On the influence of a leaky tight junction on water and solute transport in epithelia

The role of a leaky tight junction in epithelia is examined by considering the flow of water and solute through a channel consisting of two sections representing the intercellular space and tight junction. Two cases are considered, flow through a channel with a circular cross-section and flow between parallel planes. Analytical solutions are obtained using the isotonic convection approximation. The flow is driven by active transport of solute and imposed concentration and pressure differences. Particular attention is paid to the flux of solute through the tight junction. It is shown that the shape of the channel cross-section is important.The theory is applied to the rat proximal tube epithelium. It is deduced that the emergent osmolarity is close to that predicted for a closed tight junction, but that transepithelial hydrostatic pressure differences are potentially important. The influence of transepithelial concentration differences appears to be unimportant in this model.     

Peristaltic flow of a couple stress fluid in an asymmetric channel

This paper presents an analysis of the peristaltic flow of a couple stress fluid in an asymmetric channel. The asymmetric nature of the flow is introduced through the peristaltic waves of different amplitudes and phases on the channel walls. Mathematical modelling corresponding to a two-dimensional flow has been carried out. The flow analysis is presented under long wavelength and low Reynolds number approximations. Closed form solutions for the axial velocity, stream function and the axial pressure gradient are given. Numerical computations have been carried out for the pressure rise per wavelength, friction forces and trapping. It is noted that there is a decrease in the pressure when the couple stress fluid parameter increases. The variation of the couple stress fluid parameter with the size of the trapped bolus is also similar to that of pressure. Furthermore, the friction force on the lower channel wall is greater than that on the upper channel wall.     

Pulsatile blood flow in a rigid pulmonary alveolar sheet with porous walls

This paper deals with the pulsatile blood flow in the lung alveolar sheets by idealizing each of them as a channel covered by porous media. As the blood flow in the lung is of low Reynolds number, a creeping flow is assumed in the channel. The analytical and numerical results for the velocity and pressure distribution in the porous medium are presented. The effect of an imposed slip condition is also studied. Comparisons with the corresponding results for the steady-state case are made at the end.     

Analysis of intracellular reducing levels in human hepatocytes on three‐dimensional focusing microchip

A novel three‐dimensional hydrodynamic focusing microfluidic device integrated with high‐throughput cell sampling and detection of intracellular contents is presented. It has a pivotal role in maintaining the reducing environment in cells. Intracellular reducing species such as vitamin C and glutathione in normal and tumor cells were labeled by a newly synthesized 2,2,6,6‐tetramethyl‐piperidine‐1‐oxyl‐based fluorescent probe. Hepatocytes are adherent cells, which are prone to attaching to the channel surface. To avoid the attachment of cells on the channel surface, a single channel microchip with three sheath‐flow channels located on both sides of and below the sampling channel was developed. Hydrostatic pressure generated by emptying the sample waste reservoir was used as driving force of fluid on the microchip. Owing to the difference between the liquid levels of the reservoirs, the labeled cells were three‐dimensional hydrodynamically focused and transported from the sample reservoir to the sample waste reservoir. Hydrostatic pressure takes advantage of its ease of generation on a microfluidic chip without any external pressure pump, which drives three sheath‐flow streams to constrain a sample flow stream into a narrow stream to avoid blockage of the sampling channel by adhered cells. The intracellular reducing levels of HepG2 cells and L02 cells were detected by home‐built laser‐induced fluorescence detector. The analysis throughput achieved in this microfluidic system was about 59–68 cells/min. Copyright © 2013 John Wiley & Sons, Ltd.     

A model of NaCl and water flow through paracellular pathways of renal proximal tubules.

