Divergent Ray Research Articles

GPU-Accelerated Target Strength Prediction Based on Multiresolution Shooting and Bouncing Ray Method

The application of the traditional planar acoustics method is limited due to the low accuracy when computing the echo characteristics of underwater targets. Based on the concept of the shooting and bouncing ray which considers multiple reflections on the basic of the geometrics optics principle, this paper presents a more efficient GPU-accelerated multiresolution grid algorithm in the shooting and bouncing ray method (SBR) to quickly predict the target strength value of complex underwater targets. The procedure of the virtual aperture plane generation, ray tracing, scattered sound field integral and subdividing the divergent ray tubes are all implemented on the GPU. Particularly, stackless KD-tree traversal is adopted to effectively improve the ray-tracing efficiency. Experiments on the rigid sphere, cylinder and corner reflector model verify the accuracy of GPU-based multiresolution SBR. Besides, the GPU-based SBR is more than 750 times faster than the CPU version because of its tremendous computing capability. Further, the proposed accelerated GPU-based multiresolution SBR improves runtime performance at least 2.4 times that of the single resolution GPU-based SBR.

New iterative reconstruction methods for fan-beam tomography

In this paper, we present a novel class of iterative reconstruction methods for severely angular undersampled or/and limited-view tomographic problems with fan-beam scanning geometry. The proposed algorithms are based on a new analytical transform which generalizes Fourier-slice theorem to divergent-beam scanning geometries. Using a non-rigid coordinate transform, divergent rays can be reorganized into parallel ones. Therefore, one can employ a simpler parallel-beam projection model instead of more complicated divergent-beam geometries. Various existing iterative reconstruction techniques for divergent-beam geometries can be easily adapted to the proposed framework. The significant advantage of this formulation is the possibility of exploiting efficient Fourier-based recovery methods without rebinning of the projections. In case of highly sparse measurements (few-view data), rebinning methods are not suitable due to error-prone angular interpolation involved. In this work, three new methods based on the novel analytical framework for fan-beam geometry are presented: the Gerchberg-Papoulis algorithm, the Neumann decomposition method and its total variation regularized version. Presented numerical experiments demonstrate that the methods can be competitive in reconstructing from few-view noisy tomographic measurements.

Dosimetric impact assessment using a general algorithm in geant4 simulations for a complex-shaped multileaf collimator

PurposeWe have developed an inhouse algorithm for the multileaf collimator (MLC) geometry model construction with an appropriate accuracy for dosimetric tests. Our purpose is to build a complex type of MLC and analyze the influence of the modeling parameters on the dose calculation. MethodsUsing radiochromic films as detector the following tests were done: (I) Density test field: to compare measured and calculated dose distributions in order to determine the tungsten alloy physical density value. (II) Leaf ends test field: to verify the penumbra shape sensitivity against the discretization level set to simulate the curved leaf ends. (III) MLC-closed field: to obtain the value of the air gap between opposite leaves for a closed configuration which completes the modeling of the MLC leakage radiation. (IV) Picket-fence field: to fit the leaf tilt angle with respect of the divergent ray emerging from the source. ResultsFor a 18.5g/cm3 density value we have obtained a maximum, minimum and mean leakage values of 0.43%, 0.36% and 0.38%, similar to the experimental ones. The best discretization level in the leaf ends field shows a 5.51mm FWHM, very close to the measured value (5.49mm). An air gap of 370μm has been used in the simulation for the separation between opposite leaves. Using a 0.44° tilt angle, we found the same pattern as the experimental values. ConclusionsOur code can reproduce complex MLC designs with a submilimetric dosimetric accuracy which implies the necessary background for dose calculation of high clinical interest small fields.

