Elastic Scattering and Light Transport in Three-Dimensional Collagen Gel Constructs: A Mathematical Model and Computer Simulation Approach

Abstract

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.

Ternary Phase Diagram of β‐Sitosterol–γ‐Oryzanol–Canola Oil

“…Biomaterials, found in nature, frequently self-assemble, molecule-by-molecule, resulting in the formation of novel supramolecular architectures stabilized by weak, non-covalent interactions [8]. Functionalized biomaterials found in nature, formed via self-assembly, have an array of novel, beneficial functionalities (i.e., silk [9], collagen [10], and tubulin [11]) as well as detrimental architectures that lead to disease (i.e., prion proteins and atherosclerotic plaques [12]). An understanding of these self-assembled supramolecular architectures allows for the future exploitation of nature to develop novel synthetic materials with unique functionalities as well as possible treatments for diseases arising from these adverse architectures.…”

Co-operative self-assembly of cholesterol and γ-oryzanol composite crystals

“…1 These supramolecular structures are stabilized by weak, noncovalent interactions including: hydrogen bonds, ionic bonds, hydrophobic interactions, and/or van der Waals interactions. 1 Functionalized biomaterials found in nature, formed via self-assembly, have an array of novel, beneficial functionalities (i.e., silk, 2 collagen, 3 and tubulin 4 ) as well as detrimental architectures that lead to disease (i.e., prion proteins and atherosclerotic plaques 5 ). An understanding of these self-assembled supramolecular architectures allows for the future exploitation of nature to develop novel synthetic materials with unique functionalities as well as possible treatments for diseases arising from these adverse architectures.…”

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“…Interest in "self-assembled fibrillar networks" (SAFINs) which include organogelator molecules exists in a wide range of research fields and industries. Many SAFINs are present in nature and consist of materials such as fibrous actin [6], clathrin [7], tubulin [8], keratin [9], insulin [10], collagen [11], silk [12], and amyloid fibrils which are found in Alzheimer's and other neurodegenerative diseases [13]. Hence, with such diverse applications, an intimate understanding of the physical chemistry of these systems is of paramount importance.…”