Abstract

We demonstrate that, for a long cylindrical applicator that interfaces concavely or convexly with a scattering-dominant medium, a unique set of spiral-shaped directions exist on the tissue–applicator interface, along which the diffuse photon remission is essentially modeled by the photon remission along a straight line on a semi-infinite interface. This interesting phenomenon, which is validated in steady state in this work by finite-element and Monte Carlo methods, may be particularly useful for simplifying deeper-tissue sensing in endoscopic imaging geometry.

© 2011 Optical Society of America

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References

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2011 (1)

2010 (2)

2009 (1)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, Commun.Numer. Meth. Engng. 25, 711 (2009).
[CrossRef]

2006 (1)

2005 (1)

1993 (1)

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, Med. Phys. 20, 299 (1993).
[CrossRef] [PubMed]

1992 (1)

S. R. Arridge, M. Cope, and D. T. Delpy, Phys. Med. Biol. 37, 1531 (1992).
[CrossRef] [PubMed]

1989 (1)

Arridge, S. R.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, Med. Phys. 20, 299 (1993).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope, and D. T. Delpy, Phys. Med. Biol. 37, 1531 (1992).
[CrossRef] [PubMed]

Bunting, C. F.

Carpenter, C. M.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, Commun.Numer. Meth. Engng. 25, 711 (2009).
[CrossRef]

Cope, M.

S. R. Arridge, M. Cope, and D. T. Delpy, Phys. Med. Biol. 37, 1531 (1992).
[CrossRef] [PubMed]

Daluwatte, C.

Davis, S. C.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, Commun.Numer. Meth. Engng. 25, 711 (2009).
[CrossRef]

Dehghani, H.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, Commun.Numer. Meth. Engng. 25, 711 (2009).
[CrossRef]

D. Piao, H. Xie, W. Zhang, J. S. Kransinski, G. Zhang, H. Dehghani, and B. W. Pogue, Opt. Lett. 31, 2876 (2006).
[CrossRef] [PubMed]

Delpy, D. T.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, Med. Phys. 20, 299 (1993).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope, and D. T. Delpy, Phys. Med. Biol. 37, 1531 (1992).
[CrossRef] [PubMed]

Eames, M. E.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, Commun.Numer. Meth. Engng. 25, 711 (2009).
[CrossRef]

Haidekker, M. A.

Hiraoka, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, Med. Phys. 20, 299 (1993).
[CrossRef] [PubMed]

Ishimaru, A.

Kienle, A.

Kransinski, J. S.

Liemert, A.

Paulsen, K. D.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, Commun.Numer. Meth. Engng. 25, 711 (2009).
[CrossRef]

Piao, D.

Pogue, B. W.

Schweiger, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, Med. Phys. 20, 299 (1993).
[CrossRef] [PubMed]

Srinivasan, S.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, Commun.Numer. Meth. Engng. 25, 711 (2009).
[CrossRef]

Xie, H.

Xu, G.

Yalavarthy, P. K.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, Commun.Numer. Meth. Engng. 25, 711 (2009).
[CrossRef]

Yao, G.

Zhang, A.

Zhang, G.

Zhang, W.

Appl. Opt. (2)

Commun.Numer. Meth. Engng. (1)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, Commun.Numer. Meth. Engng. 25, 711 (2009).
[CrossRef]

J. Opt. Soc. Am. A (2)

Med. Phys. (1)

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, Med. Phys. 20, 299 (1993).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Med. Biol. (1)

S. R. Arridge, M. Cope, and D. T. Delpy, Phys. Med. Biol. 37, 1531 (1992).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1
Fig. 1

(a) Source–detector pair on the cylindrical applicator’s surface decomposes to a longitudinal distance and an azimuth distance. (b) Three options for moving the detector one step away from the source. (c) Region containing the path of moving the detector in a coarse grid. (d) Path of moving the detector in a dense grid using the region in (c) as a prior. (e) Three-dimensional (3D) rendering of the spiral-shaped loops when a path similar to that in (d) is mapped to the cylindrical interfaces of concave and convex geometries.

Fig. 2
Fig. 2

Finite-element discretization of the medium that interfaces with (a) concave or (b) convex cylindrical applicator. The indicated curve is one quarter of the 3D spiral-shaped profiles shown in (c). Note that in (c) the spiral profile for convex-geometry is not in a closed-loop, due to the limit of the longitudinal dimensions. The photon remission along the indicated spiral directions is compared to the semi-infinite model, FEM, and MC simulation for (d) concave geometry and (e) convex geometry.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

ln ( Ψ · d 2 ) d = { k 0 + 1 2 k 0 R b ( R 0 R a ) [ 2 R 0 R a + 2 R b 4 R 0 R b ( R 0 R a ) ] · cos α · d }
ln ( Ψ · d 2 ) d = { k 0 1 2 k 0 R b ( R 0 + R a ) + [ 2 R 0 + R a 2 R b 4 R 0 R b ( R 0 + R a ) ] · cos α · d } ,
cos α = 1 k 0 d 2 R 0 2 R 0 R a + 2 R b
cos α = 1 k 0 d 2 R 0 2 R 0 + R a 2 R b

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