The influence of out-of-plane geometry on pulsatile flow within a distal end-to-side anastomosis

We present an experimental and computational investigation of time-varying flow in an idealized fully occluded 45 degrees distal end-to-side anastomosis. Two geometric configurations are assessed, one where the centerlines of host and bypass vessels lie within a plane, and one where the bypass vessel is deformed out of the plane of symmetry, respectively, termed planar and non-planar. Flow experiments were conducted by magnetic resonance imaging in rigid wall models and computations were performed using a high order spectral/hp algorithm. Results indicate a significant change in the spatial distribution of wall shear stress and a reduction of the time-averaged peak wall shear stress magnitude by 10% in the non-planar model as compared to the planar configuration. In the planar geometry the stagnation point follows a straight-line path along the host artery bed with a path length of 0.8 diameters. By contrast in the non-planar case the stagnation point oscillates about a center that is located off the symmetry plane intersection with the host artery bed wall, and follows a parabolic path with a 0.7 diameter longitudinal and 0.5 diameter transverse excursion. A definition of the oscillatory shear index (OSI) is introduced that varies between 0 and 0.5 and that accounts for a continuous range of wall shear stress vector angles. In both models, regions of elevated oscillatory shear were spatially associated with regions of separated or oscillating stagnation point flow. The mean oscillatory shear magnitude (considering sites where OSI>0.1) in the non-planar geometry was reduced by 22% as compared to the planar configuration. These changes in the dynamic behavior of the stagnation point and the oscillatory shear distribution introduced by out-of-plane graft curvature may influence the localization of vessel wall sites exposed to physiologically unfavorable flow conditions.     

Distributions of vascular pressure and resistance in the lung

The low-viscosity bolus method was used to determine the longitudinal distributions of vascular resistance and intravascular pressure with respect to cumulative vascular volume from the lobar artery to the lobar vein in isolated dog lung lobes near functional residual capacity under zone 3 conditions. We found that the resistance distribution had two modes, a larger one upstream and a smaller one downstream from a local minimum. Over the range of vascular pressures studied the total vascular resistance decreased and the vascular volume increased with increasing vascular pressure. However, the shape of the normalized resistance distribution was independent of vascular pressure. Comparisons of the resistance distributions with the distributions of arterial, capillary, and venous volumes suggest that the modes represent regions of relatively high resistance proximal and distal to the capillary bed. These results are consistent with the concept that within the lobar vascular bed the highest resistance per unit blood volume is in the smallest arteries and veins, as suggested by morphometric data from other sources.     

Stability analysis of a continuum-based constrained mixture model for vascular growth and remodeling

A stabilizing criterion is derived for equations governing vascular growth and remodeling. We start from the integral state equations of the continuum-based constrained mixture theory of vascular growth and remodeling and obtain a system of time-delayed differential equations describing vascular growth. By employing an exponential form of the constituent survival function, the delayed differential equations can be reduced to a nonlinear ODE system. We demonstrate the degeneracy of the linearized system about the homeostatic state, which is a fundamental cause of the neutral stability observations reported in prior studies. Due to this degeneracy, stability conclusions for the original nonlinear system cannot be directly inferred. To resolve this problem, a sub-system is constructed by recognizing a linear relation between two states. Subsequently, Lyapunov’s indirect method is used to connect stability properties between the linearized system and the original nonlinear system, to rigorously establish the neutral stability properties of the original system. In particular, this analysis leads to a stability criterion for vascular expansion in terms of growth and remodeling kinetic parameters, geometric quantities and material properties. Numerical simulations were conducted to evaluate the theoretical stability criterion under broader conditions, as well as study the influence of key parameters and physical factors on growth properties. The theoretical results are also compared with prior numerical and experimental findings in the literature.     

Kinetic measurements of gas exchange in the intact pulmonary microcirculation.

