The original Delta-Eddington phase function rigidly defines the parameters f and h as g 2 and g/(1+ g), respectively. The phase function is a linear combination of the weakly anisotropic scattering and the strongly peaked forward scattering. Where f ∈ is the weight factor measuring the anisotropy of the photon scattering, which we call the anisotropy weight and h is a asymmetry factor of the phase function to modulate the weakly anisotropic scattering. The solution of the system of integral equations enables a highly accurate prediction for the photon propagation in biological tissue over a wide range of optical parameters of biomedical interest. Based on this new definition of Delta-Eddington phase function, the RTE can be reduced to a system of integral equations with respect to both the photon fluence rate and the flux vector. In this paper, we present a generalized Delta-Eddington function to approximate the real phase function. 2, 13 However, the RTE with the HG phase function is difficult to simplify further. 21 The HG function was proven to be the most accurate in terms of the angular dependence of single scattering events in biological tissues. 20 The inverse problem of optical parameters was presented based on the RTE with the Delta-Eddington function. Based on the Delta-Eddington phase function, a generalized diffusion model was presented to simulate photon propagation in highly absorbing medium and smaller source-detector separations. These two functions can be written in closed forms with a single free parameter g, called the anisotropic factor, which is often considered to be independent of the tissue scattering and absorption. Because the exact form of the phase function is currently unknown, the popular Henyey-Greenstein (HG) function 18 and the Delta-Eddington function 19 are usually used to approximate the true phase functions in biomedical applications. In the RTE, the phase functions describe the scattering characteristics of the medium and significantly influence the precision of the solution and the efficiency of the computation. 16 It is also not suitable for modeling light propagation in the visible spectrum in which biological tissue present significant photon absorption. Nevertheless, DA assumes weakly anisotropic scattering and works well only in a highly scattering and weakly absorbing medium. The popular diffusion approximation 14, 15 (DA) to RTE is widely used in the field of biophotonics because of its high computational efficiency. However, due to its statistical nature, the MC method has the disadvantage of requiring a long computation time therefore, it is usually used as a reference method for other approaches. 13 The MC method is well established to produce accurate estimates for light propagation in tissues. 11, 12 Monte Carlo (MC) is a statistical simulation method in which the paths of photons are traced as they are scattered and absorbed within the medium. 1, 2 Analytical solutions for the RTE are available for few simple geometries, and numerical solutions, such as the discrete ordinate method 3, 4 and the spherical harmonic method, 5 often lead to enormous computational cost, especially to solve inverse problems such as optical tomography, 6 bioluminescence tomography, 7 – 10 and fluorescence tomography. 1, 2 The radiative transfer equation (RTE) is considered the golden standard for biomedical applications. The photon propagation model provides insight into the interaction between light and tissues and is essential for tomographic imaging with visible and near-IR light. The current induced in the coil creates another field, in the opposite direction of the bar magnet’s to oppose the increase.The propagation of light through the biological tissue is a complicated process involving both absorption and scattering. Lenz’ Law: (a) When this bar magnet is thrust into the coil, the strength of the magnetic field increases in the coil. Faraday was aware of the direction, but Lenz stated it, so he is credited for its discovery. The direction (given by the minus sign) of the EMF is so important that it is called Lenz’ law after the Russian Heinrich Lenz (1804–1865), who, like Faraday and Henry, independently investigated aspects of induction. The minus means that the EMF creates a current I and magnetic field B that oppose the change in flux Δthis is known as Lenz’ law. The minus sign in Faraday’s law of induction is very important. The units for EMF are volts, as is usual. This relationship is known as Faraday’s law of induction.
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