Bed expansion and pressure drop studies in a liquid-solid inverse fluidised bed reactor

Hydrodynamic characteristics (bed expansion and pressure drop) of a different type of two phase fluidised bed reactor termed as liquid-solid inverse fluidised bed reactor in which low density particles are fluidised with downward flow of liquid are studied in the present investigation. Experiments were conducted using 6?mm diameter spherical particles of low density polyethylene (LDPE) and polypropylene (PP) with water and aqueous solutions of Carboxy methyl cellulose (CMC). It was found that the minimum fluidisation velocity, U _mf decreased with increase in CMC concentration and solid density. A dimensionless correlation was proposed for the prediction of bed height at fully fluidised conditions.     

Theory of non-Newtonian viscosity of red blood cell suspension: effect of red cell deformation

The effects of the deformation of red blood cells on non-Newtonian viscosity of a concentrated red cell suspension are investigated theoretically. To simplify the problem an elastic spherical shell filled with an incompressible Newtonian fluid is considered as a model of a normal red cell. The equation of the surface of the shell suspended in a steady simple shear flow is calculated on the assumption that the deformation from a spherical shape is very small. The relative viscosity of a concentrated suspension of such particles is obtained based on the "free surface cell" method proposed by Happel. It is shown that the relative viscosity decreases as the shear rate increases.     

Dynamics of a relativistic electron beam in the vicinity of a spherical injecting body in space plasma

The dynamics of a relativistic electron beam in the vicinity of an injector in the form of a spherical conducting body in a space plasma is considered. An equation describing the radial evolution of a steady electron beam with a self-similar density profile in the electric field of the injector is formulated. A method for calculating the radial evolution of a relativistic electron beam in the vicinity of an injector is developed. The method is based on the numerical integration of a set of ordinary differential equations for the beam radius and field potential in the space charge region under the relevant boundary conditions at the injector surface. Results are presented from numerical simulations of the radial dynamics of an electron beam in the vicinity of a spherical screen system for neutralizing the electric charge carried away by the beam. The numerical results show that the electric field of the injector hastens the beam expansion.     

The effect of shape on the margination dynamics of non-neutrally buoyant particles in two-dimensional shear flows

The margination dynamics of microparticles with different shapes has been analyzed within a laminar flow mimicking the hydrodynamic conditions in the microcirculation. Silica spherical particles, quasi-hemispherical and discoidal silicon particles have been perfused in a parallel plate flow chamber. The effect of the shape and density on their margination propensity has been investigated at different physiologically relevant shear rates S. Simple scaling laws have been derived showing that the number n of marginating particles scales as S(-0.63) for the spheres; S(-0.85) for discoidal and S(-1) for quasi-hemispherical particles, regardless of their density and size. Within the range considered for the shear rate, discoidal particles marginate in a larger number compared to quasi-hemispherical and spherical particles. These results may be of interest in drug delivery and bio-imaging applications, where particles are expected to drift towards and interact with the walls of the blood vessels.     

Design of bio-mimetic particles with enhanced vascular interaction

The majority of particle-based delivery systems for the ‘smart’ administration of therapeutic and imaging agents have a spherical shape, are made by polymeric or lipid materials, have a size in the order of few hundreds of nanometers and a negligibly small relative density to aqueous solutions. In the microcirculation and deep airways of the lungs, where the creeping flow assumption holds, such small spheres move by following the flow stream lines and are not affected by external volume force fields. A delivery system should be designed to drift across the stream lines and interact repeatedly with the vessel walls, so that vascular interaction could be enhanced. The numerical approach presented in [Gavze, E., Shapiro, M., 1997. Particles in a shear flow near a solid wall: effect of nonsphericity on forces and velocities. International Journal of Multiphase Flow 23, 155–182.] is, here, proposed as a tool to analyze the dynamics of arbitrarily shaped particles in a creeping flow, and has been extended to include the contribution of external force fields. As an example, ellipsoidal particles with aspect ratio 0.5 are considered. In the absence of external volume forces, a net lateral drift (margination) of the particles has been observed for Stokes number larger than unity (St>1); whereas, for smaller St, the particles oscillate with no net lateral motion. Under these conditions, margination is governed solely by particle inertia (geometry and particle-to-fluid density ratio). In the presence of volume forces, even for fairly small St, margination is observed but in a direction dictated by the external force field. It is concluded that a fine balance between size, shape and density can lead to EVI particles (particles with enhanced vascular interaction) that are able to sense endothelial cells for biological and biophysical abnormalities, mimicking circulating platelets and leukocytes.     

