Adjacent Angles Research Articles

SU‐E‐J‐122: Planning Four‐Dimensional Intensity‐Modulated Arc Therapy for Tumor Tracking

Purpose: We propose a practical four‐dimensional (4D) planning scheme of intensity‐modulated arc therapy (IMAT) for tumor tracking using dynamic multileaf collimators (MLC). Methods: We contour the target and critical structures on each image set of 4DCT associated with each breathing phase. Transformation vectors of the target from a reference phase to other phases are derived. A 3D‐IMAT plan is first optimized on the reference phase without motion‐induced margin. Assuming delivery starts at a predetermined breathing phase and the patient breathes the same way as during 4DCT imaging, we know the phases at which each planned segment will be delivered. Then, we transform the optimized segments from the reference phase to the phases of their delivery based on projections of transformation vectors of the target in the beamˈs eye‐view. The connectivity of the transformed segments between adjacent beam angles is enforced. The dose for each phase is calculated using segments delivered at that phase, and transformed to the reference phase to obtain cumulative dose. The resulting 4D plan is compared with the 3D plan without considering respiratory motion and with motion‐induced margins. Effects of enforcing connectivity on the plan quality are also evaluated. Results: Compared to the PTV dose of 3D plan without tumor tracking, the 4D PTV dose is more conformal and uniform, and it approaches the ideal situation of the patient being static. The 4D plan also showed better critical organ sparing than the 3D plan with motion‐induced margins. Adding MLC motion required for tracking to the planned motion rarely causes physical constraints to be exceeded, and enforcing connectivity thus has little effect on plan quality. Conclusions: The proposed scheme of 4D‐IMAT planning for tumor tracking is a feasible and practical approach under the current clinical planning environment. Dosimetric benefits of 4D planning have been clearly demonstrated.This stusy is supported in part by NIH R01 grant 1R01CA133539‐01A2

Experimental Study on Effect of Cold-Forming Procedures to Cold-Formed Steel Members on Power Transmission Tower

The cold-formed steel member can arrange the most suitable shape of section according to the material needed. It can increase the load capacity and decrease the weight index when it is used for power transmission towers. The effect of cold-forming procedures to cold-formed steel members is different according to the thickness of steel plate or strip. The design method of cold-formed steel members considering the strength in Chinese code of cold-formed thin-wall steel is proposed when the thickness is less than or equals 6mm. In order to study the effect of cold-forming procedures on the strength of steel, the mechanical property tests are developed on flat plates, adjacent angles and angles, which are cut from cold-formed thick-wall lipped angles. According results of test, advices on improving the formula is proposed, which is used to design the member(t≤6mm) in China, and the design method of cold-formed thick-wall steel members considering their strength is proposed. These will provides technical supports that the cold-formed steel member can be used on power transmission tower broadly.

Joint angle affects volitional and magnetically-evoked neuromuscular performance differentially

This study examined the volitional and magnetically-evoked neuromuscular performance of the quadriceps femoris at functional knee joint angles adjacent to full extension. Indices of volitional and magnetically-evoked neuromuscular performance ( N = 15 healthy males, 23.5 ± 2.9 years, 71.5 ± 5.4 kg, 176.5 ± 5.5 cm) were obtained at 25°, 35° and 45° of knee flexion. Results showed that volitional and magnetically-evoked peak force (PF V and P TF E, respectively) and electromechanical delay (EMD V and EMD E, respectively) were enhanced by increased knee flexion. However, greater relative improvements in volitional compared to evoked indices of neuromuscular performance were observed with increasing flexion from 25° to 45° (e.g. EMD V, EMD E: 36% vs. 11% improvement, respectively; F [2,14] = 6.8, p < 0.05). There were no significant correlations between EMD V and EMD E or PF V and P TF E, at analogous joint positions. These findings suggest that the extent of the relative differential between volitional and evoked neuromuscular performance capabilities is joint angle-specific and not correlated with performance capabilities at adjacent angles, but tends to be smaller with increased flexion. As such, effective prediction of volitional from evoked performance capabilities at both analogous and adjacent knee joint positions would lack robustness.

Geometry of kinked protein helices from NMR data

Mathematical questions related to determining the structure of a protein from NMR orientational restraints are discussed. The protein segment is a kinked alpha helix modeled as a regular alpha helix in which two adjacent torsion angles have been varied from their ideal values. Varying these torsion angles breaks the helix into two regular helical segments joined at a kink. The problem is to find the torsion angles at the kink from the relationship of the helical segments to the direction of the magnetic field.