Assessment of the dosimetric impact when modelling complex-shaped multi-leaf collimators in Monte Carlo simulations

Introduction We present a code, developed with the Geant 4 Monte Carlo (MC) toolkit, to model automatically complex-shaped multi-leaf collimators (MLC) by means of geometrical parameters provided by the vendor. In this work, we reproduce the Siemens 160-MLC, which leaves present a complex curved shape, and assess the dose impact found in small fields when using geometry models of different levels of detail. Purpose To evaluate with MC simulations the dosimetric impact of using a simplified geometry model of the 160-MLC and of certain geometry parameters of this MLC design. Materials and methods Dose measurements were carried out with radiochromic films inserted between solid water slabs. The dosimetric tests were: (I) Leaf ends field, to verify the penumbra shape sensitivity against the discretization level set to simulate the curved leaf ends. (II) Transmission, to adjust leaf density and real distance between opposite leaves from intra- and interleaf radiation leakage profiles. (III) Picket fence, to fit the leaf tilt angle with respect of the divergent ray emerging from the source. Results We found a variation in penumbra tails of up to 0.5 mm for varying leaf end discretization levels. Picket fence dose distributions showed that a 0.1°variation of the leaf tilt angle can lead to an underdosage variation on the dose distribution larger than 3%. Conclusion We present a versatile code which can reproduce accurately the singularities of complex MLC designs, which is of key importance for dose calculation of small fields with likely clinical implications. Disclosure Authors have no conflicts of interest.

Translating bed total body irradiation lung shielding and dose optimization using asymmetric MLC apertures.

A revised translating bed total body irradiation (TBI) technique is developed for shielding organs at risk (lungs) to tolerance dose limits, and optimizing dose distribution in three dimensions (3D) using an asymmetrically‐adjusted, dynamic multileaf collimator. We present a dosimetric comparison of this technique with a previously developed symmetric MLC‐based TBI technique. An anthropomorphic RANDO phantom is CT scanned with 3 mm slice thickness. Radiological depths (RD) are calculated on individual CT slices along the divergent ray lines. Asymmetric MLC apertures are defined every 9 mm over the phantom length in the craniocaudal direction. Individual asymmetric MLC leaf positions are optimized based on RD values of all slices for uniform dose distributions. Dose calculations are performed in the Eclipse treatment planning system over these optimized MLC apertures. Dose uniformity along midline of the RANDO phantom is within the confidence limit (CL) of 2.1% (with a confidence probability p=0.065). The issue of over‐ and underdose at the interfaces that is observed when symmetric MLC apertures are used is reduced from more than ±4% to less than ±1.5% with asymmetric MLC apertures. Lungs are shielded by 20%, 30%, and 40% of the prescribed dose by adjusting the MLC apertures. Dose‐volume histogram analysis confirms that the revised technique provides effective lung shielding, as well as a homogeneous dose coverage to the whole body. The asymmetric technique also reduces hot and cold spots at lung‐tissue interfaces compared to previous symmetric MLC‐based TBI technique. MLC‐based shielding of OARs eliminates the need to fabricate and setup cumbersome patient‐specific physical blocks.PACS number(s): 87.55.‐x, 87.55.de, 87.55.D‐

SU‐C‐BRB‐02: Symmetric and Asymmetric MLC Based Lung Shielding and Dose Optimization During Translating Bed TBI