To explain how hydrostatic pressure differences between tubule lumen and interstitium modulate isotonic reabsorption rates, we developed a model of NaCl and water flow through paracellular pathways of the proximal tubule. Structural elements of the model are a tight junction membrane, an intercellular channel whose walls transport NaCl actively at a constant rate, and a basement membrane. Equations of change were derived for the channel, boundary conditions were formulated from irreversible thermodynamics, and a pressure-area relationship typical of thin-walled tubing was assumed. The boundary value problem was solved numerically. The principal conclusions are: 1) channel NaCl concentration must remain within a few mOsm of isotonic values for reabsorption rates to be modulated by transtubular pressure differences known to affect this system: 2) basement membrane and channel wall parameters determine reabsorbate tonicity; tight junction parameters affect the sensitivity of reabsorption to transmural pressure; 3) channel NaCl concentration varies inversely with transmural pressure difference; this concentration variation controls NaCl diffusion through the tight junction; 4) modulation of NaCl diffusion through the tight junction controls the rate of isotonic reabsorption; modulation of water flow can increase sensitivity to transmural pressure; 5) no pressure-induced change in permeability of the tight junction or basement membrane is needed for pressure to modulate reabsorption; and 6) system performance is indifferent to the distribution of active transport sites, to the numerical value of the compliance function, and to the relationship between lumen and cell pressures.     

Experiments on steady and oscillatory flows at moderate Reynolds numbers in a quasi-two-dimensional channel with a throat.

The study of steady and unsteady oscillatory static fluid pressures acting on the internal wall of a collapsible tube is essential for investigation of the complicated behavior observed when a flow is conveyed inside a tube. To examine the validity of two one-dimensional nonsteady theoretical flow models, this paper presents basic experimental observations of flow separation and reattachment and measured data on the static pressure distributions of the flow in a quasi-two-dimensional channel with a throat, together with information on the corresponding shape of the wall deflection and motion. For combinations of moderate Reynolds numbers and angles of the divergent segment of the channel, a smooth flow is separated from the wall downstream of the minimum cross section and reattached to the wall farther downstream. The measured data are compared with numerical results calculated by the two flow models.     

A stochastic model of cell aggregation under planar flow in the dilute regime

Models of the adhesion of a population of cells in a plane flow are developed, considering the dilute regime. Cells considered as rigid punctual entities are virtually injected at regular times within a plane channel limited by two fixed planes. The pressure profile is supposed to be triangular (constant gradient), in accordance with the assumptions of a Poiseuille flow. The cell adherence to the channel wall is governed by the balance of forces, accounting for gravity, non-specific physical interactions, such as electrostatic effects (repulsive) and Van der Waals forces (attractive), specific adhesive forces representing the ligand–receptor interactions, and friction between cells and the fluid in the vicinity of the endothelium wall. The spatial distribution of the adhesion molecules along the wall is supposed to be a random event, accounted for by a stochastic spatial variability of the dipolar moments of those molecules, according to a Gaussian process. Experimental trends reported for the rate of aggregation of L-selectin mediated leukocytes under shear flow are in qualitative accordance with the evolution versus time of adhering cells obtained by the present simulations. The effect of the maximal injection pressure on those kinetics is assessed.     

Flow around cells adhered to a microvessel wall II: comparison to flow around adherent cells in channel flow

The flow around adherent cells in a parallel-plate channel and that in a circular cylindrical tube are numerically analyzed, and their effects on the adherent cells are compared. The cells are modeled as rigid spherical particles and they are assumed to be attached to a wall of a 2D channel uniformly in a square array, or a wall of a circular tube regularly in a line along the tube axis. It is found that, when the size ratios of the particle-to-channel height and the particle-to-tube diameter are smaller than approximately 0.2, the distributions of the shear stress and the pressure exerted on the surface of an adherent particle as well as the drag force and torque acting on it compare favorably in the 2D channel flow and tube flow. As the size ratios increase from 0.2, the differences between the 2D channel and the tube increase drastically, especially when separation distances between neighboring particles are large.     

