Monte Carlo methods for light propagation in biological tissues
- Vinckenbosch, Laura Inria, BIGS, Villers-lès-Nancy, France - Université de Fribourg, Département de Mathématiques, Switzerland
- Lacaux, Céline Inria, BIGS, Villers-lès-Nancy, France - Université de Lorraine, Institut Élie Cartan de Lorraine, Vandœuvre-lès-Nancy, France
- Tindel, Samy Inria, BIGS, Villers-lès-Nancy, France - Université de Lorraine, Institut Élie Cartan de Lorraine, Vandœuvre-lès-Nancy, France
- Thomassin, Magalie Université de Lorraine, Vandœuvre-lès-Nancy, France
- Obara, Tiphaine Université de Lorraine, Vandœuvre-lès-Nancy, France
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08.09.2015
Published in:
- Mathematical Biosciences. - 2015, vol. 269, p. 48–60
Light propagation
Equation of radiative transfer
Markov chain Monte Carlo methods
Parameter estimation
English
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
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 257984
- DOI 10.1016/j.mbs.2015.08.017
- Persistent URL
- https://folia.unifr.ch/unifr/documents/304656
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