Purpose:The primary aim was to introduce a dose optimization method for translating bed total body irradiation technique that ensures lung shielding dynamically. Symmetric and asymmetric dynamic MLC apertures were employed for this purpose.Methods:The MLC aperture sizes were defined based on the radiological depth values along the divergent ray lines passing through the individual CT slices. Based on these RD values, asymmetrically shaped MLC apertures were defined every 9 mm of the phantom in superior‐inferior direction. Individual MLC files were created with MATLAB™ and were imported into Eclipse™ treatment planning system for dose calculations. Lungs can be shielded to an optimum level by reducing the MLC aperture width over the lungs. The process was repeated with symmetrically shaped apertures.Results:Dose‐volume histogram (DVH) analysis shows that the asymmetric MLC based technique provides better dose coverage to the body and optimum shielding of the lungs compared to symmetrically shaped beam apertures. Midline dose homogeneity is within ±3% with asymmetric MLC apertures whereas it remains within ±4.5% with symmetric ones (except head region where it drops down to −7%). The substantial over and under dosage of ±5% at tissue interfaces has been reduced to ±2% with asymmetric MLC technique. Lungs dose can be reduced to any desired limit. In this experiment lungs dose was reduced to 80% of the prescribed dose, as was desired.Conclusion:The novel asymmetric MLC based technique assures optimum shielding of OARs (e.g. lungs) and better 3‐D dose homogeneity and body‐dose coverage in comparison with the symmetric MLC aperture optimization.The authors acknowledge the financial and infrastructural support provided by Pakistan Institute of Engineering & Applied Sciences (PIEAS), Islamabad and Aga Khan University Hospital (AKUH), Karachi during the course of this research project. Authors have no conflict of interest with any national / international body for the presented work.

Singular value decomposition for the cone-beam transform in the ball

Abstract The X-ray computerized tomography is concerned to the reconstruction of a function f from line (ray) integrals of f. In general, we may have the parallel ray or divergent ray geometry. In this paper we develop an analytical singular value decomposition method for the cone-beam transform in divergent ray geometry. For the parallel ray transform a singular value decomposition has been derived by P. Maass in 1987.

Using Ancient Chinese and Greek Astronomical Data: A Training Sequence in Elementary Astronomy for Pre-Service Primary School Teachers

A great amount of research has been carried out world-wide to promote history of science as a powerful science teaching tool. Because the ways of choosing and using historical elements depend on teachers’ or researchers’ educational purpose, any attempt to support a single model-to-use seems difficult and probably irrelevant. However, specific purposes may reflect specific and prescriptive terms for using historical materials. Our work aims to show up this aspect. It is an attempt to make elements of the history of astronomy involved in the elaboration of a training session for future primary school teachers. Here, ancients’ Greek and Chinese historical elements are chosen and organized according to specific educational and conceptual constraints that include the construction of the quasi-parallelism of solar rays reaching Earths’ surface, and the spontaneous modeling of the propagation of Sunlight leaning on divergent rays. This leads to an original teaching sequence were historical elements are mixed with non historical ones. This organization forms the support of a pre-service training session developed for future primary school teachers. This session aims to provide future teachers with elementary cosmological knowledge (parallelism of Sunrays, shape and size of the Earth, Sun-Earth distance…), to provide some reference marks of history of ancient cosmologies (spherical and flat Earth) resulting from two distinct contexts, and to approach some aspects associated with Nature of Science (NOS).

On the horoboundary and the geometry of rays of negatively curved manifolds

We study the Gromov compactification of quotients X= G of a Hadamard space X by a discrete group of isometries G, pointing out the main differences with the simply connected case. We prove a criterion for the Busemann equivalence of rays on these quotients and show that the “visual” description of the Gromov boundary breaks down, producing examples for the main pathologies that may occur in the nonsimply connected case, such as: divergent rays having the same Busemann functions, points on the Gromov boundary that are not Busemann functions of any ray, and discontinuity of the Busemann functions with respect to the initial conditions. Finally, for geometrically finite quotients X= G, we recover a simple description of the Gromov boundary, and prove that in this case the compactification is a singular manifold with boundary, with a finite number of conical singularities.

