An ABC of near infrared photon migration in tissues: the diffusive regime of propagation

In this paper, the theories commonly used for the study of photon migration through biological tissues and for biomedical applications are reviewed. The concepts of absorption and scattering are introduced with particular reference to biological tissues and to the near infrared wavelength range. In particular, the basic definitions of optical properties and their statistical meaning, the Beer–Lambert law, the modified Beer–Lambert law, the radiative transfer equation and the diffusion equation are examined and described. The main frame of the theories is provided in the time domain, in the continuous wave domain and in the frequency domain and the principal solutions of the radiative transfer equation and of the diffusion equation are reviewed. The propagation of photons through biological tissue can be accurately described with solutions of the radiative transfer equation, while solutions of the diffusion equation are subjected to intrinsic approximations that limit their range of validity. Whenever the solutions of the diffusion equation provide a sufficiently accurate description of photon migration, we have a diffusive regime of propagation and the media where this happens can be denoted as diffusive as well. A rule to identify the diffusive regime of propagation has been provided. For many biological tissues, the diffusive regime of propagation can be established, even near the source, provided the photons have travelled trajectories with lengths greater than four times the transport mean free path.