Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles

Wyman, D. R.; Patterson, Michael S.; Wilson, Brian C.

doi:10.1016/0021-9991(89)90067-3

Cited by 62 publications

(29 citation statements)

References 12 publications

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“…(1), which we rewrite as (8) with the same boundary conditions (2). Once again expanding the single scattering phase function f in Legendre polynomials, and rearranging, (8) may be rewritten (9) where is the scattering mean free path in the medium. Now by introducing a parameter called the excess mean free path, λ s and constants a n (λ s ) that depend on it by means of the equation the equation (10) where replaces (9) and is algebraically identical to it.…”

Section: Improved Models: Transport Condensed History (Tch) Methodsmentioning

confidence: 99%

“…Once again expanding the single scattering phase function f in Legendre polynomials, and rearranging, (8) may be rewritten (9) where is the scattering mean free path in the medium. Now by introducing a parameter called the excess mean free path, λ s and constants a n (λ s ) that depend on it by means of the equation the equation (10) where replaces (9) and is algebraically identical to it. This equation incorporates an enlarged scattering mean free path λ + λ s that approaches the original scattering mean free path λ as the excess mean free path, λ s , approaches 0.…”

Section: Improved Models: Transport Condensed History (Tch) Methodsmentioning

confidence: 99%

“…This approach is based on the observation that accuracy in a CH model might be based upon the replacement of the single scattering pdf by another that preserves a certain number of loworder angular moments of the original. The so-called similarity theory (ST) suggested by Wyman et al [9] represents one attempt to use this approach to accelerate the simulation of photons, while the more recent suggestion by Prinja and Franke [10] to replace the original scattering pdf by one based exclusively on a discrete set of scattering angles (DSA), is another that was proposed for electron transport. For both of these methods the Lewis-Larsen theory provides a theoretical context.…”

Section: Overviewmentioning

confidence: 99%

“…This CH type algorithm for efficient simulation of photon transport was developed by Wyman et al [9]; we outline their derivation below.…”

Section: Similarity Theory (St Model)mentioning

confidence: 99%

“…To implement the simulation, we could reconstruct f* according to its Legendre expansion. To simplify the sampling from f*, the authors [9] defined f* as a linear combination of orthogonal step functions on [−1, 1], constructed using Legendre polynomials. We describe our implementation of this construction for orders S = 2, 4, 12 in Section 8.…”

Section: Similarity Theory (St Model)mentioning

confidence: 99%

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Condensed history Monte Carlo methods for photon transport problems

Bhan

Spanier

2007

Journal of Computational Physics

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We study methods for accelerating Monte Carlo simulations that retain most of the accuracy of conventional Monte Carlo algorithms. These methods -called Condensed History (CH) methodshave been very successfully used to model the transport of ionizing radiation in turbid systems. Our primary objective is to determine whether or not such methods might apply equally well to the transport of photons in biological tissue. In an attempt to unify the derivations, we invoke results obtained first by Lewis, Goudsmit and Saunderson and later improved by Larsen and Tolar. We outline how two of the most promising of the CH models -one based on satisfying certain similarity relations and the second making use of a scattering phase function that permits only discrete directional changes -can be developed using these approaches. The main idea is to exploit the connection between the space-angle moments of the radiance and the angular moments of the scattering phase function. We compare the results obtained when the two CH models studied are used to simulate an idealized tissue transport problem. The numerical results support our findings based on the theoretical derivations and suggest that CH models should play a useful role in modeling light-tissue interactions.

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