Effectiveness factors for substrate and product inhibition

The transformation technique of Na and Na (Math. Biosci., 6 , 25, 1970) is extended to convert boundary-value problems involving the steady-state diffusion equation for spherical immobilized enzyme particles exhibiting substrate and product inhibition to initial-value problems. This allows a study of the influence of external mass transfer resistances on the effectiveness factors. It also considerably reduces the number of calculations required to investigate the effect of changes in the kinetic parameters on the overall rate of reaction. The existence of multiple steady states for substrate inhibition kinetics in spherical catalyst particles is illustrated and a criterion for uniqueness of steady states is developed. Effectiveness factors for competitive and noncompetitive product inhibition increase with increasing value of the Sherwood number for the substrate and increasing value of the ratio of substrate to product effective diffusivities within the particle.     

Dynamic Finite Size Effects in Spiking Neural Networks

We investigate the dynamics of a deterministic finite-sized network of synaptically coupled spiking neurons and present a formalism for computing the network statistics in a perturbative expansion. The small parameter for the expansion is the inverse number of neurons in the network. The network dynamics are fully characterized by a neuron population density that obeys a conservation law analogous to the Klimontovich equation in the kinetic theory of plasmas. The Klimontovich equation does not possess well-behaved solutions but can be recast in terms of a coupled system of well-behaved moment equations, known as a moment hierarchy. The moment hierarchy is impossible to solve but in the mean field limit of an infinite number of neurons, it reduces to a single well-behaved conservation law for the mean neuron density. For a large but finite system, the moment hierarchy can be truncated perturbatively with the inverse system size as a small parameter but the resulting set of reduced moment equations that are still very difficult to solve. However, the entire moment hierarchy can also be re-expressed in terms of a functional probability distribution of the neuron density. The moments can then be computed perturbatively using methods from statistical field theory. Here we derive the complete mean field theory and the lowest order second moment corrections for physiologically relevant quantities. Although we focus on finite-size corrections, our method can be used to compute perturbative expansions in any parameter.     

Simple pulsatile flow in an artery with a constriction

A smooth isolated, axisymmetric occlusion in a straight vascular tube is a tractable problem for pulsatile flow calculations via finite-difference approximations to the Navier-Stokes equation. Steady flow depends on the Reynolds number and two geometric parameters which describe the stenosis. The mere addition of a simple harmonic to the mean flow adds two more parameters. One is the reduced frequency, or Strokes number, and the other epsilon, the ratio of unsteady to steady flux. After describing steady stenosis flow examples, the dynamic patterns of pulsatile flow are illustrated indicating the inadequacy of basing hypotheses of atherosclerosis on mean (steady) flow.     

Approximation and visualization of large-scale motion of protein surfaces

We present a method for the approximation and real-time visualization of large-scale motion of protein surfaces. A molecular surface is represented by an expansion of spherical harmonic functions, and the motion of protein atoms around their equilibrium positions is computed by normal mode analysis. The motion of the surface is approximated by projecting the normal mode vectors of the solvent-accessible atoms to the spherical harmonic representation of the molecular surface. These surface motion vectors are represented by a separated spherical harmonic expansion. Representing the surface geometry and the surface motion vectors by spherical harmonic expansions allows variable-resolution analysis and real-time display of the large-scale surface motion. This technique has been applied to interactive visualization, interactive surface manipulation, and animation.     

