Failure analysis of a beam-column under oblique-eccentric loading: potential failure surfaces for cervical spine trauma.

For a cantilever beam-column with one end built-in and the free end subjected to an oblique-eccentric arbitrary concentrated force, general formulas to produce failure were derived. The original generalized uniform solution to the oblique-eccentric buckling problem was obtained. The Secant formula and Euler's formula were proved to be specific cases in this general solution. The load ratio, F/aE, was derived as functions of the force acting direction, alpha, the slenderness ratio, L/r, as well as the eccentricity ratio, ec/r2. Material and buckling failures aspects were combined in a uniform structural failure analysis. Safe regions for the load ratio, F/aE, were visualized in the three-dimensional (F/aE)-alpha-(L/r) space with the eccentricity ratios, ec/r2, as a parameter. The column failure factor, kL, was shown to be a key index controlling both aspects of failure as well as the orientation of the second stiffest region. The angle alpha E = tan-1 (2L/pi e) for kL = pi/2 is the singular point for both strength and buckling failure, and alpha II = tan-1 (2L/3e) for KL = 0 is the upper bound of the second stiffest region. The feasible domain of the second stiffest region is bounded by alpha E and alpha II both of which are only functions of geometrical properties. The implications of these analyses for the experimental validation of cervical spine trauma are discussed.     

Plug Effect of Erythrocytes in Capillary Blood Vessels

As an idealized problem of the motion of blood in small capillary blood vessels, the low Reynolds number flow of plasma (a newtonian fluid) in a circular cylindrical tube involving a series of circular disks is studied. It is assumed in this study that the suspended disks are equally spaced along the axis of the tube, and that their centers remain on the axis of the tube and that their faces are perpendicular to the tube axis. The inertial force of the fluid due to the convective acceleration is neglected on the basis of the smallness of the Reynolds number. The solution of the problem is derived for a quasi-steady flow involving infinitesimally thin disks. The numerical calculation is carried out for a set of different combinations of the interdisk distance and the ratio of the disk radius to the tube radius. The ratio of the velocity of the disk to the average velocity of the fluid is calculated. The different rates of transport of red blood cells and of plasma in capillary blood vessels are discussed. The average pressure gradient along the axis of the tube is computed, and the dependence of the effective viscosity of the blood on the hematocrit and the diameter of the capillary vessel is discussed.     

Common Slope Tests for Bivariate Errors‐in‐Variables Models

Likelihood ratio tests are derived for bivariate normal structural relationships in the presence of group structure. These tests may also be applied to less restrictive models where only errors are assumed to be normally distributed. Tests for a common slope amongst those from several datasets are derived for three different cases – when the assumed ratio of error variances is the same across datasets and either known or unknown, and when the standardised major axis model is used. Estimation of the slope in the case where the ratio of error variances is unknown could be considered as a maximum likelihood grouping method. The derivations are accompanied by some small sample simulations, and the tests are applied to data arising from work on seed allometry.     

Resonant ultrasound spectroscopy measurements of the elastic constants of human dentin

The technique of resonant ultrasound spectroscopy (RUS) was used to measure the second-order elastic constants of hydrated human dentin. Specimens were placed between two transducers, and the resonant frequencies of vibration were measured between 0.5 and 1.4 MHz. The elastic constants determined from the measured resonant frequencies in hydrated dentin exhibited slight hexagonal anisotropy, with the stiffest direction being perpendicular to the axis of the tubules (E11 = 25.1GPA) This hexagonal anisotropy was small (E33/E11 = 0.92), and almost disappeared when the specimens were dried. In addition, there was a pronounced anisotropy in the Poisson's ratio of wet dentin: v21 = 0.45; v31 = 0.29. With drying in air, this anisotropy vanished: v21 = v31 = 0.29. The isotropic Young's modulus of dried dentin was 28.1 GPa. RUS shows promise for determining the elastic constants in mineralized tissues.     

Dichroic Optical Properties of Uniaxially Oriented Gold Nanorods in Polymer Films

Applications based on the optical excitation of the longitudinal surface plasmon resonance of gold nanorods (AuNRs) work at highest efficiency if all component AuNRs can be maximally excited simultaneously. This can be achieved in aligned AuNR structures, such as those embedded in uniaxially stretched polymer films. Since too high heating temperatures during film stretching cause reshaping and alteration of optical properties of the rods, a maximum allowable heating temperature is determined. The alignment of the rods is quantified by an orientational order parameter of 0.92 based on a statistically significant sample of assumed t distributed means and obtained by scanning electron microscopy. We show that a stretched AuNRs-PVA composite film has optical properties that approach the dichroic properties of an idealized ensemble of fully aligned, identical, and non-interacting AuNRs embedded in a PVA film. The idealized system is provided by FDTD simulations of a single AuNR, which we carried out using the size- and shape-adapted dielectric function of gold and the software RSOFT.     

