scholarly journals Improvements in Simulations for Radiotherapy Wedge Filter dose and AAA-Convolution Factor Algorithms

2019 ◽  
pp. 194-219
Author(s):  
Francisco Casesnoves
Keyword(s):  
Integral Equation ◽  
Gaussian Model ◽  
Spherical Geometry ◽  
Numerical Data ◽  
Integral Form ◽  
Dose Delivery ◽  
Equation Resolution ◽  
Exponential Factor ◽  
Multi Leaf Collimator ◽  
Series Development

Analytical-convoluted and numerical Gaussian models have been used in recent decades for radiotherapy treatment planning software/calculations, to perform accurately radiation dose delivery –numerical, analytical, or numerical-analytical. The objective of this evoluted-contribution was to obtain an exact dose delivery, 3D analytical-integral-equation solution, for the triple Gaussian model of wedge filters, since previous/initial 2D approximations of other authors, although correct, were not completely exact. Additionally, to set conceptual and mathematical-geometrical differences between the beam modification created by Multi-Leaf Collimator and Wedge Filters, either standard or Conformal. Ever the precision, from mathematical theory algorithms to real laboratory measurements, a series of simulations are presented. The generic triple Gaussian model of Ulmer and Harder sets an Attenuation Exponential Factor, AEF, well approximated in 2 variables, namely, u and z. This evoluted contribution of the research contribution was specially focused on numerical methods and approximation analysis of the integral equation resolution –with extent details about numerical data, Appendix 3. In this paper we set a detailed spatial-spherical geometry discussion/proof towards the determination of a 3D integral form of the delivery dose in water. In other words, with an AEF for magnitude-values of variables u,v, and z. Simulations, based on these new determinations were shown with sharp presentation of the numerical-computational software and functional programming series development. Computing encode techniques are explained with some practical examples for numerical radiotherapy calculus.

scholarly journals Entire Solutions of an Integral Equation in R5

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Xin Feng ◽  
Xingwang Xu
Keyword(s):  
Integral Equation ◽  
Closed Form ◽  
Integral Form ◽  
Entire Solution ◽  
Entire Solutions ◽  
Positive Entire Solution ◽  
Moving Sphere Method

We will study the entire positive C0 solution of the geometrically and analytically interesting integral equation: u(x)=1/C5∫R5‍|x-y|u-q(y)dy with 0<q in R5. We will show that only when q=11, there are positive entire solutions which are given by the closed form u(x)=c(1+|x|2)1/2 up to dilation and translation. The paper consists of two parts. The first part is devoted to showing that q must be equal to 11 if there exists a positive entire solution to the integral equation. The tool to reach this conclusion is the well-known Pohozev identity. The amazing cancelation occurred in Pohozev’s identity helps us to conclude the claim. It is this exponent which makes the moving sphere method work. In the second part, as normal, we adopt the moving sphere method based on the integral form to solve the integral equation.

scholarly journals Splash formation at the nose of a smoothly curved body in a stream

1999 ◽  
Vol 40 (4) ◽  
pp. 421-436 ◽  
Author(s):  
E. O. Tuck ◽  
S. T. Simakov
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Velocity Potential ◽  
Integral Form ◽  
The Body ◽  
Front Face ◽  
Separation Condition ◽  
Polygonal Approximation ◽  
Side Condition ◽  
Two Dimensional Flow

AbstractIn two-dimensional flow past a body close to a free surface, the upwardly diverted portion may separate to form a splash. We model the nose of such a body by a semi-infinite obstacle of finite draft with a smoothly curved front face. This problem leads to a nonlinear integral equation with a side condition, a separation condition and an integral constraint requiring the far-upstream free surface to be asymptotically plane. The integral equation, called Villat's equation, connects a natural parametrisation of the curved front face with the parametrisation by the velocity potential near the body. The side condition fixes the position of the separation point, whereas the separation condition, known as the Brillouin-Villat condition, imposes a continuity relation to be satisfied at separation. For the described flow we derive the Brillouin-Villat condition in integral form and give a numerical solution to the problem using a polygonal approximation to the front face.

