Helical flow around arterial bends for varying body mass

The three dimensionally curved aortic arch is modeled as a portion of a helical pipe. Pulsatile blood flow therein is calculated assuming helical symmetry and an experimentally measured pressure pulse. Appropriate values for the Womersley and Reynolds numbers are taken from allometric scaling relations for a variety of body masses. The flow structure is discussed with particular reference to the wall shear, which is believed to be important in the inhibition of atheroma. It is found that nonplanar curvature limits the severity of flow separation at the inner bend, and reduces spatial variation of wall shear.     

Fluid-Dynamic Optimal Design of Helical Vascular Graft for Stenotic Disturbed Flow

Although a helical configuration of a prosthetic vascular graft appears to be clinically beneficial in suppressing thrombosis and intimal hyperplasia, an optimization of a helical design has yet to be achieved because of the lack of a detailed understanding on hemodynamic features in helical grafts and their fluid dynamic influences. In the present study, the swirling flow in a helical graft was hypothesized to have beneficial influences on a disturbed flow structure such as stenotic flow. The characteristics of swirling flows generated by helical tubes with various helical pitches and curvatures were investigated to prove the hypothesis. The fluid dynamic influences of these helical tubes on stenotic flow were quantitatively analysed by using a particle image velocimetry technique. Results showed that the swirling intensity and helicity of the swirling flow have a linear relation with a modified Germano number (Gn*) of the helical pipe. In addition, the swirling flow generated a beneficial flow structure at the stenosis by reducing the size of the recirculation flow under steady and pulsatile flow conditions. Therefore, the beneficial effects of a helical graft on the flow field can be estimated by using the magnitude of Gn*. Finally, an optimized helical design with a maximum Gn* was suggested for the future design of a vascular graft.     

Influence of the arrangement and secondary structure of melittin peptides on the formation and stability of toroidal pores

Melittin interactions with lipid bilayers and melittin formed pores are extensively studied to understand the mechanism of the toroidal pore formation. Early experimental studies suggested that melittin peptide molecules are anchored by their positively charged residues located next to the C-terminus to only one leaflet of the lipid bilayer (asymmetric arrangement). However, the recent non-linear spectroscopic experiment suggests a symmetric arrangement of the peptides with the C-terminus of the peptides anchored to both bilayers. Therefore, we present here a computational study that compares the effect of symmetric and asymmetric arrangements of melittin peptides in the toroidal pore formation. We also investigate the role of the peptide secondary structure during the pore formation. Two sets of the symmetric and asymmetric pores are prepared, one with a helical peptide from the crystal structure and the other set with a less helical peptide. We observe a stable toroidal pore being formed only in the system with a symmetric arrangement of the less helical peptides. Based on the simulation results we propose that the symmetric arrangement of the peptides might be more favorable than the asymmetric arrangement, and that the helical secondary structure is not a prerequisite for the formation of the toroidal pore.     

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

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

Geometrical correspondence identified and a new interaction unit suggested in striated muscle

It has long been believed that the periodic structure of the myosin helix is a consequence only of compressing the actin-myosin interaction sites. Here, we identify a length correspondence between the smallest helical unit on the thick filament and the helical pitch of the actin filaments in two different contractile muscles. This suggests a rotation/swing of the filaments that creates a new interaction unit in addition to the single interaction between an actin filament and a myosin head. Numerical characteristics of the single interaction are estimated from discussion about an in vivo interaction utilizing the new unit. The estimated twisted angle of the actin filaments is consistent with that calculated from its torsion rigidity and the evaluated step sizes per cross-bridge can be performed by a single bend of a myosin head. By comparing our evaluated step sizes with experimental results, we conclude that the most plausible mechanism at the force-recovery stage involves swings or rotations of both filaments in the same direction (clockwise).     