The kinetics of gas exchange are monitored in an isolated perfused lung preparation contained within a plethysmograph. The lungs are perfused with buffer, and there is no gas exchange until a 2.0-ml bolus of reactant is injected into the perfusion system. Subsequent gas exchange produces a pressure transient that is related to the corresponding volume of exchanged gas. The observed rate of volume change is the result of two separate processes: 1) the rate of gas exchange during transit through the capillary bed and 2) the distribution of vascular transit times between the point of injection and the capillary bed. The latter is assessed by a control injection containing a dissolved inert gas that is liberated in the alveoli as the bolus enters the capillary bed. Analysis of the experimental curves permits the separation of these two processes. A model of exchange kinetics indicates that this method has the capability of measuring kinetic events occurring during gas exchange in the microcirculation under physiological conditions.     

Numerical simulation of local blood flow in the carotid and cerebral arteries under altered gravity

A computational fluid dynamics (CFD) approach was presented to model the blood flows in the carotid bifurcation and the brain arteries under altered gravity. Physical models required for CFD simulation were introduced including a model for arterial wall motion due to fluid-wall interactions, a shear thinning fluid model of blood, a vascular bed model for outflow boundary conditions, and a model for autoregulation mechanism. The three-dimensional unsteady incompressible Navier-Stokes equations coupled with these models were solved iteratively using the pseudocompressibility method and dual time stepping. Gravity source terms were added to the Navier-Stokes equations to take the effect of gravity into account. For the treatment of complex geometry, a chimera overset grid technique was adopted to obtain connectivity between arterial branches. For code validation, computed results were compared with experimental data for both steady-state and time-dependent flows. This computational approach was then applied to blood flows through a realistic carotid bifurcation and two Circle of Willis models, one using an idealized geometry and the other using an anatomical data set. A three-dimensional Circle of Willis configuration was reconstructed from subject-specific magnetic resonance images using an image segmentation method. Through the numerical simulation of blood flow in two model problems, namely, the carotid bifurcation and the brain arteries, it was observed that the altered gravity has considerable effects on arterial contraction/dilatation and consequent changes in flow conditions.     

Mechanical properties of the coronary vasculature: indirect evaluation.

Information on the mechanical properties of the coronary vascular bed can be obtained indirectly by modelling the vascular system. This indirect approach, unlike 'in vitro' measurements, allows to take into account the vasomotor conditions of the circulatory district as well as the effect of the surrounding embedding tissue on the vascular performance. An experimental manoeuvre of sudden occlusion and subsequent release of the thoracic descendent aorta on 5 anaesthetized dogs with open pericardium induces a step-like variation in the coronary perfusion pressure and the occurrence of oscillations in the mean coronary flow. Such a behaviour can be described using a second-order model ('windkessel'+inductance, which takes into account blood inertia in the large vessels). The value of the coefficients entering the equations have been obtained with a 'best-fit' procedure (minimum of the chi-squared variable) on the haemodynamical data. Coefficient variations are in agreement with the direct estimation of the myocardial compliance and volume, measured by Ultrasound Echocardiographic imaging (4-chamber projection mode).     

A functional model of the rat kidney

Summary A mathematical model of the nephron was developed by writing a set of material balance equations for the flow of urea, salt and water along the length of the nephron. The geometric proportions have been elaborated in a foregoing study and are taken here as a basis, in particular the model configuration of the collecting duct system. The medullary interstitial solute concentration profiles are taken to increase linearly in outer and inner zone. The several transepithelial fluxes are driven by diffusion, osmosis, solvent drag and active transport. The development of osmotic gradient in the inner medulla is taken here to be caused by active secretion of salt into the descending limb of Henle's loop. The parameters in the flux equations for all parts of the nephron and the concentration values at the end of each tubular section are determined by collecting and averaging the values given in literature and by extrapolating the measurement data.The simulation of the model equations with these averaged parameters resulted in concentration profiles which at the ends of the several tubular sections were consistent with the values observed in experimental investigations.This work was supported by the Deutsche Forschungsgemeinschaft.     

