of LCA. The use of Newtonian blood model is a good approximation for steady as well as transient blood flow boundary conditions if shear rate is above 100 s-1. However, the assumption of steady blood flow results in underestimating the values of flow parameters such as wall shear stress, pressure and velocity.     

广西岩溶区稻田土壤优先路径的空间分布

田间土壤优先路径空间分布影响优先流的发生和运动。通过野外土壤染色示踪试验,利用形态学图像解析技术,并结合群落生态学分析方法,对广西岩溶区秸秆覆盖(CM)和非覆盖(CK)下的水稻田进行土壤优先路径空间分布研究。结果表明: 在相同的外部供水状况下,随土壤深度的增加,秸秆覆盖水稻田的土壤水平染色由整体分布向团块状聚集分布转变;非秸秆覆盖水稻田以枝状染色为主,其平均染色斑块形状系数为21.69,染色形态规则,是秸秆覆盖水稻田的1.04倍。秸秆覆盖与非覆盖水稻田的土壤优先路径均呈聚集分布,秸秆覆盖水稻田内优先路径的Morisita指数为1.28,且田间优先路径以影响半径＜1.0 mm为主(重要值0.31),非秸秆覆盖水稻田内影响半径＜1.0 mm的优先路径重要值为0.28。秸秆覆盖影响稻田土壤优先路径,有助于改善田间作物的水肥利用状况。     

Numerical Modeling of Interstitial Fluid Flow Coupled with Blood Flow through a Remodeled Solid Tumor Microvascular Network

Modeling of interstitial fluid flow involves processes such as fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. To date, majority of microvascular flow modeling has been done at different levels and scales mostly on simple tumor shapes with their capillaries. However, with our proposed numerical model, more complex and realistic tumor shapes and capillary networks can be studied. Both blood flow through a capillary network, which is induced by a solid tumor, and fluid flow in tumor’s surrounding tissue are formulated. First, governing equations of angiogenesis are implemented to specify the different domains for the network and interstitium. Then, governing equations for flow modeling are introduced for different domains. The conservation laws for mass and momentum (including continuity equation, Darcy’s law for tissue, and simplified Navier–Stokes equation for blood flow through capillaries) are used for simulating interstitial and intravascular flows and Starling’s law is used for closing this system of equations and coupling the intravascular and extravascular flows. This is the first study of flow modeling in solid tumors to naturalistically couple intravascular and extravascular flow through a network. This network is generated by sprouting angiogenesis and consisting of one parent vessel connected to the network while taking into account the non-continuous behavior of blood, adaptability of capillary diameter to hemodynamics and metabolic stimuli, non-Newtonian blood flow, and phase separation of blood flow in capillary bifurcation. The incorporation of the outlined components beyond the previous models provides a more realistic prediction of interstitial fluid flow pattern in solid tumors and surrounding tissues. Results predict higher interstitial pressure, almost two times, for realistic model compared to the simplified model.     

贡嘎山暗针叶林生态系统基于KDW运动-弥散波模型的优先流研究

利用自制的土柱装置,开展室内土柱实验,并与野外实地示踪影像分析相结合,针对研究区域土壤包气带根系层中水分快速运动的优先流展开研究,其目的在于系统分析优先流对径流过程的影响,为长江上游暗针叶林生态系统土壤水分运动规律研究及有效流域管理提供理论支持。研究采用雷诺数计算及野外示踪映像分析方法,判定证明在所研究地区,有优先流现象发生,优先流是处于层流及紊流之间的过渡流。同时针对成熟林坡积物土壤的水分运移状况分析表明研究区域的壤中流过程主要表现为优先流,而土壤中的基质部分,则表现为不动区域。研究在以往优先流模型构建的基础上,综合考虑了研究区域的实地情况,应用融入弥散波的运动波模型(KDW优先流模型),利用交叉模拟方法和统计分析方法将此模型与实地实验检验分析,认定KDW优先流模型实用性强、可靠程度较高,可较好地模拟贡嘎山暗针叶林生态系统实地。     

Poroelastic analysis of interstitial fluid flow in a single lamellar trabecula subjected to cyclic loading

