HAL CCSD
Multiscale modeling of light absorption in tissues: limitations of classical homogenization approach.
Mottin, Stéphane
Panasenko, Grigory
Ganesh, S Sivaji
Laboratoire Hubert Curien (LHC) ; Institut d'Optique Graduate School (IOGS)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)
Laboratoire de Mathématiques de l'Université de Saint-Etienne (LAMUSE) ; Université Jean Monnet - Saint-Étienne (UJM)
Indian Institute of Technology Bombay (IIT Bombay)
International audience
ISSN: 1932-6203
EISSN: 1932-6203
PLoS ONE
Public Library of Science
ujm-00628784
https://ujm.hal.science/ujm-00628784
https://ujm.hal.science/ujm-00628784/document
https://ujm.hal.science/ujm-00628784/file/journal.pone.0014350.pdf
https://ujm.hal.science/ujm-00628784
PLoS ONE, 2010, 5 (12), pp.e14350. ⟨10.1371/journal.pone.0014350⟩
DOI: 10.1371/journal.pone.0014350
info:eu-repo/semantics/altIdentifier/doi/10.1371/journal.pone.0014350
PUBMED: 21217816
info:eu-repo/semantics/altIdentifier/pmid/21217816
en
MESH: Algorithms
MESH: Optics and Photonics
MESH: Light
MESH: Mathematics
MESH: Models, Theoretical
MESH: Photons
MESH: Scattering, Radiation
MESH: Absorption
MESH: Animals
MESH: Biophysics
MESH: Blood
MESH: Blood Vessels
MESH: Humans
[SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
[PHYS.PHYS.PHYS-OPTICS]Physics [physics]/Physics [physics]/Optics [physics.optics]
info:eu-repo/semantics/article
Journal articles
In biophotonics, the light absorption in a tissue is usually modeled by the Helmholtz equation with two constant parameters, the scattering coefficient and the absorption coefficient. This classic approximation of "haemoglobin diluted everywhere" (constant absorption coefficient) corresponds to the classical homogenization approach. The paper discusses the limitations of this approach. The scattering coefficient is supposed to be constant (equal to one) while the absorption coefficient is equal to zero everywhere except for a periodic set of thin parallel strips simulating the blood vessels, where it is a large parameter ω. The problem contains two other parameters which are small: ε, the ratio of the distance between the axes of vessels to the characteristic macroscopic size, and δ, the ratio of the thickness of thin vessels and the period. We construct asymptotic expansion in two cases: ε --> 0, ω --> ∞, δ --> 0, ωδ --> ∞, ε2ωδ --> 0 and ε --> 0, ω --> ∞, δ --> 0, ε2ωδ --> ∞, and and prove that in the first case the classical homogenization (averaging) of the differential equation is true while in the second case it is wrong. This result may be applied in the biomedical optics, for instance, in the modeling of the skin and cosmetics.
2010
info:eu-repo/semantics/OpenAccess