A descriptive theory of cell migration on surfaces

Analytical expressions are derived for the first and second spatial moments pertaining to the surface locomotion of a model class of biological cells. The model is distinguished by orientation dependent step-length distributions, which result in drift motion along a preferred axis.     

Collagen fiber orientation at the tendon to bone insertion and its influence on stress concentrations

The tendon to bone insertion serves the mechanical role of transferring loads from a relatively compliant tendon to a relatively rigid bone. The details of the mechanism of load transfer are of great importance, since current surgical procedures for tendon reattachment have high failure rates. We hypothesized that the microscopic structure of the insertion is optimized to minimize stress concentrations associated with this load transfer. To explore this, collagen fiber orientation distributions were measured in the supraspinatus tendons of rats. The angular deviation of fibers was fairly uniform across the insertion, and the mean angles of the local distributions deviated mildly from the tendon axis. To explore how these observed property distributions could influence load transfer, these distributions were used to derive material properties for an idealized two-dimensional mechanical model of an insertion. Comparison between stress concentrations in this idealized model and those in three comparison models suggests that the microstructure serves to (1) simultaneously reduce stress concentrations and material mass, and (2) shield the insertion's outward splay from the highest stresses.     

Constant (optimum) power electrophoresis

The electrical field used in electrophoresis can be produced by various types of electrical power supplies. The optimum power supply, with respect to the ratio of migration velocity to heating, produces the maximum voltage gradient consistent with the maximum allowable rate of heating. The voltage and current change only to compensate for changes in the resistance of the electrophoretic system. A circuit is given which produces such constant power and its operation is compared with other types of regulation.     

Calculation of dose components in head phantom for boron neutron capture therapy.

Application of neutrons to cancer treatment has been a subject of considerable clinical and research interest since the discovery of the neutron by Chadwick in 1932 (3). Boron neutron capture therapy (BNCT) is a technique of radiation oncology which is used in treating brain cancer (glioblastoma multiform) or melanoma and that consists of preferentially loading a compound containing 10B into the tumor location, followed by the irradiation of the patient with a beam of neutron. Dose distribution for BNCT is mainly based on Monte Carlo simulations. In this work, the absorbed dose spatial distribution resultant from an idealized neutron beam incident upon ahead phantom is investigated using the Monte Carlo N-particles code, MCNP 4B. The phantom model used is based on the geometry of a circular cylinder on which sits an elliptical cylinder capped by half an ellipsoid representing the neck and head, both filled with tissue-equivalent material. The neutron flux and the contribution of individual absorbed dose components, as a function of depths and of radial distance from the beam axis (dose profiles) in phantom model, is presented and discussed. For the studied beam the maximum thermal neutron flux is at a depth of 2 cm and the maximum gamma dose at a depth of 4 cm.     

Static and dynamic finite element analyses of an idealized structural model of vertebral trabecular bone.

An idealized three-dimensional finite element model of a rodlike trabecular bone structure was developed to study its static and dynamic responses under compressive loading, considering the effects of bone marrow and apparent density. Static analysis of the model predicted hydraulic stiffening of trabecular bone due to the presence of bone marrow. The predicted power equation relating trabecular bone apparent elastic modulus to its apparent density was in good agreement with those of the reported experimental investigations. The ratio of the maximum stress in the trabecular bone tissue to its apparent stress had a high value, decreasing with increasing bone apparent density. Frequency analyses of the model predicted higher natural frequencies for the bone without marrow than those for the bone with marrow. Adding a mass relatively large compared to that of bone rendered a single-degree-of-freedom response. In this case, the resonant frequency was higher for the bone with marrow than that for the bone without marrow. The predicted vibrational measurement of apparent modulus was in good agreement with that of the static measurement, suggesting vibrational testing as a method for nondestructive measurement of trabecular bone elastic moduli.     

The theory of case-control studies for early detection programs

Although case-control studies are widely used for evaluating the benefit of early detection programs, the theoretical basis underlying this application has not been well developed. In this paper the properties of chronic disease case-control studies for evaluating early detection programs are investigated. An idealized case-control study is analyzed and the theoretical expression for the odds ratio associated with the benefit of screening is derived. The odds ratio is related to the natural history of disease and the screening program. Our results indicate that case-control studies result in odds ratios that are surprisingly close to unity and consequently have low power.     

