Horizontal transport induced by upwelling in a canyon-shaped reservoir

Several processes associated with spatial variations in buoyancy flux and mixing set up local and lake-wide horizontal temperature gradients, that in turn drive slow gravitational currents. These motions can dominate the horizontal transport and re-distribution of biological and chemical material. Here intrusions, indicative of horizontal transport, are identified in field data from a small drinking water reservoir, and the origin and character of the flows investigated using a 3-dimensional (3D) hydrodynamic model. It is shown that a horizontal temperature gradient is set up along the surface layer, due to upwelling shifting the metalimnion closer to the surface towards the upwind region, leading to a spatial variation in entrainment. The flows driven by these gradients form significant mass flux paths, enhancing exchange with the boundaries and controlling the fate of upwelled fluid. Further, the interaction of these currents with other hydrodynamic conditions is explored; namely the interaction with surface wind-driven currents, and the influence of different internal seiches generated by alternative lake bathymetries. Handling editor: D. Hamilton     

Patterning and polarization of cells by intracellular flows

Beginning with Turing's seminal work [1], decades of research have demonstrated the fundamental ability of biochemical networks to generate and sustain the formation of patterns. However, it is increasingly appreciated that biochemical networks also both shape and are shaped by physical and mechanical processes [2, 3, 4]. One such process is fluid flow. In many respects, the cytoplasm, membrane and actin cortex all function as fluids, and as they flow, they drive bulk transport of molecules throughout the cell. By coupling biochemical activity to long-range molecular transport, flows can shape the distributions of molecules in space. Here, we review the various types of flows that exist in cells, with the aim of highlighting recent advances in our understanding of how flows are generated and how they contribute to intracellular patterning processes, such as the establishment of cell polarity.     

Groundwater and pore water inputs to the coastal zone

Both terrestrial and marine forces drive underground fluid flows in the coastal zone. Hydraulic gradients on land result in groundwater seepage near shore and may contribute to flows further out on the shelf from confined aquifers. Marine processes such as tidal pumping and current-induced pressure gradients may induce interfacial fluid flow anywhere on the shelf where permeable sediments are present. The terrestrial and oceanic forces overlap spatially so measured fluid advection through coastal sediments may be a result of composite forcing. We thus define “submarine groundwater discharge” (SGD) as any and all flow of water on continental margins from the seabed to the coastal ocean, regardless of fluid composition or driving force. SGD is typically characterized by low specific flow rates that make detection and quantification difficult. However, because such flows occur over very large areas, the total flux is significant. Discharging fluids, whether derived from land or composed of re-circulated seawater, will react with sediment components. These reactions may increase substantially the concentrations of nutrients, carbon, and metals in the fluids. These fluids are thus a source of biogeochemically important constituents to the coastal ocean. Terrestrially-derived fluids represent a pathway for new material fluxes to the coastal zone. This may result in diffuse pollution in areas where contaminated groundwaters occur. This paper presents an historical context of SGD studies, defines the process in a form that is consistent with our current understanding of the driving forces as well as our assessment techniques, and reviews the estimated global fluxes and biogeochemical implications. We conclude that to fully characterize marine geochemical budgets, one must give due consideration to SGD. New methodologies, technologies, and modeling approaches are required to discriminate among the various forces that drive SGD and to evaluate these fluxes more precisely.     

Arterial pulsation-driven cerebrospinal fluid flow in the perivascular space: a computational model

This study was conducted to determine whether local arterial pulsations are sufficient to cause cerebrospinal fluid (CSF) flow along perivascular spaces (PVS) within the spinal cord. A theoretical model of the perivascular space surrounding a "typical" small artery was analysed using computational fluid dynamics. Systolic pulsations were modelled as travelling waves on the arterial wall. The effects of wave geometry and variable pressure conditions on fluid flow were investigated. Arterial pulsations induce fluid movement in the PVS in the direction of arterial wave travel. Perivascular flow continues even in the presence of adverse pressure gradients of a few kilopascals. Flow rates are greater with increasing pulse wave velocities and arterial deformation, as both an absolute amplitude and as a proportion of the PVS. The model suggests that arterial pulsations are sufficient to cause fluid flow in the perivascular space even against modest adverse pressure gradients. Local increases in flow in this perivascular pumping mechanism or reduction in outflow may be important in the etiology of syringomyelia.     