Spherical reconstruction: a method for structure determination of membrane proteins from cryo-EM images

We propose a new method for single-particle reconstruction, which should be generally applicable to structure determination for membrane proteins. After reconstitution into a small spherical vesicle, a membrane protein takes a particular orientation relative to the membrane normal, and its position in the projected image of the vesicle directly defines two of its three Euler angles of orientation. The spherical constraint imposed by the vesicle effectively reduces the dimensionality of the alignment search from 5 to 3 and simplifies the detection of the particle. Projection images of particles in vesicles collectively take all possible orientations and therefore cover the whole Fourier space. Analysis of images of vesicles in ice showed that the vesicle density is well described by a simple model for membrane electron scattering density. In fitting this model we found that osmotically swollen vesicles remain nearly spherical through the freezing process. These results satisfy the basic experimental requirements for spherical reconstruction. A computer simulation of particles in vesicles showed that this method provides good estimates of the two Euler angles and thus may improve single-particle reconstruction and extend it to smaller membrane proteins.     

Three-dimensional focusing of red blood cells in microchannel flows for bio-sensing applications

Three-dimensional (3D) focusing of particles in microchannels has been a long-standing issue in the design of biochemical/biomedical microdevices. Current microdevices for 3D cell or bioparticle focusing involve complex channel geometries in view of their fabrication because they require multiple layers and/or sheath flows. This paper proposes a simple method for 3D focusing of red blood cells (RBCs) in a single circular microcapillary, without any sheath flows, which is inspired from the fluid dynamics phenomenon in that a spherical particle lagging behind a Poiseuille flow migrates toward and along the channel axis. More explicitly, electrophoresis of RBCs superimposed on the pressure-driven flow is utilized to generate an RBC migration mode analogous to this phenomenon. A particle-tracking scheme with a sub-pixel resolution is implemented to spatially position red blood cells flowing through the channel, so that a probability density function (PDF) is constructed to evaluate the tightness of the cell focusing. Above a specific strength of the electric field, approximately 90% of the sheep RBCs laden in the flow are tightly focused within a beam diameter that is three times the cell dimension. Particle shape effect on the focusing is discussed by making comparisons between the RBCs and the spherical particles. The lateral migration velocity, predicted by an existing theoretical model, is in good agreement with the present experimental data. It is noteworthy that 3D focusing of non-spherical particles, such as RBCs, has been achieved in a circular microchannel, which is a significant improvement over previous focusing methodologies.     

Comparison of hard-cylinder and screened coulomb interactions in the modeling of supercoiled DNAs

A 1000 base pair (bp) model supercoiled DNA is simulated using spherical screened Coulomb interactions between subunits on one hand and equivalent hard-cylinder interactions on the other. The amplitudes, or effective charges, of the spherical screened Coulomb electrostatic potentials are chosen so that the electrostatic potential surrounding the middle of a linear array of 2001 subunits (31.8 Å diameter) closely matches the solution of the nonlinear Poisson-Boltzmann equation for a cylinder with 12 Å radius and the full linear charge density of DNA at all distances beyond the 24 Å hard-core diameter. This superposition of spherical screened Coulomb potentials is practically identical to the particular solution of the cylindrical linearized Poisson-Boltzmann equation that matches the solution of the nonlinear Poisson-Boltzmann equation at large distances. The interaction energy between subunits is reckoned from the effective charges according to the standard DLVO expression. The equivalent hard-cylinder diameter is chosen following Stigter's protocol for matching second virial coefficients, but for the full linear charge density of DNA. The electrostatic persistence length of the model with screened Coulomb interactions is extremely sensitive to the (arbitrarily) chosen subunit length at the higher salt concentrations. The persistence length of the hard-cylinder model is adjusted to match that of the screened Coulomb model for each ionic condition. Simulations for a superhelix density σ = -0.05 using a spherical screened Coulomb interaction plus a 24 Å hard-cylinder core (SCPHC) potential indicate that the radius of gyration of this 1000 bp DNA actually undergoes a slight increase as the NaCl concentration is raised from 0.01 to 1.0M. Thus, merely softening the potential from hard-cylinder to screened Coulomb form does not produce a large decrease in radius of gyration with increasing NaCl concentration for DNAs of this size. Radii of gyration, static structure factors, and diffusion coefficients obtained using the equivalent hard-cylinder (EHC) potential agree well with those obtained using the SCPHC potential in 1.0M NaCl, but in 0.1M NaCl the agreement is not as good, and in 0.01M NaCl the agreement is definitely unsatisfactory. These conclusions differ in significant respects from those obtained in previous studies. © 1997 John Wiley & Sons, Inc. Biopoly 42: 455–470, 1997     