Optimal allocation of multi-sensor passive localization

To improve multi-sensor passive localization precision, the optimal allocation form of multi-sensor bearing-only localization is analyzed from the perspective of the geometric dilution of precision (GDOP) of the least squares (LS) algorithm. This paper indicates that whether the target lies inside the closed region formed by the sensors or not, the optimal allocation is when each adjacent cut angle between a sensor pair is identical, and all sensors are located on the border of the circle that has the target (which is also the origin of the coordinate system) as its center. When there is no restriction on the adjacent cut angle in the above allocation, the optimal estimate of the LS algorithm in the sense of minimum variance can be acquired. When the LS algorithm achieves the optimal estimate and the sensors present the optimal allocation, the respective consistencies are analyzed. Simulation results verify the analysis of the optimal allocation form above, which can be used in multi-sensor passive localization algorithms based on sensor management.

Morley’s theorem revisited: Origami construction and automated proof

Morley’s theorem states that for any triangle, the intersections of its adjacent angle trisectors form an equilateral triangle. The construction of Morley’s triangle by the straightedge and compass method is impossible because of the well-known impossibility result for angle trisection. However, by origami, the construction of an angle trisector is possible, and hence that of Morley’s triangle. In this paper we present a computational origami construction of Morley’s triangle and an automated correctness proof of the generalized Morley’s theorem. During the computational origami construction, geometrical constraints in symbolic representation are generated and accumulated. Those constraints are then transformed into algebraic forms, i.e. a set of polynomials, which in turn are used to prove the correctness of the construction. The automated proof is based on the Gröbner bases method. The timings of the experiments of the Gröbner bases computations for our proofs are given. They vary greatly depending on the origami construction methods, the algorithms for the Gröbner bases computation, and variable orderings.

Effect of Cage Geometry on Sagittal Alignment after Posterior Lumbar Interbody Fusion for Degenerative Disc Disease

To compare the sagittal alignment of the lumbar spine after one-segment posterior lumbar interbody fusion (PLIF) using the horizontal cylinder (HC) or open box (OB) type cage. 66 patients underwent instrumented one-segment PLIF with bone grafting for lower lumbar degenerative disease. HC-type cages were used in 33 men and 13 women aged 20 to 73 (mean, 47) years between September 2001 and July 2004. OB-type cages with a 3-degree lordotic angle were used in 9 men and 11 women aged 25 to 70 (mean, 53) years between July 2004 and September 2006. Pre- and post-operative lumbar lordosis and intervertebral body angles in the fused and upper adjacent levels in the 2 groups were compared. There was no significant difference between the 2 groups with regard to changes in the lumbar lordosis and intervertebral body angle in the fused and upper adjacent levels. In both groups, the upper adjacent intervertebral body angle increased significantly by about 2 degrees. Lumbar alignment was similar after the use of the HC- or OB-type cages. This may be due to the surgical procedure and insufficient cage lordotic angle.

Silicon nanotubes with distinct bond lengths

In this paper, we extend both the rolled-up and the polyhedral models for single-walled silicon nanotubes with equal bond lengths to models having distinct bond lengths. The silicon nanotubes considered here are assumed to be formed by sp3 hybridization with different bond lengths so that the nanotube lattice is assumed to comprise only skew rhombi. Beginning with the three postulates that all bonds lying on the same helix are equal, all adjacent bond angles are equal, and all atoms are equidistant from a common axis of symmetry, we derive exact formulae for the polyhedral geometric parameters such as chiral angles, bond angles, radius and unit cell length. The polyhedral model presented here with distinct bond lengths includes both the rolled-up model with distinct bond lengths which arises from the first term of an asymptotic expansion, and an existing polyhedral model of the authors which assumes equal bond lengths. Finally, some molecular dynamics simulations are undertaken for comparison with the geometric model. These simulations start with equal bond lengths and then stabilize in such a way that two distinct bond lengths emerge.

Stochastic versus deterministic kernel-based superposition approaches for dose calculation of intensity-modulated arcs

Dose calculations for radiation arc therapy are traditionally performed by approximating continuous delivery arcs with multiple static beams. For 3D conformal arc treatments, the shape and weight variation per degree is usually small enough to allow arcs to be approximated by static beams separated by 5°–10°. But with intensity-modulated arc therapy (IMAT), the variation in shape and dose per degree can be large enough to require a finer angular spacing. With the increase in the number of beams, a deterministic dose calculation method, such as collapsed-cone convolution/superposition, will require proportionally longer computational times, which may not be practical clinically. We propose to use a homegrown Monte Carlo kernel-superposition technique (MCKS) to compute doses for rotational delivery. The IMAT plans were generated with 36 static beams, which were subsequently interpolated into finer angular intervals for dose calculation to mimic the continuous arc delivery. Since MCKS uses random sampling of photons, the dose computation time only increased insignificantly for the interpolated-static-beam plans that may involve up to 720 beams. Ten past IMRT cases were selected for this study. Each case took approximately 15–30 min to compute on a single CPU running Mac OS X using the MCKS method. The need for a finer beam spacing is dictated by how fast the beam weights and aperture shapes change between the adjacent static planning beam angles. MCKS, however, obviates the concern by allowing hundreds of beams to be calculated in practically the same time as for a few beams. For more than 43 beams, MCKS usually takes less CPU time than the collapsed-cone algorithm used by the Pinnacle3 planning system.