Pressure and flow in the umbilical cord

A fluid dynamic study of blood flow within the umbilical vessels of the human maternal-fetal circulatory system is considered. It is found that the umbilical coiling index (UCI) is unable to distinguish between cords of significantly varying pressure and flow characteristics, which are typically determined by the vessel curvature, torsion and length. Larger scale geometric non-uniformities superposed over the inherent coiling, including cords exhibiting width and/or local UCI variations as well as loose true knots, typically produce a small effect on the total pressure drop. Crucially, this implies that a helical geometry of mean coiling may be used to determine the steady vessel pressure drop through a more complex cord. The presence of vessel constriction, however, drastically increases the steady pressure drop and alters the flow profile. For pulsatile-flow within the arteries, the steady pressure approximates the time-averaged value with high accuracy over a wide range of cords. Furthermore, the relative peak systolic pressure measured over the period is virtually constant and approximately 25% below the equivalent straight-pipe value for a large range of non-straight vessels. Interestingly, this suggests that the presence of vessel helicity dampens extreme pressures within the arterial cycle and may provide another possible evolutionary benefit to the coiled structure of the cord.     

Arterial Pulsation-driven Cerebrospinal Fluid Flow in the Perivascular Space: A Computational Model

This study was conducted to determine whether local arterial pulsations are sufficient to cause cerebrospinal fluid (CSF) flow along perivascular spaces (PVS) within the spinal cord. A theoretical model of the perivascular space surrounding a "typical" small artery was analysed using computational fluid dynamics. Systolic pulsations were modelled as travelling waves on the arterial wall. The effects of wave geometry and variable pressure conditions on fluid flow were investigated. Arterial pulsations induce fluid movement in the PVS in the direction of arterial wave travel. Perivascular flow continues even in the presence of adverse pressure gradients of a few kilopascals. Flow rates are greater with increasing pulse wave velocities and arterial deformation, as both an absolute amplitude and as a proportion of the PVS. The model suggests that arterial pulsations are sufficient to cause fluid flow in the perivascular space even against modest adverse pressure gradients. Local increases in flow in this perivascular pumping mechanism or reduction in outflow may be important in the etiology of syringomyelia.     

Epithelial water transport in a balanced gradient system.

The relationship between epithelial fluid transport, standing osmotic gradients, and standing hydrostatic pressure gradients has been investigated using a perturbation expansion of the governing equations. The assumptions used in the expansion are: (a) the volume of lateral intercellular space per unit volume of epithelium is small; (b) the membrane osmotic permeability is much larger than the solute permeability. We find that the rate of fluid reabsorption is set by the rate of active solute transport across lateral membranes. The fluid that crosses the lateral membranes and enters the intercellular cleft is driven longitudinally by small gradients in hydrostatic pressure. The small hydrostatic pressure in the intercellular space is capable of causing significant transmembrane fluid movement, however, the transmembrane effect is countered by the presence of a small standing osmotic gradient. Longitudinal hydrostatic and osmotic gradients balance such that their combined effect on transmembrane fluid flow is zero, whereas longitudinal flow is driven by the hydrostatic gradient. Because of this balance, standing gradients within intercellular clefts are effectively uncoupled from the rate of fluid reabsorption, which is driven by small, localized osmotic gradients within the cells. Water enters the cells across apical membranes and leaves across the lateral intercellular membranes. Fluid that enters the intercellular clefts can, in principle, exit either the basal end or be secreted from the apical end through tight junctions. Fluid flow through tight junctions is shown to depend on a dimensionless parameter, which scales the resistance to solute flow of the entire cleft relative to that of the junction. Estimates of the value of this parameter suggest that an electrically leaky epithelium may be effectively a tight epithelium in regard to fluid flow.     

Evidence for a central role for electro-osmosis in fluid transport by corneal endothelium

The mechanism of transepithelial fluid transport remains unclear. The prevailing explanation is that transport of electrolytes across cell membranes results in local concentration gradients and transcellular osmosis. However, when transporting fluid, the corneal endothelium spontaneously generates a locally circulating current of approximately 25 microA cm(-2), and we report here that electrical currents (0 to +/-15 microA cm(-2)) imposed across this layer induce fluid movements linear with the currents. As the imposed currents must be approximately 98% paracellular, the direction of induced fluid movements and the rapidity with which they follow current imposition (rise time < or =3 sec) is consistent with electro-osmosis driven by sodium movement across the paracellular pathway. The value of the coupling coefficient between current and fluid movements found here (2.37 +/- 0.11 microm cm(2) hr(-1) microA (-1), suggests that: 1) the local endothelial current accounts for spontaneous transendothelial fluid transport; 2) the fluid transported becomes isotonically equilibrated. Ca(++)-free solutions or endothelial damage eliminate the coupling, pointing to the cells and particularly their intercellular junctions as a main site of electro-osmosis. The polycation polylysine, which is expected to affect surface charges, reverses the direction of current-induced fluid movements. Fluid transport is proportional to the electrical resistance of the ambient medium. Taken together, the results suggest that electro-osmosis through the intercellular junctions is the primary process in a sequence of events that results in fluid transport across this preparation.     

