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.     

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.     

Secondary flow velocity patterns in a pulmonary artery model with varying degrees of valvular pulmonic stenosis: pulsatile in vitro studies

The objective of this study was to characterize in detail the secondary flow velocity patterns in an in vitro model of a human (adult) pulmonary artery with varying degrees of valvular pulmonic stenosis. A two-dimensional laser Doppler anemometer (LDA) system was used to map the flow fields in the main (MPA), left (LPA), and right (RPA) branches of the pulmonary artery model. The study was conducted in the Georgia Tech right heart pulse duplicator system. A pair of counter-rotating secondary flows were observed in each daughter branch in which the fluid moved outwardly along the side walls and then circled back inwardly toward the center of the vessel. For the case of the "normal" valve, the two counter-rotating secondary flows were symmetric about the centerline. The strength of secondary flows in the RPA was much stronger than in the LPA. However, as the pulmonic valve became more stenotic, the two counter-rotating secondary flows in both the LPA and RPA were no longer symmetric. In addition, the strength of secondary flows in both daughter branches increased with increasing degree of valvular stenosis. The increment in the LPA was, however, greater than in the RPA. The study demonstrates the importance of analyzing complex biological flows from a three-dimensional viewpoint.     

Derecruitment in cat liver: extension of undistributed parallel tube model to effects of low hepatic blood flow on ethanol uptake

Previous studies showed two deviations from the predictions of the undistributed parallel tube model for hepatic uptake of substrates: a small deviation at high flows and a large deviation at low flows. We have examined whether these deviations could be described by a single correction factor. In cats anesthetized with pentobarbital, a hepatic venous long-circuit technique with an extracorporeal reservoir was used to vary portal flow and hepatic venous pressure, and allow repeated sampling of arterial, portal, and hepatic venous blood without depletion of the cat's blood volume. Hepatic uptake of ethanol was measured over a wide range of blood flows and when intrahepatic pressure was increased at low flows. This uptake could be described by the parallel tube model with a correction for hepatic blood flow: Uptake = Vmax max.(1 - e-kF).c/(Km + c). In 22 cats, Vmax max = 90 +/- 5 mumols/(min.100 g liver), k = 0.021 +/- 0.0015 when flow (F) was in millilitres per minute per 100 g liver, and Km = 150 +/- 20 microM when c is the log mean sinusoidal concentration. (1 - e-kF) represents the proportion of sinusoids perfused and metabolically active. A dynamic interpretation of this proportion is related to intermittency (derecruitment) of sinusoidal flow. Half the sinusoids were perfused at a flow of 33 mL/(min.100 g liver) and the liver was essentially completely perfused (greater than 95%) at the normal flow of 150 mL/(min.100 g liver). Derecruitment was not changed by raising hepatic venous pressure, and it was not related to hepatic venous resistance.     

Experimental study of pulsatile and steady flow through a smooth tube and an atherosclerotic coronary artery casting of man

In vitro investigation of pulsatile and steady flows through a smooth, straight circular tube and a diseased human coronary artery cast was conducted with sugar-water solutions simulating the viscosity of blood. Time averaged pressure drops for pulsatile flows measured in the circular tube over a Reynolds number ranging from 50 to 1,000 were found to be identical to those for steady flows in the same tube, both of which were in excellent agreement with the Poiseuille flow prediction. For the polyurethane case (# 124) made from a human main coronary with significant but 'non obstructive' diffuse atherosclerotic disease, pressure drops for steady flows were found to be greater than Poiseuille flow predictions by a factor of 3-8 in the physiological Reynolds number range from about 100 to 400. Pulsatile flows in the same artery cast resulted in additional 30% increases in time averaged pressure drops, and thus flow resistance, compared to the steady flow data. Steady and pulsatile flow data measured in a straight, axisymmetric model of cast # 124 showed considerably smaller increases in flow resistance than those observed in # 124 casting.     

Increasing hydrologic variability threatens depleted anadromous fish populations

Predicting effects of climate change on species and ecosystems depend on understanding responses to shifts in means (such as trends in global temperatures), but also shifts in climate variability. To evaluate potential responses of anadromous fish populations to an increasingly variable environment, we performed a hierarchical analysis of 21 Chinook salmon populations from the Pacific Northwest, examining support for changes in river flows and flow variability on population growth. More than half of the rivers analyzed have already experienced significant increases in flow variability over the last 60 years, and this study shows that this increase in variability in freshwater flows has a more negative effect than any other climate signal included in our model. Climate change models predict that this region will experience warmer winters and more variable flows, which may limit the ability of these populations to recover.     