Using small molecule crystal structure data to obtain information about sulfonamide conformation

Understanding the conformations adopted by the sulfonamide group is essential to the understanding of the way that sulfa drugs act upon the body. The relative energies of these conformations in the solid state are estimated from the Cambridge Structural Database (CSD) using cluster analysis, and are used to confirm earlier findings that many high-level ab initio calculations do not reproduce the observed solid-state structure. These conformational studies have been extended to the adjacent torsion angles, and it has been shown that the sulfonamide group significantly affects the form adopted. The relative energies of the observed forms in the solid state have been estimated using data available in the CSD.

Differentiable, multi-dimensional, knowledge-based energy terms for torsion angle probabilities and propensities

Rotatable torsion angles are the major degrees of freedom in proteins. Adjacent angles are highly correlated and energy terms that rely on these correlations are intensively used in molecular modeling. However, the utility of torsion based terms is not yet fully exploited. Many of these terms do not capture the full scale of the correlations. Other terms, which rely on lookup tables, cannot be used in the context of force-driven algorithms because they are not fully differentiable. This study aims to extend the usability of torsion terms by presenting a set of high-dimensional and fully-differentiable energy terms that are derived from high-resolution structures. The set includes terms that describe backbone conformational probabilities and propensities, side-chain rotamer probabilities, and an elaborate term that couples all the torsion angles within the same residue. The terms are constructed by cubic spline interpolation with periodic boundary conditions that enable full differentiability and high computational efficiency. We show that the spline implementation does not compromise the accuracy of the original database statistics. We further show that the side-chain relevant terms are compatible with established rotamer probabilities. Despite their very local characteristics, the new terms are often able to identify native and native-like structures within decoy sets. Finally, force-based minimization of NMR structures with the new terms improves their torsion angle statistics with minor structural distortion (0.5 A RMSD on average). The new terms are freely available in the MESHI molecular modeling package. The spline coefficients are also available as a documented MATLAB file.

Crystal structure of tricyclo-DNA: an unusual compensatory change of two adjacent backbone torsion angles

The crystal structure of a DNA duplex with tricyclo-DNA (tc-DNA) residues explains the increased RNA affinity of tc-DNA relative to DNA and tc-DNA's superior resistance to nucleases.

UNIFORM GAIN POWER-SPECTRUM ANTENNA-PATTERN THEOREM AND ITS POSSIBLE APPLICATIONS

For certain applications in radio astronomy, viz. radio spectrographs, spectrum monitoring etc., only the amplitude power spectrum coverage within an angle of observation could be of interest. Ideally, the antenna structures of such instruments should illuminate this covering angle with a fixed uniform gain. This might be achieved using a combination of dipole antennas, a single vertical dipole, a loop antenna etc., but are subjected to limited bandwidth. This limitation could be overcome if many electrically-identical wideband antennas are positioned across the perimeter of a circle lying in the horizontal plane such that the antennas' adjacent half power beam angles touch each other. It has been theoretically observed that if two identical antennas are positioned at an angle with respect to one-another in such a way that their adjacent half power beam angles coincide, then if the amplitude power spectrums of the two are added, the result is effectively an amplitude power spectrum obtained from a single antenna having an uniform gain and uniform signal to noise ratio within the angle subtended by them. This angle also happens to be equal to the half power beamwidth of the individual antennas. A proper design using frequency independent antennas might possibly result to an user specified uniform amplitude power spectrum gain coverage across any required angle, with a theoretically unlimited bandwidth. More number of identical antennas might be positioned in similar fashion for extending the angular coverage.

Equipartition of a continuous mass distribution

Here are three samples of results. (1) Let m be a finite (absolutely) continuous mass distribution in ℝ2, and let l = {l1, ..., l5 ⊂ ℝ2} be a quintuple of rays with common origin such that any two adjacent angles between them make a sum of at most π. Then an affine image of l subdivides m into five parts with any prescribed ratios.