Steady propagation of a liquid plug in a two-dimensional channel

In this study, we investigate the steady propagation of a liquid plug within a two-dimensional channel lined by a uniform, thin liquid film. The Navier-Stokes equations with free-surface boundary conditions are solved using the finite volume numerical scheme. We examine the effect of varying plug propagation speed and plug length in both the Stokes flow limit and for finite Reynolds number (Re). For a fixed plug length, the trailing film thickness increases with plug propagation speed. If the plug length is greater than the channel width, the trailing film thickness agrees with previous theories for semi-infinite bubble propagation. As the plug length decreases below the channel width, the trailing film thickness decreases, and for finite Re there is significant interaction between the leading and trailing menisci and their local flow effects. A recirculation flow forms inside the plug core and is skewed towards the rear meniscus as Re increases. The recirculation velocity between both tips decreases with the plug length. The macroscopic pressure gradient, which is the pressure drop between the leading and trailing gas phases divided by the plug length, is a function of U and U2, where U is the plug propagation speed, when the fluid property and the channel geometry are fixed. The U2 term becomes dominant at small values of the plug length. A capillary wave develops at the front meniscus, with an amplitude that increases with Re, and this causes large local changes in wall shear stresses and pressures.     

Simulation of two-dimensional fully developed laminar flow for a magneto-hydrodynamic (MHD) pump

MHD micro-pumps circumvent the wear and fatigue caused by high pressure-drop across the check valves of mechanical micro-pumps in micro-fluidic systems. Early analyses of the fluid flow for MHD micro-pumps were mostly made possible by the Poiseuille flow theory; however, this conventional laminar approach cannot illustrate the effects of various channel sizes and shapes. This paper, therefore, presents a simplified MHD flow model based upon steady state, incompressible and fully developed laminar flow theory to investigate the characteristics of a MHD pump. Inside the pump, flowing along the channel is the electrically conducting fluid flowing driven by the Lorentz forces in the direction perpendicular to both dc magnetic field and applied electric currents. The Lorentz forces were converted into a hydrostatic pressure gradient in the momentum equations of the MHD channel flow model. The numerical simulations conducted with the explicit finite difference method show that the channel dimensions and the induced Lorentz forces have significant influences on the flow velocity profile. Furthermore, the simulation results agree well with the experimental results published by other researchers.     

High concentration biotherapeutic formulation and ultrafiltration: Part 1 pressure limits

High therapeutic dosage requirements and the desire for ease of administration drive the trend to subcutaneous administration using delivery systems such as subcutaneous pumps and prefilled syringes. Because of dosage volume limits, prefilled syringe administration requires higher concentration liquid formulations, limited to about 30 cP or roughly 100–300 g L^?1 for mAb's. Ultrafiltration (UF) processes are routinely used to formulate biological therapeutics. This article considers pressure constraints on the UF process that may limit its ability to achieve high final product concentrations. A system hardware analysis shows that the ultrafiltration cassette pressure drop is the major factor limiting UF systems. Additional system design recommendations are also provided. The design and performance of a new cassette with a lower feed channel flow resistance is described along with 3D modeling of feed channel pressure drop. The implications of variations in cassette flow channel resistance for scaling up and setting specifications are considered. A recommendation for a maximum pressure specification is provided. A review of viscosity data and theory shows that molecular engineering, temperature, and the use of viscosity modifying excipients including pH adjustment can be used to achieve higher concentrations. The combined use of a low pressure drop cassette with excipients further increased final concentrations by 35%. Guidance is provided on system operation to control hydraulics during final concentration. These recommendations should allow one to design and operate systems to routinely achieve the 30 cP target final viscosity capable of delivery using a pre‐filled syringe. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 33:113–124, 2017     

An analysis of the flow of a power law fluid due to ciliary motion in an infinite channel

The propulsion mechanics of cilia-induced flow is studied through a mathematical model. The problem of two-dimensional motion of a power law fluid inside a channel with ciliated walls is considered. The characteristics of ciliary systems are determined by the dominance of viscous effects over inertial effects using the long-wavelength approximation. Solutions for the longitudinal, transverse, and resultant velocities are obtained. The pressure gradient and volume flow rate for different values of the power law index are also calculated. The flow properties for the power law fluid are determined as a function of the cilia and metachronal wave velocity. The viscous and power law fluid are compared and discussed graphically.     