Trabecula, an anatomical unit of the cancellous bone, is a porous material that consists of a lamellar bone matrix and interstitial fluid in a lacuno-canalicular porosity. The flow of interstitial fluid caused by deformation of the bone matrix is believed to initiate a mechanical response in osteocytes for bone remodeling. In order to clarify the effect of the lamellar structure of the bone matrix—i.e., variations in material properties—on the fluid flow stimuli to osteocytes embedded in trabeculae, we investigated the mechanical behavior of an individual trabecula subjected to cyclic loading based on poroelasticity. We focused on variations in the trabecular permeability and developed an analytical solution containing both transient and steady-state responses for interstitial fluid pressure in a single trabecular model represented by a multilayered two-dimensional poroelastic slab. Based on the obtained solution, we calculated the pressure and seepage velocity of the interstitial fluid in lacuno-canalicular porosity, within the single trabecula, under various permeability distributions. Poroelastic analysis showed that a heterogeneous distribution of permeability produces remarkable variations in the fluid pressure and seepage velocity in the cross section of the individual trabecula, and suggests that fluid flow stimuli to osteocytes are mostly governed by the value of permeability in the neighborhood of the trabecular surfaces if there is no difference in the average permeability in a single trabecula.     

Casson fluid model for pulsatile flow of blood under periodic body acceleration

Pulsatile flow of a Casson fluid under the influence of a periodic body acceleration has been studied in this paper. An implicit finite difference numerical procedure has been used to analyze the flow. Applicability of this method has been checked by comparing the obtained results with the analytical solution for Newtonian flow and explicit scheme solution. The agreement between the implicit and explicit scheme solutions and the analytical solution is good (error less than 1%). Flow variables have been computed at three locations in cardiovascular system (wide (femoral) and narrow (arteriole and coronary) tubes). Effects of yield stress, tube radius and pressure gradient combined, body acceleration amplitude and frequency etc., on flow have been studied. The following observations have been made: (i) Initial transient time It changes with yield stress in narrow tubes are insignificant, whereas in wide tubes It decreases with yield stress; (ii) The axial velocity and fluid acceleration variations with yield stress are uniform (changes only quantitatively, profiles shape remain same) in narrow tubes, whereas in wide tubes these variations are non-uniform (profiles change qualitatively as well as quantitatively); (iii) Yield stress effects on wall shear amplitude are insignificant in narrow tubes (congruent to 0.3% in arteriole and congruent to 6% in femoral); and (iv) For Newtonian fluid, mean flow rate does not change with body acceleration amplitude a0 and frequency fb but it increases (decreases) with a0(fb) for Casson fluid.     

Soil preferential flow in the dark coniferous forest of Gongga Mountain based on the kinetic wave model with dispersion wave (KDW preferential flow model)

Based on the law of soil water movement in unsaturated zones, the study discusses the effect of preferential flow on the movement of the researched soil through a soil column experiment using homemade experimental apparatus in four successive stages—young, middle-aged, mature and over-mature and combining dye-tracer analyses of the field process. The study proves that the preferential flow occurs in the area, and as indicated by the Reynolds numerical calculation of the preferential flow path in the 4 different successive stages, the preferential flow in the Gongga Mountain forest ecosystem is a transition flow between the laminar flow and the turbulent flow. By applying the kinetic wave model with dispersion wave (KDW preferential flow model) and comparing this model with the field experiment, the study finds that the preferential flow model has good practicability and high credibility. Verifying the KDW preferential flow model through statistic analysis indicates that the model can simulate the water movement in columns very well and the results are better in low rainfall than in high rainfall.     

Hemodynamic diagnostics of epicardial coronary stenoses: <Emphasis Type="Italic">in-vitro</Emphasis> experimental and computational study

Background  

The severity of epicardial coronary stenosis can be assessed by invasive measurements of trans-stenotic pressure drop and flow. A pressure or flow sensor-tipped guidewire inserted across the coronary stenosis causes an overestimation in true trans-stenotic pressure drop and reduction in coronary flow. This may mask the true severity of coronary stenosis. In order to unmask the true severity of epicardial stenosis, we evaluate a diagnostic parameter, which is obtained from fundamental fluid dynamics principles. This experimental and numerical study focuses on the characterization of the diagnostic parameter, pressure drop coefficient, and also evaluates the pressure recovery downstream of stenoses.     