Total body irradiation dose optimization based on radiological depth

We have previously demonstrated the use of Eclipse fluence optimization to define aperture sizes for a novel aperture modulated translating bed total body irradiation (TBI) technique. The purposes of the present study were to identify, characterize, and correct for sources of error inherent in our previous fluence optimization technique, and to develop a clinically viable fluence optimization module for the translating bed TBI technique. Aperture modulated TBI is delivered by translating the patient at constant speed on a custom bed under a modulated radiation beam. The patient is then turned from supine to prone and the process repeated, resulting in an AP‐PA treatment. Radiological depths were calculated along divergent ray lines through individual CT slices of a RANDO phantom. Beam apertures, defined using a dynamic multileaf collimator (DMLC), were generated using calculated radiological depths and calibration factors that relate fluence to aperture size in a dynamic environment. These apertures were defined every 9 mm along the phantom superior‐inferior axis. The calculated beam apertures were further modified to account for scatter within the patient. For dose calculation purposes the individual MLC files were imported into Eclipse. For treatment delivery, dynamic MLC files for both AP and PA beams were generated and delivered dynamically. Dose homogeneity in the head and neck region of the RANDO phantom was within ± 4% of the prescribed dose with this novel technique compared to −5% to +7% with our previous aperture modulated technique based on Eclipse fluence optimization. Fluence optimization and beam aperture calculation using the new technique offers a ten‐fold reduction in planning time and significantly reduces the likelihood of user error during the planning process. In conclusion, a clinically viable aperture modulated translating bed TBI technique that employs dynamically shaped MLC‐defined beam apertures based on radiological depth calculations, has been developed.PACS numbers: 87.55.‐x, 87.55.D‐

Regions of high correlation of acoustic waves in oceanic waveguides

We discuss the role of weakly divergent rays in the formation of regions with high correlation of waves in inhomogeneous stationary random media. The geometrical-acoustic approximation is used. Theoretical study is supported by numerical calculations.

SU-E-T-730: Aperture Modulated Total Body Irradiation Dose Optimization Based on the Calculation of Radiological Depth

Purpose: Total body irradiation (TBI) techniques aim to deliver a uniform and accurate radiation dose to the entire anatomy of the patient. Given irregular patient shapes and internal inhomogeneities achieving a dose homogeneity within ±10 % of the prescribed dose represents a non trivial challenge. We propose a novel TBI technique which is capable of delivering a more uniform dose to the entire patient than conventional TBI techniques. Methods: Radiological depth calculations are performed along divergent ray lines through transverse CT slices of an anthropomorphic Rando® phantom. The radiological depths take into account both body contour variation and internal inhomogeneities. Based on the calculated radiological depths, multiple beam apertures can be generated using dynamic multileaf collimation (DMLC). To account for the scatter contribution, scatter kernels are derived using the concept of the scatter maximum ratios (SMR). Based on the scatter calculation the calculated beam apertures are modified. For dose calculation purposes the individual MLC files are imported into the Eclipse™ treatment planning system. However for treatment delivery, a single MLC file with multiple control points is generated and delivered while the phantom is translated on a motorized bed close to the floor through a stationary radiation beam with 0° gantry angle. Results: In comparison to fixed open beam translating bed TBI the dose deviation along the midline was reduced from ±8% to less than ±4% of the prescribed dose with this new technique. Lungdose was reduced by more than 15%. Agreement between calculated and measured doses was better than 3% in Rando®. Conclusions: A novel, aperture modulated translating bed TBI technique that employs dynamically shaped MLC defined beams has been developed for improving dose uniformity in three dimensions. In comparison with the open fixed beam TBI technique, the dose distribution homogeneity is greatly improved.

Weakly divergent ray and diffraction beams in oceanic waveguides

Conditions that should be satisfied by the sound velocity profile of an oceanic waveguide for the dependence of the ray cycle length on the ray phase velocity to contain smooth extrema are formulated. The extrema correspond to weakly divergent ray beams forming “caustic” beams. It is found that diffraction effects cause a considerable smoothing of the sharp extrema that occur in the dependence of the interference period of neighboring modes on their phase velocity. As a result, in addition to the weakly divergent ray beams, weakly divergent diffraction beams and the corresponding “diffraction” caustics can be formed.

