## Transport theory for light propagation in biological tissue

JOSA A, Vol. 21, Issue 5, pp. 820-827 (2004)

http://dx.doi.org/10.1364/JOSAA.21.000820

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### Abstract

We study light propagation in biological tissue using the radiative transport equation. The Green’s function is the fundamental solution to the radiative transport equation from which all other solutions can be computed. We compute the Green’s function as an expansion in plane-wave modes. We calculate these plane-wave modes numerically using the discrete-ordinate method. When scattering is sharply peaked, calculating the plane-wave modes for the transport equation is difficult. For that case we replace it with the Fokker–Planck equation since the latter gives a good approximation to the transport equation and requires less work to solve. We calculate the plane-wave modes for the Fokker–Planck equation numerically using a finite-difference approximation. The method of computing the Green’s function for it is the same as for the transport equation. We demonstrate the use of the Green’s function for the transport and Fokker–Planck equations by computing the point-spread function in a half-space composed of a uniform scattering and absorbing medium.

© 2004 Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(030.5620) Coherence and statistical optics : Radiative transfer

(170.3660) Medical optics and biotechnology : Light propagation in tissues

**History**

Original Manuscript: June 17, 2003

Revised Manuscript: November 11, 2003

Manuscript Accepted: November 11, 2003

Published: May 1, 2004

**Citation**

Arnold D. Kim, "Transport theory for light propagation in biological tissue," J. Opt. Soc. Am. A **21**, 820-827 (2004)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-5-820

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### References

- A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE Press, Piscataway, N.J., 1996).
- K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).
- K. M. Case, “On boundary value problems of linear transport theory,” in Proceedings of the Symposium in Applied Mathematics, Vol. 1, R. Bellman, G. Birkhoff, I. Abu-Shumays, eds. (American Mathematical Society, Providence, R.I., 1969), pp. 17–36.
- A. D. Kim, J. B. Keller, “Light propagation in biological tissue,” J. Opt. Soc. Am. A 20, 92–98 (2003). [CrossRef]
- J. E. Morel, “An improved Fokker–Planck angular differencing scheme,” Nucl. Sci. Eng. 89, 131–136 (1985).
- C. L. Leakeas, E. W. Larsen, “Generalized Fokker–Planck approximations of particle transport with highly forward-peaked scattering,” Nucl. Sci. Eng. 137, 236–250 (2001).

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