Applying Ecological Input-Output Flow Analysis to Material Flows in Industrial Systems: Part I: Tracing Flows

Input-output mathematics, which allows a modeler to fully consider direct and indirect relationships among conserved flows in a system, has a long history in economics with prominent use dating to Leontief in the 1930s. Nearly all previous industrial applications of input-output analysis have been grounded in the monetary flows of an economy. Here however, because of the central nature of physical flows in the environmental impact of industry, we consider physical flows to be a fundamental component of an industrial economy. Hence, we propose an input-output based approach for modeling physical flows in industry independent of their monetary implications.
In this first part of a two-part article, a framework for using input-output mathematics to model material and energy flows is constructed from a foundation laid by previous research in nutrient and energy cycling in natural ecosystems. The mathematics of input-output flow analysis is presented from an ecological perspective, culminating in two core capabilities: tracing of flows with environs (investigated in this article) and characterizing system behavior with flow metrics (presented in the second article). We assert that environ analysis is an effective means for tracing flows through industrial systems while fully considering direct and indirect flow paths. We explore material flows of aluminum and five other metals in depth using environ analysis in this article.     

Effect of turbulent models on left ventricle diastolic flow patterns simulation

Abstract

Vortex structures, as one of the most important features of cardiac flow, have a crucial impact on the left ventricle function and pathological conditions. These swirling flows are closely related to the presence of turbulence in left ventricle which is investigated in the current study. Using an extended model of the left heart, including a fluid-structure interaction (FSI) model of the mitral valve with a realistic geometry, the effect of using two numerical turbulent models, k-ε and Spalart-Allmaras (SA), on diastolic flow patterns is studied and compared with results from laminar flow model. As a result of the higher dissipation rate in turbulent models (k-ε and SA), vortices are larger and stronger in the laminar flow model. Comparing E/A ratio in the three models (Laminar, k-ε, and SA) with experimental data from healthy subjects, it is concluded that the results from k-ε model are more accurate.     

Airway dynamics in transition between peak and maximal expiratory flow

Expiratory flow-volume curves with periodic interruption of flow showed flow transients exceeding maximal flow (Vmax) measured on the maximum expiratory flow-volume (MEFV) curve in a mechanical lung model and in five tracheotomized, vagotomized, open-chest, anesthetized dogs. Direct measurement of flow from the collapsing model airway showed that the volume of the flow transients in excess of the MEFV envelope was greater than that from the collapsing airway. Determination of wave-speed flows from local airway transmural pressure-area curves (J. Appl. Physiol. 52: 357-369, 1982) and photography of the airway led to the following conclusions. Flow transients exceeding Vmax are wave-speed flows determined by an initial and unstable configuration of the flow-limiting segment (FLS) with maximum compression in the midportion. The drop in flow from the peak to the following plateau is due to development of a more stable airway configuration with maximum compression at the mouthward end with a smaller area and a smaller maximal flow. When FLS jumps to a more peripheral position, the more distal airways may pass through similar configurational changes that are responsible for the sudden decrease of flow (the "knee") seen on most MEFV curves from dogs.     

A novel solution for fluid flow problems based on the lattice Boltzmann method

Recently, phase separation and fluid flow problems have represented an important development in fluid dynamics, which has many important industrial applications. Lattice Boltzmann method (LBM) is the numerical method that explains the behaviour of fluid dynamics in mesoscopic scale single-component single-phase and multi-component multiphase flows. In this paper, we study the lattice Boltzmann models (LBMs) in two dimensions (2D) with nine directions (Q9), that is the D2Q9 model was used to study the phase separation and observe that the phenomenon of fluid flow in a cylinder has obstacle and square cavity. The simulation results show that fluid flows in the square cavity and in the cylinder, present phase separation of single-component multiphase fluid flow.     

Flow patterns at the major T-junctions of the dog descending aorta

Using a novel technique developed in our own laboratory, an isolated transparent arterial segment containing the whole descending aorta and its four major branches was prepared from a dog. The flow patterns at each aortic T-junction were studied in detail under the conditions of steady flow by means of flow visualization and cinemicrographic techniques. It was found that a standing recirculation zone consisting of a pair of thin-layered spiral secondary flows located symmetrically about the common median plane of the aorta and side branches was formed at each T-junction over a wide range of flow conditions including the time-averaged estimated mean values of physiological flow rates and flow rate ratios. The results support the recent in vivo findings by other investigators that flow reversal occurs at some junctions of the dog abdominal aorta during each cardiac cycle. The flow patterns at the aortic T-junctions were very much similar to those previously observed in various glass model T-junctions. However, due to the particular anatomical structure of the vessel wall at each branching site (the curvature of the wall was very sharp at the flow divider, but gently rounded at the bend opposite to it) no recirculation zone was formed in the side branches. At a given flow rate ratio, the measured critical Reynolds numbers for the formation of spiral secondary flows and fully developed disturbed flows were much higher in aortic T-junctions than those in glass model T-junctions having equivalent branching angles and diameter ratios. These results indicate that, in the circulation, conditions at arterial T-junctions appear to be optimal for minimizing the formation of disturbed flows.     

