Corrigendum to "Solution of Radiative Transfer Equation with a Continuous and Stochastic Varying Refractive Index by Legendre Transform Method".

[This corrects the article DOI: 10.1155/2014/814929.].

Solution of radiative transfer equation with a continuous and stochastic varying refractive index by legendre transform method.

The present paper gives a new computational framework within which radiative transfer in a varying refractive index biological tissue can be studied. In our previous works, Legendre transform was used as an innovative view to handle the angular derivative terms in the case of uniform refractive index spherical medium. In biomedical optics, our analysis can be considered as a forward problem solution in a diffuse optical tomography imaging scheme. We consider a rectangular biological tissue-like domain with spatially varying refractive index submitted to a near infrared continuous light source. Interaction of radiation with the biological material into the medium is handled by a radiative transfer model. In the studied situation, the model displays two angular redistribution terms that are treated with Legendre integral transform. The model is used to study a possible detection of abnormalities in a general biological tissue. The effect of the embedded nonhomogeneous objects on the transmitted signal is studied. Particularly, detection of targets of localized heterogeneous inclusions within the tissue is discussed. Results show that models accounting for variation of refractive index can yield useful predictions about the target and the location of abnormal inclusions within the tissue.

Computational laser spectroscopy in a biological tissue.

We present a numerical spectroscopic study of visible and infrared laser radiation in a biological tissue. We derive a solution of a general two-dimensional time dependent radiative transfer equation in a tissue-like medium. The used model is suitable for many situations especially when the external source is time-dependent or continuous. We use a control volume-discrete ordinate method associated with an implicit three-level second-order time differencing scheme. We consider a very thin rectangular biological-tissue-like medium submitted to a visible or a near infrared light sources. The RTE is solved for a set of different wavelength source. All sources are assumed to be monochromatic and collimated. The energetic fluence rate is computed at a set of detector points on the boundaries. According to the source type, we investigate either the steady-state or transient response of the medium. The used model is validated in the case of a heterogeneous tissue-like medium using referencing experimental results from the literature. Also, the developed model is used to study changes on transmitted light in a rat-liver tissue-like medium. Optical properties depend on the source wavelength and they are taken from the literature. In particular, light-transmission in the medium is studied for continuous wave and for short pulse.

Visible and near-infrared laser radiation in a biological tissue. A forward model for medical imaging by optical tomography.

We present a numerical model for the study of a general, two-dimensional, time-dependent, laser radiation transfer problem in a biological tissue. The model is suitable for many situations, especially when the external laser source is pulsed or continuous. We used a control volume discrete-ordinate method associated with an implicit, three-level, second-order, time-differencing scheme. In medical imaging by laser techniques, this could be an optical tomography forward model. We considered a very thin rectangular biological tissue-like medium submitted to a visible or a near-infrared laser source. Different cases were treated numerically. The source was assumed to be monochromatic and collimated. We used either a continuous source or a short-pulsed source. The transmitted radiance was computed in detector points on the boundaries. Also, the distribution of the internal radiation intensity for different instants is presented. According to the source type, we examined either the steady-state response or the transient response of the medium. First, our model was validated by experimental results from the literature for a homogeneous biological tissue. The space and angular grid independency of our results is shown. Next, the proposed model was used to study changes in transmitted radiation for a homogeneous background medium in which were imbedded two heterogeneous objects. As a last investigation, we studied a multilayered biological tissue. We simulated near-infrared radiation in human skin, fat and muscle. Some results concerning the effects of fat thickness and positions of the detector source on the reflected radiation are presented.