On the paths of fluid particles in an axisymmetrical aneurysm

The aim of this study is the characterization of the pulsatile flow field by demonstration of the paths of single particles in a model of an axisymmetric aneurysm. The detailed analysis of the flow field can give additional information on the flow pattern and the time of transition of blood particles in the segment. The basis of the calculations is the system of the Navier-Stokes equations for incompressible Newtonian fluid flow. To solve these equations numerically the finite element method was used. The trajectory equations for a fluid particle were solved by use of a predictor-corrector procedure. The results of the computer simulation demonstrate the development, shift and disappearance of vortices in the excavation and give references to zones of stasis. This behavior can be an important factor in thrombogenesis.     

On the Importance of Hysteresis in Numerical Modeling of Surfactant-Induced Unsaturated Flow

It is known that surfactants can induce flow in unsaturated porous media due to the dependence of capillary pressure on surface tension. A commonly observed feature in systems with surfactant-induced flow is a transient wetting/drying/wetting sequence associated with the propagation of a surfactant solute front under monotonic flow conditions. Previous efforts to model surfactant-induced flow in relatively complex (e.g., two-dimensional systems) have not successfully incorporated hysteretic moisture retention properties. In this research, hysteretic, two-dimensional simulations of surfactant-induced flow were performed to assess the potential importance of considering hysteresis in such simulations. Hysteretic simulation results were compared to experimental data and to non-hysteretic simulations. The results suggest that the inclusion of hysteresis in numerical simulations can improve the match between simulated and experimental results in systems with surfactant-induced unsaturated flow. Furthermore, the inclusion of hysteresis in numerical simulations played a significant role in predicting the distribution of the contaminant and correct pressure head/moisture condition at the end of the experiment.     

Original article submission: Platelet stress accumulation analysis to predict thrombogenicity of an artificial kidney

An implantable artificial kidney using a hemofilter constructed from an array of silicon membranes to provide ultrafiltration requires a suitable blood flow path to ensure stable operation in vivo. Two types of flow paths distributing blood to the array of membranes were evaluated: parallel and serpentine. Computational fluid dynamics (CFD) simulations were used to guide the development of the blood flow paths. Pressure data from animal tests were used to obtain pulsatile flow conditions imposed in the transient simulations. A key consideration for stable operation in vivo is limiting platelet stress accumulation to avoid platelet activation and thrombus formation. Platelet stress exposure was evaluated by CFD particle tracking methods through the devices to provide distributions of platelet stress accumulation. The distributions of stress accumulation over the duration of a platelet lifetime for each device revealed that stress accumulation for the serpentine flow path exceeded levels expected to cause platelet activation while the accumulated stress for the parallel flow path was below expected activation levels.     

Numerical simulation of blood flow in the left ventricle and aortic sinus using magnetic resonance imaging and computational fluid dynamics

Understanding cardiac blood flow patterns has many applications in analysing haemodynamics and for the clinical assessment of heart function. In this study, numerical simulations of blood flow in a patient-specific anatomical model of the left ventricle (LV) and the aortic sinus are presented. The realistic 3D geometry of both LV and aortic sinus is extracted from the processing of magnetic resonance imaging (MRI). Furthermore, motion of inner walls of LV and aortic sinus is obtained from cine-MR image analysis and is used as a constraint to a numerical computational fluid dynamics (CFD) model based on the moving boundary approach. Arbitrary Lagrangian–Eulerian finite element method formulation is used for the numerical solution of the transient dynamic equations of the fluid domain. Simulation results include detailed flow characteristics such as velocity, pressure and wall shear stress for the whole domain. The aortic outflow is compared with data obtained by phase-contrast MRI. Good agreement was found between simulation results and these measurements.     