Computation in the rabbit aorta of a new metric – the transverse wall shear stress – to quantify the multidirectional character of disturbed blood flow

Spatial variation of the haemodynamic stresses acting on the arterial wall is commonly assumed to explain the focal development of atherosclerosis. Disturbed flow in particular is thought to play a key role. However, widely-used metrics developed to quantify its extent are unable to distinguish between uniaxial and multidirectional flows. We analysed pulsatile flow fields obtained in idealised and anatomically-realistic arterial geometries using computational fluid dynamics techniques, and in particular investigated the multidirectionality of the flow fields, capturing this aspect of near-wall blood flow with a new metric – the transverse wall shear stress (transWSS) – calculated as the time-average of wall shear stress components perpendicular to the mean flow direction. In the idealised branching geometry, multidirectional flow was observed downstream of the branch ostium, a region of flow stagnation, and to the sides of the ostium. The distribution of the transWSS was different from the pattern of traditional haemodynamic metrics and more dependent on the velocity waveform imposed at the branch outlet. In rabbit aortas, transWSS patterns were again different from patterns of traditional metrics. The near-branch pattern varied between intercostal ostia, as is the case for lesion distribution; for some branches there were striking resemblances to the age-dependent patterns of disease seen in rabbit and human aortas. The new metric may lead to improved understanding of atherogenesis.     

Plasmastatic models of galathea traps with magnetically transparent boundaries

Mathematical models and results of calculation of plasma equilibrium in a circular cylinder with three helical or straight imbedded current-carrying conductors (i.e., in a straightened analog of a toroidal Galathea trap) are presented. The equilibrium is described in the framework of two-dimensional boundary value problems with plane and helical analogs of the Grad-Shafranov equation for the scalar magnetic flux function. Problems with first-kind boundary conditions corresponding to a magnetically transparent boundary of the cylinder and problems with second-kind boundary conditions and a given value of the electric current flowing in plasma (in addition to those flowing in the conductors) are considered. Deformations of magnetoplasma configurations in the cylinder for different formulations of the above-specified problems are investigated numerically.     

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

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

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

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

Reduced MHD equations with allowance for slow magnetosonic waves

The so-called reduced magnetohydrodynamics, which deals with the motion of incompressible fluids and is usually applied to describe plasma flows in a strong toroidal magnetic field, has a number of drawbacks and, in some cases, fails to produce correct results. The equations proposed here are simpler than the original MHD equations and are free of these drawbacks. These equations, like reduced MHD equations, make it possible to remove from consideration fast magnetosonic waves and to introduce the vector potential for the poloidal magnetic field. However, our equations differ from the reduced MHD equations in that they completely incorporate slow magnetosonic waves, the specific features of the toroidal geometry, and the effects of the toroidal velocity.     

Distributed torsion angle grid search in high dimensions: A systematic approach to NMR structure determination

Two complementary approaches for systematic search in torsion angle space are described for the generation of all conformations of polypeptides which satisfy experimental NMR restraints, hard-sphere van der Waals radii, and rigid covalent geometry. The first procedure is based on a recursive, tree search algorithm for the examination of linear chains of torsion angles, and uses a novel treatment to propagate the search results to neighboring regions so that the structural consequences of the restraints are fully realized. The second procedure is based on a binary combination of torsion vector spaces for connected submolecules, and produces intermediate results in Cartesian space for a more robust restraint analysis. Restraints for NMR applications include bounds on torsion angles and internuclear distances, including relational and degenerate restraints involving equivalent and nonstereoassigned protons. To illustrate these methods, conformation search results are given for the tetrapeptide APGA restrained to an idealized -turn conformation, an alanine octapeptide restrained to a right-handed helical conformation, and the structured region of the peptide SYPFDV.     

Steady and oscillatory transnasal pressure-flow relationships in healthy adults.