A Jump-Growth Model for Predator–Prey Dynamics: Derivation and Application to Marine Ecosystems

This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we call the deterministic jump-growth equation, and a linear Fokker–Planck equation for the stochastic fluctuations. The McKendrick–von Foerster equation, used in previous studies, is shown to be a first-order approximation, appropriate in equilibrium systems where predators are much larger than their prey. The model has a power-law steady state consistent with the approximate constancy of mass density in logarithmic intervals of body mass often observed in marine ecosystems. The behaviours of the stochastic process, the deterministic jump-growth equation, and the McKendrick–von Foerster equation are compared using numerical methods. The numerical analysis shows two classes of attractors: steady states and travelling waves.     

Structural characterization (shape and dimensions) and stability of polysaccharide/lipid nanoparticles

The structure of a new supramolecular drug carrier (named Biovectors—BV) was studied using light scattering and scanning electronic microscopy techniques. This system consists of a polysaccharide core of chemically cross-linked maltodextrins to which phospholipids (and, in some cases, cholesterol) are added. Both polysaccharide cores and BV cross-linked with phosphate (negatively charged) and epichlorhydrin (no net charge) are spherical particles. The increase in the ionic strength of the medium increases the density of the charged polysaccharide cores. The lipid strongly interacts with neutral and negatively charged cores, decreasing both intra- and interparticle interactions. The results (mainly, ρ = R_g/R_h < 0.775 in some cases) suggest that BV are gel-like particles of variable density, referred to as microgels or soft spheres. Neutral polysaccharides have a strong tendency to self-aggregate. This self-aggregation of polysaccharide neutral cores is prevented by the addition of lipid or dimethylsulfoxide. © 1997 John Wiley & Sons, Inc. Biopoly 41: 511–520, 1997     

Microstructural Modeling of Collagen Network Mechanics and Interactions with the Proteoglycan Gel in Articular Cartilage

Cartilage matrix mechanical function is largely determined by interactions between the collagen fibrillar network and the proteoglycan gel. Although the molecular physics of these matrix constituents have been characterized and modern imaging methods are capable of localized measurement of molecular densities and orientation distributions, theoretical tools for using this information for prediction of cartilage mechanical behavior are lacking. We introduce a means to model collagen network contributions to cartilage mechanics based upon accessible microstructural information (fibril density and orientation distributions) and which self-consistently follows changes in microstructural geometry with matrix deformations. The interplay between the molecular physics of the collagen network and the proteoglycan gel is scaled up to determine matrix material properties, with features such as collagen fibril pre-stress in free-swelling cartilage emerging naturally and without introduction of ad hoc parameters. Methods are developed for theoretical treatment of the collagen network as a continuum-like distribution of fibrils, such that mechanical analysis of the network may be simplified by consideration of the spherical harmonic components of functions of the fibril orientation, strain, and stress distributions. Expressions for the collagen network contributions to matrix stress and stiffness tensors are derived, illustrating that only spherical harmonic components of orders 0 and 2 contribute to the stress, while orders 0, 2, and 4 contribute to the stiffness. Depth- and compression-dependent equilibrium mechanical properties of cartilage matrix are modeled, and advantages of the approach are illustrated by exploration of orientation and strain distributions of collagen fibrils in compressed cartilage. Results highlight collagen-proteoglycan interactions, especially for very small physiological strains where experimental data are relatively sparse. These methods for determining matrix mechanical properties from measurable quantities at the microscale (composition, structure, and molecular physics) may be useful for investigating cartilage structure-function relationships relevant to load-bearing, injury, and repair.     

