Flow and sediment transport in vegetated waterways: a review

One of the most important waterway components is vegetation, which play a pivotal role in the flow and sediment transport. Vegetation environment and characteristics, including vegetation porosity or density, shape, flexibility and vegetation height, are significantly affected in vegetated channels. Various vegetation positions and arrangements such as patches significantly affect the sediment deposition rate and flow turbulence. This paper reviews recent works conducted on vegetated open channels, which include the effect of different vegetation arrangements and vegetation characteristics on mass transport and turbulence structure. Studies based on laboratory, field works, and modeling, have been reviewed based on previous methods used by different researchers. Methods used in vegetation porosity evaluation, rate of flow and sediment transport properties are presented. In short, flow and transport depend on the vegetation properties and flow structure conditions.     

Analytical basis for the determination of the lacunar–canalicular permeability of bone using cyclic loading

An analytical model for the determination of the permeability in the lacunar-canalicular porosity of bone using cyclic loading is described in this contribution. The objective of the analysis presented is to relate the lacunar-canalicular permeability to a particular phase angle that is measurable when the bone is subjected to infinitesimal cyclic strain. The phase angle of interest is the lag angle between the applied strain and the resultant stress. Cyclic strain causes the interstitial fluid to move. This movement is essential for the viability of osteocytes and is believed to play a major role in the bone mechanotransduction mechanism. However, certain bone fluid flow properties, notably the permeability of the lacunar-canalicular porosity, are still not accurately determined. In this paper, formulas for the phase angle as a function of permeability for infinitesimal cyclic strain are presented and mathematical expressions for the storage modulus, loss modulus, and loss tangent are obtained. An accurate determination of the PLC permeability will improve our ability to understand mechanotransduction and mechanosensory mechanisms, which are fundamental to the understanding of how to treat osteoporosis, how to cope with microgravity in long-term manned space flights, and how to increase the longevity of prostheses that are implanted in bone tissue.     

Engineered tissue scaffolds with variational porous architecture

This paper presents a novel computer-aided modeling of 3D tissue scaffolds with a controlled internal architecture. The complex internal architecture of scaffolds is biomimetically modeled with controlled micro-architecture to satisfy different and sometimes conflicting functional requirements. A functionally gradient porosity function is used to vary the porosity of the designed scaffolds spatially to mimic the functionality of tissues or organs. The three-dimensional porous structures of the scaffold are geometrically partition into functionally uniform porosity regions with a novel offsetting operation technique described in this paper. After determining the functionally uniform porous regions, an optimized deposition-path planning is presented to generate the variational internal porosity architecture with enhanced control of interconnected channel networks and continuous filament deposition. The presented methods are implemented, and illustrative examples are presented in this paper. Moreover, a sample optimized tool path for each example is fabricated layer-by-layer using a micronozzle biomaterial deposition system.     

Use of high-resolution MRI for investigation of fluid flow and global permeability in a material with interconnected porosity

We present a multi-scale experimental approach designed to improve the investigation of both localized and global fluid flow in biomaterials with randomly interconnected porosity. Coralline hydroxyapatite (ProOsteon 500 from Interpore-Cross), having a relatively well-defined porosity, was used as an in vitro model of typical bone architecture. Axial fluid velocity profiles within the pores of a cylindrical hydroxyapatite sample were characterized using high-resolution MRI in conjunction with the measurement of global flow and associated permeability based on the Darcy-type relationship. Assuming Newtonian fluid behaviour, image analysis permitted computation of local porosity, intra-pore fluid shear, and visualization of flow heterogeneity within the sample. These results may benefit applications in biomaterials for the evaluation of factors influencing bony incorporation in porous scaffolds and on porous implant and bone surfaces. Normal and diseased biological tissues are also clinical relevant applications.     

