Elastic scattering and light transport in three-dimensional collagen gel constructs: A mathematical model and computer simulation approach

A mathematical modeling approach for elastic scattering and light propagation is presented, which can be used to obtain the scattering coefficient, the index of refraction, and the distribution of the collagen fibrils in a gel. Collagen fibrils can be realistically represented by small cylindrical particles. The analysis of the scattering of light by such particles provides the scattering coefficient. Light transport in multilayered tissues has been modeled and the collagen fibrils scattering coefficient has been considered as main input parameters. Assuming that a gel is composed of fibrils with the same diameter, it is possible to obtain all the input parameters of the model and, therefore, a simulated spectrum. This can be repeated for several diameters. Considering a gel composed of fibrils with different diameters, it is possible to obtain a best-fitting simulated spectrum as a weighted sum (least-square-error based) of the spectra corresponding to several fibril diameters, and, therefore, obtain an estimate of the percentages of fibrils of each diameter in the gel. Moreover, the scattering coefficient and refractive index, which are also provided by the model, are relevant parameters as they relate to tissue properties in their own right.