Conformational structure, dynamics, and solvation energies of small alanine peptides in water and carbon tetrachloride

The rate-limiting barrier for peptide transport across lipid bilayers is the nonpolar hydrocarbon interior. Permeating peptides may undergo conformational changes during their transfer from an aqueous solution into the barrier domain, thus facilitating peptide transport. To test this hypothesis, all-atom and explicit-solvent molecular dynamics (MD) simulations have been conducted on a series of small peptides, p-toluyl-Ala(n) (n = 0-3) used previously in transport experiments, to explore their conformational structures, dynamics and solvation free energies in water and carbon tetrachloride (CCl(4)). The conformations of the p-toluyl alanine di- and tri-peptides in water were found to be far from random coils, with P(II) and alpha(R) dominating but with smaller populations of seven-membered (c(7)) and five-membered rings (c(5)). In contrast, the seven-membered ring, c(7), along with c(5) dominated in CCl(4). These results indicate that the conformational preferences of the alanine peptides are highly sensitive to solvent. Dynamically, stable seven-membered ring formation occurred on a time scale of 10 ps while larger ring-sizes (e.g., 10-membered rings) were observed much less frequently. The values of adjacent torsional angles (phi(1), psi(1)) were dependent on neighboring torsional angles. Thermal motions of neighboring torsions leading to transitions between c(7), c(5), alpha(R), and P(II) conformers were highly cooperative while longer range correlations between transitions of adjacent sets of torsions (phi(1), psi(1)) and (phi(2), psi(2)) were less evident. Peptide folding in CCl(4) lowers the intramolecular electrostatic energies. This, along with hydrophobic interactions, favors partitioning into CCl(4). These effects only partially offset other types of intramolecular interactions and peptide-solvent polar interactions that are more favorable in water, leading to net transfer free energies (3-7 kcal/mol) that disfavor peptide transfer from water into carbon tetrachloride.

Sharpening of directional responses along the auditory pathway of the oyster toadfish, Opsanus tau

Our previous studies have shown that the peripheral auditory system of the toadfish encodes the direction of a sound source. Here, we compare directional responses of peripheral saccular afferents, cells in the descending octaval nucleus (DON) of the medulla, and the torus semicircularis (TS) of the midbrain. Recording locations in the brain were labeled with neurobiotin to confirm the site. To compare directional responses among cells, we calculated an index [sharpening ratio (SR)] that weights the relative strength of responses to the best direction for that cell and to the adjacent stimulus angles tested. Unsharpened saccular afferents tend to have a cosinusoidal directional response pattern (DRP) with an expected SR of 0.87. In DON, more than 60% of the cells exhibited directional sharpening (defined as SR <0.8). In TS, more than 80% of the cells exhibited directional sharpening. We conclude that directional auditory sharpening first occurs in DON and some additional sharpening occurs in the ascending pathway to the midbrain, particularly in azimuth. The sharpening of directional selectivity is likely to be an important component of the neural computations underlying directional hearing.

The behavior of electroplated hard-chromium on Cr–Mo steel subject to long-term annealing at 250 °C

A hard Cr-deposit was annealed at 250 °C for various periods after electroplating. From the results of the DSC analysis and hardness measurement, the softened microstructure in the Cr-deposit was developed after 30 min annealing. By examining the TEM-cross-sectional annealed specimen, a recrystallization zone of the soften microstructure was found, in which equiaxed grains with relative lower dislocation density were examined from place to place and many voids were found among the triple grain boundary. However, most parts of as-plated Cr-deposit grew slightly and were still in texture after long-term annealing at 250 °C. On the interface between the Cr-deposit and the steel initiated equiaxed grains that grew by merging adjacent grain and small angle grain boundary were observed.

The Poisson-Voronoi tessellation: relationships for edges

In a unified approach, this paper presents distributional properties of a Voronoi tessellation generated by a homogeneous Poisson point process in the Euclidean space of arbitrary dimension. Probability density functions and moments are given for characteristics of the ‘typical’ edge in lower-dimensional section hyperplanes (edge lengths, adjacent angles). We investigate relationships between edges and their neighbours, called Poisson points or centres; namely angular distributions, distances, and positions of neighbours relative to the edge. The approach is analytical, and the results are given partly explicitly and partly as integral expressions, which are suitable for the numerical calculations also presented.

The Poisson-Voronoi tessellation: relationships for edges

In a unified approach, this paper presents distributional properties of a Voronoi tessellation generated by a homogeneous Poisson point process in the Euclidean space of arbitrary dimension. Probability density functions and moments are given for characteristics of the ‘typical’ edge in lower-dimensional section hyperplanes (edge lengths, adjacent angles). We investigate relationships between edges and their neighbours, called Poisson points or centres; namely angular distributions, distances, and positions of neighbours relative to the edge. The approach is analytical, and the results are given partly explicitly and partly as integral expressions, which are suitable for the numerical calculations also presented.

Correlation between ω and ψ Dihedral Angles in Protein Structures

The planarity of the peptide group is one of the fundamental features of protein structure that is described in every chemistry and biochemistry textbook. By surveying a dataset of 163 atomic resolution protein structures we here identify the stereochemical conditions that favor significant deformations of peptide bond planarity. In particular, we demonstrate that the values of the omega dihedral angle are strictly correlated to the values of the adjacent psi angle. This trend is also observed in highly strained states such as those occurring in vicinal disulfide bridges. These findings provide direct evidence for the mutual influence of the geometrical parameters that describe the protein structure.