Nonequilibrium Distributions and Hydrodynamic Coupling Distort the Measurement of Nanoscale Forces near Interfaces

We calculate the displacement of a single spherical particle from the minimum of a harmonic well positioned near a plane wall and immersed in a uniform flow. A failure to account for the fluctuations in particle position orthogonal to the plane (leading to fluctuations in hydrodynamic drag) results in large discrepancies, with the naive displacement calculated by assuming no fluctuations in the balance of forces. The chief criterion for neglecting such fluctuations is that the stiffness of the harmonic potential exceeds the thermal stresses on the particle by at least two orders of magnitude. For micrometer-diameter particles typically employed in force spectroscopy of DNA, macromolecules, and molecular motors, this can lead to errors of up to 100% in the measured properties. The Supporting Material to the article provides an implementation of this model intended to fit experimental measurements for the stiffness of the harmonic potential constraining the particle.     

A Population Density Approach That Facilitates Large-Scale Modeling of Neural Networks: Analysis and an Application to Orientation Tuning

We explore a computationally efficient method of simulating realistic networks of neurons introduced by Knight, Manin, and Sirovich (1996) in which integrate-and-fire neurons are grouped into large populations of similar neurons. For each population, we form a probability density that represents the distribution of neurons over all possible states. The populations are coupled via stochastic synapses in which the conductance of a neuron is modulated according to the firing rates of its presynaptic populations. The evolution equation for each of these probability densities is a partial differential-integral equation, which we solve numerically. Results obtained for several example networks are tested against conventional computations for groups of individual neurons.We apply this approach to modeling orientation tuning in the visual cortex. Our population density model is based on the recurrent feedback model of a hypercolumn in cat visual cortex of Somers et al. (1995). We simulate the response to oriented flashed bars. As in the Somers model, a weak orientation bias provided by feed-forward lateral geniculate input is transformed by intracortical circuitry into sharper orientation tuning that is independent of stimulus contrast.The population density approach appears to be a viable method for simulating large neural networks. Its computational efficiency overcomes some of the restrictions imposed by computation time in individual neuron simulations, allowing one to build more complex networks and to explore parameter space more easily. The method produces smooth rate functions with one pass of the stimulus and does not require signal averaging. At the same time, this model captures the dynamics of single-neuron activity that are missed in simple firing-rate models.     

On multipole representation of current generators

In Yeh, Martinek, and de Beaumont (Bull. Math. Biophysics,20, 203–216, 1958), multipole representations of current generators in a volume conductor are used, based upon the Taylor series expansion of the potential function. In Yeh, (Bull. Math. Biophysics,23, 263–276, 1961) multipole representations of current generators in a spherical volume conductor are used, based upon the spherical harmonic expansion. This paper correlates these two systems of multipole representations so that formulations in terms of one system of the representations may be readily transformed into formulations in terms of the other system. Since the Taylor series representation is more graphic, whereas the spherical harmonic representation is more compact, such a transformation between these two systems of formulations can serve useful purposes in the application of the theory of electrocardiography. This investigation was supported by the National Heart Institute under Research Grant H-2263 (c-4).     

In vivo studies of HDL assembly and metabolism using adenovirus-mediated transfer of ApoA-I mutants in ApoA-I-deficient mice.

We have used adenovirus-mediated gene transfer in apoA-I-deficient (A-I-/-) mice to probe the in vivo assembly and metabolism of HDL using apoA-I variants, focusing primarily on the role of the C-terminal 32 amino acids (helices 9-10). Lipid, lipoprotein, and apoA-I analyses showed that plasma levels of apoA-I and HDL of the mutants were 40-88% lower than that of wild type (WT) human apoA-I despite comparable levels of expression in the liver. WT apoA-I and mutant 1 (P165A, E172A) formed spherical particles with the size and density of HDL2 and HDL3. Mutant 2 (E234A, E235A, K238A, K239A) generated spherical particles with density between HDL2 and HDL3. Mutant 3 (L211V, L214V, L218V, L219V) and mutant 4 (L222K, F225K, F229K), which have substitutions of hydrophobic residues in the C-terminus, generated discoidal HDL particles indicating a defect in their conversion to mature spherical HDL. Significant amounts of mutant 4 and mutant 5 (truncated at residue 219) were found in the lipid poor fractions after ultracentrifugation of the plasma (18 and 35%, respectively, of total apoA-I). These findings suggest that hydrophobic residues in and/or between helices 9 and 10 are important for the maturation of HDL in vivo.