Light transport algorithms generate realistic images by simulating the emission and scattering of light in an artificial environment. Applications include lighting design, architecture, and computer animation, while related engineering disciplines include neutron transport and radiative heat transfer. The main challenge with these algorithms is the high complexity of the geometric, scattering, and illumination models that are typically used. In this dissertation, we develop new Monte Carlo techniques that greatly extend the range of input models for which light transport simulations are practical. Our contributions include new theoretical models, statistical methods, and rendering algorithms. We start by developing a rigorous theoretical basis for bidirectional light transport algorithms (those that combine direct and adjoint techniques). First, we propose a linear operator formulation that does not depend on any assumptions about the physical validity of the input scene. We show how to obtain mathematically correct results using a variety of bidirectional techniques. Next we derive a different formulation, such that for any physically valid input scene, the transport operators are symmetric. This symmetry is important for both theory and implementations, and is based on a new reciprocity condition that we derive for transmissive materials. Finally, we show how light transport can be formulated as an integral over a space of paths. This framework allows new sampling and integration techniques to be applied, such as the Metropolis sampling algorithm. We also use this model to investigate the limitations of unbiased Monte Carlo methods, and to show that certain kinds of paths cannot be sampled. Our statistical contributions include a new technique called multiple importance sampling, which can greatly increase the robustness of Monte Carlo integration. It uses more than one sampling technique to evaluate an integral, and then combines these samples in a

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Robust Monte Carlo methods for light transport simulation

/pdf/the-egsnrc-code-system-monte-carlo-simulation-of-electron-1ijb3klmhd.pdf

The EGSnrc Code System: Monte Carlo Simulation of Electron and Photon Transport

Radiation heat transfer in combustion systems

This chapter presents a finite-volume (FV) method for computing radiation heat transfer processes The main ingredients of the calculation procedure were presented by Chai et al [1] The resulting method has been tested, refined and extended to account for various geometrical and physical complexities

Finite volume method for radiation heat transfer

The charge of Task Group 186 (TG-186) is to provide guidance for early adopters of model-based dose calculation algorithms (MBDCAs) for brachytherapy (BT) dose calculations to ensure practice uniformity. Contrary to external beam radiotherapy, heterogeneity correction algorithms have only recently been made available to the BT community. Yet, BT dose calculation accuracy is highly dependent on scatter conditions and photoelectric effect cross-sections relative to water. In specific situations, differences between the current water-based BT dose calculation formalism (TG-43) and MBDCAs can lead to differences in calculated doses exceeding a factor of 10. MBDCAs raise three major issues that are not addressed by current guidance documents: (1) MBDCA calculated doses are sensitive to the dose specification medium, resulting in energy-dependent differences between dose calculated to water in a homogeneous water geometry (TG-43), dose calculated to the local medium in the heterogeneous medium, and the intermediate scenario of dose calculated to a small volume of water in the heterogeneous medium. (2) MBDCA doses are sensitive to voxel-by-voxel interaction cross sections. Neither conventional single-energy CT nor ICRU∕ICRP tissue composition compilations provide useful guidance for the task of assigning interaction cross sections to each voxel. (3) Since each patient-source-applicator combination is unique, having reference data for each possible combination to benchmark MBDCAs is an impractical strategy. Hence, a new commissioning process is required. TG-186 addresses in detail the above issues through the literature review and provides explicit recommendations based on the current state of knowledge. TG-43-based dose prescription and dose calculation remain in effect, with MBDCA dose reporting performed in parallel when available. In using MBDCAs, it is recommended that the radiation transport should be performed in the heterogeneous medium and, at minimum, the dose to the local medium be reported along with the TG-43 calculated doses. Assignments of voxel-by-voxel cross sections represent a particular challenge. Electron density information is readily extracted from CT imaging, but cannot be used to distinguish between different materials having the same density. Therefore, a recommendation is made to use a number of standardized materials to maintain uniformity across institutions. Sensitivity analysis shows that this recommendation offers increased accuracy over TG-43. MBDCA commissioning will share commonalities with current TG-43-based systems, but in addition there will be algorithm-specific tasks. Two levels of commissioning are recommended: reproducing TG-43 dose parameters and testing the advanced capabilities of MBDCAs. For validation of heterogeneity and scatter conditions, MBDCAs should mimic the 3D dose distributions from reference virtual geometries. Potential changes in BT dose prescriptions and MBDCA limitations are discussed. When data required for full MBDCA implementation are insufficient, interim recommendations are made and potential areas of research are identified. Application of TG-186 guidance should retain practice uniformity in transitioning from the TG-43 to the MBDCA approach.

Report of the Task Group 186 on model-based dose calculation methods in brachytherapy beyond the TG-43 formalism: current status and recommendations for clinical implementation.

This books presents a balanced overview of the major methods currently available for obtaining numerical solutions in neutron and gamma ray transport. It focuses on methods particularly suited to the complex problems encountered in the analysis of reactors, fusion devices, radiation shielding, and other nuclear systems. Derivations are given for each of the methods showing how the transport equation is reduced to sets of algebraic equations suitable for solution on a digital computer. The limitations of the methods and their suitability for different classes of problems are discussed in terms of computer memory, time requirements, and accuracy.

W. F. Miller

Papers

Computational Methods of Neutron Transport