Flutter in collapsible tubes: a theoretical model of wheezes

A mathematical analysis of flow through a flexible channel is examined as a model of flow-induced flutter oscillations that pertain to the production of wheezing breath sounds. The model provides predictions for the critical fluid speed that will initiate flutter waves of the wall, as well as their frequency and wavelength. The mathematical results are separated into linear theory (small oscillations) and nonlinear theory (larger oscillations). Linear theory determines the onset of the flutter, whereas nonlinear theory determines the relationships between the fluid speed and both the wave amplitudes and frequencies. The linear theory predictions correlate well with data taken at the onset of flutter and flow limitation during experiments of airflow in thick-walled collapsible tubes. The nonlinear theory predictions correlate well with data taken as these flows are forced to higher velocities while keeping the flow rate constant. Particular ranges of the parameters are selected to investigate and discuss the applications to airway flows. According to this theory, the mechanism of generation of wheezes is based in the interactions of fluid forces and friction and wall elastic-restoring forces and damping. In particular, a phase delay between the fluid pressure and wall motion is necessary. The wave speed theory of flow limitation is discussed with respect to the specific data and the flutter model.     

Seasonal Invasion Dynamics in a Spatially Heterogeneous River with Fluctuating Flows

A key problem in environmental flow assessment is the explicit linking of the flow regime with ecological dynamics. We present a hybrid modeling approach to couple hydrodynamic and biological processes, focusing on the combined impact of spatial heterogeneity and temporal variability on population dynamics. Studying periodically alternating pool-riffle rivers that are subjected to seasonally varying flows, we obtain an invasion ratchet mechanism. We analyze the ratchet process for a caricature model and a hybrid physical–biological model. The water depth and current are derived from a hydrodynamic equation for variable stream bed water flows and these quantities feed into a reaction-diffusion-advection model that governs population dynamics of a river species. We establish the existence of spreading speeds and the invasion ratchet phenomenon, using a mixture of mathematical approximations and numerical computations. Finally, we illustrate the invasion ratchet phenomenon in a spatially two-dimensional hydraulic simulation model of a meandering river structure. Our hybrid modeling approach strengthens the ecological component of stream hydraulics and allows us to gain a mechanistic understanding as to how flow patterns affect population survival.     

Squeezing flows of vaginal gel formulations relevant to microbicide drug delivery

Efficacy of topical microbicidal drug delivery formulations against HIV depends in part on their ability to coat, distribute, and be retained on epithelium. Once applied to the vagina, a formulation is distributed by physical forces including: gravity, surface tension, shearing, and normal forces from surrounding tissues, i.e., squeezing forces. The present study focused on vaginal microbicide distribution due to squeezing forces. Mathematical simulations of squeezing flows were compared with squeezing experiments, using model vaginal gel formulations. Our objectives were: (1) to determine if mathematical simulations can accurately describe squeezing flows of vaginal gel formulations; (2) to find the best model and optimized parameter sets to describe these gels; and (3) to examine vaginal coating due to squeezing using the best models and summary parameters for each gel. Squeezing flow experiments revealed large differences in spreadability between formulations, suggesting different coating distributions in vivo. We determined the best squeezing flow models and summary parameters for six test gels of two compositions, cellulose and polyacrylic acid (PAA). We found that for some gels it was preferable to deduce model input parameters directly from squeezing flow experiments. For the cellulose gels, slip conditions in squeezing flow experiments needed to be evaluated. For PAA gels, we found that in the absence of squeezing experiments, rotational viscometry measurements (to determine Herschel-Bulkley parameters) led to reasonably accurate predictions of squeezing flows. Results indicated that yield stresses may be a strong determinant of squeezing flow mechanics. This study serves as a template for further investigations of other gels and determination of which sources of rheological data best characterize potential microbicidal formulations. These mathematical simulations can serve as useful tools for exploring drug delivery parameters, and optimizing formulations, prior to costly clinical trials.     

