TH-E-BRE-02: A Forward Scattering Approximation to Dose Calculation Using the Linear Boltzmann Transport Equation

2014 ◽  
Vol 41 (6Part33) ◽  
pp. 565-566
Author(s):  
B Catt ◽  
M Snyder
Keyword(s):  
Transport Equation ◽  
Boltzmann Transport Equation ◽  
Dose Calculation ◽  
Forward Scattering ◽  
Boltzmann Transport ◽  
Scattering Approximation

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

Solving Nongray Boltzmann Transport Equation in Gallium Nitride

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Ajit K. Vallabhaneni ◽  
Liang Chen ◽  
Man P. Gupta ◽  
Satish Kumar
Keyword(s):  
Gallium Nitride ◽  
Transport Equation ◽  
Thermal Transport ◽  
Hot Spot ◽  
Boltzmann Transport Equation ◽  
Significant Loss ◽  
Computational Time ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Fourier Model

Several studies have validated that diffusive Fourier model is inadequate to model thermal transport at submicron length scales. Hence, Boltzmann transport equation (BTE) is being utilized to improve thermal predictions in electronic devices, where ballistic effects dominate. In this work, we investigated the steady-state thermal transport in a gallium nitride (GaN) film using the BTE. The phonon properties of GaN for BTE simulations are calculated from first principles—density functional theory (DFT). Despite parallelization, solving the BTE is quite expensive and requires significant computational resources. Here, we propose two methods to accelerate the process of solving the BTE without significant loss of accuracy in temperature prediction. The first one is to use the Fourier model away from the hot-spot in the device where ballistic effects can be neglected and then couple it with a BTE model for the region close to hot-spot. The second method is to accelerate the BTE model itself by using an adaptive model which is faster to solve as BTE for phonon modes with low Knudsen number is replaced with a Fourier like equation. Both these methods involve choosing a cutoff parameter based on the phonon mean free path (mfp). For a GaN-based device considered in the present work, the first method decreases the computational time by about 70%, whereas the adaptive method reduces it by 60% compared to the case where full BTE is solved across the entire domain. Using both the methods together reduces the overall computational time by more than 85%. The methods proposed here are general and can be used for any material. These approaches are quite valuable for multiscale thermal modeling in solving device level problems at a faster pace without a significant loss of accuracy.

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