The influence of flow characteristics and gas physical properties on nasal resistance (NR) is difficult to ascertain with traditional rhinomanometric methods because the respiratory airflows used in these methods are largely uncontrolled. As an alternative, we used a novel method of rhinomanometry in which an externally generated flow is passed through the nasal passage via a mouthpiece. The transnasal pressure-flow relationships for both quasi-steady and oscillating flows and with different gases were obtained in five healthy adults with this method. For quasi-steady nasal flows the dimensionless pressure losses were largely independent of physical properties of the gas and a function of the Reynolds number (Re) of the flow. Values of NR for quasi-steady flows were largely independent of flow direction for Re up to roughly 3,000 in all five subjects and for Re up to roughly 19,000 in two of the five subjects. Airway collapse occurred in two subjects at Re greater than 3,000, suggesting that the nonrigid segments of the nasal passage contribute to the intersubject variations in NR at high flow rates. Pressure losses associated with oscillating flows measured at frequencies between 1 and 16 Hz were similar to steady flow losses provided that Re was less than roughly 3,000. For Re greater than 3,000 the oscillating flow resistances were affected by the phasic redistribution of flow into compliant segments of the nasal passage. These results indicate that, for flow rates and harmonic frequencies associated with breathing at rest, the nasal passage behaves as a rigid rough-walled pipe in which pressure losses are largely determined by forces relating to viscous friction and convective accelerations.     

Developing oscillatory flow in a circular pipe: a new solution

The problem of oscillatory flow in a circular pipe was analyzed by Atabek and associates more than two decades ago. Their formulas for velocity and pressure distributions in developing pipe flows under oscillatory conditions have been often cited. However, the application of these formulas for flow field computations requires a rather complex procedure involving plotting of a set of curves and predetermination of the phase angles. This paper presents a method using the imaginary argument of the Bessel function to solve the Navier-Stokes equations. A different set of solution formulas are obtained. A comparison of the formulas obtained in this paper with those of Atabek shows that the former is considerably simpler and more convenient to use in flow computations. Numerical results computed using this paper's formulas are consistent with Atabek's and with the experimental measurements.     

Core flexibility of a truncated metazoan mitochondrial tRNA

Secondary and tertiary structures of tRNAs are remarkably preserved from bacteria to humans, the notable exception being the mitochondrial (m) tRNAs of metazoans, which often deviate substantially from the canonical cloverleaf (secondary) or ‘L’-shaped (tertiary) structure. Many metazoan mtRNAs lack either the TψC (T) or dihydrouridine (D) loops of the canonical cloverleaf, which are known to confer structural rigidity to the folded structure. Thus, the absence of canonical TψC–D interactions likely results in greater dispersion of anticodon-acceptor interstem angle than for canonical tRNAs. To test this hypothesis, we have assessed the dispersion of the anticodon-acceptor angle for bovine mtRNA^Ser(AGY), which lacks the canonical D arm and is thus incapable of forming stabilizing interarm interactions. Using the method of transient electric birefringence (TEB), and by changing the helical torsion angle between a core mtRNA bend and a second bend of known angle/rigidity, we have demonstrated that the core of mtRNA^Ser(AGY) has substantially greater flexibility than its well-characterized canonical counterpart, yeast cytoplasmic tRNA^Phe. These results suggest that increased flexibility, in addition to a more open interstem angle, would allow both noncanonical and canonical mtRNAs to utilize the same protein synthetic apparatus.     

