Light Propagation through Biological Tissue and Other Diffusive Media: Theory, Solutions, and Software

Light Propagation through Biological Tissue and Other Diffusive Media: Theory, Solutions, and Software
Author(s):    Fabrizio Martelli; Samuele Del Bianco; Andrea Ismaelli; Giovanni Zaccanti
Published:   2010
DOI:             10.1117/3.824746
eISBN: 9780819481832  |  Print ISBN13: 9780819476586
Description:

This book provides foundational information on modeling light propagation through diffusive media, with special emphasis on biological tissue. A summary of the theoretical background on light propagation through diffusive media is provided with the aid of easy-to-use software designed to calculate the solutions of the diffusion equation. The book also provides:

The basic theory of photon transport with the analytical solutions of the diffusion equation for several geometries

Detailed coverage of the radiative transfer equation and the diffusion equation

The theories and the formulae based on the diffusion equation that have been widely used for biomedical applications

The general concepts and the physical quantities necessary to describe light propagation through absorbing and scattering media

A description of the software provided on the CD-ROM, along with the accuracy of the presented solutions.

Although the theoretical and computational tools provided with this book and CD-ROM have their primary use in the field of biomedical optics, there are many other applications in which they can be used, including agricultural products, forest products, food products, plastic materials, pharmaceutical products, and many others.

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The purpose of this book and the enclosed software is to provide a tool with dual functionality. The text summarizes the theory of light propagation through diffusive media, while the software serves as a computational tool giving users an interactive approach to understanding the link between theory and real calculations. Through this two-pronged approach, the authors believe that this tool will be valuable both for research investigations and educational purposes.

The software on the CD-ROM is designed to calculate the solutions of the diffusion equation (DE) — solutions that can be verified by comparing against the enclosed set of reference Monte Carlo (MC) results. The text describes the basic theory of photon transport along with analytical solutions of the diffusion equation for several geometries. The book also includes a description of the software, related materials, and their use.

We will show that propagation of light through turbid media (i.e., media with scattering and absorption properties) can be accurately described with the radiative transfer equation (RTE), a complex integro-differential equation of which analytical solutions are not available for geometries of practical interest. The DE is an approximation that can be obtained from the RTE by making some simplifying assumptions. For the DE, analytical solutions are available in many geometries, but it is necessary to stress that these solutions are approximate. Therefore, each application should be checked to verify that the accuracy of these approximations is sufficient. This check can be performed by comparing the approximate solutions against reference solutions of the RTE. For this purpose, the CD-ROM also includes examples of numerical solutions of the RTE obtained with MC simulations for different geometries.

Diffusive media are turbid media for which the solutions of the DE provide a sufficiently accurate description of light propagation. Through these media, photons propagate in a diffusive regime, i.e., the path followed by any photon migrating from the source to the detector looks like a random walk (zigzag trajectory). This occurs when photons undergo a sufficiently high number of scattering events that their trajectories become randomized. Section 2.5 lists a number of media common in daily life for which a diffusive regime of propagation can be assumed. This list includes highly scattering media like biological tissues, agricultural products, wood, paper, plastic materials, sugar, salt, and milk, for which the diffusive regime can be reached even when the volume of the medium is of a few cubic centimeters. The list also includes slightly scattering media like clouds of gas and dust in the interstellar medium, in which case an extremely large volume is necessary.

In the book, a review is presented of the theories and the formulae based on the DE that have been widely used for biomedical applications. These theories and formulae are the basis of the programs provided with the CD-ROM. The contents of the book are divided into three parts. The first part (Chapters 2 and 3) presents the basic theory of photon transport. In Chapter 2, the general concepts and the physical quantities necessary to describe light propagation through absorbing and scattering media are introduced. In Chapter 3, the RTE and the DE are described and discussed. In the second part (Chapters 4, 5, 6 and 7), various solutions of the RTE are presented. Chapter 4 is devoted to solutions of the DE for homogeneous media. Chapter 5 is dedicated to hybrid solutions for the homogeneous slab based on solutions of the RTE and the telegrapher equation. In Chapter 6, a solution of the DE for a two-layer medium is described. In Chapter 7, solutions of the perturbed DE when small defects are introduced into the medium are obtained with the Born approximation. In the third part (Chapters 8, 9 and 10), the software provided with the CD-ROM is described, and the accuracy of the solutions presented is investigated and discussed. In Chapter 8, the software included in the CD-ROM is described. Chapters 9 and 10 are dedicated to the validation of the solutions and of the software described in the previous chapters. The validation is done by means of comparisons with the results of MC simulations. In Chapter 9, a detailed description of the MC programs employed is provided, and in Chapter 10 the results of the comparisons are described and discussed.

In the CD-ROM, all the programs for calculating the solutions presented in the book are provided with the results of MC simulations that can be used as a standard reference. The CD-ROM is divided into three parts: the first includes the software named Diffusion&Perturbation; the second contains all the source code for the solutions found in the book; and the third part contains the results of MC simulations that can be used as a standard reference.

© 2010 Society of Photo-Optical Instrumentation Engineers

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