Designing and testing of backflow-free catheters

Convection-enhanced delivery (CED) is a drug delivery technique used to target specific regions of the central nervous system (CNS) for the treatment of neurodegenerative diseases and cancer while bypassing the blood-brain barrier (BBB). The application of CED is limited by low volumetric flow rate infusions in order to prevent the possibility of backflow. Consequently, a small convective flow produces poor drug distribution inside the treatment region, which can render CED treatment ineffective. Novel catheter designs and CED protocols are needed in order to improve the drug distribution inside the treatment region and prevent backflow. In order to develop novel backflow-free catheter designs, the impact of the micro-fluid injection into deformable porous media was investigated experimentally as well as numerically. Fluid injection into the porous media has a considerable effect on local transport properties such as porosity and hydraulic conductivity because of the local media deformation. These phenomena not only alter the bulk flow velocity distribution of the micro-fluid flow due to the changing porosity, but significantly modify the flow direction, and even the volumetric flow distribution, due to induced local hydraulic conductivity anisotropy. These findings help us to design backflow-free catheters with safe volumetric flow rates up to 10 μl/min. A first catheter design reduces porous media deformation in order to improve catheter performance and control an agent volumetric distribution. A second design prevents the backflow by reducing the porosity and hydraulic conductivity along a catheter's shaft. A third synergistic catheter design is a combination of two previous designs. Novel channel-inducing and dual-action catheters, as well as a synergistic catheter, were successfully tested without the occurrence of backflow and are recommended for future animal experiments.     

Effects of stent porosity on hemodynamics in a sidewall aneurysm model

Computation and experiment have been complementarily performed to study the fluid flow inside a stented lateral aneurysm anchored on the straight parent vessel. The implicit solver was based on the time-dependent incompressible Navier-Stokes equations of laminar flow. Solutions were generated by a cell-center finite-volume method that used second-order upwind and second-order center flux difference splitting for the convection and diffusion term, respectively. The second-order Crank-Nicolson method was used in the time integration term. Experimental techniques used were flow visualization (FV) and particle tracking velocimetry (PTV). Experimentally, the straight afferent vessel had an inner diameter 10mm. The diameters of the aneurysmal orifice, neck, and fundus were 14, 10, and 15 mm, respectively, and the distance between the orifice and dome measured 20mm. A 30 mm long helix-shaped stent was tested. Four stent porosities of 100%, 70%, 50%, and 25% were examined. Volume-flow rate waveform of a cerebral artery was considered with a maximum Reynolds number of 250 and Womersley number of 3.9. Results are presented in terms of the pulsatile main and secondary flow velocity vector fields, the volume inflow rates into the aneurysm, and the wall shear stress (WSS) and wall pressure at the aneurysm dome. Some comparisons of computed results with the present FV and PTV results and with the data available from the literature are also made. The maximum flow velocity inside the aneurysm ostium and the WSS in the dome region at the peak flow can, respectively, be suppressed to less than 5% of the parent vessel bulk velocity (or 20% of the unstented case) and 8% of the unstented case if the stent porosity is smaller than 40% (about the porosity of the two-layer stents). In general, the three-layer stents seem not as effective as the two-layer stents in reducing the magnitude of aneurysm inflow rate and WSS.     

Numerical simulation of the effect of permeability on the hydrodynamics in a parallel-plate coculture flow chamber

To study the effect of the porous membrane permeability on the hydrodynamics in a parallel-plate coculture flow chamber (PPcFC), we demonstrated the permeability of the porous membrane as a function of some parameters, such as porosity, membrane thickness, pore size and shape of the membrane. The effect of permeability on the flow in the PPcFC was analysed using the commercial software – Fluent. Results showed that the permeability was directly proportional to the thickness, the porosity and the pore size of the membrane, and inversely proportional to the surface shape factor. To ensure the best flow pattern, the inlet velocity range was limited by the membrane permeability and fluid viscosity, and then restricted the available magnitudes of shear rate on the permeable membrane. Our findings are helpful in designing and preparing the biomaterials that have adequate mechanical properties for the functional vascular grafts production, and in using of the flow chamber in various investigations.     