Results and prospects for the study of the morphologic basis of microcirculation of the blood

The survey of the works, performed during the 11th five-year period in studying general biological regularities of microcirculation, demonstrates certain success in investigations developed in the following directions: functional geometry of the hemo-microcirculatory bed; elaboration of quantitative and qualitative analysis methods of the microcirculatory system elements; functional morphology of the vascular endothelium; experimental analysis of adaptive mechanisms of the microcirculatory bed; clinical-morphological investigations of microcirculation. Formation of structural-functional units, ensuring specialization of microcirculation in organs, forms the base of the functional geometry of the microcirculatory bed. This makes necessary conditions for compartmentalization of some micro-region in an organ and spatial distribution of various liquid media in dependence of certain topology of microvessels. The most perspective ways in development of morphological investigations, concerning the general biological regularities of microcirculation, are discussed.     

Hydrodynamic and Sediment Responses of Open Channels to Exposed Pipe Encasements

The effects of exposed pipe encasements on the local variation of hydrodynamic and sediment conditions in a river channel are examined. Laboratory experiments are performed to assess the response of water level, flow regime and bed deformation to several representative types of concrete encasements. The experimental conditions considered are: three types of exposed pipe encasements exposed on the bed, including trapezoidal shape, circular-arc shape and polygonal shape, and three sets of discharges, including annual discharge, once-in-3-year flood, and once-in-50-year flood. Our experiments show that: (1) the amount of backwater definitely depends on the encasement geometric shape and the background discharge; (2) smaller discharges generally tend to induce local scour of river bed downstream of the encasement, and the order of sensitivity of bed deformation to the encasement geometric shape is trapezoidal > circular-arc > polygonal; (3) comparatively speaking, the polygonal encasement may be considered as a suitable protective structure for pipelines across alluvial rivers, with relatively modest effects on the local hydrodynamic conditions and bed stabilization.     

Comparative analysis of the theoretical models of a hot dense plasma and the density functional theory

A general set of self-consistent field equations that describes the state of the whole ensemble of atoms and ions in a hot dense plasma is derived using the density functional theory. The set of equations is used to obtain equations of the Thomas-Fermi model, the Hartree-Fock-Slater model, the detail configuration account method, and the ion model. This approach makes it possible to identify the physical approximations underlying the theoretical models and to analyze their applicability ranges. Some of the results obtained from the Hartree-Fock-Slater model, the detail configuration account method, and the ion model are compared with the experimental data.     

A dynamic mathematical model for sequential leach bed anaerobic digestion of organic fraction of municipal solid waste

A mathematical model that describes the operation of a sequential leach bed process for anaerobic digestion of organic fraction of municipal solid waste (MSW) is developed and validated. This model assumes that ultimate mineralisation of the organic component of the waste occurs in three steps, namely solubilisation of particulate matter, fermentation to volatile organic acids (modelled as acetic acid) along with liberation of carbon dioxide and hydrogen, and methanogenesis from acetate and hydrogen. The model incorporates the ionic equilibrium equations arising due to dissolution of carbon dioxide, generation of alkalinity from breakdown of solids and dissociation of acetic acid. Rather than a charge balance, a mass balance on the hydronium and hydroxide ions is used to calculate pH. The flow of liquid through the bed is modelled as occurring through two zones—a permeable zone with high flushing rates and the other more stagnant. Some of the kinetic parameters for the biological processes were obtained from batch MSW digestion experiments. The parameters for flow model were obtained from residence time distribution studies conducted using tritium as a tracer. The model was validated using data from leach bed digestion experiments in which a leachate volume equal to 10% of the fresh waste bed volume was sequenced. The model was then tested, without altering any kinetic or flow parameters, by varying volume of leachate that is sequenced between the beds. Simulations for sequencing/recirculating 5 and 30% of the bed volume are presented and compared with experimental results.     

Comparison of the effects of prostaglandins F1alpha, F2alpha, F1beta, and F2beta on the canine pulmonary vascular bed.

The effects of four F series prostaglandins on the pulmonary vascular bed were compared under conditions of controlled pulmonary blood flow in the intact spontaneously breathing dog. PGF1alpha and PGF2alpha increased lobar arterial pressure whereas PGF1beta and PGF2beta had little if any effect when infused into the lobar artery. The increase in lobar arterial pressure in response to PGF1alpha and PGF2alpha was associated with a significant increase in lobar venous pressure but no change in left atrial pressure. These data indicate that PGF1alpha and PGF2alpha increase pulmonary vascular resistance by constricting lobar veins and vessels upstream to small veins, presumed to be small arteries. It is concluded that in the pulmonary vascular bed the configuration of the hydroxyl group at carbon 9 is an important determinant of pressor activity.     

