Verification method of Monte Carlo codes for transport processes with arbitrary accuracy

Abstract In this work, we present a robust and powerful method for the verification, with arbitrary accuracy, of Monte Carlo codes for simulating random walks in complex media. Such random walks are typical of photon propagation in turbid media, scattering of particles, i.e., neutrons in a nuclear r...

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Autores principales:	Fabrizio Martelli, Federico Tommasi, Angelo Sassaroli, Lorenzo Fini, Stefano Cavalieri
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/dc557ce17a434d84b6833f6403e8b78d
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spelling	oai:doaj.org-article:dc557ce17a434d84b6833f6403e8b78d2021-12-02T18:51:35ZVerification method of Monte Carlo codes for transport processes with arbitrary accuracy10.1038/s41598-021-98429-32045-2322https://doaj.org/article/dc557ce17a434d84b6833f6403e8b78d2021-09-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-98429-3https://doaj.org/toc/2045-2322Abstract In this work, we present a robust and powerful method for the verification, with arbitrary accuracy, of Monte Carlo codes for simulating random walks in complex media. Such random walks are typical of photon propagation in turbid media, scattering of particles, i.e., neutrons in a nuclear reactor or animal/humans’ migration. Among the numerous applications, Monte Carlo method is also considered a gold standard for numerically “solving” the scalar radiative transport equation even in complex geometries and distributions of the optical properties. In this work, we apply the verification method to a Monte Carlo code which is a forward problem solver extensively used for typical applications in the field of tissue optics. The method is based on the well-known law of average path length invariance when the entrance of the entities/particles in a medium obeys to a simple cosine law, i.e., Lambertian entrance, and annihilation of particles inside the medium is absent. By using this law we achieve two important points: (1) the invariance of the average path length guarantees that the expected value is known regardless of the complexity of the medium; (2) the accuracy of a Monte Carlo code can be assessed by simple statistical tests. We will show that we can reach an arbitrary accuracy of the estimated average pathlength as the number of simulated trajectories increases. The method can be applied in complete generality versus the scattering and geometrical properties of the medium, as well as in presence of refractive index mismatches in the optical case. In particular, this verification method is reliable to detect inaccuracies in the treatment of boundaries of finite media. The results presented in this paper, obtained by a standard computer machine, show a verification of our Monte Carlo code up to the sixth decimal digit. We discuss how this method can provide a fundamental tool for the verification of Monte Carlo codes in the geometry of interest, without resorting to simpler geometries and uniform distribution of the scattering properties.Fabrizio MartelliFederico TommasiAngelo SassaroliLorenzo FiniStefano CavalieriNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-12 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Fabrizio Martelli Federico Tommasi Angelo Sassaroli Lorenzo Fini Stefano Cavalieri Verification method of Monte Carlo codes for transport processes with arbitrary accuracy
description	Abstract In this work, we present a robust and powerful method for the verification, with arbitrary accuracy, of Monte Carlo codes for simulating random walks in complex media. Such random walks are typical of photon propagation in turbid media, scattering of particles, i.e., neutrons in a nuclear reactor or animal/humans’ migration. Among the numerous applications, Monte Carlo method is also considered a gold standard for numerically “solving” the scalar radiative transport equation even in complex geometries and distributions of the optical properties. In this work, we apply the verification method to a Monte Carlo code which is a forward problem solver extensively used for typical applications in the field of tissue optics. The method is based on the well-known law of average path length invariance when the entrance of the entities/particles in a medium obeys to a simple cosine law, i.e., Lambertian entrance, and annihilation of particles inside the medium is absent. By using this law we achieve two important points: (1) the invariance of the average path length guarantees that the expected value is known regardless of the complexity of the medium; (2) the accuracy of a Monte Carlo code can be assessed by simple statistical tests. We will show that we can reach an arbitrary accuracy of the estimated average pathlength as the number of simulated trajectories increases. The method can be applied in complete generality versus the scattering and geometrical properties of the medium, as well as in presence of refractive index mismatches in the optical case. In particular, this verification method is reliable to detect inaccuracies in the treatment of boundaries of finite media. The results presented in this paper, obtained by a standard computer machine, show a verification of our Monte Carlo code up to the sixth decimal digit. We discuss how this method can provide a fundamental tool for the verification of Monte Carlo codes in the geometry of interest, without resorting to simpler geometries and uniform distribution of the scattering properties.
format	article
author	Fabrizio Martelli Federico Tommasi Angelo Sassaroli Lorenzo Fini Stefano Cavalieri
author_facet	Fabrizio Martelli Federico Tommasi Angelo Sassaroli Lorenzo Fini Stefano Cavalieri
author_sort	Fabrizio Martelli
title	Verification method of Monte Carlo codes for transport processes with arbitrary accuracy
title_short	Verification method of Monte Carlo codes for transport processes with arbitrary accuracy
title_full	Verification method of Monte Carlo codes for transport processes with arbitrary accuracy
title_fullStr	Verification method of Monte Carlo codes for transport processes with arbitrary accuracy
title_full_unstemmed	Verification method of Monte Carlo codes for transport processes with arbitrary accuracy
title_sort	verification method of monte carlo codes for transport processes with arbitrary accuracy
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/dc557ce17a434d84b6833f6403e8b78d
work_keys_str_mv	AT fabriziomartelli verificationmethodofmontecarlocodesfortransportprocesseswitharbitraryaccuracy AT federicotommasi verificationmethodofmontecarlocodesfortransportprocesseswitharbitraryaccuracy AT angelosassaroli verificationmethodofmontecarlocodesfortransportprocesseswitharbitraryaccuracy AT lorenzofini verificationmethodofmontecarlocodesfortransportprocesseswitharbitraryaccuracy AT stefanocavalieri verificationmethodofmontecarlocodesfortransportprocesseswitharbitraryaccuracy
_version_	1718377416696528896

Verification method of Monte Carlo codes for transport processes with arbitrary accuracy

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