Assessment of Model Based (Input) Impedance,Pulse Wave Velocity,and Wave Reflection in the Asklepios Cohort

Objectives

Arterial stiffness and wave reflection parameters assessed from both invasive and non-invasive pressure and flow readings are used as surrogates for ventricular and vascular load. They have been reported to predict adverse cardiovascular events, but clinical assessment is laborious and may limit widespread use. This study aims to investigate measures of arterial stiffness and central hemodynamics provided by arterial tonometry alone and in combination with aortic root flows derived by echocardiography against surrogates derived by a mathematical pressure and flow model in a healthy middle-aged cohort.

Methods

Measurements of carotid artery tonometry and echocardiography were performed on 2226 ASKLEPIOS study participants and parameters of systemic hemodynamics, arterial stiffness and wave reflection based on pressure and flow were measured. In a second step, the analysis was repeated but echocardiography derived flows were substituted by flows provided by a novel mathematical model. This was followed by a quantitative method comparison.

Results

All investigated parameters showed a significant association between the methods. Overall agreement was acceptable for all parameters (mean differences: -0.0102 (0.033 SD) mmHg*s/ml for characteristic impedance, 0.36 (4.21 SD) mmHg for forward pressure amplitude, 2.26 (3.51 SD) mmHg for backward pressure amplitude and 0.717 (1.25 SD) m/s for pulse wave velocity).

Conclusion

The results indicate that the use of model-based surrogates in a healthy middle aged cohort is feasible and deserves further attention.     

A variational calculus approach to the suspension flow problem using the minimal force hypothesis

Analytic expressions for the velocity profile and distribution of neutrally buoyant particles in laminar flow were obtained as functions of the radial distance. A modified Einstein viscosity model and the hypothesis that the total force on all the particles flowing in the tube is a minimum were used. The methods of the variational calculus were used in the mathematical development. A velocity profile differing only slightly from the parabolic form of that for Hagan-Poiseuille flow was obtained. For particle distribution the equations developed predict a maximum concentration along the center-line for some flows and a maximum concentration in a ring some distance from the center line in other flows. Both of these concentration profiles have been observed experimentally. Quantitative predictions from the equations derived must await further experimental work to permit calculation of the parameters included in the equations.     

A tridomain model for potassium clearance in optic nerve of Necturus

Complex fluids flow in complex ways in complex structures. Transport of water and various organic and inorganic molecules in the central nervous system are important in a wide range of biological and medical processes. However, the exact driving mechanisms are often not known. In this work, we investigate flows induced by action potentials in an optic nerve as a prototype of the central nervous system. Different from traditional fluid dynamics problems, flows in biological tissues such as the central nervous system are coupled with ion transport. They are driven by osmosis created by concentration gradient of ionic solutions, which in turn influence the transport of ions. Our mathematical model is based on the known structural and biophysical properties of the experimental system used by the Harvard group Orkand et al. Asymptotic analysis and numerical computation show the significant role of water in convective ion transport. The full model (including water) and the electrodiffusion model (excluding water) are compared in detail to reveal an interesting interplay between water and ion transport. In the full model, convection due to water flow dominates inside the glial domain. This water flow in the glia contributes significantly to the spatial buffering of potassium in the extracellular space. Convection in the extracellular domain does not contribute significantly to spatial buffering. Electrodiffusion is the dominant mechanism for flows confined to the extracellular domain.     

介绍一种建立池塘能流模型的方法

系统生态学是对生物群落的生存、成长和死亡进行宏观研究。其系统方法论有多种处理问题的方法,特别是框图模型的应用尤其广泛,如在海洋、经济、城市、水体和陆地生态系统均有应用,但仅局限于画画框图讨论而已,并没有指出其应用的实际意义。还有一种系统动力学框图,属臆造模型。     

Minimizing Chlorine Use: Assessing the Trade-offs Between Cost and Chlorine Reduction in Chemical Manufacturing

A mathematical model ofthe material and energy flows in the chemical manufacturing industries was used to evaluate trade-offs between cost and chlorine use in chemical manufaduring. The model was also used to assess the impact that new technologies could have on chlorine use. Although the cost data in the model were subject to considerable uncertainty, the results did provide general guidance in choosing chemical manufacturing technologies that reduce chlorine use in a cost-effective way More significant, the modeling demonstrates that material flow data can play a critical role in assessing the environmental implications of industrial systems.     

