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.     

Computation of steady three-dimensional flow in a model of the basilar artery

The flow in the basilar artery arises from the merging of the flows from the two vertebral arteries. To study the flow phenomena in the basilar artery, computations have been performed using a finite element (FE) method. We consider steady flow in a geometrically symmetric confluence. For simplicity, channels with a rectangular cross-section have been used. Both symmetric and asymmetric flow cases have been considered. The results show that for the Reynolds number of interest the flow downstream of the junction is highly three-dimensional, and that the flow at the end of the basilar artery, where it splits again, will not be fully developed. The computed phenomena have been confirmed by laser Doppler velocity measurements.     

Heat balance of the human body: influence of variations of locally distributed parameters

Human body temperature control is characterized by a local dependence of system variables and parameters. Essential properties regarding inhomogeneity of the passive system have been investigated using mathematical methods. The general diffusion-equation has been solved using implicit finite difference methods with nonlinear boundary conditions. In order to allow comparison with experimental results, a simple ideal controller has been defined. On the basis of an inhomogeneous cylinder model with four concentric layers, influences of variations due to differences between tissues and individuals or measurements of parameters such as basal metabolism and conductivity have been studied. Stationary temperature profiles calculated for homogeneous and inhomogeneous conditions have been compared. Finally, the influence of blood flow has been discussed, as well as the stationary behaviour of profiles due to blood flow and blood flow control. The change of sign of curvature of temperature profile is possible only if blood flow mechanisms and the local distribution of metabolism are taken into account.     

A hydrodynamical study of the flow in renal tubules

The hydrodynamical problem of flow in proximal renal tubule is investigated by considering axisymmetric flow of a viscous, incompressible fluid through a long narrow tube of varying cross-section with reabsorption at the wall. Two cases for reabsorption have been studied (i) when the bulk flow,Q, decays exponentially with the axial distancex, and (ii) whenQ is an arbitrary function ofx such thatQ-Q ₀ can be expressed as a Fourier integral (whereQ ₀ is the flux atx=0). The analytic expressions for flow variables have been obtained by applying perturbation method in terms of wall parameter ε. The effects of ε on pressure drop across the tube, radial velocity and wall shear have been studied in the case of exponentially decaying bulk flow and it has been found that the results are in agreement with the existing ones for the renal tubules.     

Effect of flow pulsatility on modeling the hemodynamics in the total cavopulmonary connection

Total cavopulmonary connection is the result of a series of palliative surgical repairs performed on patients with single ventricle heart defects. The resulting anatomy has complex and unsteady hemodynamics characterized by flow mixing and flow separation. Although varying degrees of flow pulsatility have been observed in vivo, non-pulsatile (time-averaged) boundary conditions have traditionally been assumed in hemodynamic modeling, and only recently have pulsatile conditions been incorporated without completely characterizing their effect or importance. In this study, 3D numerical simulations with both pulsatile and non-pulsatile boundary conditions were performed for 24 patients with different anatomies and flow boundary conditions from Georgia Tech database. Flow structures, energy dissipation rates and pressure drops were compared under rest and simulated exercise conditions. It was found that flow pulsatility is the primary factor in determining the appropriate choice of boundary conditions, whereas the anatomic configuration and cardiac output had secondary effects. Results show that the hemodynamics can be strongly influenced by the presence of pulsatile flow. However, there was a minimum pulsatility threshold, identified by defining a weighted pulsatility index (wPI), above which the influence was significant. It was shown that when wPI<30%, the relative error in hemodynamic predictions using time-averaged boundary conditions was less than 10% compared to pulsatile simulations. In addition, when wPI<50, the relative error was less than 20%. A correlation was introduced to relate wPI to the relative error in predicting the flow metrics with non-pulsatile flow conditions.     

Effects of peripheral layer viscosity on blood flow through the artery with mild stenosis

The effects of peripheral layer viscosity on physiological characteristics of blood flow through the artery with mild stenosis have been studied. It has been shown that the resistance to flow and the wall shear decrease as the peripheral layer viscosity decreases.     

A study on the non-linear flow of blood through arteries

The pulsatile flow of blood through arteries is investigated in this paper by treating the blood vessel as a thin-walled anisotropic, non-linearly viscoelastic, incompressible circular cylindrical shell; nonlinearities of the flow of blood are also paid due consideration. The displacement components of the vessel wall are obtained from the equations of equilibrium which have been linearized by employing the principle of superimposition of a small deformation on a state of known finite deformation. The influence of the wall deformation on the flow properties of blood, has been accounted for by considering suitably formulated continuity conditions. A finitedifference scheme is employed for solving the flow equations together with the boundary and initial conditions by using the locally measured values of pressure and pressure gradient. Numerical results obtained for the velocity profile of blood flowing in a canine middle descending thoracic aorta have been presented through figures.     

