Subcritical flutter in collapsible tube flow: a model of expiratory flow in the trachea

Using an axisymmetric geometry that retains certain qualitative features of the trachea, we extend one-dimensional modeling of flow in collapsible tubes to include both curved shell effects and, for untethered tubes, wall inertia. A systematic scaling of the finite deformation membrane equations leads to an approximate set which is consistent with the one-dimensional fluid model; axial and normal wall variables are coupled elastically, but only axial inertia is retained. Transverse curvature causes elastic coupling that can give rise to axial wall motion and a flutter instability. The source of instability is the product of a nonzero reference axial curvature with axial tension variation due to axial stretching. The numerical results suggest that this mechanism may be significant even in processes which cannot be assumed one-dimensional.     

One-dimensional model of the Debye layer near a dielectric surface

A study is made of the processes occurring in a low-density plasma near a dielectric wall. A one-dimensional non-steady-state model of the electron dynamics is constructed that takes into account secondary electron emission. The Vlasov-Poisson equations are solved numerically. According to the results obtained, the steady-state potential distribution that forms at a low temperature of the incident electrons gives rise to a wall layer whose characteristic thickness is about several Debye lengths and in which the electrons are decelerated. In this case, the electron density is lowest near the wall. The situation in which the temperature of the incident electrons is high is far more complicated: the solution is quasi-periodic in character and the electron density near the wall is the highest.     

Flow-tissue interaction with compliance mismatch in a model stented artery

The insertion of an endovascular prosthesis is known to have a thrombogenic effect that is also a consequence of the interaction between the flowing blood and the stented arterial segment; in fact the prosthesis induces a compliance mismatch and a possible small expansion along the vessel that eventually gives rise to an anomalous distribution of wall shear stresses. The fluid dynamics inside a rectilinear elastic vessel with compliance and section variation is studied here numerically. A recently introduced perturbative approach is employed to model the interaction between the fluid and the elastic tissue; this approximate technique is first validated by comparison with a complete solution within a simple one-dimensional model of the same system. Then it is applied to an axisymmetric model in order to evaluate the flow dynamics and the distribution of wall shear stress in the stented vessel. Compliance mismatch is shown to produce more intense negative wall shear stresses in the stented segment while rapid variations of wall shear stress are found at the stent ends. These effects are enhanced when the prosthesis is accompanied by a small increase of the vessel lumen.     

Traveling wave solutions of a reaction diffusion model for competing pioneer and climax species

Presented is a reaction-diffusion model for the interaction of pioneer and climax species. For certain parameters the system exhibits bistability and traveling wave solutions. Specifically, we show that when the climax species diffuses at a slow rate there are traveling wave solutions which correspond to extinction waves of either the pioneer or climax species. A leading order analysis is used in the one-dimensional spatial case to estimate the wave speed sign that determines which species becomes extinct. Results of these analyses are then compared to numerical simulations of wave front propagation for the model on one and two-dimensional spatial domains. A simple mechanism for harvesting is also introduced.     

Ultrastructural organization of the transition from the distal nephron to the collecting duct in the desert rodent Psammomys obesus

Summary The transition from the nephron to the collecting duct is formed by three tubular segments (convoluted part of the distal tubule, connecting tubule, cortical collecting duct), which in the desert rodent, Psammomys obesus, transform gradually from one segment to the next, due to intermingling of their different cell types.The convoluted part of the distal tubule (DTC) starts abruptly, shortly beyond the macula densa and initially is homogeneously composed of characteristic DTC-cells. Subsequently, the DTC-cells intermingle with intercalated cells. The first appearance of the connecting-tubule cell, which gradually replaces the DTC-cell, is regarded as the beginning of the connecting tubule. The major portion of the connecting tubule is lined by connecting-tubule cells and intercalated cells. The first appearance of the principal cell between them defines the beginning of the cortical collecting duct, which in the medullary ray is lined by principal and intercalated cells only.Each cell type is described in detail and discussed in relation to the assumed function of the tubular segments.Interspecies differences in the cellular composition of the transitional zone from the nephron to the collecting duct are discussed in relation to the different organization of the collecting duct system.     

