The dependence of computed tomography number to relative electron density conversion on phantom geometry and its impact on planned dose

A computed tomography number to relative electron density (CT-RED) calibration is performed when commissioning a radiotherapy CT scanner by imaging a calibration phantom with inserts of specified RED and recording the CT number displayed. In this work, CT-RED calibrations were generated using several commercially available phantoms to observe the effect of phantom geometry on conversion to electron density and, ultimately, the dose calculation in a treatment planning system. Using an anthropomorphic phantom as a gold standard, the CT number of a material was found to depend strongly on the amount and type of scattering material surrounding the volume of interest, with the largest variation observed for the highest density material tested, cortical bone. Cortical bone gave a maximum CT number difference of 1,110 when a cylindrical insert of diameter 28 mm scanned free in air was compared to that in the form of a 30 × 30 cm2 slab. The effect of using each CT-RED calibration on planned dose to a patient was quantified using a commercially available treatment planning system. When all calibrations were compared to the anthropomorphic calibration, the largest percentage dose difference was 4.2 % which occurred when the CT-RED calibration curve was acquired with heterogeneity inserts removed from the phantom and scanned free in air. The maximum dose difference observed between two dedicated CT-RED phantoms was ±2.1 %. A phantom that is to be used for CT-RED calibrations must have sufficient water equivalent scattering material surrounding the heterogeneous objects that are to be used for calibration.

Some remarks on the symplectic pairing on the moduli space of representations of the fundamental group of surfaces

This work grew out of an attempt to understand a conjectural remark made by Professor Kyoji Saito to the author about a possible link between the Fox-calculus description of the symplectic structure on the moduli space of representations of the fundamental group of surfaces into a Lie group and pairs of mutually dual sets of generators of the fundamental group. In fact in his paper [3] , Prof. Kyoji Saito gives an explicit description of the system of dual generators of the fundamental group.

Void Geometry Driven Spin Crossover in Zeolite-Encapsulated Cobalt Tris(bipyridyl) Complex Ion

The cobalt(II) tris(bipyridyl) complex ion encapsulated in zeolite-Y supercages exhibits a thermally driven interconversion between a low-spin and a high-spin state-a phenomenon not observed for this ion either in solid state or in solution. From a comparative study of the magnetism and optical spectroscopy of the encapsulated and unencapsulated complex ion, supported by molecular modeling, such spin behavior is shown to be intramolecular in origin. In the unencapsulated or free state, the [Co(bipy)(3)](2+) ion exhibits a marked trigonal prismatic distortion, but on encapsulation, the topology of the supercage forces it to adopt a near-octahedral geometry. An analysis using the angular overlap ligand field model with spectroscopically derived parameters shows that the geometry does indeed give rise to a low-spin ground state, and suggests a possible scenario for the spin state interconversion.

The equilibrium geometry and electronic structure of Bi nanolines on clean and hydrogenated Si(001) surfaces

The equilibrium geometry, electronic structure and energetic stability of Bi nanolines on clean and hydrogenated Si(001) surfaces have been examined by means of ab initio total energy calculations and scanning tunnelling microscopy. For the Bi nanolines on a clean Si surface the two most plausible structural models, the Miki or M model (Miki et al 1999 Phys. Rev. B 59 14868) and the Haiku or H model (Owen et al 2002 Phys. Rev. Lett. 88 226104), have been examined in detail. The results of the total energy calculations support the stability of the H model over the M model, in agreement with previous theoretical results. For Bi nanolines on the hydrogenated Si(001) surface, we find that an atomic configuration derived from the H model is also more stable than an atomic configuration derived from the M model. However, the energetically less stable (M) model exhibits better agreement with experimental measurements for equilibrium geometry. The electronic structures of the H and M models are very similar. Both models exhibit a semiconducting character, with the highest occupied Bi-derived bands lying at ~0.5 eV below the valence band maximum. Simulated and experimental STM images confirm that at a low negative bias the Bi lines exhibit an 'antiwire' property for both structural models.

The geometry of Bi nanolines on Si(0 0 1)

A study of the Bi nanoline geometry on Si(0 0 1) has been performed using a combination of ab initio theoretical technique and scanning tunnelling microscopy (STM). Our calculations demonstrate decisively that the recently proposed Haiku geometry is a lower energy configuration than any of the previously proposed line geometries. Furthermore, we have made comparisons between STM constant-current topographs of the lines and Tersoff–Haman STM simulations. Although the Haiku and the Miki geometries both reproduce the main features of the constant-current topographs, the simulated STM images of the Miki geometry have a dark stripe between the dimer rows that does not correspond well with experiment.

Collision-Geometry-Based Pulsed Guidance Law for Exoatmospheric Interception

No abstract is available.