Dependence of mechanical behavior of the murine tail disc on regional material properties: a parametric finite element study

In vivo rodent tail models are becoming more widely used for exploring the role of mechanical loading on the initiation and progression of intervertebral disc degeneration. Historically, finite element models (FEMs) have been useful for predicting disc mechanics in humans. However, differences in geometry and tissue properties may limit the predictive utility of these models for rodent discs. Clearly, models that are specific for rodent tail discs and accurately simulate the disc's transient mechanical behavior would serve as important tools for clarifying disc mechanics in these animal models. An FEM was developed based on the structure, geometry, and scale of the mouse tail disc. Importantly, two sources of time-dependent mechanical behavior were incorporated: viscoelasticity of the matrix, and fluid permeation. In addition, a novel strain-dependent swelling pressure was implemented through the introduction of a dilatational stress in nuclear elements. The model was then validated against data from quasi-static tension-compression and compressive creep experiments performed previously using mouse tail discs. Finally, sensitivity analyses were performed in which material parameters of each disc subregion were individually varied. During disc compression, matrix consolidation was observed to occur preferentially at the periphery of the nucleus pulposus. Sensitivity analyses revealed that disc mechanics was greatly influenced by changes in nucleus pulposus material properties, but rather insensitive to variations in any of the endplate properties. Moreover, three key features of the model-nuclear swelling pressure, lamellar collagen viscoelasticity, and interstitial fluid permeation-were found to be critical for accurate simulation of disc mechanics. In particular, collagen viscoelasticity dominated the transient behavior of the disc during the initial 2200 s of creep loading, while fluid permeation governed disc deformation thereafter. The FEM developed in this study exhibited excellent agreement with transient creep behavior of intact mouse tail motion segments. Notably, the model was able to produce spatial variations in nucleus pulposus matrix consolidation that are consistent with previous observations in nuclear cell morphology made in mouse discs using confocal microscopy. Results of this study emphasize the need for including nucleus swelling pressure, collagen viscoelasticity, and fluid permeation when simulating transient changes in matrix and fluid stress/strain. Sensitivity analyses suggest that further characterization of nucleus pulposus material properties should be pursued, due to its significance in steady-state and transient disc mechanical response.     

A model of fluid-biofilm interaction using a Burger material law

A two-dimensional finite element model of the biofilm response to flow was developed. The numerical code sequentially coupled the fluid dynamics of turbulent, incompressible flow with the mechanical response of a single hemispherical biofilm cluster (approximately 100 microm) attached to the flow boundary. A non-linear Burger material law was used to represent the viscoelastic response of a representative microbial biofilm. This constitutive law was incorporated into the numerical model as a Prony series representation of the biofilm's relaxation modulus. Model simulations illuminated interesting details of this fluid-structure interaction. Simulations revealed that softer biofilms (characterized by lower elastic moduli) were highly susceptible to lift forces and consequently were subject to even greater drag forces found higher in the velocity field. A bimodal deformation path due to the two Burger relaxation times was also observed in several simulations. This suggested that interfacial biofilm may be most susceptible to hydrodynamically induced detachment during the initial relaxation time. This result may prove useful in developing removal strategies. Additionally, plots of lift versus drag suggested that the deformation paths taken by viscoelastic biofilms are largely insensitive to specific material coefficients. Softer biofilms merely seem to follow the same path (as a stiffer biofilm) at a faster rate. These relationships may be useful in estimating the hydrodynamic forces acting on an attached biofilm based on changes in scale and cataloged material properties.     

Validation of a fluid–structure interaction numerical model for predicting flow transients in arteries

Fluid–structure interaction (FSI) numerical models are now widely used in predicting blood flow transients. This is because of the importance of the interaction between the flowing blood and the deforming arterial wall to blood flow behaviour. Unfortunately, most of these FSI models lack rigorous validation and, thus, cannot guarantee the accuracy of their predictions. This paper presents the comprehensive validation of a two-way coupled FSI numerical model, developed to predict flow transients in compliant conduits such as arteries. The model is validated using analytical solutions and experiments conducted on polyurethane mock artery. Flow parameters such as pressure and axial stress (and precursor) wave speeds, wall deformations and oscillating frequency, fluid velocity and Poisson coupling effects, were used as the basis of this validation. Results show very good comparison between numerical predictions, analytical solutions and experimental data. The agreement between the three approaches is generally over 95%. The model also shows accurate prediction of Poisson coupling effects in unsteady flows through flexible pipes, which up to this stage have only being predicted analytically. Therefore, this numerical model can accurately predict flow transients in compliant vessels such as arteries.     