Transmural difference in coronary arteriolar dilation to adenosine: effect of luminal pressure and K(ATP) channels

Coronary blood flow in the subendocardium is preferentially increased by adenosine but is redistributed to the subepicardium during ischemia in association with coronary pressure reduction. The mechanism for this flow redistribution remains unclear. Since adenosine is released during ischemia, it is possible that the coronary microcirculation exhibits a transmural difference in vasomotor responsiveness to adenosine at various intraluminal pressures. Although the ATP-sensitive K(+) (K(ATP)) channel has been shown to be involved in coronary arteriolar dilation to adenosine, its role in the transmural adenosine response remains elusive. To address these issues, pig subepicardial and subendocardial arterioles (60-120 micrometer) were isolated, cannulated, and pressurized to 20, 40, 60, or 80 cmH(2)O without flow for in vitro study. At each of these pressures, vessels developed basal tone and dilated concentration dependently to adenosine and the K(ATP) channel opener pinacidil. Subepicardial and subendocardial arterioles dilated equally to adenosine and pinacidil at 60 and 80 cmH(2)O luminal pressure. At lower luminal pressures (i.e., 20 and 40 cmH(2)O), vasodilation in both vessel types was enhanced. Enhanced vasodilatory responses were not affected by removal of endothelium but were abolished by the K(ATP) channel inhibitor glibenclamide. In a manner similar to reducing pressure, a subthreshold dose of pinacidil potentiated vasodilation to adenosine. In contrast to adenosine, dilation of coronary arterioles to sodium nitroprusside was independent of pressure changes. These results indicate that coronary microvascular dilation to adenosine is enhanced at lower intraluminal pressures by selective activation of smooth muscle K(ATP) channels. Since microvascular pressure has been shown to be consistently lower in the subendocardium than in the subepicardium, it is likely that the inherent pressure gradient in the coronary microcirculation across the ventricular wall may be an important determinant of transmural flow in vivo during resting conditions or under metabolic stress with adenosine release.     

A one-dimensional unsteady separable and reattachable flow model for collapsible tube-flow analysis

Taking into account both flow separation and reattachment observed in available experimental results on flows in a quasi-two-dimensional channel, we present a one-dimensional unsteady flow model, which is applicable to a flow in a collapsible tube. The flow model has been derived from the two-dimensional Navier-Stokes equations by introducing the concept of a dividing streamline, which divides a separated flow into a jet and a dead-water zone. We also present a criterion for the determination of a separation point. Numerical results show that the locations of the predicted separation points agree well with the experimental data. The predicted static pressure of the separated flow is almost constant downstream of the separation point and increases quickly just before the reattachment point as observed in the experiment. Finally, using the present flow model and the separation criterion, we examine the oscillatory behavior of an unsteady flow in a symmetric channel whose walls move sinusoidally.     

Particle Image Velocimetry Study of Pulsatile Flow in Bi-leaflet Mechanical Heart Valves with Image Compensation Method

Particle Image Velocimetry (PIV) is an important technique in studying blood flow in heart valves. Previous PIV studies of flow around prosthetic heart valves had different research concentrations, and thus never provided the physical flow field pictures in a complete heart cycle, which compromised their pertinence for a better understanding of the valvular mechanism. In this study, a digital PIV (DPIV) investigation was carried out with improved accuracy, to analyse the pulsatile flow field around the bi-leaflet mechanical heart valve (MHV) in a complete heart cycle. For this purpose a pulsatile flow test rig was constructed to provide the necessary in vitro test environment, and the flow field around a St. Jude size 29 bi-leaflet MHV and a similar MHV model were studied under a simulated physiological pressure waveform with flow rate of 5.2 l/min and pulse rate at 72 beats/min. A phase-locking method was applied to gate the dynamic process of valve leaflet motions. A special image-processing program was applied to eliminate optical distortion caused by the difference in refractive indexes between the blood analogue fluid and the test section. Results clearly showed that, due to the presence of the two leaflets, the valvular flow conduit was partitioned into three flow channels. In the opening process, flow in the two side channels was first to develop under the presence of the forward pressure gradient. The flow in the central channel was developed much later at about the mid-stage of the opening process. Forward flows in all three channels were observed at the late stage of the opening process. At the early closing process, a backward flow developed first in the central channel. Under the influence of the reverse pressure gradient, the flow in the central channel first appeared to be disturbed, which was then transformed into backward flow. The backward flow in the central channel was found to be the main driving factor for the leaflet rotation in the valve closing process. After the valve was fully closed, local flow activities in the proximity of the valve region persisted for a certain time before slowly dying out. In both the valve opening and closing processes, maximum velocity always appeared near the leaflet trailing edges. The flow field features revealed in the present paper improved our understanding of valve motion mechanism under physiological conditions, and this knowledge is very helpful in designing the new generation of MHVs.     

