## Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator. III. Synthetic study of continuous-wave photon fluence rate along unique spiral paths |

JOSA A, Vol. 29, Issue 4, pp. 545-558 (2012)

http://dx.doi.org/10.1364/JOSAA.29.000545

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### Abstract

This is Part III of the work that examines photon diffusion in a scattering-dominant medium *enclosed by* a “concave” circular cylindrical applicator or *enclosing* a “convex” circular cylindrical applicator. In Part II of this work Zhang et al. [J. Opt. Soc. Am. A 28, 66 (2011)] predicted that, on the tissue-applicator interface of either “concave” or “convex” geometry, there exists a unique set of spiral paths, along which the steady-state photon fluence rate decays at a rate equal to that along a straight line on a planar semi-infinite interface, for the same line-of-sight source–detector distance. This phenomenon of steady-state photon diffusion is referred to as “straight-line-resembling-spiral paths” (abbreviated as “spiral paths”). This Part III study develops analytic approaches to the spiral paths associated with geometry of a large radial dimension and presents spiral paths found numerically for geometry of a small radial dimension. This Part III study also examines whether the spiral paths associated with a homogeneous medium are a good approximation for the medium containing heterogeneity. The heterogeneity is limited to an anomaly that is aligned azimuthally with the spiral paths and has either positive or negative contrast of the absorption or scattering coefficient over the background medium. For a weak-contrast anomaly the perturbation by it to the photon fluence rate along the spiral paths is found by applying a well-established perturbation analysis in cylindrical coordinates. For a strong-contrast anomaly the change by it to the photon fluence rate along the spiral paths is computed using the finite-element method. For the investigated heterogeneous-medium cases the photon fluence rate along the homogeneous-medium associated spiral paths is macroscopically indistinguishable from, and microscopically close to, that along a straight line on a planar semi-infinite interface.

© 2012 Optical Society of America

**OCIS Codes**

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

(170.5280) Medical optics and biotechnology : Photon migration

(170.6960) Medical optics and biotechnology : Tomography

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: September 28, 2011

Revised Manuscript: November 30, 2011

Manuscript Accepted: December 1, 2011

Published: March 22, 2012

**Virtual Issues**

Vol. 7, Iss. 6 *Virtual Journal for Biomedical Optics*

**Citation**

Anqi Zhang, Daqing Piao, and Charles F. Bunting, "Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator. III. Synthetic study of continuous-wave photon fluence rate along unique spiral paths," J. Opt. Soc. Am. A **29**, 545-558 (2012)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-29-4-545

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### References

- A. Ishimaru, “Diffusion of light in turbid material,” Appl. Opt. 28, 2210–2215 (1989). [CrossRef]
- W. Jost, “Diffusion and electrolytic conduction in crystals (ionic semiconductors),” J. Chem. Phys. 1, 466–475 (1933). [CrossRef]
- A. M. Weinberg and E. P. Wigner, The Physical Theory of Neutron Chain Reactors (University of Chicago Press, 1958).
- D. L. Cummings, R. L. Reuben, and D. A. Blackburn, “The effect of pressure modulation on the flow of gas through a solid membrane: permeation and diffusion of hydrogen through nickel,” Metall. Trans. A 15, 639–648 (1984). [CrossRef]
- L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, 1973).
- E. A. Mason, R. J. Munn, and F. J. Smith, “Thermal diffusion in gases,” in Advances in Atomic and Molecular Physics(Academic, 1966), pp. 33–91.
- W. K. Hocking, S. Fukao, M. Yamamoto, T. Tsuda, and S. Kato, “Viscosity waves and thermal-conduction waves as a cause of ‘specular’ reflectors in radar studies of the atmosphere,” Radio Sci. 26, 1281–1303 (1991). [CrossRef]
- A. Mandelis, Diffusion-Wave Fields: Mathematical Methods and Green Functions (Springer-Verlag, 2001).
- S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992). [CrossRef]
- R. L. Barbour, H. Graber, R. Aronson, and J. Lubowsky, “Model for 3-D optical imaging of tissue,” Remote Sensing Science for the Nineties, IGARSS ’90, 1395–1399 (1990). http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?isNumber=3531&arNumber=688761&isnumber=3531&arnumber=688761&tag=1 [CrossRef]
- S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993). [CrossRef]
- A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998). [CrossRef]
- S. J. Madsen, B. C. Wilson, M. S. Patterson, Y. D. Park, S. L. Jacques, and Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992). [CrossRef]
- S. Fantini, M. A. Franceschini, and E. Gratton, “Semi-infinite-geometry boundary problem for light migration in highly scattering media: a frequency-domain study in the diffusion approximation,” J. Opt. Soc. Am. B 11, 2128–2138 (1994). [CrossRef]
- A. Zhang, D. Piao, C. F. Bunting, and B. W. Pogue, “Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator. I. Steady-state theory,” J. Opt. Soc. Am. A 27, 648–662 (2010). [CrossRef]
- A. Zhang, G. Xu, C. Daluwatte, G. Yao, C. F. Bunting, B. W. Pogue, and D. Piao, “Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator. II. Quantitative examinations of the steady-state theory,” J. Opt. Soc. Am. A 28, 66–75 (2011). [CrossRef]
- A. Zhang, D. Piao, G. Yao, C. F. Bunting, and Y. Jiang, “Diffuse photon remission along unique spiral paths on a cylindrical interface is modeled by photon remission along a straight line on a semi-infinite interface,” Opt. Lett. 36, 654–656 (2011). [CrossRef]
- S. R. Arridge, P. van der Zee, M. Cope, and D. T. Delpy, “Reconstruction methods for infra-red absorption imaging,” Proc. SPIE 1431, 204–215 (1991). [CrossRef]
- M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20, 426–428 (1995). [CrossRef]
- L. V. Wang and H. Wu, Biomedical Optics, Principles and Imaging (Wiley, 2007).
- H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009). [CrossRef]

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