Abstract

Near-infrared optical techniques permit tissue diagnosis by surface measurement. However, the geometrical shape of this interface profiles the intensity of the surface measurement, which is found to have an iso-pathlength (IPL) point allowing for absorption identification independent of tissue scattering. The IPL point was projected in Monte Carlo (MC) simulation, validated experimentally in cylindrical tissues, but remains under-appreciated through analytical approaches. In this work, we present an analytical solution of an IPL point for steady-state diffusion based on the extrapolated zero-boundary condition. The same IPL points were found when comparing this solution to 3-D MC simulations for a tissue radius range of 5-8mm.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. K. P. Nadeau, T. B. Rice, A. J. Durkin, and B. J. Tromberg, “Multifrequency synthesis and extraction using square wave projection patterns for quantitative tissue imaging,” J. Biomed. Opt. 20(11), 116005 (2015).
    [Crossref] [PubMed]
  2. V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7(8), 603–614 (2010).
    [Crossref] [PubMed]
  3. V. V. Tuchin, Optical clearing of tissues and blood (SPIE Press, Bellingham, WA, 2006).‏
  4. T. D. O’Sullivan, A. E. Cerussi, D. J. Cuccia, and B. J. Tromberg, “Diffuse optical imaging using spatially and temporally modulated light,” J. Biomed. Opt. 17(7), 071311 (2012).
    [PubMed]
  5. O. Wieben, in Design of Pulse Oximeters, edited by J.G. Webster (Taylor & Francis, 1997), p. 40–55.
  6. J. T. B. Moyle, in Pulse Oximetry (BMJ Books London, 2002).
  7. L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
    [Crossref] [PubMed]
  8. S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
    [Crossref] [PubMed]
  9. 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(7), 1531–1560 (1992).
    [Crossref] [PubMed]
  10. B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39(7), 1157–1180 (1994).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  13. 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(3), 648–662 (2010).
    [Crossref] [PubMed]
  14. R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11(10), 2727–2741 (1994).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  17. I. Feder, H. Duadi, and D. Fixler, “Experimental system for measuring the full scattering profile of circular phantoms,” Biomed. Opt. Express 6(8), 2877–2886 (2015).
    [Crossref] [PubMed]
  18. H. Duadi, I. Feder and D. Fixler, ” Near‐infrared human finger measurements based on self‐calibration point: Simulation and in vivo experiments,” J. Biophot. 11 (2018)
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    [Crossref] [PubMed]
  20. I. Feder, H. Duadi, R. Chakraborty, and D. Fixler, “Self-Calibration Phenomenon for Near-Infrared Clinical Measurements: Theory, Simulation, and Experiments,” ACS Omega 3(3), 2837–2844 (2018).
    [Crossref] [PubMed]
  21. D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, “Speckle random coding for 2D super resolving fluorescent microscopic imaging,” Micron 38(2), 121–128 (2007).
    [Crossref] [PubMed]
  22. D Fixler, Y Namer, Y Yishay, and M. Deutsch‏, “Influence of fluorescence anisotropy on fluorescence intensity and lifetime measurement: theory, simulations and experiments,” IEEE Trans. Biomed. Eng. 53(6), 1141–1152‏ (2006).

2018 (1)

I. Feder, H. Duadi, R. Chakraborty, and D. Fixler, “Self-Calibration Phenomenon for Near-Infrared Clinical Measurements: Theory, Simulation, and Experiments,” ACS Omega 3(3), 2837–2844 (2018).
[Crossref] [PubMed]

2017 (1)

2015 (3)

I. Feder, H. Duadi, and D. Fixler, “Experimental system for measuring the full scattering profile of circular phantoms,” Biomed. Opt. Express 6(8), 2877–2886 (2015).
[Crossref] [PubMed]

D. Piao, R. L. Barbour, H. L. Graber, and D. C. Lee, “On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium,” J. Biomed. Opt. 20(10), 105005 (2015).
[Crossref] [PubMed]

K. P. Nadeau, T. B. Rice, A. J. Durkin, and B. J. Tromberg, “Multifrequency synthesis and extraction using square wave projection patterns for quantitative tissue imaging,” J. Biomed. Opt. 20(11), 116005 (2015).
[Crossref] [PubMed]

2014 (1)

H. Duadi, I. Feder, and D. Fixler, “Linear dependency of full scattering profile isobaric point on tissue diameter,” J. Biomed. Opt. 19(2), 026007 (2014).
[Crossref] [PubMed]

2012 (1)