Model-based fitting of single-channel dwell-time distributions

Single-channel recordings provide unprecedented resolutions on kinetics of conformational changes of ion channels. Several approaches exist for analysis of the data, including the dwell-time histogram fittings and the full maximal-likelihood approaches that fit either the idealized dwell-time sequence or more ambitiously the noisy data directly using hidden Markov modeling. Although the full maximum likelihood approaches are statistically advantageous, they can be time-consuming especially for large datasets and/or complex models. We present here an alternative approach for model-based fitting of one-dimensional and two-dimensional dwell-time histograms. To improve performance, we derived analytical expressions for the derivatives of one-dimensional and two-dimensional dwell-time distribution functions and employed the gradient-based variable metric method for fast search of optimal rate constants in a model. The algorithm also has the ability to allow for a first-order correction for the effects of missed events, global fitting across different experimental conditions, and imposition of typical constraints on rate constants including microscopic reversibility. Numerical examples are presented to illustrate the performance of the algorithm, and comparisons with the full maximum likelihood fitting are discussed.     

1H-NMR stereospecific assignments by conformational data-base searches

A search procedure is described for making stereospecific assignments at prochiral centers in proteins on the basis of nuclear Overhauser enhancement and coupling constant data derived from nmr experiments. A data base comprising torsion angles, associated 1H-1H coupling constants and interproton distances is searched by a computer algorithm for sets of values that match the experimental data within specified error limits. Two different data bases are used. The first is a crystallographic data base derived from 34 well-refined crystal structures; the second is a systematic data base derived from conformations of a short peptide fragment with idealized geometry by systematically varying the phi, psi, and chi 1 torsion angles. Both approaches are tested for beta-methylene groups with model data obtained from 20 crystal structures. The results for the two methods are similar though not identical, so that a combination of the two methods appears to be useful. With an appropriate choice of error estimates, around 80% of the beta-methylene groups could be assigned in the test calculations. In addition, results with experimental nmr data indicate that a similar percentage of stereospecific assignments can be made in practical situations.     

Supramolecular organization of lysophosphatidylcholine-packaged Gramicidin A

Heat derived gramicidin A'/L-alpha-lysophosphatidylcholine complexes were separated on a sucrose gradient to form two fractions: Fraction A which had an approximately constant Gramicidin A' to phospholipid ratio of 8 to 10 lipid molecules per Gramicidin A' molecule and Fraction B which had a larger but variable ratio. Fluorescence and circular dichroism studies confirmed Fraction A to be a lipid-incorporated channel state. Electron microscopic studies, using uranyl acetate negative staining, showed fraction A to be a membranous state with the formation of bilayer vesicles, that is, the interaction of peptide and phospholipid micelles causes the lipid to reorganize into a bilayer structure. Freeze-fracture replicas of the channel incorporated state demonstrated the presence of a supramolecular organization of particles exhibiting a tendency to form rows with a 50-60 A periodicity along the row and with 70-80 A distance between rows. An idealized working model for the incorporated state is presented.     

Elements of metacommunity structure of Paraguayan bats: multiple gradients require analysis of multiple ordination axes

Techniques to evaluate elements of metacommunity structure (EMS; coherence, species turnover and range boundary clumping) have been available for several years. Such approaches are capable of determining which idealized pattern of species distribution best describes distributions in a metacommunity. Nonetheless, this approach rarely is employed and such aspects of metacommunity structure remain poorly understood. We expanded an extant method to better investigate metacommunity structure for systems that respond to multiple environmental gradients. We used data obtained from 26 sites throughout Paraguay as a model system to demonstrate application of this methodology. Using presence–absence data for bats, we evaluated coherence, species turnover and boundary clumping to distinguish among six idealized patterns of species distribution. Analyses were conducted for all bats as well as for each of three feeding ensembles (aerial insectivores, frugivores and molossid insectivores). For each group of bats, analyses were conducted separately for primary and secondary axes of ordination as defined by reciprocal averaging. The Paraguayan bat metacommunity evinced Clementsian distributions for primary and secondary ordination axes. Patterns of species distribution for aerial insectivores were dependent on ordination axis, showing Gleasonian distributions when ordinated according to the primary axis and Clementsian distributions when ordinated according to the secondary axis. Distribution patterns for frugivores and molossid insectivores were best described as random. Analysis of metacommunities using multiple ordination axes can provide a more complete picture of environmental variables that mold patterns of species distribution. Moreover, analysis of EMS along defined gradients (e.g., latitude, elevation and depth) or based on alternative ordination techniques may complement insights based on reciprocal averaging because the fundamental questions addressed in analyses are contingent on the ordination technique that is employed.     

Power of the classical twin design revisited.