A finite element analysis for the prediction of load-induced fluid flow and mechanochemical transduction in bone

Interstitial fluid flow through the lacunocanalicular cavities of mechanically loaded bone provides the biophysical basis for a number of postulates regarding mechanotransduction in bone. Recently, the existence of load-induced fluid flow and its influence on molecular transport through bone has been confirmed using tracer methods to visualize fluid flow induced by in vivo four-point-bending of rat tibiae. In this paper, we present a theoretical two-stage approach for the calculation of load-induced flow fields and for the evaluation of their influence on molecular transport in bone loaded in four-point bending, analogous to the aforementioned experimental model. In the first stage, the fluid velocities are calculated using a three-dimensional, poroelastic finite element model. In the second stage, mass transport analysis, this calculated fluid flow serves as a forced convection flow and its contribution to the total transport potential is determined. Based on this combined approach, the overall tracer concentration in the loaded bone is significantly higher than that in the unloaded bone. Furthermore, augmentation of mass transport through convective flow is more pronounced in the tension band of the tissue, as compared to the compression band. In general, augmentation of tracer concentration via convective mechanisms is most pronounced in areas corresponding to lowest fluid velocities, which is indicative of fluid flow direction and areas of increased "dwell time" or accumulation during the loading cycle. This theoretical model, in combination with the corresponding experimental model, provides unique insight into the role of mechanical loads in modulating local flow distributions and concentration gradients within bone tissue.     

Corneal endothelium transports fluid in the absence of net solute transport

The corneal endothelium transports fluid from the corneal stroma to the aqueous humor, thus maintaining stromal transparency by keeping it relatively dehydrated. This fluid transport mechanism is thought to be driven by the transcellular transports of HCO(3)(-) and Cl(-) in the same direction, from stroma to aqueous. In parallel to these anion movements, for electroneutrality, there are paracellular Na(+) and transcellular K(+) transports in the same direction. The resulting net flow of solute might generate local osmotic gradients that drive fluid transport. However, there are reports that some 50% residual fluid transport remains in nominally HCO(3)(-) free solutions. We have examined the driving force for this residual fluid transport. We confirm that in nominally HCO(3)(-) free solutions, 48% of control fluid transport remains. When in addition Cl(-) channels are inhibited, 30% of control fluid movement still remains. Addition of a carbonic anhydrase inhibitor has no further effect. These manipulations combined inhibit the transcellular transport of all anions, without which there cannot be any net transport of solute and consequently no local osmotic gradients, yet there is residual fluid movement. Only the further addition of benzamil, an inhibitor of epithelial Na(+) channels, abolishes fluid transport completely. Our data are inconsistent with transcellular local osmosis and instead support the paradigm of paracellular fluid transport driven by electro-osmotic coupling.     

Development,persistence and regeneration of foraging ectomycorrhizal mycelial systems in soil microcosms

Development of extraradical mycelia of two strains each of Paxillus involutus and Suillus bovinus in ectomycorrhizal association with Pinus sylvestris seedlings was studied in two dimensions in non-sterile soil microcosms. There were significant inter- and intra-specific differences in extraradical mycelial growth and morphology. The mycelial systems of both strains of P. involutus were diffuse and extended more rapidly than those of S. bovinus. Depending on the strain, P. involutus mycelia were either highly plane filled, with high mass fractal dimension (a measure of space filling) or sparse, low mass fractal dimension systems. Older mycelial systems persisted as linear cords interlinking ectomycorrhizal tips. S. bovinus produced either a mycelium with a mixture of mycelial cords and diffuse fans that rapidly filled explorable area, or a predominately corded mycelium of minimal area cover. In the soil microcosms, mass fractal dimension and mycelial cover tended to increase with time, mycelia encountering litter having significantly greater values. Results are discussed in terms of the ecology of these fungi, their foraging activities and functional importance in forest ecosystems.     

