TH-E-BRE-01: A 3D Solver of Linear Boltzmann Transport Equation Based On a New Angular Discretization Method with Positivity for Photon Dose Calculation Benchmarked with Geant4

2014 ◽  
Vol 41 (6Part33) ◽  
pp. 565-565
Author(s):  
X Hong ◽  
H Gao
Keyword(s):  
Transport Equation ◽  
Boltzmann Transport Equation ◽  
Dose Calculation ◽  
Discretization Method ◽  
Boltzmann Transport ◽  
Photon Dose ◽  
Angular Discretization

INVERSE RADIOTHERAPY TREATMENT PLANNING MODEL APPLYING BOLTZMANN-TRANSPORT EQUATION

2002 ◽  
Vol 12 (01) ◽  
pp. 109-141 ◽  
Author(s):  
JOUKO TERVO ◽  
PEKKA KOLMONEN
Keyword(s):  
Radiation Therapy ◽  
Transport Equation ◽  
Treatment Planning ◽  
Dose Distribution ◽  
Treatment Plan ◽  
Boltzmann Transport Equation ◽  
Dose Calculation ◽  
Calculation Model ◽  
Boltzmann Transport ◽  
Delivery Technique

In the external radiation therapy the source of radiation is from outside. The healthy tissue and some organs, called critical organs which are quite intolerable for radiation, are always irradiated, too. Therefore, the careful treatment plan has to be constructed to ensure high and homogeneous dose in the tumor, but on the other hand to spare the normal tissue and critical organs possibly well. In the radiation therapy treatment planning one tries to optimize the dose distribution in the way that the above aim is satisfied. The dose distributions can be generated with different techniques. The most recent of them is the so-called multileaf collimator (MLC) delivery technique. Calculation of the dose distribution demands some dose calculation model. The paper gives a model and theoretical basis of planning applying the Boltzmann-transport equation in dose calculation and MLC delivery technique. The existence of solutions and the optimal treatment planning are considered. A preliminary artificial computer simulation is included.

scholarly journals A fast, linear Boltzmann transport equation solver for computed tomography dose calculation (Acuros CTD )

2018 ◽  
Vol 46 (2) ◽  
pp. 925-933 ◽  
Author(s):  
Adam Wang ◽  
Alexander Maslowski ◽  
Todd Wareing ◽  
Josh Star‐Lack ◽  
Taly Gilat Schmidt
Keyword(s):  
Computed Tomography ◽  
Transport Equation ◽  
Boltzmann Transport Equation ◽  
Dose Calculation ◽  
Boltzmann Transport

scholarly journals An Evaluation of an Improper Integral Arises from an Analytic Solution of a Model Boltzmann Equation for Photon Transport

2016 ◽  
Vol 35 ◽  
pp. 87-94
Author(s):  
Taposh Kumar Das
Keyword(s):  
Mathematical Model ◽  
Boltzmann Equation ◽  
Transport Equation ◽  
Analytic Solution ◽  
Boltzmann Transport Equation ◽  
Dose Calculation ◽  
Boltzmann Transport ◽  
Photon Transport ◽  
Improper Integral ◽  
The Mathematical Model

In this article we adopted the Mathematical model of solution of an improper integral which is created from the solution of the Boltzmann Transport equation (BTE) for photons. For the dose calculation of radiotherapy for cancer treatment, we need to solve the Boltzmann Transport equation. This improper integral is the important part of the BTE. Also the calculating time of the dose calculation is mostly dependent on the calculating time of this improper integral. For reducing the calculating time we need the minimum integrating area which is explained in this paper.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 87-94

Hybrid Ballistic-Diffusive Solution of the Frequency-Dependent Phonon Boltzmann Transport Equation

2016 ◽  
Author(s):  
Pareekshith Allu ◽  
Sandip Mazumder
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Transport Equation ◽  
Knudsen Number ◽  
Spherical Harmonics ◽  
Hybrid Method ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport ◽  
Partial Differential ◽  
Angular Discretization

The phonon Boltzmann Transport Equation (BTE) is difficult to solve on account of the directional and spectral nature of the phonon intensity, which necessitates angular and spectral discretization, and ultimately results in a large number (typically few hundreds) of four-dimensional partial differential equations. In the ballistic (large Knudsen number) regime, the phonon intensity is highly anisotropic, and therefore, angular resolution is desirable. However, in the diffusive (small Knudsen number) regime, the intensity is fairly isotropic, and hence, angular discretization is wasteful. In such scenarios, the method of spherical harmonics may be effectively used to reduce the large number of directional BTEs to a few partial differential equations. Since the Knudsen number is frequency dependent, the decision to preserve or eliminate angular discretization may be made frequency by frequency based on whether the spectral Knudsen number is large or small. In this article, a hybrid method is proposed in which for some frequency intervals (bands), full angular discretization is used, while for others, the first order spherical harmonics (P1) is invoked to reduce the number of directional BTEs. The accuracy and efficiency of the hybrid method is tested by solving several steady state and transient nanoscale heat conduction problems in two and three-dimensional geometries. Silicon is used as the candidate material. It is found that hybridization is effective in significantly improving the efficiency of solution of the BTE — sometimes by a factor of three — without significant penalty on the accuracy.

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