Rms Displacement Research Articles

Semi-empirical formulation of multiple scattering for the Gaussian beam model of heavy charged particles stopping in tissue-like matter

Dose calculation for radiotherapy with protons and heavier ions deals with a large volume of path integrals involving a scattering power of body tissue. This work provides a simple model for such demanding applications. There is an approximate linearity between RMS end-point displacement and range of incident particles in water, empirically found in measurements and detailed calculations. This fact was translated into a simple linear formula, from which the scattering power that is only inversely proportional to the residual range was derived. The simplicity enabled the analytical formulation for ions stopping in water, which was designed to be equivalent with the extended Highland model and agreed with measurements within 2% or 0.02 cm in RMS displacement. The simplicity will also improve the efficiency of numerical path integrals in the presence of heterogeneity.

Residue energy and mobility in sequence to global structure and dynamics of a HIV-1 protease (1DIFA) by a coarse-grained Monte Carlo simulation

Energy, mobility, and structural profiles of residues in a specific sequence of human immunodeficiency virus (HIV)-1 protease chain and its global conformation and dynamics are studied by a coarse-grained computer simulation model on a cubic lattice. HIV-1 protease is described by a chain of 99 residues (nodes) in a specific sequence (1DIFA) with N- and C-terminals on the lattice, where empty lattice sites represent an effective solvent medium. Internal structures of the residues are ignored but their specificities are captured via an interaction (epsilon(ij)) matrix (residue-residue, residue-solvent) of the coefficient (fepsilon(ij)) of the Lennard-Jones potential. Simulations are performed for a range of interaction strength (f) with the solvent-residue interaction describing the quality of the solvent. Snapshots of the protein show considerable changes in the conformation of the protein on varying the interaction. From the mobility and energy profiles of the residues, it is possible to identify the active (and not so active) segments of the protein and consequently their role in proteolysis. Contrary to interaction thermodynamics, the hydrophobic residues possess higher configurational energy and lower mobility while the electrostatic and polar residues are more mobile despite their lower interaction energy. Segments of hydrophobic core residues, crucial for the structural evolution of the protein are identified-some of which are consistent with recent molecular dynamics simulation in context to possible clinical observations. Global energy and radius of gyration of the protein exhibit nonmonotonic dependence on the interaction strength (f) with opposite trends, e.g., rapid transition into globular structure with higher energy. Variations of the rms displacement of the protein and that of a tracer residue, Gly(49), with the time steps show how they slow down on increasing the interaction strength.

Alternative scattering power for Gaussian beam model of heavy charged particles

This study provides an accurate, efficient and simple multiple scattering formulation for heavy charged particles such as protons and heavier ions with a new form of scattering power that is a key quantity for beam transport in matter. The Highland formula for multiple scattering angle was modified to a scattering power formula to be used within the Fermi–Eyges theory in the presence of heterogeneity. An analytical formula for RMS end-point displacement in homogeneous matter was also derived for arbitrary ions. The formulation was examined in terms of RMS angles and displacements in comparison with other formulations and measurements. The results for protons, helium ions and carbon ions in water agreed with them at a level of 2% or the differences were discussed.

Development and preliminary evaluation of a prototype audiovisual biofeedback device incorporating a patient-specific guiding waveform

The aim of this research was to investigate the effectiveness of a novel audio-visual biofeedback respiratory training tool to reduce respiratory irregularity. The audiovisual biofeedback system acquires sample respiratory waveforms of a particular patient and computes a patient-specific waveform to guide the patient's subsequent breathing. Two visual feedback models with different displays and cognitive loads were investigated: a bar model and a wave model. The audio instructions were ascending/descending musical tones played at inhale and exhale respectively to assist in maintaining the breathing period. Free-breathing, bar model and wave model training was performed on ten volunteers for 5 min for three repeat sessions. A total of 90 respiratory waveforms were acquired. It was found that the bar model was superior to free breathing with overall rms displacement variations of 0.10 and 0.16 cm, respectively, and rms period variations of 0.77 and 0.33 s, respectively. The wave model was superior to the bar model and free breathing for all volunteers, with an overall rms displacement of 0.08 cm and rms periods of 0.2 s. The reduction in the displacement and period variations for the bar model compared with free breathing was statistically significant (p = 0.005 and 0.002, respectively); the wave model was significantly better than the bar model (p = 0.006 and 0.005, respectively). Audiovisual biofeedback with a patient-specific guiding waveform significantly reduces variations in breathing. The wave model approach reduces cycle-to-cycle variations in displacement by greater than 50% and variations in period by over 70% compared with free breathing. The planned application of this device is anatomic and functional imaging procedures and radiation therapy delivery.

