Abstract
We present an analytical model of optical fluence for multiple cylindrical inhomogeneities embedded in an otherwise homogeneous turbid medium. The model is based on the diffusion equation and represents the optical fluence distribution inside and outside inhomogeneities as a series of modified Bessel functions. We take into account the interplay between cylindrical inhomogeneities by introducing new boundary conditions on the surface of inhomogeneities. The model is compared with the numerical solution of the diffusion equation with NIRFAST software. The fluences inside the inhomogeneities obtained by the two methods are in close agreement. This permits the use of the model as a forward model for quantitative photoacoustic imaging.
Highlights
The forward model of optical fluence in biological tissues is an important topic in diffuse optical tomography (DOT) [1,2,3] and in quantitative photoacoustic (PA) imaging [4,5,6]
There are three types of forward models: (1) Monte Carlo (MC) methods [7,8,9] are based on a stochastic model and need significant computation time to achieve sufficient precision; (2) numerical methods, e.g., finite element (FEM) [10,11,12,13,14,15,16], involve matrix inversion and are computationally costly; (3) analytical methods involve less computation time, and should be more suitable for real-time PA imaging
Little work has been done on the analytical model of multiple inhomogeneities embedded in an otherwise homogeneous turbid medium, probably because this model can hardly be integrated in a DOT reconstruction process for tissues
Summary
The forward model of optical fluence in biological tissues is an important topic in diffuse optical tomography (DOT) [1,2,3] and in quantitative photoacoustic (PA) imaging [4,5,6]. Boas et al developed analytical models for an inhomogeneity embedded in an otherwise homogeneous turbid medium. Ripoll et al developed analytical models based on the Kirchhoff approximation [22,23], assuming that the total intensity at a certain point in the medium is equal to the sum of the incident field and the wave reflected from the plane tangent to the interface. These studies focused on DOT, and the optical fluence is mainly investigated at the detector position.
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