The interaction effect between two neutron absorbers using Wallace's method

2000 ◽  
Vol 78 (12) ◽  
pp. 1035-1054 ◽  
Author(s):  
M MR Williams
Keyword(s):  
Integral Equation ◽  
Transport Equation ◽  
Absorption Rate ◽  
Exact Result ◽  
Integral Form ◽  
High Accuracy ◽  
Approximation Procedure ◽  
Plate Separation ◽  
Source Sink ◽  
Constant Source

The dependence of Galanin's constant on fuel-plate separation is studied. Galanin's constant arises in the source–sink method of lattice calculations and normally its value for an isolated fuel plate is used. Our calculations therefore enable the accuracy of that assumption to be assessed. To illustrate the problem, two absorbing and scattering plates, embedded in an infinite moderator and separated by a distance b are considered, with a source in the moderator region. The calculations are carried out via the integral form of the transport equation using the little-known method of Wallace. This approach enables the integral equation to be cast into a particularly useful form for evaluation of the flux and absorption rate in the plates. A variational method and a numerical solution provide results that show that there are significant deviations from the isolated plate approximation. Tables and figures are provided to illustrate these conclusions. In addition to the main result, we take the opportunity to show how Wallace's method can be used to simplify the transport equation for an infinitely reflected slab reactor. We also obtain results for the flux in a half-space in which there is a constant source, using a novel approximation procedure. Comparison with the exact result shows high accuracy.

scholarly journals Physical and Dosimetric Aspect of Euromechanics Add-on Multileaf Collimator on Varian Clinac 2100 C/D

2019 ◽  
Vol 9 (1Feb) ◽  
Author(s):  
S A Rohani ◽  
S R Mahdavi ◽  
A Mostaar ◽  
S Ueltzhöffer ◽  
R Mohammadi ◽  
...  
Keyword(s):  
Quality Assurance ◽  
Full Width Half Maximum ◽  
Intensity Modulated Radiation Therapy ◽  
Multileaf Collimator ◽  
Dose Delivery ◽  
Positional Accuracy ◽  
Position Accuracy ◽  
Multi Leaf Collimator ◽  
Radiation Transmission ◽  
Study Application

Background: Before treatment planning and dose delivery, quality assurance of multi-leaf collimator (MLC) has an important role in intensity-modulated radiation therapy (IMRT) due to the creation of multiple segments from optimization process.Objective: The purpose of this study is to assess the quality control of MLC leaves using EBT3 Gafchromic films.Material and Methods: Leaf Position accuracy and leaf gap reproducibility were checked with Garden fence test. The garden fence test consists of 5 thin bands A) 0.2 Cm width spaced at 2 Cm intervals and B) 1 Cm width spaced at 1 Cm intervals. Each leaf accuracy was analyzed with measuring the full-width half-maximum (FWHM). Maximum and average leaf transmission were measured with gafchromic EBT3 films from Ashland for both 6 MV and 18 MV beams.Results: Leaf positions were found to be in a range between 1.78 – 2.53 mm, instead of nominal 2 mm for the test A and between 9.09 – 10.36 mm, instead of nominal 10 mm for the test B. The Average radiation transmission of the MLC was noted 1.79% and 1.98% of the open 10x10 Cm2 field at isocenter for 6 MV and 18 MV beams, respectively. Maximum radiation transmission was noted 4.1% and 4.4% for 6 MV and 18 MV beams, respectively.Conclusion: In this study, application of gafchromic EBT3 films for the quality assurance of Euromechanics multileaf collimator was studied. Our results showed that the average leaf leakage and positional accuracy of this type of MLC were in the acceptance level based on the Protocols.