Influence of vascular porosity on fluid flow and nutrient transport in loaded cortical bone

Load-induced fluid flow is a key factor in triggering bone modeling and remodeling processes that maintain bone mass and architecture. To provide an enhanced understanding of fluid flow in bone, unique computational models of a tibial section were developed. The purpose of the study was to examine the effects of incorporating vascular porosity on pore fluid pressure and resulting lacunocanalicular flow and to determine the role of load-induced fluid flow in tracer transport. Simulations revealed large local pressure gradients surrounding the vascular canals that were dependent on the magnitude and state (i.e., compressive or tensile) of the stress. Fluid velocity magnitudes were increased by over an order of magnitude in the dual-porosity model, relative to the single-porosity model. Fluid flow had a marked effect on tracer perfusion within the cortex. After 10 loading cycles, a 9-fold increase in tracer concentration, relative to diffusion alone, was observed in the compressive region where fluid exchange was greatest between the lacunocanalicular porosity and the vascular canals. Agreement was achieved between computational results and experimental investigations of electrokinetic phenomenon, tracer transport, cellular stimulation, and functional adaptation. The models produced substantial improvements in bone fluid flow simulation and underscored the significance of incorporating vascular porosity in models designed to quantify fluid pressure and flow characteristics within mechanically loaded cortical bone.     

Numerical study of the impact of non-Newtonian blood behavior on flow over a two-dimensional backward facing step

Endothelial cell (EC) responsiveness to shear stress is essential for vasoregulation and plays a role in atherogenesis. Although blood is a non-Newtonian fluid, EC flow studies in vitro are typically performed using Newtonian fluids. The goal of the present study was to determine the impact of non-Newtonian behavior on the flow field within a model flow chamber capable of producing flow disturbance and whose dimensions permit Reynolds and Womersley numbers comparable to those present in vivo. We performed two-dimensional computational fluid dynamic simulations of steady and pulsatile laminar flow of Newtonian and non-Newtonian fluids over a backward facing step. In the non-Newtonian simulations, the fluid was modeled as a shear-thinning Carreau fluid. Steady flow results demonstrate that for Re in the range 50-400, the flow recirculation zone downstream of the step is 22-63% larger for the Newtonian fluid than for the non-Newtonian fluid, while spatial gradients of shear stress are larger for the non-Newtonian fluid. In pulsatile flow, the temporal gradients of shear stress within the flow recirculation zone are significantly larger for the Newtonian fluid than for the non-Newtonian fluid. These findings raise the possibility that in regions of flow disturbance, EC mechanotransduction pathways stimulated by Newtonian and non-Newtonian fluids may be different.     

Oxygen transport and cell viability in an annular flow bioreactor: comparison of laminar Couette and Taylor-vortex flow regimes

Rotating wall vessel bioreactors have been proposed as a means of controlling the fluid dynamic environment during long-term culture of mammalian cells and engineered tissues. In this study, we show how the delivery of oxygen to cells in an annular flow bioreactor is enhanced by the forced convective transport afforded by Taylor vortex flows. A fiberoptic oxygen probe with negligible lag time was used to measure the dissolved oxygen concentration in real time and under carefully controlled aeration conditions. From these data, the overall mass transfer coefficients were calculated and mass transport correlations determined under laminar Couette flow conditions and discrete Taylor vortex flow regimes, including laminar, wavy, and turbulent flows. While oxygen transport in Taylor vortex flows was significantly greater, and the available oxygen exceeded that consumed by murine fibroblasts in free suspension, the proportion of cells that remained viable decreased with increasing Reynolds number (101.8 < Rei < 1018), which we attribute to the action of fluid shear stresses on the cells as opposed to any limitation in mass transport. Nevertheless, the results of this study suggest that laminar Taylor-vortex flow regimes provide an effective means of maintaining the levels of oxygen transport required for long-term cell culture.     

Non-Newtonian flow-induced deformation from pressurized cavities in absorbing porous tissues

We investigate the behavior of a spherical cavity in a soft biological tissue modeled as a deformable porous material during an injection of non-Newtonian fluid that follows a power law model. Fluid flows into the neighboring tissue due to high cavity pressure where it is absorbed by capillaries and lymphatics at a rate proportional to the local pressure. Power law fluid pressure and displacement of a solid in the tissue are computed as function of radial distance and time. Numerical solutions indicate that shear thickening fluids exhibit less fluid pressure and induce small solid deformation as compared to shear thinning fluids. Absorption in the biological tissue increases as a consequence of flow-induced deformation for power law fluids. In most cases non-Newtonian results are compared with the viscous fluid case to magnify the differences.     