Direct visualization of hemolymph flow in the heart of a grasshopper (Schistocerca americana)

Background  

Hemolymph flow patterns in opaque insects have never been directly visualized due to the lack of an appropriate imaging technique. The required spatial and temporal resolutions, together with the lack of contrast between the hemolymph and the surrounding soft tissue, are major challenges. Previously, indirect techniques have been used to infer insect heart motion and hemolymph flow, but such methods fail to reveal fine-scale kinematics of heartbeat and details of intra-heart flow patterns.     

Asymmetric introgression between the M and S forms of the malaria vector, Anopheles gambiae, maintains divergence despite extensive hybridization

The suggestion that genetic divergence can arise and/or be maintained in the face of gene flow has been contentious since first proposed. This controversy and a rarity of good examples have limited our understanding of this process. Partially reproductively isolated taxa have been highlighted as offering unique opportunities for identifying the mechanisms underlying divergence with gene flow. The African malaria vector, Anopheles gambiae s.s., is widely regarded as consisting of two sympatric forms, thought by many to represent incipient species, the M and S molecular forms. However, there has been much debate about the extent of reproductive isolation between M and S, with one view positing that divergence may have arisen and is being maintained in the presence of gene flow, and the other proposing a more advanced speciation process with little realized gene flow because of low hybrid fitness. These hypotheses have been difficult to address because hybrids are typically rare (<1%). Here, we assess samples from an area of high hybridization and demonstrate that hybrids are fit and responsible for extensive introgression. Nonetheless, we show that strong divergent selection at a subset of loci combined with highly asymmetric introgression has enabled M and S to remain genetically differentiated despite extensive gene flow. We propose that the extent of reproductive isolation between M and S varies across West Africa resulting in a 'geographic mosaic of reproductive isolation'; a finding which adds further complexity to our understanding of divergence in this taxon and which has considerable implications for transgenic control strategies.     

A mathematical model of the flow in the circle of Willis

A mathematical model of the flow in the circle of Willis has been designed and the effects of (a) the large anatomical variation of the communicating arteries and (b) physiological changes of the resistances of the vertebral arteries have been studied. The influence of the posterior perforating arteries on the flow in the posterior communicating arteries has been investigated as well, with special attention being paid to the possible occurrence of a 'dead point'. In the model, the influence of diameters of the communicating arteries on the flow in the afferent vessels and the segments of the circle turns out to be considerable, especially in the range of the anatomical variation of the diameters. Within this range flow reductions due to an increased resistance of the vertebral artery will be compensated for by the system. Assuming that the values and ratios of the peripheral resistances are within the physiological range, a dead point is not to be expected in the flow in the posterior communicating arteries.     

Numerical 3D analysis of oscillatory flow in the time-varying laryngeal channel

Three-dimensional flow through an anatomically representative model of the human larynx has been numerically simulated. This model includes the vestibular folds, the vocal cords and the glottic and subglottic areas. Pseudo-time-varying glottic aperture and flow conditions have been considered during quiet breathing, with a peak volume flow rate of 0.75 l/s and a frequency of 0.25 Hz. Because of the severe constriction, jet-like configurations have been observed. Minor differences have been outlined between the inspiration and expiration profiles. Simulations demonstrated the presence of a backflow region which may extend to 60 mm from the glottis at peak inspiration and occupy 20% of the tracheal cross section. Because of its rolling, this backflow region appears in the sagittal plane close to the anterior wall, only one diameter from the laryngeal constriction and extends over about 40 mm. The evolution of the streamwise velocity contours and of the corresponding secondary vector plots at six critical stations, including the glottic section, has also been described. A double pair of counter-rotating vortices develops shortly downstream/upstream from the orifice respectively at inspiration/expiration and merges near the frontal plane about 25 mm from the glottis. The effect of the incoming flow has been evaluated by including the pharyngeal channel; no major difference has been observed in the computed flow patterns.     