Effect of macroscale formation of intraluminal thrombus on blood flow in abdominal aortic aneurysms

A mathematical approach of blood flow within an abdominal aortic aneurysm (AAA) with intraluminal thrombus (ILT) is presented. The macroscale formation of ILT is modeled as a growing porous medium with variable porosity and permeability according to values proposed in the literature. The model outlines the effect of a porous ILT on blood flow in AAAs. The numerical solution is obtained by employing a structured computational mesh of an idealized fusiform AAA geometry and applying the Galerkin weighted residual method in generalized curvilinear coordinates. Results on velocity and pressure fields of independent cases with and without ILT are presented and discussed. The vortices that develop within the aneurysmal cavity are studied and visualized as ILT becomes more condensed. From a mechanistic point of view, the reduction of bulge pressure, as ILT is thickening, supports the observation that ILT could protect the AAA from a possible rupture. The model also predicts a relocation of the maximum pressure region toward the zone proximal to the neck of the aneurysm. However, other mechanisms, such as the gradual wall weakening that usually accompany AAA and ILT formation, which are not included in this study, may offset this effect.     

Particle Imaging Velocimetry Evaluation of Intracranial Stents in Sidewall Aneurysm: Hemodynamic Transition Related to the Stent Design

We investigated the flow modifications induced by a large panel of commercial-off-the-shelf (COTS) intracranial stents in an idealized sidewall intracranial aneurysm (IA). Flow velocities in IA silicone model were assessed with and without stent implantation using particle imaging velocimetry (PIV). The use of the recently developed multi-time-lag method has allowed for uniform and precise measurements of both high and low velocities at IA neck and dome, respectively. Flow modification analysis of both regular (RSs) and flow diverter stents (FDSs) was subsequently correlated with relevant geometrical stent parameters. Flow reduction was found to be highly sensitive to stent porosity variations for regular stents RSs and moderately sensitive for FDSs. Consequently, two distinct IA flow change trends, with velocity reductions up to 50% and 90%, were identified for high-porosity RS and low-porosity FDS, respectively. The intermediate porosity (88%) regular braided stent provided the limit at which the transition in flow change trend occurred with a flow reduction of 84%. This transition occurred with decreasing stent porosity, as the driving force in IA neck changed from shear stress to differential pressure. Therefore, these results suggest that stents with intermediate porosities could possibly provide similar flow change patterns to FDS, favourable to curative thrombogenesis in IAs.     

Numerical model for intraosseous infusion of the human calvarium for hydrocephalus shunting

Hydrocephaly is the defective absorption of cerebrospinal fluid (CSF) into the blood stream. This work is an experimental and computational fluid dynamic modelling study to determine the permeability of the diploë as a potential receptor for CSF. Human calvariae were studied by micro-CT to measure their porosity, the area of flow and develop model geometry. Pressure-flow measurements were conducted on specimens to determine their permeability in the physiological and transverse flow directions to compare with numerical results. The overall porosity and permeability of the calvaria were spatially variable. Results suggest an order of magnitude increase in permeability for a 14% increase in overall porosity based on a small number of samples. Numerical results fell within the experimental infusion tests results. Due to the difficulty and ethical considerations in obtaining adolescent skull samples to perform large-scale testing, the developed model will be invaluable.     

Controls on diagenesis and dolomitization of peritidal facies,Early Cretaceous Lower Edwards Group,central Texas,USA