A novel extracellular role for tissue transglutaminase in matrix-bound VEGF-mediated angiogenesis

The importance of tissue transglutaminase (TG2) in angiogenesis is unclear and contradictory. Here we show that inhibition of extracellular TG2 protein crosslinking or downregulation of TG2 expression leads to inhibition of angiogenesis in cell culture, the aorta ring assay and in vivo models. In a human umbilical vein endothelial cell (HUVEC) co-culture model, inhibition of extracellular TG2 activity can halt the progression of angiogenesis, even when introduced after tubule formation has commenced and after addition of excess vascular endothelial growth factor (VEGF). In both cases, this leads to a significant reduction in tubule branching. Knockdown of TG2 by short hairpin (shRNA) results in inhibition of HUVEC migration and tubule formation, which can be restored by add back of wt TG2, but not by the transamidation-defective but GTP-binding mutant W241A. TG2 inhibition results in inhibition of fibronectin deposition in HUVEC monocultures with a parallel reduction in matrix-bound VEGFA, leading to a reduction in phosphorylated VEGF receptor 2 (VEGFR2) at Tyr¹²¹⁴ and its downstream effectors Akt and ERK1/2, and importantly its association with β1 integrin. We propose a mechanism for the involvement of matrix-bound VEGFA in angiogenesis that is dependent on extracellular TG2-related activity.     

A critical reevaluation of the structure of the rat uriniferous tubule as revealed by scanning electron microscopy

Summary The fine structure of luminal surface of clearly identified portions of uriniferous tubules has been studied by scanning electron microscopy to elucidate some controversies concerning the topography of certain surface formations. The results show a characteristic pattern of the luminal surface in the region of Henle's loop, which was assumed by previous authors, to belong to the collecting tubule. Furthermore it is demonstrated that no cilia are present within the terminal portion of the collecting tubules.     

Experimental validation of a time-domain-based wave propagation model of blood flow in viscoelastic vessels

Time-domain-based one-dimensional wave propagation models of the arterial system are preferable over one-dimensional wave propagation models in the frequency domain since the latter neglect the non-linear convection forces present in the physiological situation, especially when the vessel is tapered. Moreover, one-dimensional wave propagation models of the arterial system can be used to provide boundary conditions for fully three-dimensional fluid-structure interaction computations that are usually defined in the time domain. In this study, a time-domain-based one-dimensional wave propagation model in a cross-sectional area, flow and pressure (A,q,p)-formulation is developed. Using this formulation, a constitutive law that includes viscoelasticity based on the mechanical behaviour of a Kelvin body, is introduced. The resulting pressure and flow waves travelling through a straight and tapered vessel are compared to experimental data obtained from measurements in an in vitro setup. The model presented shows to be well suited to predict wave propagation through these straight and tapered vessels with viscoelastic wall properties and hereto can serve as a time-domain-based method to model wave propagation in the human arterial system.     

Clonal analysis of immortalized renal proximal tubule cells: Na(+)/glucose cotransport system levels are maintained despite a decline in transport function