The study of cerebral venous blood flow disturbance peculiarity in the norm and under the extravasal compression of brachiocephalic veins with the use of magnetic resonance venography and ultrasound duplex scanning

The MR-venography of the veins and brain venous sinuses, brachiocephalic veins an internal jugular veins duplex scanning have been performed in order to study the distinctions of cerebral venous hemodynamics of healthy people and the patients with venous encephalopathy caused by the extravasal compression of the brachiocephalic veins at the neck level and the superior sections of mediastinum. It has been revealed that the blood flow reducing in transverse brain sinuses occurs not only in the case of outflow disorder in the distal sections of the venous system, but also in norm. This reducing depends on anatomic constitution of confluens sinuum and the venous angle type of brachiocephalic veins. The three venous angle types of brachiocephalic veins have been distinguished: y-type, mu-type and Y-type. It has been registered that in case of the mu-type angle the blood flow can be reduced in norm due to peripheral resistance increase at the physiological bends of nearly a right angle type. The distinctions of hemodynamics in case of venous obstruction in contrast to arterial obstruction have been described. It has been registered that in case of outflow trouble in one of the internal jugular veins the speed and the volume of the blood flow in it are progressively reduced depending on the duration and the manifestation of compression. All this results in narrowing of the vein diameter from the affected side, and in compensatory distention of the diameter and increase of blood flow volume in the contralateral internal jugular vein, vertebral and external jugular veins, in succession.     

Properties and principles of mycelial flow: experiments with a tube rheometer

The flow behavior of a penicillin mash has been investigated with a tube rheometer and compared with rotational viscometer observations. In the low-shear regions plug flow and breakdown of the plug have been studied. For turbulent flow turbulence damping was demonstrated. The Theological development during the fermentation was followed. At low deformation rates the pressure drop increased during the fermentation. In turbulent regions the opposite tendency was observed. The possible underlying flow mechanisms are discussed, and the influence of a number of physical parameters have been investigated.     

Estimation of age-related changes in the regulation of peripheral blood flow in humans

The age-dependent features in the state of skin microvascular bed has been studied with laser Doppler flowmetry in healthy volunteers of different age groups. To reveal the reaction of skin blood flow in response to short-term ischemia, the occlusive test has been carried out. To estimate the contribution of rhythmic components to blood flow signal, continuous wavelet-transform spectral analysis was used. Age-dependent increase of pulse-wave amplitude and decrease of respiratory wave amplitude reflecting age-dependent changes in functioning of arteriolar and venular links of microvascular bed have been observed at rest. In response to short-term ischemia the age-dependent reduction of reserve resources has been revealed in functioning of arteriolar link of microvascular bed. The reduction of activity of myogenic, neurogenic and endothelial regulation systems have been shown at rest in ageing.     

The intestinal fatty acid binding protein: the role of turns in fast and slow folding processes

The intestinal fatty acid binding protein is one of a family of proteins that are composed of two beta-sheets surrounding a large interior cavity into which the ligand binds. Glycine residues occur in many of the turns between adjacent antiparallel beta-strands. In previous work, the effect of replacing these glycine residues with valine has been examined with stopped flow instrumentation using intrinsic tryptophan fluorescence spectroscopy [Kim and Frieden (1998) Protein Sci. 7, 1821-1828]. To resolve the burst phase missing in the stopped flow measurements, these valine mutants have been reexamined with sub-millisecond continuous flow instrumentation. Some of the glycine residues have also been replaced with proline, and the folding reactions of these proline mutants have been compared with those of their valine counterparts. In all cases, the stability of the protein is decreased, but some turns appear to be more critical for final structure stabilization than others. Surprisingly, the rate constants observed for all the mutants measured by sub-millisecond continuous flow methods are quite similar (1400-3000 s(-1)), and in all the mutants, there is a shift in the fluorescence emission maximum from that of the unfolded protein to lower wavelengths, suggesting some collapse of the unfolded state within 200 micros. In contrast to the rate constants observed for the initial folding events measured by the sub-millisecond continuous flow method, the rate constants for the slower phase observed in the stopped flow instrument vary widely for the different mutants. The latter step appears to be related to side chain stabilization rather than secondary structure formation. It is also shown that the ligand binds tightly only to the native protein and not to any intermediate forms.     