T. D. O’Sullivan, A. E. Cerussi, D. J. Cuccia, and B. J. Tromberg, “Diffuse optical imaging using spatially and temporally modulated light,” J. Biomed. Opt. 17(7), 071311 (2012).
[PubMed]

2010 (2)

2008 (1)

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[Crossref] [PubMed]

2007 (1)

D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, “Speckle random coding for 2D super resolving fluorescent microscopic imaging,” Micron 38(2), 121–128 (2007).
[Crossref] [PubMed]

2001 (1)

2000 (1)

1995 (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

1994 (2)

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39(7), 1157–1180 (1994).
[Crossref] [PubMed]

R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11(10), 2727–2741 (1994).
[Crossref] [PubMed]

1992 (1)

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(7), 1531–1560 (1992).
[Crossref] [PubMed]

Arridge, S. R.

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(7), 1531–1560 (1992).
[Crossref] [PubMed]

Barbour, R. L.

D. Piao, R. L. Barbour, H. L. Graber, and D. C. Lee, “On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium,” J. Biomed. Opt. 20(10), 105005 (2015).
[Crossref] [PubMed]

Bunting, C. F.

Cerussi, A. E.

T. D. O’Sullivan, A. E. Cerussi, D. J. Cuccia, and B. J. Tromberg, “Diffuse optical imaging using spatially and temporally modulated light,” J. Biomed. Opt. 17(7), 071311 (2012).
[PubMed]

Chakraborty, R.

I. Feder, H. Duadi, R. Chakraborty, and D. Fixler, “Self-Calibration Phenomenon for Near-Infrared Clinical Measurements: Theory, Simulation, and Experiments,” ACS Omega 3(3), 2837–2844 (2018).
[Crossref] [PubMed]

Cope, M.

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(7), 1531–1560 (1992).
[Crossref] [PubMed]

Cuccia, D. J.

T. D. O’Sullivan, A. E. Cerussi, D. J. Cuccia, and B. J. Tromberg, “Diffuse optical imaging using spatially and temporally modulated light,” J. Biomed. Opt. 17(7), 071311 (2012).
[PubMed]

Delpy, D. T.

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(7), 1531–1560 (1992).
[Crossref] [PubMed]

Deutsch, M.

D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, “Speckle random coding for 2D super resolving fluorescent microscopic imaging,” Micron 38(2), 121–128 (2007).
[Crossref] [PubMed]

Duadi, H.

I. Feder, H. Duadi, R. Chakraborty, and D. Fixler, “Self-Calibration Phenomenon for Near-Infrared Clinical Measurements: Theory, Simulation, and Experiments,” ACS Omega 3(3), 2837–2844 (2018).
[Crossref] [PubMed]

I. Feder, H. Duadi, and D. Fixler, “Experimental system for measuring the full scattering profile of circular phantoms,” Biomed. Opt. Express 6(8), 2877–2886 (2015).
[Crossref] [PubMed]

H. Duadi, I. Feder, and D. Fixler, “Linear dependency of full scattering profile isobaric point on tissue diameter,” J. Biomed. Opt. 19(2), 026007 (2014).
[Crossref] [PubMed]

Durkin, A. J.

K. P. Nadeau, T. B. Rice, A. J. Durkin, and B. J. Tromberg, “Multifrequency synthesis and extraction using square wave projection patterns for quantitative tissue imaging,” J. Biomed. Opt. 20(11), 116005 (2015).
[Crossref] [PubMed]

Feder, I.

I. Feder, H. Duadi, R. Chakraborty, and D. Fixler, “Self-Calibration Phenomenon for Near-Infrared Clinical Measurements: Theory, Simulation, and Experiments,” ACS Omega 3(3), 2837–2844 (2018).
[Crossref] [PubMed]

I. Feder, H. Duadi, and D. Fixler, “Experimental system for measuring the full scattering profile of circular phantoms,” Biomed. Opt. Express 6(8), 2877–2886 (2015).
[Crossref] [PubMed]

H. Duadi, I. Feder, and D. Fixler, “Linear dependency of full scattering profile isobaric point on tissue diameter,” J. Biomed. Opt. 19(2), 026007 (2014).
[Crossref] [PubMed]

Feng, T. C.

Fixler, D.