Primary rabbit kidney proximal tubule (RPT) cells (S.D. Chung et al., 1982, J. Cell Biol. 95, 118-126) were transfected with the vector pRSV-T, which contains SV40 early region genes. After the third passage (when normal cells had stopped dividing), individual colonies formed in cultures transfected with pRSV-T. Clonal isolates (RPT-I cells) could be obtained in a simple and reproducible manner. Southern analysis of clone RPT-I8 indicated the presence of SV40 early region genes. Nuclear SV40 T was detected. After 23 passages, and subcloning, RPT-I8 (and subclones) was found to express renal proximal tubule markers to a similar extent, indicating that the phenotype was stable. Nevertheless, the activities of the Na(+)/glucose cotransport system, gamma-glutamyl transpeptidase and alkaline phosphatase, were reduced as compared with primary cultures. Western analysis indicated that the level of Na(+)/glucose cotransporters was maintained in RPT-I8 cells, when compared with intact proximal tubules and primary cultures. Thus, the reduction in alpha-MG uptake in RPT-I8 cells may be attributed to other types of cellular alterations, including changes in energy metabolism. Indeed, growth in glucose-free medium was not observed in RPT-I8 cell cultures, suggesting that unlike primary RPT cells (J. C. Chung et al., 1992, J. Cell. Physiol. 150, 243-250), the gluconeogenic pathway was not intact.     

Tubular fluid flow and distal NaCl delivery mediated by tubuloglomerular feedback in the rat kidney

The glomerular filtration rate in the kidney is controlled, in part, by the tubuloglomerular feedback (TGF) system, which is a negative feedback loop that mediates oscillations in tubular fluid flow and in fluid NaCl concentration of the loop of Henle. In this study, we developed a mathematical model of the TGF system that represents NaCl transport along a short loop of Henle with compliant walls. The proximal tubule and the outer-stripe segment of the descending limb are assumed to be highly water permeable; the thick ascending limb (TAL) is assumed to be water impermeable and have active NaCl transport. A bifurcation analysis of the TGF model equations was performed by computing parameter boundaries, as functions of TGF gain and delay, that separate differing model behaviors. The analysis revealed a complex parameter region that allows a variety of qualitatively different model equations: a regime having one stable, time-independent steady-state solution and regimes having stable oscillatory solutions of different frequencies. A comparison with a previous model, which represents only the TAL explicitly and other segments using phenomenological relations, indicates that explicit representation of the proximal tubule and descending limb of the loop of Henle lowers the stability of the TGF system. Model simulations also suggest that the onset of limit-cycle oscillations results in increases in the time-averaged distal NaCl delivery, whereas distal fluid delivery is not much affected.     

Transimmortalized proximal tubule and collecting duct cell lines derived from the kidneys of transgenic mice

This review summarizes the strategy of cellular immortalization based on the principle of targeted oncogenesis in transgenic mice, used to establish models of transimmortalized renal proximal tubule cells, referred to as PKSV-PCT and PKSV-PR-cells, and collecting duct principal cells, referred to as mpkCCD_cl4 cells. These cell lines have maintained for long-term passages the main biochemical and functional properties of the parental cells from which they were derived. Proximal tubule PKSV-PCT and PKSV-PR cells have been proved to be suitable cell systems for toxicological and pharmacological studies. They also permitted the establishment of a model of multidrug-resistant (MDR) renal epithelial tubule cells, PKSV-PR_col50, which have served for the study of both MDR-dependent extrusion of chemotherapeutic drugs and inappropriate accumulation of weak base anthracyclines in intracellular acidic organelles. The novel collecting duct cell line mpkCCD_cl4, which has maintained the characteristics of tight epithelial cells, in particular Na⁺ absorption stimulated by aldosterone, has been extensively used for pharmacological studies related to the regulation of ion transport. These cells have permitted the identification of several aldosterone-induced proteins playing a key role in the regulation of Na⁺ absorption mediated by the epithelial Na⁺ channel ENaC. Recent studies have also provided evidence that these cell lines represent valuable cell systems for the study of host–pathogen interactions and the analysis of the role of renal tubule epithelial cells in the induction of inflammatory response caused by uropathogens that may lead to severe renal damage.     