Pendelluft flow in symmetric airway bifurcations.

We propose a mathematical model for pendelluft flow in a single airway bifurcation. The model is motivated by an apparatus used in an experimental study of the pendelluft by Ultman et al. (1988). We derive differential equations governing the fluid flow, which directly connect physiological parameters to the variables determining the pendelluft; this approach allows us to include nonlinearity in the model. If nonlinearity is neglected, our model is identical to the R-I-C circuits used by previous investigators. If nonlinearity is retained, we show that pendelluft can occur even in perfectly symmetric airway bifurcations. For the specific apparatus used in the experiments of High et al. (1991), we demonstrate that two qualitatively different pendelluft flows can occur in the system.     

Fish response to the temporal hierarchy of the natural flow regime in the Daly River, northern Australia

In this study, relationships between flow variation across multiple temporal scales and the distribution and abundance of three fish species, western rainbowfish Melanotaenia australis, sooty grunter Hephaestus fuliginosus and barramundi Lates calcarifer were examined at eight sampling reaches in the Daly River, Northern Territory, Australia. Discharge was highly seasonal during the study period of 2006-2010 with a distinct wet-dry discharge pattern. Significant catchment-wide correlations were identified between species abundance and hydrologic variables across several scales describing the magnitude and variability of flow. A Bayesian hierarchical model which accounted for >80% of variation in abundances for all species and age classes (i.e. juvenile and adult), identified the extent to which the influence of short-term flow variation was dependent upon the historical flow regime. There were distinct ontogenetic differences in these relationships for H. fuliginosus, with variability of recent flows having a negative effect on juveniles which was stronger at locations with higher historical mean daily flow. Lates calcarifer also displayed ontogenetic differences in relationships to flow variation with adults showing a positive association with increase in recent flows and juveniles showing a negative one. The effect of increased magnitude of wet-season flows on M. australis was negative in locations with lower historical mean daily flow but positive in locations with higher historical mean daily flow. The results highlighted how interactions between multiple scales of flow variability influence the abundance of fish species according to their life-history requirements.     

Fractal properties of perfusion heterogeneity in optimized arterial trees: a model study

Regional blood flows in the heart muscle are remarkably heterogeneous. It is very likely that the most important factor for this heterogeneity is the metabolic need of the tissue rather than flow dispersion by the branching network of the coronary vasculature. To model the contribution of tissue needs to the observed flow heterogeneities we use arterial trees generated on the computer by constrained constructive optimization. This method allows to prescribe terminal flows as independent boundary conditions, rather than obtaining these flows by the dispersive effects of the tree structure. We study two specific cases: equal terminal flows (model 1) and terminal flows set proportional to the volumes of Voronoi polyhedra used as a model for blood supply regions of terminal segments (model 2). Model 1 predicts, depending on the number Nterm of end-points, fractal dimensions D of perfusion heterogeneities in the range 1.20 to 1.40 and positively correlated nearest-neighbor regional flows, in good agreement with experimental data of the normal heart. Although model 2 yields reasonable terminal flows well approximated by a lognormal distribution, it fails to predict D and nearest-neighbor correlation coefficients r1 of regional flows under normal physiologic conditions: model 2 gives D = 1.69 +/- 0.02 and r1 = -0.18 +/- 0.03 (n = 5), independent of Nterm and consistent with experimental data observed under coronary stenosis and under the reduction of coronary perfusion pressure. In conclusion, flow heterogeneity can be modeled by terminal positions compatible with an existing tree structure without resorting to the flow-dispersive effects of a specific branching tree model to assign terminal flows.     

Computational aspects of motion perception in natural and artificial vision systems.