A Hybrid Analytical/Numerical Model for the Characterization of Preferential Flow Path with Non-Darcy Flow

Due to the long-term fluid-solid interactions in waterflooding, the tremendous variation of oil reservoir formation parameters will lead to the widespread evolution of preferential flow paths, thereby preventing the further enhancement of recovery efficiency because of unstable fingering and premature breakthrough. To improve oil recovery, the characterization of preferential flow paths is essential and imperative. In efforts that have been previously documented, fluid flow characteristics within preferential paths are assumed to obey Darcy''s equation. However, the occurrence of non-Darcy flow behavior has been increasingly suggested. To examine this conjecture, the Forchheimer number with the inertial coefficient estimated from different empirical formulas is applied as the criterion. Considering a 10% non-Darcy effect, the fluid flow in a preferential path may do experience non-Darcy behavior. With the objective of characterizing the preferential path with non-Darcy flow, a hybrid analytical/numerical model has been developed to investigate the pressure transient response, which dynamically couples a numerical model describing the non-Darcy effect of a preferential flow path with an analytical reservoir model. The characteristics of the pressure transient behavior and the sensitivities of corresponding parameters have also been discussed. In addition, an interpretation approach for pressure transient testing is also proposed, in which the Gravitational Search Algorithm is employed as a non-linear regression technology to match measured pressure with this hybrid model. Examples of applications from different oilfields are also presented to illustrate this method. This cost-effective approach provides more accurate characterization of a preferential flow path with non-Darcy flow, which will lay a solid foundation for the design and operation of conformance control treatments, as well as several other Enhanced Oil Recovery projects.     

Modeling of arterial stenosis and its applications to blood diseases

Blood flow in a stenosed tube has been modeled in the present studies. Blood flow is assumed to be represented by a couple stress fluid. Flow parameters such as velocity, resistance to flow, and shear stress distribution have been computed for different suspension concentrations (haematocrit), and for the blood diseases; polycythemia, plasma cell dyscrasias, and for Hb SS (sickle cell). The results have been compared with the case of normal blood and for other theoretical models. The importance of size effects in blood flow studies has been highlighted.     

Numerical simulations of the blood flow through vertebral arteries

Vertebral arteries are two arteries whose structure and location in human body result in development of special flow conditions. For some of the arteries, one can observe a significant difference between flow rates in the left and the right arteries during ultrasonography diagnosis. Usually the reason of such a difference was connected with pathology of the artery in which a smaller flow rate was detected. Simulations of the flow through the selected type of the vertebral artery geometry for twenty five cases of artery diameters have been carried out. The main aim of the presented experiment was to visualize the flow in the region of vertebral arteries junction in the origin of the basilar artery. It is extremely difficult to examine this part of human circulation system, thus numerical experiments may be helpful in understanding the phenomena occurring when two relatively large arteries join together to form one vessel. The obtained results have shown that an individual configuration and diameters of particular arteries can exert an influence on the flow in them and affect a significant difference between flow rates for vertebral arteries. It has been assumed in the investigations that modelled arteries were absolutely normal, without any pathology. In the numerical experiment, the non-Newtonian model of blood was employed.     

Nonocclusive Hemorrhagic Necrosis of the Intestine

Hemorrhagic intestinal necrosis occurs without demonstrable mechanical obstruction of the mesenteric vascular supply. The etiologic factors include (1) congestive heart failure, (2) cardiac arrhythmia, (3) dehydration, and (4) digitalis therapy with or without digitalis toxicity. All of these factors have been shown to result in a decrease in splanchnic blood flow. The outcome of this disease has invariably been fatal. Early recognition and nonoperative management directed toward increasing splanchnic blood flow are the most significant factors in the survival of patients.     

Preface: Blasts from the past and back to the future

The invasion of dreissenid mussels into inland waters of the Northern Hemisphere has received considerable attention and, both zebra mussels and quagga mussels continue to spread westward. Despite studies aimed at understanding the biology of dreissenid mussels, relatively few studies have focused on water velocity and other hydrodynamic characteristics of water flow. The objective of this review was to identify, through a search of online databases, the papers that have been made available that directly have assessed the influence of hydrodynamic characteristics of water flow on dreissenid mussel biology. Using Thompson Reuters Web of Science, Google Scholar, and other resources, 46 papers were identified. These papers detailed that metrics associated with hydrodynamics of water flow, including current, wave action, velocity, flow rate, and discharge, can influence the biology of dreissenid mussels (primarily zebra mussel, which were studied far more than quagga mussel). Hydrodynamic characteristics influenced external fertilization, larval development and settlement, juvenile recruitment and attachment, and suspension feeding, growth and abundance of adults. In most cases, the impact of higher flow rates were locally negative and may present an opportunity for applications of water flow to control the spread or establishment of dreissenid mussels. Several knowledge gaps have been identified.