The transepithelial shunt pathway in the renal proximal tubule of newt kidney

The transepithelial shunt pathway of newt proximal tubule was examined with glass micro-electrode and electron microscopic methods. The input resistance of the peritubular (basal) membrane and tubular wall were found to be $\text{4.2 ± 0.1 · 10}{}^6$ ($\text{mean ± S.E.}\text{, n = 16}$) and $\text{11.4 ± 0.2 · 10}{}^4\text{(n = 11)}$, respectively. The input resistance of the peritubular membrane was approximately 40-times larger than that of the tubular wall. When the kidneys were perfused in a lanthanum solution, the lanthanum ions were then observed in the junctional complexes and in the intercellular spaces on both the basal and apical sides. The results indicate that the electrical shunt pathway corresponds to the apical junctional complexes and the intercellular spaces, and that the tight junctions are not truly ‘tight’ for the transepithelial movement of small ions in the proximal tubule of the newt kidney.     

Stability analysis for a peri-implant osseointegration model

We investigate stability of the solution of a set of partial differential equations, which is used to model a peri-implant osseointegration process. For certain parameter values, the solution has a ‘wave-like’ profile, which appears in the distribution of osteogenic cells, osteoblasts, growth factor and bone matrix. This ‘wave-like’ profile contradicts experimental observations. In our study we investigate the conditions, under which such profile appears in the solution. Those conditions are determined in terms of model parameters, by means of linear stability analysis, carried out at one of the constant solutions of the simplified system. The stability analysis was carried out for the reduced system of PDE’s, of which we prove, that it is equivalent to the original system of equations, with respect to the stability properties of constant solutions. The conclusions, derived from the linear stability analysis, are extended for the case of large perturbations. If the constant solution is unstable, then the solution of the system never converges to this constant solution. The analytical results are validated with finite element simulations. The simulations show, that stability of the constant solution could determine the behavior of the solution of the whole system, if certain initial conditions are considered.     

Albumin handling by renal tubular epithelial cells in a microfluidic bioreactor

Epithelial cells in the proximal tubule of the kidney reclaim and metabolize protein from the glomerular filtrate. Proteinuria, an overabundance of protein in the urine, affects tubular cell function and is a major factor in the progression of chronic kidney disease. By developing experimental systems to study tubular protein handling in a setting that simulates some of the environmental conditions of the kidney tubule in vivo, we can better understand how microenviromental conditions affect cellular protein handling to determine if these conditions are relevant in disease. To this end, we used two in vitro microfluidic models to evaluate albumin handling by renal proximal tubule cells. For the first system, cells were grown in a microfluidic channel and perfused with physiological levels of shear stress to evaluate the effect of mechanical stress on protein uptake. In the second system, a porous membrane was used to separate an apical and basolateral compartment to evaluate the fate of protein following cellular metabolism. Opossum kidney (OK) epithelial cells were exposed to fluorescently labeled albumin, and cellular uptake was determined by measuring the fluorescence of cell lysates. Confocal fluorescence microscopy was used to compare uptake in cells grown under flow and static conditions. Albumin processed by the cells was examined by size exclusion chromatography (SEC) and SDS-PAGE. Results showed that cellular uptake and/or degradation was significantly increased in cells exposed to flow compared to static conditions. This was confirmed by confocal microscopy. Size exclusion chromatography and SDS-PAGE showed that albumin was broken down into small molecular weight fragments and excreted by the cells. No trace of intact albumin was detectable by either SEC or SDS-PAGE. These results indicate that fluid shear stress is an important factor mediating cellular protein handling, and the microfluidic bioreactor provides a novel tool to investigate this process.     

Proteomic analysis of AQP11-null kidney: Proximal tubular type polycystic kidney disease