In this paper a computational scheme for motion perception in artificial and natural vision systems is described. The scheme is motivated by a mathematical analysis in which first-order spatial properties of optical flow, such as singular points and elementary components of optical flow, are shown to be salient features for the computation and analysis of visual motion. The fact that different methods for the computation of optical flow produce similar results is explained in terms of the simple spatial structure of the image motion of rigid bodies. Singular points and elementary flow components are used to compute motion parameters, such as time-to-collision and angular velocity, and also to segment the visual field into areas which correspond to different motions. Then a number of biological implications are discussed. Electrophysiological findings suggest that the brain perceives visual motion by detecting and analysing optical flow components. However, the cortical neurons, which seem to detect elementary flow components, are not able to extract these components from more complex flows. A simple model for the organization of the receptive field of these cells, which is consistent with anatomical and electrophysiological data, is described at the end of the paper.     

Computational fluid dynamics simulations on a Devonian spiriferid Paraspirifer bownockeri (Brachiopoda): Generating mechanism of passive feeding flows

A mechanism of generating passive feeding flow for the Devonian spiriferide brachiopod Paraspirifer bownockeri was theoretically elucidated through fluid dynamics simulations for flow around rigid shells. The RANS equations were used as a turbulence model, and the unsteady incompressible flow was solved using the finite volume method. Two directions of ventral and dorsal flows were investigated as typical cases where little exchange flow occurs inside the shells. The digital model of the shell was constructed using image processing of X-ray CT images of a shell replica made by molding a polycarbonate plate to a well-preserved fossil specimen of Paraspirifer. To examine the effect of flow velocity, three conditions of ambient flow velocity were adopted for both the ventral and dorsal flows. The pressure distribution along the gape showed that a relatively high pressure occurred around the sulcus in all simulated cases. This high pressure generated inflow from the sulcus and subsequent spiral internal flow, especially in fast ambient flows. This means that the sulcus generated the considerable pressure gradient around the gape passively and generated the stable intake of seawater and a spiral flow of water inside the shell for feeding. We conclude that the shell form of certain spiriferides could generate spiral flows so as to promote passive feeding, and the sulcus is interpreted as an important form for the passive intake of water.     

Effect of high altitude exposure on the hemodynamics of the bidirectional Glenn physiology: Modeling incremented pulmonary vascular resistance and heart rate

The considerable blood mixing in the bidirectional Glenn (BDG) physiology further limits the capacity of the single working ventricle to pump enough oxygenated blood to the circulatory system. This condition is exacerbated under severe conditions such as physical activity or high altitude. In this study, the effect of high altitude exposure on hemodynamics and ventricular function of the BDG physiology is investigated. For this purpose, a mathematical approach based on a lumped parameter model was developed to model the BDG circulation. Catheterization data from 39 BDG patients at stabilized oxygen conditions was used to determine baseline flows and pressures for the model. The effect of high altitude exposure was modeled by increasing the pulmonary vascular resistance (PVR) and heart rate (HR) in increments up to 80% and 40%, respectively. The resulting differences in vascular flows, pressures and ventricular function parameters were analyzed. By simultaneously increasing PVR and HR, significant changes (p <0.05) were observed in cardiac index (11% increase at an 80% PVR and 40% HR increase) and pulmonary flow (26% decrease at an 80% PVR and 40% HR increase). Significant increase in mean systemic pressure (9%) was observed at 80% PVR (40% HR) increase. The results show that the poor ventricular function fails to overcome the increased preload and implied low oxygenation in BDG patients at higher altitudes, especially for those with high baseline PVRs. The presented mathematical model provides a framework to estimate the hemodynamic performance of BDG patients at different PVR increments.     