The Early Cretaceous Fort Terrett Formation of Mason County, central Texas, is a succession of subtidal to peritidal mud-dominated facies with minor intervals of bioclastic packstone–grainstone, rudist floatstone, and interbedded chert nodules. The strata conformably overlie the Hensel Formation, which was deposited unconformably on Precambrian basement. The Hensel Formation also contains a significant percentage of dolomite, precipitated within a fine-grained clayey matrix. The Hensel and Fort Terrett Formations were deposited during a transgressive episode, which provided the conditions for the extensive shallow-water Comanche carbonate platform. Siliciclastic and carbonate sediments were deposited along the coastal margin in subtidal, intertidal to supratidal areas. Previous dolomitization models have suggested that high permeability layers are required for dolomitizing brines to flow through a carbonate succession. Although, interparticle porosity in muddy tidal-flat successions can be significant, it has a limited flow capacity. However, interconnected fenestral porosity can allow sufficient fluid flow to move dolomitizing fluids more efficiently through the succession. Thus, it is hypothesized that interconnected fenestral porosity could have had a significant impact on permeability within this muddy succession and provided the pathways and conduits for Mg-rich brines. Four types of dolomite are recognized in the Fort Terrett succession. Three of these dolomite types formed largely by replacement and they occur throughout the succession. Features such as crystal size, crystal face geometry and zonation reflect the progressive development and recrystallization of the dolomite types. Only type 4 dolomite formed as a cement in void spaces during a late diagenetic stage. The direction of the dolomitizing fluid movement is difficult to determine, but it was likely downward in this case, controlled by a density-head driving-mechanism generated by dense hypersaline fluids from an evaporating lagoon.     

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.     

Porosity development and distribution in the Rüdersdorfer Schaumkalk (Middle Triassic) of the Gas Store Berlin,Germany

Gas is stored in the Triassic Buntsandstein units above the salt-pillow structure of Spandau. Brines obtained collaterally when bringing the gas back to the surface are reinjected into the oomoldic limestone of the Lower Muschelkalk. Cores of the limestone were investigated with respect to microfacies, diagnetic development, porosity, and permeability to provide the input for modeling reservoir configuration and capacity of this unit. In the porous portions of this unit, six microfacies types were distinguished by varying proportions of ooids, peloids and biogenic (skeletal) particles. Microfacies types do not correlate with porosity and permeability. The rocks were altered by varying successions of dissolution and cementation stages; four diagenetic grades were defined on the basis of development of moldic pores and their fillings. The diagenetic grades correlate with porosity and permeability showing that kind and intensity of diagenetic alterations largely overprinted initial control of microfacies on fluid flow.     

Effect of percolation rate on nutrient kinetics and rice yield in tropical rice soils

A model is presented with which the contribution of longitudinal oxygen diffusion to total oxygen requirement of a root can be estimated. Oxygen transport in and respiration of the soil are taken into account. Given the air-filled root porosity, root diameter, coefficient of oxygen transfer between root and soil, root and soil respiration rate, and the coefficient for oxygen diffusion in the soil, the maximum length a root can attain with an adequate oxygen supply to the root tip can be calculated. Results show the importance of root porosity for root aeration, also in unsaturated soils. For thick roots (radius >0.03 cm), diffusion along the internal pathway can provide 50–75% of the total oxygen requirement even, at modest values of the root porosity.     

Predicting fracture of the femoral neck

A prediction of the probability of safe loading of the femoral neck, based on queueing theory, is presented. The following methods have been applied: (I) criterion of bone fracture was formulated, taking into consideration the complex state of stress-strain in the porosity zones of the bone; (II) tensile stresses around pores in the stretched zone of the bone were evaluated; (III) the influence of random events of the critical regimes of loading was modeled. The evaluation of the probability of safe loading of bones was obtained based on the levels of the tensile stresses, Young's moduli and ultimate tensile stresses which are affected by the increase in bone porosity and the distribution of the pores. Examples of analysis involving typical mechanical properties of bone in areas of vascular and lacunar-canalicular porosity are demonstrated. The ranges of initial average values of effective Young's moduli and ultimate tensile strengths were taken as 15.8-17.5GPa and 83-95MPa, respectively. The present analysis discovers the existence of three levels of safe loading: (1) a relatively safe level of the nominal tensile stresses (smaller than (2.8-3.2)MPa) where the probability of safe loading is of the order of 0.95 for the bone porosity which is less than 0.15; (2) an intermediate level of safety where the nominal tensile stresses are below (4.2-4.8)MPa and the probability of safe loading is 0.89 or higher, for the same level of bone porosity; (3) a critical level of safe loading where the nominal tensile stresses are about (8.3-9.5)MPa; they lead to sharp drop of probabilities of safe loading to 0.85-0.8 if the porosity is about 0.10 and to probabilities of 0.41-0.4 if the porosity is about 0.15.     