Autosomal Dominant Polycystic Kidney Disease (ADPKD) is caused by the mutation of polycystins (PC-1 or PC-2), in which cysts start from the collecting duct to extend to all nephron segments with eventual end stage renal failure. The cyst development is attenuated by a vasopressin V2 receptor antagonist tolvaptan which, however, will not affect proximal tubule cysts devoid of V2 receptor. Aquaporin-11 (AQP11) is expressed selectively in the proximal tubule of the kidney and AQP11-null kidneys have a disruptive PC-1 trafficking to the plasma membrane to develop polycystic kidneys. Here, we analyzed AQP11-null kidneys at the beginning of cyst formation by quantitative proteomic analysis using Tandem Mass Tag (TMT). Among ~ 1200 identified proteins, 124 proteins were differently expressed by > 1.5 or < 0.8 fold change. A pancreatic stone inhibitor or a growth factor, lithostathine-1 (Reg1) was most enhanced by 5 folds which was confirmed by western blot, while mitochondria-related proteins were downregulated. The identified proteins will be new target molecules for the treatment of proximal tubular cysts and helpful to explore the functional roles of AQP11 in the kidney.     

Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis

We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system well-posed. We firstly consider one-dimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In two-dimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two sub-models, only one of which is capable of generating pattern. We thus focus on this particular sub-model. We present a nonlinear analysis of spatio-temporal patterns exhibited by the sub-model on a square domain and discuss mode interaction. Our analysis shows that when a two-dimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation.     

Validation of a patient-specific one-dimensional model of the systemic arterial tree

The aim of this study is to develop and validate a patient-specific distributed model of the systemic arterial tree. This model is built using geometric and hemodynamic data measured on a specific person and validated with noninvasive measurements of flow and pressure on the same person, providing thus a patient-specific model and validation. The systemic arterial tree geometry was obtained from MR angiographic measurements. A nonlinear viscoelastic constitutive law for the arterial wall is considered. Arterial wall distensibility is based on literature data and adapted to match the wave propagation velocity of the main arteries of the specific subject, which were estimated by pressure waves traveling time. The intimal shear stress is modeled using the Witzig-Womersley theory. Blood pressure is measured using applanation tonometry and flow rate using transcranial ultrasound and phase-contrast-MRI. The model predicts pressure and flow waveforms in good qualitative and quantitative agreement with the in vivo measurements, in terms of wave shape and specific wave features. Comparison with a generic one-dimensional model shows that the patient-specific model better predicts pressure and flow at specific arterial sites. These results obtained let us conclude that a patient-specific one-dimensional model of the arterial tree is able to predict well pressure and flow waveforms in the main systemic circulation, whereas this is not always the case for a generic one-dimensional model.     

A one-dimensional mathematical model of collecting lymphatics coupled with an electro-fluid-mechanical contraction model and valve dynamics

We propose a one-dimensional model for collecting lymphatics coupled with a novel Electro-Fluid-Mechanical Contraction (EFMC) model for dynamical contractions, based on a modified FitzHugh–Nagumo model for action potentials. The one-dimensional model for a deformable lymphatic vessel is a nonlinear system of hyperbolic Partial Differential Equations (PDEs). The EFMC model combines the electrical activity of lymphangions (action potentials) with fluid-mechanical feedback (circumferential stretch of the lymphatic wall and wall shear stress) and lymphatic vessel wall contractions. The EFMC model is governed by four Ordinary Differential Equations (ODEs) and phenomenologically relies on: (1) environmental calcium influx, (2) stretch-activated calcium influx, and (3) contraction inhibitions induced by wall shear stresses. We carried out a stability analysis of the stationary state of the EFMC model. Contractions turn out to be triggered by the instability of the stationary state. Overall, the EFMC model allows emulating the influence of pressure and wall shear stress on the frequency of contractions observed experimentally. Lymphatic valves are modelled by extending an existing lumped-parameter model for blood vessels. Modern numerical methods are employed for the one-dimensional model (PDEs), for the EFMC model and valve dynamics (ODEs). Adopting the geometrical structure of collecting lymphatics from rat mesentery, we apply the full mathematical model to a carefully selected suite of test problems inspired by experiments. We analysed several indices of a single lymphangion for a wide range of upstream and downstream pressure combinations which included both favourable and adverse pressure gradients. The most influential model parameters were identified by performing two sensitivity analyses for favourable and adverse pressure gradients.