A mathematical model of proximal tubule absorption

A previous model of the mechanisms of flow through epithelia was modified and extended to include hydrostatic and osmotic pressures in the cells and in the peritubular capillaries. The differential equations for flow and concentration in each region of the proximal tubule were derived. The equations were solved numerically by a finite difference method. The principal conclusions are: (i) Cell NaCl concentration remains essentially isotonic over the pressure variations considered; (ii) channel NaCl concentration varies only a few mosmol from isotonicity, and the hydrostatic and osmotic pressure differences across the cell wall are of the same order of magnitude; (iii) both reabsorbate osmolality and pressure-induced flow are relatively insensitive to the geometry of the system; (iv) a strong equilibrating mechanism exists in the sensitivity of the reabsorbate osmolality to luminal osmolality; this mechanism is far more significant than any other parameter change.     

Waveform dependence of pulsatile flow in a stenosed channel

Bloodflow in arteries often shows a rich variety of vortical flows, which are dominated by the complex geometry of blood vessels, the dynamic pulsation of blood flow, and the complicated boundary conditions. With a two-dimensional model of unsteady flow in a stenosed channel, the pulsatile influence on such vortical fluid dynamics has been numerically studied in terms of waveform dependence on physiological pulsation. Results are presented for unsteady flows downstream of the stenosed portion with variation in the wavefiorms of systole and diastole. Overall, a train of propagating vortex waves is observed for all the cases, but it shows great sensitivity to the waveforms. The generation and development of the vortex waves may be linked to the presence of an adverse pressure gradient within a specific interval between two points of inflection of the systolic waveform. The adverse pressure gradient consists of a global pressure gradient that is found to be closely related to the dynamnics of' the pulsation, and a local pressure gradient, which is obsented to be dominated by the nonlinear vortex dynamics.     

Interaction of Peristaltic Flow with Pulsatile Couple-Stress Fluid

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Finite element analysis of the lift on a slightly deformable and freely rotating and translating cylinder in two-dimensional channel flow

Motivated by the lateral migration phenomena of fresh and glutaraldehyde-fixed red blood cells in a field flow fractionation (FFF) separation system, we studied the transverse hydrodynamic lift on a slightly flexible cylinder in a two-dimensional channel flow. The finite element method was used to analyze the flow field with the cylinder at different transverse locations in the channel. The shape of the cylinder was determined by the pressure on the surface of the cylinder from the flow field solution and by the internal elastic stress. The cylinder deformation and the flow field were solved simultaneously. The transverse lift exerted on the cylinder was then calculated. The axial and angular speed of the cylinder were iterated such that the drag and torque on the cylinder were nulled to represent a freely translating and rotating state. The results showed that the transverse lift on a deformable cylinder increased greatly and the equilibrium position moved closer to the center of the channel compared to a rigid cylinder. Also, with the same elastic modulus but a higher flow rate, a larger deformation and higher equilibrium location were found. The maximum deformation of the cylinder occurred when the cylinder was closest to the wall where a larger shear rate existed. The numerical results and experimental studies are discussed.