Weak geodesic topology and fixed finite subgraph theorems in infinite partial cubes II. Fixed subgraph properties and infinite treelike partial cubes

We prove that if a partial cube G contains no divergent rays, then: (i) there exists a non-empty finite convex subgraph of G which is fixed by every automorphism of G; (ii) every self-contraction of G fixes a non-empty finite isometric subgraph of G; (iii) for every commuting family F of self-contractions of G, there exists a non-empty finite isometric subgraph of G which is fixed by every element of F. Moreover, we show that those fixed subgraphs can be specified for some particular partial cubes, as is the case for median graphs and more generally for netlike partial cubes. We give new examples of such special graphs by extending the finite concept of treelike partial cubes [B. Brešar et al., Tree-like isometric subgraphs of hypercubes, Discussiones Mathematicae–Graph Theory 23 (2003), 227–240] to the infinite case, and by introducing what we call faithful-treelike, convex-treelike and strongly treelike partial cubes.

SU‐GG‐T‐511: Towards Real‐Time Radiation Therapy: Superposition/Convolution at 4fps

Purpose: To enable novel radiation therapy workflows by providing superposition/convolution dose calculation at interactive rates. Method and Materials: The Superposition/Convolution (S/C) dose computation algorithm utilizes ray‐tracing techniques extensively and is well suited to acceleration using consumer graphics processing units (GPU). The standard S/C algorithm was parallelized and implemented using NVIDIA's CUDA GPU programming environment. The basic S/C method generates incident fluence, using a source model, and transports it from the radiation source, using ray‐tracing, to deposit a TERMA grid. Then superposition spreads the dose deposition kernel out by ray‐tracing from each point in the TERMA grid. There are several issues with parallelizing this algorithm. Calculation of the TERMA grid suffers from read‐write conflicts. We solve this by running groups of spatially separated divergent rays. The forward S/C kernel also suffers from read‐write conflicts, but the inverse kernel does not. We reduced memory bandwidth by using a variable step ray‐tracer, independently attenuating each spectral energy bin and caching lookup‐tables. We explored the concept of using volumetric mip‐maps to approximate the ray as a true solid angle. Results: We compared our implementation to Pinnacle3 for low (64×64×64 cube with 4 mm voxels) and high resolution (128×128×128 cube with 2mm voxels) water phantoms using as similar settings as possible. Pinnacle3 (Philips ‐ Madison, WI) was run on a SunFire v250 machine with times of 30.961s and 365.944s respectively. We performed our calculations on a single NVIDIA GeForce 8800 GTX with times of 0.217s and 2.197s respectively. Preliminary experiments using volumetric mip‐maps showed additional performance improvements with minor accuracy loss. Conclusion: We have completed a GPU accelerated superposition/convolution dose engine, providing a substantial performance gain over CPU based implementations — indicating that real time dose computation is feasible with the accuracy levels of the S/C algorithm.

Efficient projection and backprojection scheme for spherically symmetric basis functions in divergent beam geometry

In cone-beam transmission tomography the measurements are performed with a divergent beam of x-rays. The reconstruction with iterative methods is an approach that offers the possibility to reconstruct the corresponding images directly from these measurements. Another approach based on spherically symmetric basis functions (blobs) has been reported with results demonstrating a better image quality for iterative reconstruction algorithms. When combining the two approaches (i.e., using blobs in iterative cone-beam reconstruction of divergent rays) the problem of blob sampling without introducing aliasing must be addressed. One solution to this problem is to select a blob size large enough to ensure a sufficient sampling, but this prevents a high resolution reconstruction, which is not desired. Another solution is a heuristic low-pass filtering, which removes this aliasing, but neglects the different contributions of blobs to the absorption depending on the spatial position in the volume and, therefore, cannot achieve the best image quality. This article presents a model of sampling the blobs which is motivated by the beam geometry. It can be used for high resolution reconstruction and can be implementedefficiently.

Sci-Thur PM Therapy-10: Is there an optimal starting gantry angle for equiangular-spaced beam arrangements in IMRT?

