The use of the Henyey–Greenstein phase function in Monte Carlo simulations in biomedical optics

Monte Carlo (MC) simulations are often at the heart of the testing procedure in biomedical optics. One of the critical points in MC simulations is to define the new photon direction after each scattering event. One of the most popular solutions is to use the Henyey-Greenstein phase function or some linear combinations of it. In this note, we demonstrate that randomly generating the angle defining the new direction of a photon after a collision, by means of the Henyey-Greenstein phase function, is not equivalent to generating the cosine of this angle, as is classically done. In practice, it is demonstrated that for a nearly isotropic medium (asymmetry parameter g approximately 0) this discrepancy is not large, however for an anisotropic medium as is typically found in vivo (e.g. g = 0.98) the two methods give completely different results.

[1]  B. Wilson,et al.  Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties. , 1989, Applied optics.

[2]  W. Gander,et al.  Adaptive Quadrature—Revisited , 2000 .

[3]  S. A. Prahl,et al.  A Monte Carlo model of light propagation in tissue , 1989, Other Conferences.

[4]  Nick Everdell,et al.  Optical tomography of the breast using a multi-channel time-resolved imager , 2005, Physics in medicine and biology.

[5]  D. Toublanc,et al.  Henyey-Greenstein and Mie phase functions in Monte Carlo radiative transfer computations. , 1996, Applied optics.

[6]  J. Briers,et al.  Laser Doppler, speckle and related techniques for blood perfusion mapping and imaging. , 2001, Physiological measurement.

[7]  B. Wilson,et al.  A Monte Carlo model for the absorption and flux distributions of light in tissue. , 1983, Medical physics.

[8]  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.

[9]  D. Delpy,et al.  An improved design for a stable and reproducible phantom material for use in near-infrared spectroscopy and imaging. , 1995, Physics in medicine and biology.

[10]  D T Delpy,et al.  Parallel operation of Monte Carlo simulations on a diverse network of computers. , 1997, Physics in medicine and biology.

[11]  S R Arridge,et al.  Recent advances in diffuse optical imaging , 2005, Physics in medicine and biology.

[12]  S. Arridge,et al.  Optical imaging in medicine: II. Modelling and reconstruction , 1997, Physics in medicine and biology.

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

[14]  L. C. Henyey,et al.  Diffuse radiation in the Galaxy , 1940 .

[15]  Leonardo Dagdug,et al.  Effects of anisotropic optical properties on photon migration in structured tissues. , 2003, Physics in medicine and biology.

[16]  W Feng,et al.  Influence of overlying tissue and probe geometry on the sensitivity of a near-infrared tissue oximeter. , 2001, Physiological measurement.

[17]  S Andersson-Engels,et al.  Real-time method for fitting time-resolved reflectance and transmittance measurements with a monte carlo model. , 1998, Applied optics.

[18]  Z. Kam,et al.  Absorption and Scattering of Light by Small Particles , 1998 .

[19]  S R Arridge,et al.  The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis. , 1992, Physics in medicine and biology.

[20]  S. Jacques,et al.  Angular dependence of HeNe laser light scattering by human dermis , 1988 .

[21]  J. Mourant,et al.  High-angle scattering events strongly affect light collection in clinically relevant measurement geometries for light transport through tissue. , 2000, Physics in medicine and biology.

[22]  L Wang,et al.  MCML--Monte Carlo modeling of light transport in multi-layered tissues. , 1995, Computer methods and programs in biomedicine.

[23]  A. Witt,et al.  Multiple scattering in reflection nebulae. I - A Monte Carlo approach. II - Uniform plane-parallel nebulae with foreground stars. III - Nebulae with embedded illuminating stars , 1977 .

[24]  G.L. Goudreau.  Computational structural mechanics. From national defense to national resource , 1994, IEEE Computational Science and Engineering.

[25]  Simon R. Arridge,et al.  Computational aspects of diffuse optical tomography , 2003, Comput. Sci. Eng..

[26]  M. Ferrari,et al.  Principles, techniques, and limitations of near infrared spectroscopy. , 2004, Canadian journal of applied physiology = Revue canadienne de physiologie appliquee.