Phase function simulation in tissue phantoms: a fractal approach

Artificial media are needed for the calibration of optical diagnostic methods in order to work on reproducible, stable and well known samples. Since the scattering and absorption coefficients can easily be adjusted by using appropriate concentrations of scattering and absorbing components, the most difficult part in the design of a good tissue phantom is to obtain an actual phase function. The most common way to create phantoms is to use scattering microspheres of equal size, but the Mie phase function of such a phantom does not match the tissue's real phase function. Moreover, we show in this paper that the similarity relations often used for the analysis of the results obtained with this type of phantom may sometimes be very inaccurate. The use of a mixture of different sized scattering particles is then considered, in order to imitate the whole phase function. However, as the determination of adequate sizes and concentrations is a difficult mathematical task, we describe a simple method to solve this problem. We first demonstrate that the extreme optical complexity of real biological samples could be simulated by a mixture of spheres with a fractal diameter distribution. Then, we present a few simple rules based on the knowledge of this fractal distribution, which can be used to obtain a realistic phase function with a limited number of sphere diameters.

[1]  Eric Tinet,et al.  Fast and accurate new Monte Carlo simulation for light propagation through turbid media , 1993, Defense, Security, and Sensing.

[2]  A. P. Shepherd,et al.  Comparison of Mie theory and the light scattering of red blood cells. , 1988, Applied optics.

[3]  H. V. Hulst Light Scattering by Small Particles , 1957 .

[4]  David T. Delpy,et al.  Optical properties of brain tissue , 1993, Photonics West - Lasers and Applications in Science and Engineering.

[5]  W. Wiscombe Improved Mie scattering algorithms. , 1980, Applied optics.

[6]  On the determination of optical parameters for turbid materials , 1994 .

[7]  M. V. van Gemert,et al.  Measurements and calculations of the energy fluence rate in a scattering and absorbing phantom at 633 nm. , 1989, Applied optics.

[8]  H. J. van Staveren,et al.  Light scattering in Intralipid-10% in the wavelength range of 400-1100 nm. , 1991, Applied optics.

[9]  Yasuo Kuga,et al.  Attenuation constant of a coherent field in a dense distribution of particles , 1982 .

[10]  M S Patterson,et al.  Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm. , 1987, Medical physics.

[11]  Sigrid Avrillier,et al.  Monte Carlo simulation of collimated beam transmission through turbid media , 1990 .

[12]  Eric Tinet,et al.  Similarity relations in multiple scattering through turbid media: a Monte Carlo evaluation , 1993, Defense, Security, and Sensing.

[13]  R Marchesini,et al.  Extinction and absorption coefficients and scattering phase functions of human tissues in vitro. , 1989, Applied optics.

[14]  Particle sizing in the Mie scattering region: singular-value analysis , 1989 .

[15]  M S Patterson,et al.  The use of India ink as an optical absorber in tissue-simulating phantoms , 1992, Physics in medicine and biology.

[16]  J. J. Bosch,et al.  Path-length distributions of photons re-emitted from turbid media illuminated by a pencil-beam , 1995 .

[17]  B. Mandelbrot Fractal Geometry of Nature , 1984 .

[18]  Christian Depeursinge,et al.  Determination of biological tissue optical coefficients from the spatial or temporal scattered profile of a collimated pulsed light source , 1995, Other Conferences.

[19]  J. Featherstone,et al.  Nature of light scattering in dental enamel and dentin at visible and near-infrared wavelengths. , 1995, Applied optics.

[20]  David T. Delpy,et al.  Development of a stable and reproducible tissue-equivalent phantom for use in infrared spectroscopy and imaging , 1993, Photonics West - Lasers and Applications in Science and Engineering.

[21]  Jaap R. Zijp,et al.  Pascal program to perform Mie calculations , 1993 .

[22]  Akira Ishimaru,et al.  Wave propagation and scattering in random media , 1997 .