Characterization and Thermal Degradation of Polyimide Derived from 5-amino-2(p-aminophenyl) Benzoxazole Monomer with Pyromellitic Dianhydride

2012 ◽  
Vol 455-456 ◽  
pp. 806-814 ◽  
Author(s):  
Xiang Li Meng ◽  
Ling Jiang ◽  
Yu Dong Huang
Keyword(s):  
Thermal Degradation ◽  
Three Dimensional ◽  
Integral Form ◽  
Polyimide Film ◽  
Amic Acid ◽  
Pyromellitic Dianhydride ◽  
Ozawa Method ◽  
Element Analysis ◽  
Exponential Factor ◽  
Good Thermal Stability

- 5-amino-2(p-aminophenyl) benzoxazole (AAPB) and its derived polyimide prepared with pyromellitic dianhydride (PMDA) were synthesized successfully. Their structures were characterized by FT-IR, 1H NMR, Element analysis, 13C NMR, Solid-state 13CNMR, DSC, TG and XRD. The polyimide was synthesized via a conventional two-stage method. The intermediate poly (amic acid) had inherent viscosity of 1.06dL/g and could be thermally converted into light yellow polyimide film. The polyimide showed excellent solvent resistance and good thermal stability. The glass transition temperature (Tg) was found to be 314°C, the decomposition started at a temperature above 500°C in air and above 550°C in argon atmosphere. The thermal degradation of the polyimide was studied by thermogravimetric analysis (TGA) in order to determine the actual reaction mechanisms of the decomposition process. The apparent activation energy (Ea) was obtained following Flynn-Wall-Ozawa method. The activation energies of different mechanism models and pre-exponential factor (A) were determined by Coats-Redfern method. Compared with the value obtained from the Ozawa method, the actual reaction mechanism obeyed three-dimensional diffusion model, Jander equation (D3) with integral form g(α)=[1-(1-α)1/3]2.

Two-Group Neutron Transport Theory for Plane and Spherical Geometry

1970 ◽  
Vol 25 (10) ◽  
pp. 1370-1374 ◽  
Author(s):  
K. O. Thielheim ◽  
W. Blöcker
Keyword(s):  
Integral Equation ◽  
Singular Integral ◽  
Fredholm Integral Equation ◽  
Transport Theory ◽  
Neutron Transport ◽  
Spherical Geometry ◽  
Singular Integral Equations ◽  
Neutron Transport Theory ◽  
Critical Problems ◽  
Expansion Coefficients

Abstract Two-Group neutron transport theory is applied to critical problems in plane and spherical geometry. The neutron flux and the density transform for plane and spherical geometry respectively are expanded into singular eigenfunctions of the transport equation. With aid of the theory of singular integral equations the problem is reduced to one Fredholm integral equation for the expansion coefficients. The critical equations are presented as additional conditions.

Simulation study of proton arc therapy with the compact single-room MEVION-S250 proton therapy system

2020 ◽  
Vol 19 (4) ◽  
pp. 347-354
Author(s):  
Sven Ferguson ◽  
Salahuddin Ahmad ◽  
Imad Ali
Keyword(s):  
Treatment Planning ◽  
Proton Therapy ◽  
Simulation Study ◽  
Double Scattering ◽  
Dose Delivery ◽  
Scattering System ◽  
Normal Tissues ◽  
Multi Leaf Collimator ◽  
Arc Therapy ◽  
Single Aperture

AbstractAim:The purpose of this study is to investigate the feasibility of proton arc therapy (PAT) using the double-scattering MEVION-S250 proton system. The treatment planning and dose delivery parameters from PAT were compared with conventional treatment planning techniques.Materials and methods:PAT was simulated with multiple conformal and fixed-aperture beams (5–15) using the MEVION-S250-double-scattering proton system. Conformal apertures were simulated with the Eclipse-treatment-planning system: (a) using a static single aperture that provides the best average conformal circular or rectangular apertures to cover the tumour from different angular views (SPAT), and (b) dynamic conformal apertures of the tumour shape at each irradiation angle that can be obtained from a multi-leaf-collimator system (DPAT).Results:The DPAT and SPAT plans provided superior dose coverage and sparing of normal tissues in comparison with conventional plans (CPT). The entrance normal tissue and skin doses (<40%) were lowered significantly by delivering dose from different directions over a wider angular view compared to conventional plans that have large entrance dose from only two fields. While the mean and minimum doses from PAT and CPT were comparable, the maximum doses from arc plans were lower than the maximum doses in conventional plans. The SPAT and DPAT plans had comparable dose parameters for regularly shaped targets. The heterogeneity index (HI) was superior in PAT plans which improved with increasing number of beams in arc plans for the different treatment sites. The conformality index (CI) depends on the treatment site and complexity of the shape of the planning target volume where for brain, pancreatic and lung tumours, PAT plans conformality was comparable and sometimes superior to CPT; and HI and CI were generally better in DPAT compared to SPAT.Conclusions:PAT plans have superior dose coverage and sparing of normal tissues compared to CPT plans using the MEVION double-scattering system as shown in this simulation study. Ideally, conformal proton arcs require beam shaping and dose delivery with the gantry moving; however, the MEVION double-scattering system lacks a multi-leaf collimator system and cannot deliver dose during gantry rotation. The single aperture conformal proton therapy technique is more time and cost effective compared with conventional techniques that are used currently with the MEVION proton therapy system because of the elimination of the need for patient-specific compensators. In present study, PAT was simulated with the MEVION double-scattering proton therapy system; however, it can be performed also with other proton therapy systems.