The effects of non-Newtonian viscoelasticity and wall elasticity on flow at a 90 degrees bifurcation

To study the fundamentals of hemodynamics in arteries, the flow parameters: pulsatility, elasticity and non-Newtonian viscoelasticity were considered in detail in a 90 degrees-T-bifurcation of a rigid and elastic model. The velocity distribution 2.5 mm behind the bifurcation in the straight tube was measured with a laser-Doppler-anemometer. The fluid used was an aqueous glycerine solution and a viscoelastic Separan mixture. Flow visualization studies were done with a sheet of laser light in the plane of the bifurcation. The velocity distribution was measured for both steady and pulsatile flows with a laser-Doppler-anemometer in a backward scattered way. From the velocity measurements the shear gradients were calculated. Substantial differences were found in the flow behavior of Newtonian and non-Newtonian fluids, especially behind the bifurcation in the main tube, where secondary flows and flow separation started. Also, differences due to the elastic and rigid wall could be seen. Very high shear gradients were found in the flow between main flow and the separation zone which can lead to a damage of the blood cells.     

Insights into interstitial flow,shear stress,and mass transport effects on ECM heterogeneity in bioreactor-cultivated engineered cartilage hydrogels

Interstitial flow in articular cartilage is secondary to compressive and shear deformations during joint motion and has been linked with the well-characterized heterogeneity in structure and composition of its extracellular matrix. In this study, we investigated the effects of introducing gradients of interstitial flow on the evolution of compositional heterogeneity in engineered cartilage. Using a parallel-plate bioreactor, we observed that Poiseuille flow stimulation of chondrocyte-seeded agarose hydrogels led to an increase in glycosaminoglycan and type II collagen deposition in the surface region of the hydrogel exposed to flow. Experimental measurements of the interstitial flow fields based on the fluorescence recovery after photobleaching technique suggested that the observed heterogeneity in composition is associated with gradients in interstitial flow in a boundary layer at the hydrogel surface. Interestingly, the interstitial flow velocity profiles were nonlinearly influenced by flow rate, which upon closer examination led us to the original observation that the apparent hydrogel permeability decreased exponentially with increased interfacial shear stress. We also observed that interstitial flow enhances convective mass transport irrespective of molecular size within the boundary layer near the hydrogel surface and that the convective contribution to transport diminishes with depth in association with interstitial flow gradients. The implications of the nonlinearly inverse relationship between the interfacial shear stress and the interstitial flux and permeability and its consequences for convective transport are important for tissue engineering, since porous scaffolds comprise networks of Poiseuille channels (pores) through which interstitial flow must navigate under mechanical stimulation or direct perfusion.     

A microscale model of bacterial and biofilm dynamics in porous media

A microscale model for the transport and coupled reaction of microbes and chemicals in an idealized two-dimensional porous media has been developed. This model includes the flow, transport, and bioreaction of nutrients, electron acceptors, and microbial cells in a saturated granular porous media. The fluid and chemicals are represented as a continuum, but the bacterial cells and solid granular particles are represented discretely. Bacterial cells can attach to the particle surfaces or be advected in the bulk fluid. The bacterial cells can also be motile and move preferentially via a run and tumble mechanism toward a chemoattractant. The bacteria consume oxygen and nutrients and alter the profiles of these chemicals. Attachment of bacterial cells to the soil matrix and growth of bacteria can change the local permeability. The coupling of mass transport and bioreaction can produce spatial gradients of nutrients and electron acceptor concentrations. We describe a numerical method for the microscale model, show results of a convergence study, and present example simulations of the model system.     

Corneal endothelium transports fluid in the absence of net solute transport

The corneal endothelium transports fluid from the corneal stroma to the aqueous humor, thus maintaining stromal transparency by keeping it relatively dehydrated. This fluid transport mechanism is thought to be driven by the transcellular transports of HCO₃⁻ and Cl⁻ in the same direction, from stroma to aqueous. In parallel to these anion movements, for electroneutrality, there are paracellular Na⁺ and transcellular K⁺ transports in the same direction. The resulting net flow of solute might generate local osmotic gradients that drive fluid transport. However, there are reports that some 50% residual fluid transport remains in nominally HCO₃⁻ free solutions. We have examined the driving force for this residual fluid transport. We confirm that in nominally HCO₃⁻ free solutions, 48% of control fluid transport remains. When in addition Cl⁻ channels are inhibited, 30% of control fluid movement still remains. Addition of a carbonic anhydrase inhibitor has no further effect. These manipulations combined inhibit the transcellular transport of all anions, without which there cannot be any net transport of solute and consequently no local osmotic gradients, yet there is residual fluid movement. Only the further addition of benzamil, an inhibitor of epithelial Na⁺ channels, abolishes fluid transport completely. Our data are inconsistent with transcellular local osmosis and instead support the paradigm of paracellular fluid transport driven by electro-osmotic coupling.