PARAMETRIC STUDY ON MULTIPLE TUNED MASS DAMPERS USING INTERCONNECTED MASSES

In this paper, the dynamic performance of a controlled high building is numerically investigated considering the effects of different numbers of mass dampers and their interconnection. The numerical analysis is conducted on a 20-story building considered as a shear frame and reduced to an SDOF system by means of the mode-superposition method. The system is subjected to harmonic load. Numerical searches are conducted based on the Min. Max. procedure in order to obtain efficient interconnected (I) multiple tuned mass dampers (MTMD). Comparisons are made among the uncontrolled system, the system controlled by non-interconnected (NI) MTMD, and the system controlled by (I) MTMD in frequency and time domain. Both (NI) and (I) MTMD reduce significantly frequency response peak amplitude. It is observed that the (I) MTMD produces great reductions on maximum displacement, rms displacement, steady-state peak response, and story displacements close to the reductions obtained by (NI) MTMD using review parameters. Mass maximum displacements analysis shows that the space required for (I) MTMD installation is smaller than (NI) MTMD.

VIV of a Composite Riser at Moderate Reynolds Number Using CFD

The vibratory response of a long slender riser, made of composite materials and subject to an ocean current, is examined for a range of conditions. A major focus of this study is the performance of composite materials when used for risers. The influence of the number of modes of vibration is studied, as is the influence of the mass ratio and the value of the damping coefficient. The flow past the riser is represented by a shear flow, ranging from Re=8000 at the lower end of the riser to Re=10,000 at the upper end of the riser. The riser vibration is treated as a coupled fluid-flow/vibration problem. The fluid-flow equations are represented by a large eddy simulation model for the wake turbulence present in the flow. Strip theory is used to represent different forcing locations along the length of the riser. Since the composite riser has a material damping that is frequency dependent (it decreases with increasing frequency), its response is different from, say, a steel riser with a constant material damping. The composite riser, with variable damping, has a larger rms displacement than a riser with constant damping, primarily because of the smaller mass ratio. The vibration amplitude is found to increase with an increase in the number of modes.

The effect of the rotational angle on MR diffusion indices in nerves: Is the rms displacement of the slow-diffusing component a good measure of fiber orientation?

In recent years, much effort has been made to increase our ability to infer nerve fiber direction through the use of diffusion MR. The present study examines the effect of the rotational angle ( α), i.e. the angle between the diffusion sensitizing gradients and the main axis of the fibers in the nerves, on different NMR indices. The indices examined were the apparent diffusion coefficient (ADC), extracted from low b-values ( b max ≈ 1200 s/mm 2), and the root mean square (rms) displacement of the fast and the slow-diffusing components extracted from high b-value q-space diffusion MR data. In addition, the effect of both the diffusion time and myelination was evaluated. We found that the most sensitive index to the rotational angle is the rms displacement of the slow-diffusing component extracted from the high b-value q-space diffusion MR experiment. For this component the rms displacement was nearly constant for α values ranging from −10° to +80° (where α = 0° is the z direction), but it changed dramatically when diffusion was measured nearly perpendicular to the nerve fiber direction, i.e., for α = 90 ± 10°. The ADC and the rms displacement of the fast-diffusing component exhibited only gradual changes, with a maximal change at α = 45 ± 15°. The sensitivity of the rms displacement of the slow-diffusing component to the rotational angle was found to be higher at longer diffusion times and in mature fully myelinated nerves. The relevance of these observations for determining the fiber direction is briefly discussed.

