title: Monte Carlo methods for light propagation in biological tissues.
abstract: Light propagation in turbid media is driven by the equation of radiative transfer. We give a formal probabilistic representation of its solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods in order to estimate the quantity of light that is received by a homogeneous tissue when emitted by an optic fiber. A variance reduction method is studied and implemented, as well as a Markov chain Monte Carlo method based on the Metropolis-Hastings algorithm. The resulting estimating methods are then compared to the so-called Wang-Prahl (or Wang) method. Finally, the formal representation allows to derive a non-linear optimization algorithm close to Levenberg-Marquardt that is used for the estimation of the scattering and absorption coefficients of the tissue from measurements.
authors.affiliation: Inria, BIGS, Villers-lès-Nancy, F-54600, France; Université de Fribourg, Département de Mathématiques, chemin du Musée 23, Fribourg CH-1700, Switzerland. Electronic address: laura.vinckenbosch@heig-vd.ch.
authors.forename: Laura
authors.initials: L
authors.lastname: Vinckenbosch
authors.affiliation: Inria, BIGS, Villers-lès-Nancy, F-54600, France; Université de Lorraine, Institut Élie Cartan de Lorraine, UMR 7502, Vandœuvre-lès-Nancy, F-54506, France.
authors.forename: Céline
authors.initials: C
authors.lastname: Lacaux
authors.affiliation: Inria, BIGS, Villers-lès-Nancy, F-54600, France; Université de Lorraine, Institut Élie Cartan de Lorraine, UMR 7502, Vandœuvre-lès-Nancy, F-54506, France.
authors.forename: Samy
authors.initials: S
authors.lastname: Tindel
authors.affiliation: Université de Lorraine, CRAN, UMR 7039, 9, avenue de la forêt de Haye, Vandœuvre-lès-Nancy, F-54516, France.
authors.forename: Magalie
authors.initials: M
authors.lastname: Thomassin
authors.affiliation: Université de Lorraine, CRAN, UMR 7039, 9, avenue de la forêt de Haye, Vandœuvre-lès-Nancy, F-54516, France.
authors.forename: Tiphaine
authors.initials: T
authors.lastname: Obara
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D008027:Light; D008390:Markov Chains; D055641:Mathematical Concepts; D008954:Models, Biological; D015233:Models, Statistical; D009010:Monte Carlo Method; D017711:Nonlinear Dynamics; D010778:Photochemotherapy
keywords: Equation of radiative transfer; Light propagation; Markov chain Monte Carlo methods; Parameter estimation