Statistics of photon penetration depth in diffusive media

The study of photon migration through highly scattering media opens the way to the non-invasive investigation of biological tissues well below the skin surface. When the medium is addressed in reflectance geometry, a key issue is to maximize the depth reached by migrating photons. By exploiting the Diffusion Approximation of the Radiative Transfer Equation, we calculated the time-resolved and continuous-wave probability density functions for the maximum depth reached by detected photons, for both a homogeneous and a layered laterally-infinite diffusive slab. From the probability density functions it is possible to calculate the mean value of the maximum depth at which detected photons have undergone scattering events.

[1]  George Zonios,et al.  Investigation of reflectance sampling depth in biological tissues for various common illumination/collection configurations , 2014, Journal of biomedical optics.

[2]  A. Darzi,et al.  Diffuse optical imaging of the healthy and diseased breast: A systematic review , 2008, Breast Cancer Research and Treatment.

[3]  Alwin Kienle,et al.  Exact and efficient solution of the radiative transport equation for the semi-infinite medium , 2013, Scientific Reports.

[4]  Davide Contini,et al.  Time domain functional NIRS imaging for human brain mapping , 2014, NeuroImage.

[5]  G H Weiss,et al.  Statistical properties of the penetration of photons into a semi-infinite turbid medium: a random-walk analysis. , 1998, Applied optics.

[6]  David A. Boas,et al.  Twenty years of functional near-infrared spectroscopy: introduction for the special issue , 2014, NeuroImage.

[7]  Ilaria Bargigia,et al.  Nondestructive optical detection of monomer uptake in wood polymer composites. , 2014, Optics letters.

[8]  Descriptive parameter for photon trajectories in a turbid medium. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  D Contini,et al.  Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory. , 1997, Applied optics.

[10]  G. Weiss,et al.  Model for photon migration in turbid biological media. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[11]  Fabrizio Martelli,et al.  Light Propagation Through Biological Tissue and Other Diffusive Media: Theory, Solutions, and Software , 2009 .

[12]  Ralph Nossal,et al.  Photon migration in layered media. , 1988, Applied optics.

[13]  R. Cubeddu,et al.  Nondestructive quantification of chemical and physical properties of fruits by time-resolved reflectance spectroscopy in the wavelength range 650-1000 nm. , 2001, Applied optics.

[14]  Alessandro Torricelli,et al.  There’s plenty of light at the bottom: statistics of photon penetration depth in random media , 2016, Scientific Reports.

[15]  Vasan Venugopalan,et al.  Radiative transport in the delta-P1 approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media. , 2004, Journal of biomedical optics.

[16]  A. Yodh,et al.  Diffuse optics for tissue monitoring and tomography , 2010, Reports on progress in physics. Physical Society.

[17]  B. Chance,et al.  Photon migration in the presence of a single defect: a perturbation analysis. , 1995, Applied optics.

[18]  George H. Weiss,et al.  A measure of photon penetration into tissue in diffusion models , 1998 .

[19]  Ilaria Bargigia,et al.  Diffuse Optical Techniques Applied to Wood Characterisation , 2013 .

[20]  A numerical study of the statistics of penetration depth of photons re-emitted from irradiated media , 1998 .

[21]  Timothy C Zhu,et al.  Reconstruction of in-vivo optical properties for human prostate using interstitial diffuse optical tomography. , 2009, Optics express.

[22]  Stefan Andersson-Engels,et al.  Broadband photon time-of-flight spectroscopy of pharmaceuticals and highly scattering plastics in the VIS and close NIR spectral ranges. , 2013, Optics express.

[23]  B. Wilson,et al.  Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths. , 1995, Applied optics.

[24]  R. Cubeddu,et al.  Time-Domain Broadband near Infrared Spectroscopy of the Female Breast: A Focused Review from Basic Principles to Future Perspectives , 2012 .

[25]  A. Berezhkovskii,et al.  Where do Brownian particles spend their time , 1998 .

[26]  G. Weiss,et al.  Statistics of the depth probed by cw measurements of photons in a turbid medium , 1998 .

[27]  B Chance,et al.  Study of photon migration depths with time-resolved spectroscopy. , 1991, Optics letters.

[28]  B. Tromberg,et al.  Optical imaging of breast cancer oxyhemoglobin flare correlates with neoadjuvant chemotherapy response one day after starting treatment , 2011, Proceedings of the National Academy of Sciences.

[29]  Marco Ferrari,et al.  A brief review on the history of human functional near-infrared spectroscopy (fNIRS) development and fields of application , 2012, NeuroImage.

[30]  George H. Weiss,et al.  Statistics of Penetration Depth of Photons Re-Emitted From Irradiated Tissue , 1989 .