scholarly journals New integral forms of generalized Mathieu series and related applications

2013 ◽  
Vol 7 (1) ◽  
pp. 180-192 ◽  
Author(s):  
Gradimir Milovanovic ◽  
Tibor Pogány
Keyword(s):  
Integral Equation ◽  
Systematic Study ◽  
Fredholm Integral Equation ◽  
Special Functions ◽  
Integral Form ◽  
Integral Representations ◽  
Integration Path ◽  
Integral Expression ◽  
Integral Forms ◽  
Mathieu Series

The main object of this article is to present a systematic study of integral representations for generalized Mathieu series and its alternating variant, and to derive a new integral expression for these special functions by contour integration using rectangular integration path. Also, by virtue of newly established integral form of generalized Mathieu series, we obtain a new integral expression for the Bessel function of the first kind of half integer order, solving a related Fredholm integral equation of the first kind with nondegenerate kernel.

scholarly journals Physical and Dosimetric Aspect of Euromechanics Add-on Multileaf Collimator on Varian Clinac 2100 C/D

2019 ◽  
Author(s):  
S A Rohani ◽  
S R Mahdavi ◽  
A Mostaar ◽  
S Ueltzhöffer ◽  
R Mohammadi ◽  
...  
Keyword(s):  
Quality Assurance ◽  
Full Width Half Maximum ◽  
Intensity Modulated Radiation Therapy ◽  
Multileaf Collimator ◽  
Dose Delivery ◽  
Positional Accuracy ◽  
Position Accuracy ◽  
Multi Leaf Collimator ◽  
Radiation Transmission ◽  
Study Application

Background: Before treatment planning and dose delivery, quality assurance of multi-leaf collimator (MLC) has an important role in intensity-modulated radiation therapy (IMRT) due to the creation of multiple segments from optimization process.Objective: The purpose of this study is to assess the quality control of MLC leaves using EBT3 Gafchromic films.Material and Methods: Leaf Position accuracy and leaf gap reproducibility were checked with Garden fence test. The garden fence test consists of 5 thin bands A) 0.2 Cm width spaced at 2 Cm intervals and B) 1 Cm width spaced at 1 Cm intervals. Each leaf accuracy was analyzed with measuring the full-width half-maximum (FWHM). Maximum and average leaf transmission were measured with gafchromic EBT3 films from Ashland for both 6 MV and 18 MV beams.Results: Leaf positions were found to be in a range between 1.78 – 2.53 mm, instead of nominal 2 mm for the test A and between 9.09 – 10.36 mm, instead of nominal 10 mm for the test B. The Average radiation transmission of the MLC was noted 1.79% and 1.98% of the open 10x10 Cm2 field at isocenter for 6 MV and 18 MV beams, respectively. Maximum radiation transmission was noted 4.1% and 4.4% for 6 MV and 18 MV beams, respectively.Conclusion: In this study, application of gafchromic EBT3 films for the quality assurance of Euromechanics multileaf collimator was studied. Our results showed that the average leaf leakage and positional accuracy of this type of MLC were in the acceptance level based on the Protocols.

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