Statistical power of the classical twin design was revisited. The approximate sampling variances of a least-squares estimate of the heritability in a univariate analysis and estimate of the genetic correlation coefficient in a bivariate analysis were derived analytically for the ACE model. Statistical power to detect additive genetic variation under the ACE model was derived analytically for least-squares, goodness-of-fit and maximum likelihood-based test statistics. The noncentrality parameter for the likelihood ratio test statistic is shown to be a simple function of the MZ and DZ intraclass correlation coefficients and the proportion of MZ and DZ twin pairs in the sample. All theoretical results were validated using simulation. The derived expressions can be used to calculate power of the classical twin design in a simple and rapid manner.     

The directional absorption properties of rhodopsin and its photoproducts.

The experimental data on the absorption of a plane polarised light by a solution of cattle rhodopsin at -196 degrees C have been theoretically analysed to model the directional absorption properties of rhodopsin and its photoproducts. It is seen that these molecules behave like planar absorbers having a ratio of about 100 : 7 between the extinction coefficients along the long axis and perpendicular to it. Using this result and the experimental observations on absorption and dichroism in the retina in situ, a model for the configuration of chromophores in the disc membranes has been derived. In this model the plane of the chromophore is perpendicular to that of the disc and the long axis of the chromophore makes an angle of 6.6 degrees with the plane of the disc. The solution of the problem depends on the assumption that the absorption axes are the same for the rhodopsin, prelumirhodopsin and isorhodopsin.     

Three-dimensional measurement of rearfoot motion during running

Excessive ranges of motion during running have been speculated to be connected to injuries to the lower extremities. Movement of the foot and lower leg has commonly been studied with two-dimensional techniques. However, differences in the alignment of the longitudinal axis of the foot with the camera axis will produce measurement errors for projected angles of the lower extremities. A three-dimensional approach would not have this limitation. The purpose of this study is to present a three-dimensional model for calculation of angles between lower leg and foot, lower leg and ground, and foot and ground, and to compare results from treadmill running derived from this model with results derived from a two-dimensional model for different alignment angles between foot axis and camera axis. A two camera Selspot system was used to obtain three-dimensional information on motion of the studied segments. It was found that several two-dimensional variables measured from a posterior view are very sensitive to the alignment angle between the foot and the camera axis. Some variables change as much as 1 degrees for every 2 degrees of change of the alignment angle. The large influence of rotations other than the measured one in two-dimensional measurements makes advisable the use of a three-dimensional model when studying motion between foot and lower leg during running.     

Study on the molecular models commonly used in the simulation of dilute polymeric solutions in flow

Three molecular models, commonly used in the simulation of polymeric solutions and melts were employed to describe the rheological behaviour of dilute, elastic and constant viscosity solution formed by bead-and-bond chain molecules immersed into a soft-sphere solvent. The intermolecular interactions for the three models were calculated by the Lennard-Jones potential. The differences amongst the models proceeded from the intramolecular restrictions: the simplest one is a Freely-Joined-Chain (FJC) model with harmonic bond potentials, in the second model bonds are restricted by a finite extensible non-linear elastic (FENE) potential plus a repulsive WCA potential, and the third model is conformed by the United Atom (UA) approach which includes bond, flexion and torsion potentials. Both Couette and Poiseuille flows were simulated using Non-Equilibrium Molecular Dynamics. Deformation displayed by the three chain models; defined in terms of their radius of gyration was calculated and according to results it was found that for Couette flow, the three chains exhibit similar response to deformation. In Poiseulle flow, the FJC and FENE models behave similarly but the UA model presents a larger resistance to deformation. For both flow regimes, the forces involved to deform the chains were estimated in terms of the first normal stress differences. From these estimations it was found that the UA model depicted the stiffest chain, followed by the FENE model, and last the FJC model.     

Supramolecular organization of lysophosphatidylcholine-packaged gramicidin A′

Heat derived gramicidin A′/l-α-lysophosphatidylcholine complexes were separated on a sucrose gradient to form two fractions: Fraction A which had an approximately constant Gramicidin A′ to phospholipid ratio of 8 to 10 lipid molecules per Gramicidin A′ molecule and Fraction B which had a larger but variable ratio. Fluorescence and circular dichroism studies confirmed Fraction A to be a lipid-incorporated channel state. Electron microscopic studies, using uranyl acetate negative staining, showed fraction A to be a membranous state with the formation of bilayer vesicles, that is, the interaction of peptide and phospholipid micelles causes the lipid to reorganize into a bilayer structure. Freeze-fracture replicas of the channel incorporated state demonstrated the presence of a supramolecular organization of particles exhibiting a tendency to form rows with a 50–60 Å periodicity along the row and with 70–80 Å distance between rows. An idealized working model for the incorporated state is presented.