Morphological plasticity in a native freshwater fish from semiarid Australia in response to variable water flows

In fishes, alterations to the natural flow regime are associated with divergence in body shape morphology compared with individuals from unaltered habitats. However, it is unclear whether this morphological divergence is attributable to evolutionary responses to modified flows, or is a result of phenotypic plasticity. Fishes inhabiting arid regions are ideal candidates for studying morphological plasticity as they are frequently exposed to extreme natural hydrological variability. We examined the effect of early exposure to flows on the development of body shape morphology in the western rainbowfish (Melanotaenia australis), a freshwater fish that is native to semiarid northwest Australia. Wild fish were collected from a region (the Hamersley Ranges) where fish in some habitats are subject to altered water flows due to mining activity. The offspring of wild‐caught fish were reared in replicated fast‐flow or slow‐flow channels, and geometric morphometric analyses were used to evaluate variation in fish body shape following 3, 6, 9, and 12 months of exposure. Water flows influenced fish morphology after 6 and 9 months of flow exposure, with fish in fast‐flow environments displaying a more robust body shape than those in slow‐flow habitats. No effect of flow exposure was observed at 3 and 12 months. Fishes also showed significant morphological variation within flow treatments, perhaps due to subtle differences in water flow among the replicate channels. Our findings suggest that early exposure to water flows can induce shifts in body shape morphology in arid zone freshwater fishes. Morphological plasticity may act to buffer arid zone populations from the impacts of anthropogenic activities, but further studies are required to link body shape plasticity with behavioral performance in habitats with modified flows.     

Phasic hemodynamics and reverse blood flows in the aortic isthmus and pulmonary arteries of preterm lambs with pulmonary vascular dysfunction

Time-domain representations of the fetal aortopulmonary circulation were carried out in lamb fetuses to study hemodynamic consequences of congenital diaphragmatic hernia (CDH) and the effects of endothelin-receptor antagonist tezosentan (3 mg/45 min). From the isthmic aortic and left pulmonary artery (PA) flows (Q) and isthmic aortic, PA, and left auricle pressures (P) on day 135 in 10 controls and 7 CDH fetuses (28 ewes), discrete-triggered P and Q waveforms were modelized as Pt and Qt functions to obtain basic hemodynamic profiles, pulsatile waves [P, Q, and entry impedance (Ze)], and P and Q hysteresis loops. In the controls, blood propelling energy was accounted for by biventricular ejection flow waves (kinetic energy) with low Ze and by flow-driven pressure waves (potential energy) with low Ze. Weak fetal pulmonary perfusion was ensured by reflux (reverse flows) from PA branches to the ductus anteriosus and aortic isthmus as reverse flows. Endothelin-receptor antagonist blockade using tezosentan slightly increased the forward flow but largely increased diastolic backward flow with a diminished left auricle pre- and postloading. In CHD fetuses, the static component overrode phasic flows that were detrimental to reverse flows and the direction of the diastolic isthmic flow changed to forward during the diastole period. Decreased cardiac output, flattened pressure waves, and increased forward Ze promoted backward flow to the detriment of forward flow (especially during diastole). Additionally, the intrapulmonary arteriovenous shunting was ineffective. The slowing of cardiac output, the dampening of energetic pressure waves and pulsatility, and the heightening of phasic impedances contributed to the lowering of aortopulmonary blood flows. We speculate that reverse pulmonary flow is a physiological requirement to protect the fetal pulmonary circulation from the prominent right ventricular stream and to enhance blood flow to the fetal heart and brain.     