Effects of dynamic loading on solute transport through the human cartilage endplate

Nutrient and metabolite transport through the cartilage endplate (CEP) is important for maintaining proper disc nutrition, but the mechanisms of solute transport remain unclear. One unresolved issue is the role of dynamic loading. In comparison to static loading, dynamic loading is thought to enhance transport by increasing convection. However, the CEP has a high resistance to fluid flow, which could limit solute convection. Here we measure solute transport through site-matched cadaveric human lumbar CEP tissues under static vs. dynamic loading, and we determine how the degree of transport enhancement from dynamic loading depends on CEP porosity and solute size. We found that dynamic loading significantly increased small and large solute transport through the CEP: on average, dynamic loading increased the transport of sodium fluorescein (376 Da) by a factor of 1.85 ± 0.64 and the transport of a large dextran (4000 Da) by a factor of 4.97 ± 3.05. Importantly, CEP porosity (0.65 ± 0.07; range: 0.47–0.76) strongly influenced the degree of transport enhancement. Specifically, for both solutes, transport enhancement was greater for CEPs with low porosity than for CEPs with high porosity. This is because the CEPs with low porosity were susceptible to larger improvements in fluid flow under dynamic loading. The CEP becomes less porous and less hydrated with aging and as disc degeneration progresses. Together, these findings suggest that as those changes occur, dynamic loading has a greater effect on solute transport through the CEP compared to static loading, and thus may play a larger role in disc nutrition.     

Flow-induced permeation of non-occlusive blood clots: an MRI study and modelling

The success of clot thrombolysis very much depends on efficient clot permeation with blood plasma carrying the thrombolytic agent. In this paper clot permeation was studied by dynamic magnetic resonance imaging (MRI) on artificial non-occlusive blood clots inserted in an artificial circulation system filled with blood plasma to which an MRI contrast agent was added. The MRI results revealed that clot permeation is much faster and more efficient at the entrance of the flow channel across the clot. Clot permeation with fluid was simulated numerically as well. The simulation was based on numerical solution of Navier-Stokes equations for the flow in the channel and within the clot. The clot was considered as a porous material with known permeability and porosity. Based on the calculated velocity profiles, concentration profiles of fluid in the clot were modelled. These agreed well with the MRI results. The presented model of clot permeation with fluid may also serve as a useful extension to numerical modelling of dissolution of non-occlusive blood clots during thrombolytic therapy.     

Estimation of bone permeability using accurate microstructural measurements

While interstitial fluid flow is necessary for the viability of osteocytes, it is also believed to play a role in bone's mechanosensory system by shearing bone cell membranes or causing cytoskeleton deformation and thus activating biochemical responses that lead to the process of bone adaptation. However, the fluid flow properties that regulate bone's adaptive response are poorly understood. In this paper, we present an analytical approach to determine the degree of anisotropy of the permeability of the lacunar-canalicular porosity in bone. First, we estimate the total number of canaliculi emanating from each osteocyte lacuna based on published measurements from parallel-fibered shaft bones of several species (chick, rabbit, bovine, horse, dog, and human). Next, we determine the local three-dimensional permeability of the lacunar-canalicular porosity for these species using recent microstructural measurements and adapting a previously developed model. Results demonstrated that the number of canaliculi per osteocyte lacuna ranged from 41 for human to 115 for horse. Permeability coefficients were found to be different in three local principal directions, indicating local orthotropic symmetry of bone permeability in parallel-fibered cortical bone for all species examined. For the range of parameters investigated, the local lacunar-canalicular permeability varied more than three orders of magnitude, with the osteocyte lacunar shape and size along with the 3-D canalicular distribution determining the degree of anisotropy of the local permeability. This two-step theoretical approach to determine the degree of anisotropy of the permeability of the lacunar-canalicular porosity will be useful for accurate quantification of interstitial fluid movement in bone.     

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.