I. Feder, H. Duadi, R. Chakraborty, and D. Fixler, “Self-Calibration Phenomenon for Near-Infrared Clinical Measurements: Theory, Simulation, and Experiments,” ACS Omega 3(3), 2837–2844 (2018).
[Crossref] [PubMed]

I. Feder, H. Duadi, and D. Fixler, “Experimental system for measuring the full scattering profile of circular phantoms,” Biomed. Opt. Express 6(8), 2877–2886 (2015).
[Crossref] [PubMed]

H. Duadi, I. Feder, and D. Fixler, “Linear dependency of full scattering profile isobaric point on tissue diameter,” J. Biomed. Opt. 19(2), 026007 (2014).
[Crossref] [PubMed]

D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, “Speckle random coding for 2D super resolving fluorescent microscopic imaging,” Micron 38(2), 121–128 (2007).
[Crossref] [PubMed]

Garcia, J.

D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, “Speckle random coding for 2D super resolving fluorescent microscopic imaging,” Micron 38(2), 121–128 (2007).
[Crossref] [PubMed]

Graaff, R.

Graber, H. L.

D. Piao, R. L. Barbour, H. L. Graber, and D. C. Lee, “On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium,” J. Biomed. Opt. 20(10), 105005 (2015).
[Crossref] [PubMed]

Haskell, R. C.

Jacques, S. L.

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[Crossref] [PubMed]

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

Lee, D. C.

D. Piao, R. L. Barbour, H. L. Graber, and D. C. Lee, “On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium,” J. Biomed. Opt. 20(10), 105005 (2015).
[Crossref] [PubMed]

Martelli, F.

McAdams, M. S.

Nadeau, K. P.

K. P. Nadeau, T. B. Rice, A. J. Durkin, and B. J. Tromberg, “Multifrequency synthesis and extraction using square wave projection patterns for quantitative tissue imaging,” J. Biomed. Opt. 20(11), 116005 (2015).
[Crossref] [PubMed]

Ntziachristos, V.

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7(8), 603–614 (2010).
[Crossref] [PubMed]

O’Sullivan, T. D.

T. D. O’Sullivan, A. E. Cerussi, D. J. Cuccia, and B. J. Tromberg, “Diffuse optical imaging using spatially and temporally modulated light,” J. Biomed. Opt. 17(7), 071311 (2012).
[PubMed]

Patel, S. G.

Patterson, M. S.

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39(7), 1157–1180 (1994).
[Crossref] [PubMed]

Piao, D.

Pogue, B. W.

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(3), 648–662 (2010).
[Crossref] [PubMed]

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[Crossref] [PubMed]

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39(7), 1157–1180 (1994).
[Crossref] [PubMed]

Rice, T. B.

K. P. Nadeau, T. B. Rice, A. J. Durkin, and B. J. Tromberg, “Multifrequency synthesis and extraction using square wave projection patterns for quantitative tissue imaging,” J. Biomed. Opt. 20(11), 116005 (2015).
[Crossref] [PubMed]

Sassaroli, A.

Svaasand, L. O.

Ten Bosch, J. J.

Tromberg, B. J.

K. P. Nadeau, T. B. Rice, A. J. Durkin, and B. J. Tromberg, “Multifrequency synthesis and extraction using square wave projection patterns for quantitative tissue imaging,” J. Biomed. Opt. 20(11), 116005 (2015).
[Crossref] [PubMed]

T. D. O’Sullivan, A. E. Cerussi, D. J. Cuccia, and B. J. Tromberg, “Diffuse optical imaging using spatially and temporally modulated light,” J. Biomed. Opt. 17(7), 071311 (2012).
[PubMed]

R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11(10), 2727–2741 (1994).
[Crossref] [PubMed]

Tsay, T. T.

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

Weiss, A.

D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, “Speckle random coding for 2D super resolving fluorescent microscopic imaging,” Micron 38(2), 121–128 (2007).
[Crossref] [PubMed]

Yamada, Y.

Zaccanti, G.

Zalevsky, Z.

D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, “Speckle random coding for 2D super resolving fluorescent microscopic imaging,” Micron 38(2), 121–128 (2007).
[Crossref] [PubMed]

Zhang, A.