The effect of temperature gradient on the transport phenomenon in roots of maize plants grown under salinity conditions. conductivity and filtration properties

An analysis of flows through primary root and first node root tissues of plants grown under conditions of salinity and nutrient deficiency induced by temperature gradients was carried out using. a mathematical model. The results obtained show that high KNO₃ concentration in Knop’s nutrient solution (salinity) causes an inhibition of volume and heat flows and that the omission of KNO₃ from Knop’s nutrient solution (deficiency) stimulates these flows. The causes of the inhibition lay in the fact that salinity reduced hydraulic, electric, and osmotic conductivity when compared with the control (Knop’s solution), but relative to nutrient deficiency, it increased osmotic conductivity, electrodiffusion, diffusion, and filtration of heat flow induced by the electric and heat power. The causes of the stimulation were that deficiency partially decreased conductivities, similarly as salinity when compared with the control, and also decreased osmotic abilities of the system. By contrast, it increased heat conductivity and corresponding filtrations (diffusion-thermal, thermoosmotic). In first node root tissues, it increased all conductivities with the exception of electric conductivity, then osmotic, electroosmotic, diffusion, electrodiffusion, and filtration of heat flow and current flow, that is the number of possible ways of solution transport through root tissues increased.     

The Effect of temperature gradient on the transport phenomenon in roots of maize plants grown under salinity conditions. substance,heat, and ion flows

An analysis of flows through primary root and first node root tissues of plants grown under conditions of salinity and nutrient deficiency induced by temperature gradients was carried out using. a mathematical model. The results obtained show that high KNO₃ concentration in Knop’s nutrient solution (salinity) causes an inhibition of volume and heat flows and that the omission of KNO₃ from Knop’s nutrient solution (deficiency) stimulates these flows. The causes of the inhibition lay in the fact that salinity reduced hydraulic, electric, and osmotic conductivity when compared with the control (Knop’s solution), but relative to nutrient deficiency, it increased osmotic conductivity, electrodiffusion, diffusion, and filtration of heat flow induced by the electric and heat power. The causes of the stimulation were that deficiency partially decreased conductivities, similarly as salinity when compared with the control, and also decreased osmotic abilities of the system. By contrast, it increased heat conductivity and corresponding filtrations (diffusion-thermal, thermoosmotic). In first node root tissues, it increased all conductivities with the exception of electric conductivity, then osmotic, electroosmotic, diffusion, electrodiffusion, and filtration of heat flow and current flow, that is the number of possible ways of solution transport through root tissues increased. Part II.     

Mathematical models of the flow in the basilar artery

The flow in the basilar artery arises from the merging of the flows from the two vertebral arteries. This study deals with the question whether a parabolic (Poiseuille) profile will have been established before the basilar artery divides into both posterior cerebral arteries. The inlet length (that is, the downstream distance needed for the flow to become approximately equal to the limiting Poiseuille flow) and velocity profiles have been computed from two- and three-dimensional mathematical models in which flow pulsatility and vessel wall distensibility have been neglected and the complex geometry of the junction has been taken into account in a simplified form. The results show that the flow at the end of the basilar artery is far from being parabolic and that an asymmetry in the entrance flow will be carried along towards the end of the basilar artery, thus affecting flows in the circle of Willis.     

A Material Flow Accounting Case Study of the Lisbon Metropolitan Area using the Urban Metabolism Analyst Model

This article describes a new methodological framework to account for urban material flows and stocks, using material flow accounting (MFA) as the underlying method. The proposed model, urban metabolism analyst (UMAn), bridges seven major gaps in previous urban metabolism studies: lack of a unified methodology; lack of material flows data at the urban level; limited categorizations of material types; limited results about material flows as they are related to economic activities; limited understanding of the origin and destination of flows; lack of understanding about the dynamics of added stock; and lack of knowledge about the magnitude of the flow of materials that are imported and then, to a great extent, exported. To explore and validate the UMAn model, a case study of the Lisbon Metropolitan Area was used. An annual time series of material flows from 2003 to 2009 is disaggregated by the model into 28 material types, 55 economic activity categories, and 18 municipalities. Additionally, an annual projection of the obsolescence of materials for 2010–2050 was performed. The results of the case study validate the proposed methodology, which broadens the contribution of existing urban MFA studies and presents pioneering information in the field of urban metabolism. In particular, the model associates material flows with economic activities and their spatial location within the urban area.