Flow cytometry: a promising technique for the study of silicone oil-induced particulate formation in protein formulations

Subvisible particles in formulations intended for parenteral administration are of concern in the biopharmaceutical industry. However, monitoring and control of subvisible particulates can be complicated by formulation components, such as the silicone oil used for the lubrication of prefilled syringes, and it is difficult to differentiate microdroplets of silicone oil from particles formed by aggregated protein. In this study, we demonstrate the ability of flow cytometry to resolve mixtures comprising subvisible bovine serum albumin (BSA) aggregate particles and silicone oil emulsion droplets with adsorbed BSA. Flow cytometry was also used to investigate the effects of silicone oil emulsions on the stability of BSA, lysozyme, abatacept, and trastuzumab formulations containing surfactant, sodium chloride, or sucrose. To aid in particle characterization, the fluorescence detection capabilities of flow cytometry were exploited by staining silicone oil with BODIPY 493/503 and model proteins with Alexa Fluor 647. Flow cytometric analyses revealed that silicone oil emulsions induced the loss of soluble protein via protein adsorption onto the silicone oil droplet surface. The addition of surfactant prevented protein from adsorbing onto the surface of silicone oil droplets. There was minimal formation of homogeneous protein aggregates due to exposure to silicone oil droplets, although oil droplets with surface-adsorbed trastuzumab exhibited flocculation. The results of this study demonstrate the utility of flow cytometry as an analytical tool for monitoring the effects of subvisible silicone oil droplets on the stability of protein formulations.     

Comparison between a generalized Newtonian model and a network-type multiscale model for hemodynamic behavior in the aortic arch: Validation with 4D MRI data for a case study

Blood is a complex fluid in which the presence of the various constituents leads to significant changes in its rheological properties. Thus, an appropriate non-Newtonian model is advisable; and we choose a Modified version of the rheological model of Phan-Thien and Tanner (MPTT). The different parameters of this model, derived from the rheology of polymers, allow characterization of the non-Newtonian nature of blood, taking into account the behavior of red blood cells in plasma. Using the MPTT model that we implemented in the open access software OpenFOAM, numerical simulations have been performed on blood flow in the thoracic aorta for a healthy patient. We started from a patient-specific model which was constructed from medical images. Exiting flow boundary conditions have been developped, based on a 3-element Windkessel model to approximate physiological conditions. The parameters of the Windkessel model were calibrated with in vivo measurements of flow rate and pressure. The influence of the selected viscosity of red blood cells on the flow and wall shear stress (WSS) was investigated. Results obtained from this model were compared to those of the Newtonian model, and to those of a generalized Newtonian model, as well as to in vivo dynamic data from 4D MRI during a cardiac cycle. Upon evaluating the results, the MPTT model shows better agreement with the MRI data during the systolic and diastolic phases than the Newtonian or generalized Newtonian model, which confirms our interest in using a complex viscoelastic model.     

The role of fibril reinforcement in the mechanical behavior of cartilage

Collagen fibril reinforcement was incorporated into a nonlinear poroelastic model for articular cartilage in unconfined compression. It was found that the radial fibrils play a predominant role in the transient mechanical behavior but a less important role in the equilibrium response of cartilage. The radial fibrils are in tension and can be highly stressed during compression, in contrast to low compressive stresses in all directions for the proteoglycan matrix after a small initial compression. The strain dependent fibril stiffening produces strong nonlinear transient response; the fibrils provide extra stiffness to balance a rising fluid pressure and to restrain stress increase in the proteoglycans. The fibril reinforcement, induced by the fluid pressure and flow, also accounts for a complex pattern of strain-magnitude and strain-rate dependence of cartilage stiffness.