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

ACS Omega (1)

I. Feder, H. Duadi, R. Chakraborty, and D. Fixler, “Self-Calibration Phenomenon for Near-Infrared Clinical Measurements: Theory, Simulation, and Experiments,” ACS Omega 3(3), 2837–2844 (2018).
[Crossref] [PubMed]

Appl. Opt. (2)

Biomed. Opt. Express (1)

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

J. Biomed. Opt. (5)

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[Crossref] [PubMed]

K. P. Nadeau, T. B. Rice, A. J. Durkin, and B. J. Tromberg, “Multifrequency synthesis and extraction using square wave projection patterns for quantitative tissue imaging,” J. Biomed. Opt. 20(11), 116005 (2015).
[Crossref] [PubMed]

T. D. O’Sullivan, A. E. Cerussi, D. J. Cuccia, and B. J. Tromberg, “Diffuse optical imaging using spatially and temporally modulated light,” J. Biomed. Opt. 17(7), 071311 (2012).
[PubMed]

H. Duadi, I. Feder, and D. Fixler, “Linear dependency of full scattering profile isobaric point on tissue diameter,” J. Biomed. Opt. 19(2), 026007 (2014).
[Crossref] [PubMed]

D. Piao, R. L. Barbour, H. L. Graber, and D. C. Lee, “On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium,” J. Biomed. Opt. 20(10), 105005 (2015).
[Crossref] [PubMed]

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

Micron (1)

D. Fixler, J. Garcia, Z. Zalevsky, A. Weiss, and M. Deutsch, “Speckle random coding for 2D super resolving fluorescent microscopic imaging,” Micron 38(2), 121–128 (2007).
[Crossref] [PubMed]

Nat. Methods (1)

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7(8), 603–614 (2010).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Med. Biol. (2)

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(7), 1531–1560 (1992).
[Crossref] [PubMed]

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39(7), 1157–1180 (1994).
[Crossref] [PubMed]

Other (5)

V. V. Tuchin, Optical clearing of tissues and blood (SPIE Press, Bellingham, WA, 2006).‏

O. Wieben, in Design of Pulse Oximeters, edited by J.G. Webster (Taylor & Francis, 1997), p. 40–55.

J. T. B. Moyle, in Pulse Oximetry (BMJ Books London, 2002).

H. Duadi, I. Feder and D. Fixler, ” Near‐infrared human finger measurements based on self‐calibration point: Simulation and in vivo experiments,” J. Biophot. 11 (2018)

D Fixler, Y Namer, Y Yishay, and M. Deutsch‏, “Influence of fluorescence anisotropy on fluorescence intensity and lifetime measurement: theory, simulations and experiments,” IEEE Trans. Biomed. Eng. 53(6), 1141–1152‏ (2006).

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Figures (4)

Fig. 1
Fig. 1 Details of a cylindrical geometry corresponding to a concave tissue medium. The red arrow indicates the incident light. The positions of the image source, the equivalent isotropic source, and the extrapolated zero-boundary (dashed line) are also illustrated.
Fig. 2
Fig. 2 FSPs and the IPL point resulted from 3-D MC simulation and diffusion theory for steady-state photon illumination into a concave cylindrical tissue domain. Tissue radius is R0 = 6mm. The FSP has an IPL point which is constant for different reduced scattering coefficients: (a) In the MC simulation gray asterisks, black squares and red triangles correspond respectively to μs' = 10, 16 and 26cm−1. (b) In the diffusion theory black dotted, blue solid, green dot-dashed and red dashed lines represent respectively μs' = 16, 18, 20 and 26 cm−1. (c) Comparison of 3-D MC simulation and diffusion theory reveals a common IPL point at 171°.
Fig. 3
Fig. 3 The influence of radius on the IPL point. IPL point from MC simulation (red circles, STD = ± 1°) and from diffusion theory (blue squares, STD = ± 0.5°).
Fig. 4
Fig. 4 The FSPs of steady-state photon diffusion for a convex geometry with a radius of 6mm, where a cylinder of air is surrounded by tissue (Eq. (7). Different reduced scattering coefficients (μs' = 16 and 26 cm−1 corresponding to black dotted and red dashed lines) have a common IPL point at 171°.

Equations (7)

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

R a =1/ μ s '.
2 Ψ( r ) μ a D Ψ( r )= S( r ) D
D= [ 3( μ a + μ s ' ) ] 1
Ψ( θ )= S 2 π 2 D m=0 k I m [ k eff ( R 0 R a ) ] K m ( k eff R 0 ) [ 1 I m ( k eff R 0 ) K m [ k eff ( R 0 + R b ) ] K m ( k eff R 0 ) I m [ k eff ( R 0 + R b ) ] ]cos( mθ )
P scatter =1 e μ ' s dr
θ new = θ old + s ˜ co s 1 ( g )
Ψ( θ )= S 2 π 2 D m=0 k I m [ k eff R 0 ] K m ( k eff ( R 0 + R a ) ) [ 1 K m ( k eff R 0 ) I m [ k eff ( R 0 R b ) ] I m ( k eff R 0 ) K m [ k eff ( R 0 R b ) ] ]cos( mθ )

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