Equiangular‐spaced beam arrangements are the standard for intensity‐modulated radiotherapy(IMRT). However, since the choice of starting gantry angle is arbitrary, the question arises of whether there exist optimal starting gantry angles which will produce clinically significant improvements. To investigate the effect of beam orientation, the starting gantry angles in a 5‐beam equiangular‐spaced arrangement were incremented by 5°. Fifteen IMRT plans were generated per patient using 6 MV photon beams with static MLC delivery for 5 prostate, 5 lung, and 5 head‐and‐neck cancer patients. The plans were compared based on Planning Target Volume (PTV) and Organ‐at‐Risk (OAR) dose‐volume histograms, PTV mean dose, OAR maximum dose, total number of segments, and total number of monitor units. A fundamental geometric PTV conformity analysis was also conducted for each increment in gantry angle. To achieve this, divergent ray tracing was performed from the beam source coordinates through the PTV Beam's‐Eye‐View to produce a 3D cone beam matrix. The geometric conformity index (ratio of beam overlap volume to PTV volume) was then calculated. Clinically insignificant variations in PTV mean dose were found for all treatment sites as the starting gantry angles were incremented. This observation was further supported by the small variation in geometric conformity index with gantry increment. The variations in rectal V 75 Gy, spinal cord DVH, and parotid V 30 Gy were clinically significant for the prostate, lung, and head‐and‐neck patients, respectively. It is evident that the choice of starting gantry angle in IMRT equiangular‐spaced beam arrangements must be chosen with care.

The ultrasonic probe for the investigating of internal object structure by ultrasound transmission tomography

The main component of every device used for investigating internal object structure by Ultrasound Transmission Tomography (UTT) is a special ultrasonic probe. This paper presents the structure of model multielement ring probe for examining objects using this method in divergent ray projection geometry. The probe is made up of 1024 rectangular separate piezoelectric transducers working at frequency f = 1.7 MHz, placed inside a ring with diameter D = 30 cm and height h = 9 cm. Each element of the probe is equipped with a quarter-wave matching layer. All the transducers function as transmitters and receivers, and can be joined in groups both during transmitting and during receiving. Some examples of admittance characteristics of a single piezoelectric transducer and examples of shapes of pulses generated and received by particular transducers were presented. Important factors affecting the measurement resolution are the sizes of the active surface of the transducers.

Propagation of whistler-mode chorus to low altitudes: divergent ray trajectories and ground accessibility

Abstract. We investigate the ray trajectories of nonductedly propagating lower-band chorus waves with respect to their initial angle θ0, between the wave vector and ambient magnetic field. Although we consider a wide range of initial angles θ0, in order to be consistent with recent satellite observations, we pay special attention to the intervals of initial angles θ0, for which the waves propagate along the field lines in the source region, i.e. we mainly focus on waves generated with &theta0 within an interval close to 0° and on waves generated within an interval close to the Gendrin angle. We demonstrate that the ray trajectories of waves generated within an interval close to the Gendrin angle with a wave vector directed towards the lower L-shells (to the Earth) significantly diverge at the frequencies typical for the lower-band chorus. Some of these diverging trajectories reach the topside ionosphere having θ close to 0°; thus, a part of the energy may leak to the ground at higher altitudes where the field lines have a nearly vertical direction. The waves generated with different initial angles are reflected. A small variation of the initial wave normal angle thus very dramatically changes the behaviour of the resulting ray. Although our approach is rather theoretical, based on the ray tracing simulation, we show that the initial angle θ0 of the waves reaching the ionosphere (possibly ground) is surprisingly close - differs just by several degrees from the initial angles which fits the observation of magnetospherically reflected chorus revealed by CLUSTER satellites. We also mention observations of diverging trajectories on low altitude satellites.

State of the autonomous (autonomic) nervous system in general diseases accompanied by myopia

Myopia is a type of refractive error of the eye characterized by the fact that the rays from the image of objects gather in focus before reaching the retina, in front of it. Divergent rays fall on the retina and create light scattering circles. To reduce these, people with myopia squint their eyes.