SU-FF-I-07: Single- and Dual-Energy CT Calibration Lines for Assessing the Calcium Content of Lung Nodules: Effects of Patient Body and Lung Nodule Size

Purpose: To determine the concentration of Ca in lung nodules for a CAD technique, lung nodule calibration lines are being derived at locations throughout lung fields. A study was performed to investigate the effects of patient body and lung nodule size on derived calibration lines. Method and Materials: Simulated spherical lung nodules of two concentrations (50 and 100mg/cc ) were employed. Three different diameter nodules (4.8mm, 9.5mm, 16mm) were scanned in a simulated thorax section “A” representing the middle of the chest with large lung regions. The 4.8mm and 9.5mm nodules were also scanned in section “B” representing the upper chest with smaller lung regions. Fat-rings were added to the phantoms to simulate larger patients. Images were acquired on a GE-VCT scanner at 80, 120 and 140kVp. The RMS CT♯ displacements between the calibration lines for phantoms with and without fat-rings were compared. Results: Body-size had a significant effect on the calibration lines for each single kVp technique. Mean RMS displacements for the 9.5mm nodules at 80, 120 and 140 kVp were 22+/−2, 19+/−3, and 18+/−2HU, respectively for phantom “A”, and 19+/−2, 14+/−1, and 14+/−1HU for “B”. Corresponding displacements for 80kVp–140kVp dual-energy were much less: 5+/–1HU (“A”) and 6+/−2HU (“B”). Results similar to the 9.5mm were obtained for the 4.8 and 16mm nodules in phantom “A” However, in phantom “B”, the 4.8mm dual-energy displacements (12+/−4 HU) were about as large as the single-energy. The phantom “B” study was repeated, and the dual-energy displacements for the 4.8mm nodules were slightly better (7+/− 4 HU) on one lung side but about as poor (10+/−7HU) on the other. Conclusion: Dual-energy CT calibration of the calcium concentration of lung nodules is less sensitive to patient body size than single-energy calibration. However, the dual-energy approach may not compensate for patient body size for smaller nodules.

Random error due to Brownian motion in microscopic particle image velocimetry

Simulations were performed to determine the applicability of the central limit theorem in predicting the experimental error in particle image velocimetry experiments caused by the random motion of seed particles due to Brownian motion. For an idealized light-sheet PIV experiment, it was found that the central limit theorem accurately predicts the experimental error when the rms particle motion due to Brownian motion is less than approximately 1 pixel. For rms particle motion greater than this, the central limit theorem underpredicts the random error due to Brownian motion. For all of the microPIV cases investigated, it was found that the central limit theorem always underpredicts the random error due to Brownian motion. This discrepancy between the predicted error and measured error was found to increase with increasing random particle displacement due to Brownian motion. Finally, an empirical formula was developed to predict the rms error due to Brownian motion. Because a direct application of the central limit theorem was found to significantly underpredict the rms error in microPIV experiments, this empirical formula could be useful in interpreting the results from microPIV experiments. The empirical formula was found accurate to within 6% for all cases investigated in the simulations. Thus, the empirical formula can provide a substantial improvement in accurately predicting rms error compared to applying the central limit theorem, which was found to underpredict the random error due to Brownian motion in microPIV experiments by as much as 54% for a 1 pixel rms displacement.

Molecular simulation of an aerosol OT reverse micelle: 2. Energy and kinetic characteristics

The effect of the structure of a reverse micelle on the energy and kinetic characteristics of system components is studied via the molecular dynamics method with the use of the coarse-grain model of a surfactant ion. Partial energies are calculated and the behavior of the local electric potential is determined. It is shown that, despite a high ion concentration, the electric potential in the surface layer of a micelle behaves itself as in the surface layer of pure water. Coefficients of translational diffusion of the components are calculated on the basis of the Einstein relation for the dependence of rms displacement on time. Autocorrelation functions of the angular velocity of eigenvectors of water molecules are obtained.

Lattice site location and annealing behavior of implanted Ca and Sr in GaN

We report on the lattice location of ion-implanted Ca and Sr in thin films of single-crystalline wurtzite GaN. Using the emission channeling technique the angular distributions of β− particles emitted by the radioactive isotopes 45Ca (t1/2=163.8 d) and 89Sr (t1/2=50.53 d) were monitored with a position-sensitive detector following 60 keV room-temperature implantation. Our experiments give direct evidence that ∼90% of Ca and >60% of Sr atoms were occupying substitutional Ga sites with root mean square displacements of the order of 0.15–0.30 Å, i.e., larger than the expected thermal vibration amplitude of 0.074 Å. Annealing the Ca implanted samples at 1100–1350 °C in high-pressure N2 atmosphere resulted in a better incorporation into the substitutional Ga site. The Sr implanted sample showed a small decrease in rms displacements for vacuum annealing up to 900 °C, while the substitutional fraction remained nearly constant. The annealing behavior of the rms displacements can explain why annealing temperatures above 1100 °C are needed to achieve electrical and optical activations, despite the fact that the majority of the acceptors are already located on Ga sites immediately after ion implantation.