Beta-turns in proteins

The X-ray atomic co-ordinates from 29 proteins of known sequence and structure were utilized to elucidate 459 β-turns in regions of chain reversals. Tetrapeptides whose αC_iαC_{(i + 3)} distances were below 7 Å and not in a helical region were characterized as β-turns. In addition, β-turns were considered to have hydrogen bonding if their computed O_(i)N_{(i + 3)} distances were ≤3.5 Å. The torsion angles of 26 proteins containing 421 β-turns were examined and classified into 11 bend types based on the (φ, ψ) dihedral angles of the i + 1 and i + 2 bend residues. The average frequency of β-turns is 32% as compared to the 38% helices and 20% β-sheets in the 29 proteins. The most frequently occurring bend residues are Asn, Cys, Asp in the first position, Pro, Ser, Lys in the second position, Asn, Asp, Gly in the third position, and Trp, Gly, Tyr in the fourth position. Residues with the highest β-turn potential in all four positions are Pro, Gly, Asn, Asp, and Ser with the most hydrophobic residues (i.e. Val, IIe, and Leu) showing the lowest bend potential. However, in the region just beyond the β-turns, hydrophobic residues occur with greater frequency than do hydrophilic residues. An environmental analysis of β-turn neighboring residues shows that reverse chain folding is stabilized by anti-parallel β-sheets as well as helix-helix and α-β interactions. The β-turn potential at the 12 positions adjacent to and including the bend were plotted for the 20 amino acids and showed dramatic positional preferences, which may be classified according to the nature of the side-chains. An examination of the 27 β-turns in elastase showed that 21 were found in identical positions as those in α-chymotrypsin. However, only 37 of the 84 bend residues were conserved, indicating that structural similarity may persist despite differences in sequence homology. A survey of residues occupying bend types I′, II′ and III′ showed that Gly appeared most frequently in the third position in bend types I′ and III′ as well as in the second position in bend types II′ and III′. Fourteen hydrogenbonded type II bends were found without a Gly at the third position, contrary to the energy calculations. Eight type VI bends with a cis Pro at the third position were also elucidated.     

Mechanistic insight into the physiological relevance of helical blood flow in the human aorta: an in vivo study

The hemodynamics within the aorta of five healthy humans were investigated to gain insight into the complex helical flow patterns that arise from the existence of asymmetries in the aortic region. The adopted approach is aimed at (1) overcoming the relative paucity of quantitative data regarding helical blood flow dynamics in the human aorta and (2) identifying common characteristics in physiological aortic flow topology, in terms of its helical content. Four-dimensional phase-contrast magnetic resonance imaging (4D PC MRI) was combined with algorithms for the calculation of advanced fluid dynamics in this study. These algorithms allowed us to obtain a 4D representation of intra-aortic flow fields and to quantify the aortic helical flow. For our purposes, helicity was used as a measure of the alignment of the velocity and the vorticity. There were two key findings of our study: (1) intra-individual analysis revealed a statistically significant difference in the helical content at different phases of systole and (2) group analysis suggested that aortic helical blood flow dynamics is an emerging behavior that is common to normal individuals. Our results also suggest that helical flow might be caused by natural optimization of fluid transport processes in the cardiovascular system, aimed at obtaining efficient perfusion. The approach here applied to assess in vivo helical blood flow could be the starting point to elucidate the role played by helicity in the generation and decay of rotating flows in the thoracic aorta.     

A model analysis of internal loads, energetics, and effects of wobbling mass during the whole-body vibration

The internal loads, energetics, and the effects of wobbling mass during the whole-body vibration are studied in terms of analysis and comparison of two models: one is a system of four degrees-of-freedom with rigid and wobbling masses in both lower body and upper body (Model A), while the other one (Model B) is a system of three degrees-of-freedom with a rigid upper body and is otherwise identical to Model A. The main findings are the following: (1) The wobbling mass in the upper body is able to reduce the total internal load on the rigid mass of the upper body considerably. (2) "Partial" internal loads on a certain part of the body may be even larger than the total load on the same part of the body because of the phase differences among the partial loads. Therefore, a full consideration of safety during the whole-body vibration has to take not only the total, but also all the partial internal loads into account. (3) The fluctuation of power input and the fluctuation of mechanical energy could be much larger than the fluctuation of dissipation rate. (4) For frequencies higher than the resonance frequency range, the amplitude of the oscillation of the centre of mass of the body is so reduced that only the change of elastic potential energy dominates in the change of mechanical energy. Thus, a simple picture of energy flow is obtained as follows: for approximately one half of the oscillation period, the energy flows from the vibrator into the human body and is mainly stored in the muscle-tendon system, while for the remaining approximate half of the period, the energy flows from the muscle-tendon system back to the vibrator with a slightly smaller amount because a small part of the flown-in energy has been dissipated.