The Atlas of Chinese World Wide Web Ecosystem Shaped by the Collective Attention Flows

The web can be regarded as an ecosystem of digital resources connected and shaped by collective successive behaviors of users. Knowing how people allocate limited attention on different resources is of great importance. To answer this, we embed the most popular Chinese web sites into a high dimensional Euclidean space based on the open flow network model of a large number of Chinese users’ collective attention flows, which both considers the connection topology of hyperlinks between the sites and the collective behaviors of the users. With these tools, we rank the web sites and compare their centralities based on flow distances with other metrics. We also study the patterns of attention flow allocation, and find that a large number of web sites concentrate on the central area of the embedding space, and only a small fraction of web sites disperse in the periphery. The entire embedding space can be separated into 3 regions(core, interim, and periphery). The sites in the core (1%) occupy a majority of the attention flows (40%), and the sites (34%) in the interim attract 40%, whereas other sites (65%) only take 20% flows. What’s more, we clustered the web sites into 4 groups according to their positions in the space, and found that similar web sites in contents and topics are grouped together. In short, by incorporating the open flow network model, we can clearly see how collective attention allocates and flows on different web sites, and how web sites connected each other.     

Neuropeptide control of thyroid blood flow and hormone secretion in the rat

The effects of peptide HI (PHI), neuropeptide Y (NPY), and substance P (SP) on thyroid blood flow and hormone levels were studied in anesthetized rats. Regional blood flows were determined using radioactive microspheres. No change in heart rate or mean left ventricular pressure occurred during these neuropeptide infusions (0.625 micrograms iv over 2 min). PHI treatment resulted in a four-fold increase in thyroid blood flow. Blood flows to the pancreas and salivary gland also increased during PHI treatment. Infusions of NPY or SP did not significantly alter thyroid blood flow. However, SP decreased blood flow to the spleen and small intestine. These neuropeptides had no effect on blood flows to the adrenal, kidney, brain, heart, and adipose tissues. Following PHI, NPY, and SP infusions, plasma triiodothyronine and thyroxine levels were not different from values in saline-treated rats. This study demonstrates that PHI, like vasoactive intestinal peptide, is a potent thyroidal vasodilator at a dose that does not affect circulating thyroid hormone secretion.     

Non-Newtonian effects of blood flow on hemodynamics in distal vascular graft anastomoses

Non-Newtonian fluid flow in a stenosed coronary bypass is investigated numerically using the Carreau-Yasuda model for the shear thinning behavior of the blood. End-to-side coronary bypass anastomosis is considered in a simplified model geometry where the host coronary artery has a 75% severity stenosis. Different locations of the bypass graft to the stenosis and different flow rates in the graft and in the host artery are studied. Particular attention is given to the non-Newtonian effect of the blood on the primary and secondary flow patterns in the host coronary artery and the wall shear stress (WSS) distribution there. Interaction between the jet flow from the stenosed artery and the flow from the graft is simulated by solving the three-dimensional Navier-Stokes equation coupled with the non-Newtonian constitutive model. Results for the non-Newtonian flow, the Newtonian flow and the rescaled Newtonian flow are presented. Significant differences in axial velocity profiles, secondary flow streamlines and WSS between the non-Newtonian and Newtonian fluid flows are revealed. However, reasonable agreement between the non-Newtonian and the rescaled Newtonian flows is found. Results from this study support the view that the residual flow in a partially occluded coronary artery interacts with flow in the bypass graft and may have significant hemodynamic effects in the host vessel downstream of the graft. Non-Newtonian property of the blood alters the flow pattern and WSS distribution and is an important factor to be considered in simulating hemodynamic effects of blood flow in arterial bypass grafts.     

Geometrical focusing of cells in a microfluidic device: an approach to separate blood plasma

It is well known that when a suspension of cells flows in small vessels (arterioles or venules), there exists a cell-free layer of a few microns adjacent to the vascular walls. Using an in vitro model, we show experimentally that for a fixed flow rate a geometrical constriction in the flow can artificially enhance the cell-free layer. Also, we show that rapid variation of the geometry coupled to the deformability of the cells can dramatically modify their spatial distribution in the channel. The effects of the constriction geometry, flow rate, suspending fluid viscosity, cell concentration, and cell deformability are studied and the results are interpreted in terms of a model of the hydrodynamic drift of an ellipsoidal cell in a shear flow. We propose a microfluidic application of this focusing effect for separation of the red blood cells from the suspending plasma.     

The feasibility of utilizing a mathematical model in studying nonlinear transport processes in living systems

On the basis of proportionality between flow and its conjugated force a mathematical model for volume, current and osmotic flows was designed and a method for the experimental measurement of flows, the transbarrier (trans-segmental) potential and the rate of flow was devised. The results obtained experimentally as well as using the mathematical model indicate that the plant root is differentiated not only according to localization, but also according to the conductivity, permeability and selectivity of these tissues.     

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.