Q‐space analysis of lung morphometry in vivo with hyperpolarized3He spectroscopy

To examine the utility of a (3)He spectroscopic q-space technique for detecting changes in lung morphometry in vivo. A diffusion-weighted spectroscopy sequence was used to collect global diffusion data from healthy adults (N = 11), healthy children (N = 5), and chronic obstructive pulmonary disease (COPD) patients (N = 2) using 40 cc of hyperpolarized (3)He gas within a two second breathhold. Displacement probability profiles (DPP) were obtained by Fourier transformation of diffusion data with respect to q. A bi-Gaussian model was used to decompose the DPPs into narrow and broad components, characterized by root-mean-square displacements X(rms1) and X(rms2), respectively. In healthy adults, the narrow component (X(rms,1)) of the DPP had a mean displacement of 188 +/- 10 microm, slightly less than the reported average size of the alveoli. The broad component (X(rms,2)) had a mean value of 474 +/- 44 microm, comparable to the diameter of the respiratory bronchioles in the acinus. In children, both X(rms1) (167 +/- 4 microm) and X(rms2) (382 +/- 22 microm) compared to healthy adults (P < 0.01). In COPD patients, the mean displacements were elevated (X(rms1): 265 +/- 71 microm; X(rms2): 530 +/- 109 microm) compared to healthy adults. Excellent correlation was found between rms displacements and age (age vs. X(rms,1): r = 0.78, P < 0.001; age vs. X(rms,2): r = 0.90, P < 0.001). The q-space parameters agreed remarkably well with published alveolar morphometry data. The results suggest that the technique may be sensitive to disease, as evident from the elevated mean displacements in COPD patients compared to healthy volunteers. Detailed lung microstructural information can be obtained using a very low volume of inhaled (3)He.

Lattice sites of implanted Cu and Ag in ZnO

The group Ib impurities Cu and Ag on substitutional Zn sites are among possible candidates for p-type doping of ZnO. In order to explore possible lattice sites of Cu and Ag in ZnO the radioactive impurities 67Cu and 111Ag were implanted at doses of 4×10 12 cm −2 to 1×10 14 cm −2 at 60 keV into ZnO single crystals. The emission channeling effects of β − particles from the decay were studied by means of position-sensitive electron detectors, giving direct evidence that in the as-implanted state large fractions of Cu and Ag atoms (60%–70% for Cu and 30% for Ag) occupy almost ideal substitutional Zn sites with root mean square (rms) displacements of 0.014–0.017 nm. However, following vacuum annealing at 600 ∘C and above both Cu and Ag were found to be located increasingly on sites that are characterized by large rms displacements (0.03–0.05 nm) from Zn sites. We conclude that in high-temperature treated ZnO Cu and Ag are most likely not simply replacing Zn atoms but are incorporated in complexes with other crystal defects or as clusters.

Prospective motion correction of X-ray images for coronary interventions

A method for prospective motion correction of X-ray imaging of the heart is presented. A 3D + t coronary model is reconstructed from a biplane coronary angiogram obtained during free breathing. The deformation field is parameterized by cardiac and respiratory phase, which enables the estimation of the state of the arteries at any phase of the cardiac-respiratory cycle. The motion of the three-dimensional (3-D) coronary model is projected onto the image planes and used to compute a dewarping function for motion correcting the images. The use of a 3-D coronary model facilitates motion correction of images acquired with the X-ray system at arbitrary orientations. The performance of the algorithm was measured by tracking the motion of selected left coronary landmarks using a template matching cross-correlation. In three patients, we motion corrected the same images used to construct their 3D + t coronary model. In this best case scenario, the algorithm reduced the motion of the landmarks by 84%-85%, from mean RMS displacements of 12.8-14.6 pixels to 2.1-2.2 pixels. Prospective motion correction was tested in five patients by building the coronary model from one dataset, and correcting a second dataset. The patient's cardiac and respiratory phase are monitored and used to calculate the appropriate correction parameters. The results showed a 48%-63% reduction in the motion of the landmarks, from a mean RMS displacement of 11.5-13.6 pixels to 4.4-7.1 pixels.