Experimental measurement of particle size distribution and voidage in an expanded bed adsorption system

This paper presents an experimental analysis of matrix bead size distribution and voidage variations with axial height in an expanded bed adsorption system. Use of a specially constructed expanded bed with side ports has enabled sampling from within the expanded bed along the vertical axis. Particles removed from within the bed were measured for their size distributions. Residence time distribution studies were used to estimate bed voidage. Measurements of axial and radial particle size distributions and axial voidage distribution have been made at different flow rates. Particle size was found to be radially constant, indicating constant stratification in the column. The particle size was found to decrease with increasing axial height. Voidage increased with axial height from a settled bed value of 0.39 to approaching unity for high liquid velocities and increased at a constant axial position with increased flowrate. This information provides key insight into bed stability and data for the improved modeling of this important unit operation.     

Modified CelliGen-packed bed bioreactors for hybridoma cell cultures

This study describes two packed bed bioreactor configurations which were used to culture a mouse-mouse hybridoma cell line (ATCC HB-57) which produces an IgG₁ monoclonal antibody. The first configuration consists of a packed column which is continuously perfused by recirculating oxygenated media through the column. In the second configuration, the packed bed is contained within a stationary basket which is suspended in the vessel of a CelliGen^™ bioreactor. In this configuration, recirculation of the oxygenated media is provided by the CelliGen Cell Lift impeller. Both configurations are packed with disk carriers made from a non-woven polyester fabric. During the steady-state phase of continuous operation, a cell density of 10⁸ cells per cm³ of bed volume was obtained in both bioreactor configurations. The high levels of productivity (0.5 gram MAb per 1 of packed bed per day) obtained in these systems demonstrates that the culture conditions achieved in these packed bed bioreactors are excellent for the continuous propagation of hybridomas using media which contains low levels (1 %) of serum as well as serum-free media. These packed bed bioreactors allow good control of pH, dissolved oxygen and temperature. The media flows evenly over the cells and produces very low shear forces. These systems are easy to set up and operate for prolonged periods of time. The potential for scale-up using Fibra-cel carriers is enhanced due to the low pressure drop and low mass transfer resistance, which creates high void fraction approaching 90% in the packed bed.     

纺织基人造血管几何特征表征的实验研究

人造血管的壁厚和松弛内径是其主要的几何特征参数。本文中首先依据国际标准ISO 7198的要求设计了测试人造血管松弛内径的测试定规,并对人造血管样品进行了测试。然后对人造血管壁厚的测试方法进行了初步探讨。     

Pattern formation of leaf veins by the positive feedback regulation between auxin flow and auxin efflux carrier

The generation of vascular pattern formation in plants is an interesting process of pattern formation in organisms. It is well known that the plant hormone auxin is involved in plant vascular differentiation and that the PIN1 protein, an auxin efflux carrier, localizes to one side of the cell membrane. Several hypotheses have been proposed to explain the formation of leaf venation. One is the canalization hypothesis that is based on the assumption that a positive feedback regulation exists between the flow of a signal molecule and the capacity of its flow. Here, we attempted to integrate the canalization hypothesis and experimental data. We investigated models of the positive feedback regulation between the auxin flow and PIN1 localization. Model 1, with conserved PIN1 amount in each cell, can generate a branching pattern similar to that of plant leaf venation. We introduced the diffusible enhancer "e" into the model as unknown factor. The obtained patterns show a quasi-periodic distribution of auxin flow paths, when the model dynamics includes domain growth. In order to understand the early initiation process that generates an inhomogeneity from an almost homogeneous distribution, we introduced model 2, a simplified version of model 1. Model 2 can generate inhomogeneity with a parameter dependency similar to that of model 1. To analyse parameter condition required for pattern development, approximated equations are obtained from model 2. The isocline analysis of the equations without spatial structure shows that the inhomogeneous distribution occurs from an almost homogeneous distribution. This parameter condition for generating inhomogeneity is consistent with the results of models 1 and 2.     