A follow up MRI-based geometry and computational fluid dynamics study of carotid bifurcation

Cardiovascular disease is the leading causes of death in the developed world. Wall shear stress (WSS) is associated with the initiation and progression of atherogenesis. This study combined the recent advances in MR imaging and computational fluid dynamics (CFD) and evaluated the patient-specific carotid bifurcation. The patient was followed up for 3 years. The geometry changes (tortuosity, curvature, ICA/CCA area ratios, central to the cross-sectional curvature, maximum stenosis) and the CFD factors (Velocity distribute, Wall Shear Stress (WSS) and Oscillatory Shear Index (OSI)) were compared at different time points.The carotid stenosis was a slight increase in the central to the cross-sectional curvature, and it was minor and variable curvature changes for carotid centerline. The OSI distribution presents ahigh-values in the same region where carotid stenosis and normal border, indicating complex flow and recirculation.The significant geometric changes observed during the follow-up may also cause significant changes in bifurcation hemodynamics.

Study of tracheal collapsibility, compliance and stress by considering its asymmetric geometry

The shape of tracheal cartilage has been widely treated as symmetric in analytical and numerical models. However, according to both histological images and in vivo medical image, tracheal cartilage is of highly asymmetric shape. Taking the cartilage as symmetric structure will induce bias in calculation of the collapse behavior, as well as compliance and muscular stress. However, this has been rarely discussed. In this paper, tracheal collapse is represented by considering its asymmetric shape. For comparison, the symmetric shape, which is reconstructed by half of the cartilage, is also presented. A comparison of cross-sectional area, compliance of airway and stress in the muscular membrane, determined by asymmetric shape and symmetric shape is made. The result indicates that the symmetric assumption brings a small error, around 5% in predicting the cross-sectional area under loading conditions. The relative error of compliance is more than 10%. Particularly when the pressure is close to zero, the error could be more than 50%. The model considering the symmetric shape results in a significant difference in predicting stress in muscular membrane by either under- or over-estimating it. In conclusion, tracheal cartilage should not be treated as a symmetric structure. The results obtained in this study are helpful in evaluating the error induced by the assumption in geometry.

Fluid-structure interaction study on human arterial plaque with patient specific geometry and boundary conditions

Atherosclerotic plaque rupture has been extensively considered as the leading cause of death in western countries. It is believed that high stresses within plaque can be an important factor on triggering the rupture of the plaque. Stress analysis in the coronary and carotid arteries with plaque have been developed by many researchers from 2D to 3-D models, from structure analysis only to the Fluid-Structure Interaction (FSI) models[1].

Geometry Of Proline And Hydroxyproline .1. An Analysis Of X-Ray Crystal-Structure Data

We have carried out an analysis of crystal structure data on prolyl and hydroxyprolyl moieties in small molecules. The flexibility of the pyrrolidine ring due to the pyramidal character of nitrogen has been defined in terms of two projection angles δ1 and δ2. The distribution of these parameters in the crystal structures is found to be consistent with results of the energy calculations carried out on prolyl moieties in our laboratory.

The mean geometry of the peptide unit from crystal structure data

The average dimensions of the peptide unit have been obtained from the data reported in recent crystal structure analyses of di- and tripeptides. The bond lengths and bond angles agree with those in common use, except for the bond angle C---N---H, which is about 4° less than the accepted value, and the angle C2α---N---H which is about 4° more. The angle τ (Cα) has a mean value of 114° for glycyl residues and 110° for non-glycyl residues. Attention is directed to these mean values as observed in crystal structures, as they are relevant for model building of peptide chain structures.

Optimum geometry for uniform deposits on a rotating substrate from a point source

The application of an algorithm shows that maximum uniformity of film thickness on a rotating substrate is achieved for a normalized source-to-substrate distance ratio, h/r =1.183.

Formal description, compression and transformation of digital pictures II. Picture algebra and geometry

In an earlier paper (Part I) we described the construction of Hermite code for multiple grey-level pictures using the concepts of vector spaces over Galois Fields. In this paper a new algebra is worked out for Hermite codes to devise algorithms for various transformations such as translation, reflection, rotation, expansion and replication of the original picture. Also other operations such as concatenation, complementation, superposition, Jordan-sum and selective segmentation are considered. It is shown that the Hermite code of a picture is very powerful and serves as a mathematical signature of the picture. The Hermite code will have extensive applications in picture processing, pattern recognition and artificial intelligence.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

Generalised quaternion methods in conformal geometry

A new approach to Penrose's twistor algebra is given. It is based on the use of a generalised quaternion algebra for the translation of statements in projective five-space into equivalent statements in twistor (conformal spinor) space. The formalism leads toSO(4, 2)-covariant formulations of the Pauli-Kofink and Fierz relations among Dirac bilinears, and generalisations of these relations.