Lattice location and thermal stability of implanted Fe in ZnO

The emission channeling technique was applied to evaluate the lattice location of implanted Fe59 in single-crystalline ZnO. The angular distribution of β− particles emitted by Fe59 was monitored with a position-sensitive electron detector, following 60 keV low dose (2.0×1013cm−2) room-temperature implantation of the precursor isotope Mn59. The emission patterns around the [0001], [1̱102],[1̱101], and [2̱113] directions revealed that following annealing at 800 °C, 95(8)% of the Fe atoms occupy ideal substitutional Zn sites with rms displacements of 0.06-0.09 Å.

Dielectric function and localized diffusion in ion conducting glasses

We present the three coupled rate equations of the mismatch generated relaxation for the accommodation and transport of ions (MIGRATION) concept that describe the ion dynamics in, for example, ion-conducting glasses and simultaneously yield scaled conductivity and permittivity spectra. Here, model spectra are compared with the experimental spectra of xNa 2O·(1- x)GeO 2 glasses for x=0.0513, 0.0902, 0.213. This allows us to estimate the long-time limit of the localized rms displacement, lim t → ∞ { < R 2 ( t ) > − 6 ⁢ D ⁢ t } 0.5 , which may be roughly interpreted as the average size of the ion cage before the dynamics become diffusive. For the three compositions considered, we obtain an approximate x −1/3 dependence of this quantity, which implies that the ion dynamics are largely governed by the Coulomb interactions between the mobile ions.

Influence of O and C co-implantation on the lattice site of Er in GaN

The lattice location of low-dose implanted Er in GaN, GaN:O, and GaN:C was investigated using the emission channeling technique. The conversion electrons emitted by the probe isotope 167mEr give direct evidence that the majority (≈90%) of Er atoms are located on substitutional Ga sites for all samples. Annealing up to 900 °C does not change these fractions, although it reduces the Er root-mean-square (rms) displacements. The only visible effect of oxygen or carbon doping is a small increase in the rms displacements with respect to the undoped sample.

X-ray structure of human gankyrin, the product of a gene linked to hepatocellular carcinoma.

X-ray structure of human gankyrin, the product of a gene linked to hepatocellular carcinoma.

Lattice location and stability of implanted Cu in ZnO

The lattice location of copper in single-crystalline zinc oxide was studied by means of the emission channeling technique. Following 60-keV room-temperature implantation at a fluence of $2.3\ifmmode\times\else\texttimes\fi{}{10}^{13}{\mathrm{cm}}^{\ensuremath{-}2},$ the angular distribution of ${\ensuremath{\beta}}^{\ensuremath{-}}$ particles emitted by the radioactive isotope ${}^{67}\mathrm{Cu}$ was measured by a position-sensitive detector. The ${\ensuremath{\beta}}^{\ensuremath{-}}$ emission patterns give direct evidence that in the as-implanted state a large fraction of Cu atoms (60%--70%) occupy almost ideal substitutional Zn sites with root-mean-square (rms) displacements of 0.16--0.17 \AA{}. However, following annealing at $600\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ and above Cu was found to be located on sites that are characterized by large rms displacements (0.3--0.5 \AA{}) from Zn sites.

CORRECTION-TO-SCALING OF RANDOM WALKS IN DISORDERED MEDIA

We study the correction to scaling of the rms displacements of random walks in disordered media consisted of connected networks of the lattice percolation in two, three, and four dimensions. The two types of ensemble averages, i.e. an infinite-network average of random walks starting from an infinite network and an all-cluster average starting from any occupied site, are investigated using both the myoptic ants and the blind ants models. We find that the rms displacements exhibit strong nonanalytic corrections in all dimensions. The correction exponent δ defined by the rms displacement of t-step random walks via Rt=At1/d w (1+Bt-δ+Ct-1+⋯) was found as δ≃0.39, 0.27, and 0.27 for, respectively, two, three, and four dimensions for an infinite-network average, and δ≃0.37, 0.28, and 0.24 for an all-cluster average.