Studies on protein adsorption in a vortex flow reactor

The performance of a vortex flow reactor (VFR) with suspended particles for protein adsorption was studied under varying operating conditions, and resin volume fractions. The VFR behaved as an expanded bed in the regimen of laminar vortices flow. Streamline DEAE was used for bovine serum albumin (BSA) adsorption. Expanded bed VFR experiments were performed with varying geometric aspect ratios (14.6, 28.6 and 40.0) and axial superficial velocity (100–300 cm h⁻¹) to investigate their influence on productivity and dynamic capacity. The results are compared with literature data on an expanded bed column (EBC). Adsorption breakthrough curves were fitting to a simple two-parameter model.     

Framework of Collagen Type I – Vasoactive Vessels Structuring Invariant Geometric Attractor in Cancer Tissues: Insight into Biological Magnetic Field

In a previous research, we have described and documented self-assembly of geometric triangular chiral hexagon crystal-like complex organizations (GTCHC) in human pathological tissues. This article documents and gathers insights into the magnetic field in cancer tissues and also how it generates an invariant functional geometric attractor constituted for collider partners in their entangled environment. The need to identify this hierarquic attractor was born out of the concern to understand how the vascular net of these complexes are organized, and to determine if the spiral vascular subpatterns observed adjacent to GTCHC complexes and their assembly are interrelational. The study focuses on cancer tissues and all the macroscopic and microscopic material in which GTCHC complexes are identified, which have been overlooked so far, and are rigorously revised. This revision follows the same parameters that were established in the initial phase of the investigation, but with a new item: the visualization and documentation of external dorsal serous vascular bed areas in spatial correlation with the localization of GTCHC complexes inside the tumors. Following the standard of the electro-optical collision model, we were able to reproduce and replicate collider patterns, that is, pairs of left and right hand spin-spiraled subpatterns, associated with the orientation of the spinning process that can be an expansion or contraction disposition of light particles. Agreement between this model and tumor data is surprisingly close; electromagnetic spiral patterns generated were identical at the spiral vascular arrangement in connection with GTCHC complexes in malignant tumors. These findings suggest that the framework of collagen type 1 – vasoactive vessels that structure geometric attractors in cancer tissues with invariant morphology sets generate collider partners in their magnetic domain with opposite biological behavior. If these principles are incorporated into nanomaterial, biomedical devices, and engineered tissues, new therapeutic strategies could be developed for cancer treatment.     

Vasoactive drugs and tumor blood flow

Different observations on the reactivity of tumor vessels to vasoactive drugs have suggested a decreased, a similar or an increased reactivity to vasoactive stimuli in the vascular bed of tumors as compared to normal tissues. No adrenergic innervation of newly developed tumor vessels has been found, while preexisting normal vessels incorporated during tumor growth may retain some innervation. In transplantable rat tumors, contractile cells, including smooth muscle cells, have been seen in tumor vessels. From recent experimental studies, it was concluded that the tumor's vascular bed is probably in a state of maximal dilatation and therefore sensitive to vasoconstriction, but less sensitive to pharmacological dilatation. These observations may correspond to regional tumor hypoxia and progressive development of tumor necrosis during tumor growth. The results of experimental tumor studies might question the reliability of diagnostic and therapeutic procedures in clinical oncology, which are based on differences in the reactivity to vasoactive drugs between normal and malignant tissues.     

Exploring geometric properties of gold nanoparticles using TEM images to explain their chaperone like activity for citrate synthase

Study on geometric properties of nanoparticles and their relation with biomolecular activities, especially protein is quite a new field to explore. This work was carried out towards this direction where images of gold nanoparticles obtained from transmission electron microscopy were processed to extract their size and area profile at different experimental conditions including and excluding a protein, citrate synthase. Since the images were ill-posed, texture of a context-window for each pixel was used as input to a back-propagation network architecture to obtain decision on its membership as nanoparticle. The segmented images were further analysed by k-means clustering to derive geometric properties of individual nanoparticles even from their assembled form. The extracted geometric information was found to be crucial to give a model featuring porous cage like configuration of nanoparticle assembly using which the chaperone like activity of gold nanoparticles can be explained.