Abstract

The method consists of measuring the perturbation provoked by a small volume of the diffusive medium on light propagating through a medium of known optical properties. The absorption and the reduced scattering coefficients of the medium are retrieved from multidistance continuous-wave measurements of transmittance. The inversion procedure is based on the solution of the diffusion equation obtained with a perturbative approach. The method has been validated with Monte Carlo results. Examples of experimental results are reported.

© 2002 Optical Society of America

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  1. S. R. Arridge, M. Cope, 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] [PubMed]
  2. F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, G. Zaccanti, “Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation,” Phys. Med. Biol. 45, 1359–1373 (2000).
    [CrossRef] [PubMed]
  3. A. Kienle, M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A 14, 246–254 (1997).
    [CrossRef]
  4. J. L. Karagiannes, Z. Zhang, B. Grossweiner, L. I. Grossweiner, “Applications of the 1-D diffusion approximation to the optics of tissues and tissue phantoms,” Appl. Opt. 28, 2311–2317 (1989).
    [CrossRef] [PubMed]
  5. S. A. Prahl, M. J. C. van Gemert, A. J. Welch, “Determining the optical properties of turbid media by using the adding-doubling method,” Appl. Opt. 32, 559–568 (1993).
    [CrossRef] [PubMed]
  6. V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
    [CrossRef] [PubMed]
  7. A. Vogel, C. Dlugos, R. Nuffer, R. Birngruber, “Optical properties of human sclera, and their consequences for transscleral laser applications,” Lasers Surg. Med. 11, 331–340 (1991).
    [CrossRef] [PubMed]
  8. T. L. Troy, D. L. Page, E. M. Sevick-Muraca, “Optical properties of normal and diseased breast tissues: prognosis for optical mammography,” J. Biomed. Opt. 3, 342–355 (1996).
    [CrossRef]
  9. O. Coquoz, L. O. Svaasand, B. J. Tromberg, “Optical property measurements of turbid media in a small-volume cuvette with frequency-domain photon migration,” Appl. Opt. 40, 6281–6291 (2001).
    [CrossRef]
  10. S. Carraresi, T. S. M. Shatir, F. Martelli, G. Zaccanti, “Accuracy of a perturbation model to predict the effect of scattering and absorbing inhomogeneities on photon migration,” Appl. Opt. 40, 4622–4632 (2001).
    [CrossRef]
  11. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1996), Vol. 1.
  12. A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, G. Zaccanti, “Monte Carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. 37, 7392–7400 (1998).
    [CrossRef]
  13. G. Zaccanti, L. Alianelli, C. Blumetti, S. Carraresi, “Method for measuring the mean time of flight spent by photons inside a volume element of a highly diffusing medium,” Opt. Lett. 24, 1290–1292 (1999).
    [CrossRef]
  14. W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [CrossRef]
  15. R. J. Hunter, M. S. Patterson, T. J. Farrel, J. E. Hayward, “Hemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of the top layer thickness,” Phys. Med. Biol. 47, 193–208 (2002).
    [CrossRef] [PubMed]
  16. A. H. Gandjbakhche, V. Chernomordik, J. C. Hebden, R. Nossal, “Time-dependent contrast functions for quantitative imaging in time-resolved transillumination experiments,” Appl. Opt. 37, 1973–1981 (1998).
    [CrossRef]
  17. V. Chernomordik, D. Hattery, A. H. Gandjbakhche, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, R. Cubeddu, “Quantification by random walk of the optical parameters of nonlocalized abnomalies embedded within tissuelike phantoms,” Opt. Lett. 25, 951–953 (2000).
    [CrossRef]

2002

R. J. Hunter, M. S. Patterson, T. J. Farrel, J. E. Hayward, “Hemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of the top layer thickness,” Phys. Med. Biol. 47, 193–208 (2002).
[CrossRef] [PubMed]

2001

2000

V. Chernomordik, D. Hattery, A. H. Gandjbakhche, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, R. Cubeddu, “Quantification by random walk of the optical parameters of nonlocalized abnomalies embedded within tissuelike phantoms,” Opt. Lett. 25, 951–953 (2000).
[CrossRef]

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, G. Zaccanti, “Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation,” Phys. Med. Biol. 45, 1359–1373 (2000).
[CrossRef] [PubMed]

1999

1998

1997

1996

T. L. Troy, D. L. Page, E. M. Sevick-Muraca, “Optical properties of normal and diseased breast tissues: prognosis for optical mammography,” J. Biomed. Opt. 3, 342–355 (1996).
[CrossRef]

1993

1992

S. R. Arridge, M. Cope, 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] [PubMed]

1991

A. Vogel, C. Dlugos, R. Nuffer, R. Birngruber, “Optical properties of human sclera, and their consequences for transscleral laser applications,” Lasers Surg. Med. 11, 331–340 (1991).
[CrossRef] [PubMed]

1990

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

1989

Alianelli, L.

Arridge, S. R.

S. R. Arridge, M. Cope, 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] [PubMed]

Bassani, M.

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, G. Zaccanti, “Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation,” Phys. Med. Biol. 45, 1359–1373 (2000).
[CrossRef] [PubMed]

Birngruber, R.

A. Vogel, C. Dlugos, R. Nuffer, R. Birngruber, “Optical properties of human sclera, and their consequences for transscleral laser applications,” Lasers Surg. Med. 11, 331–340 (1991).
[CrossRef] [PubMed]

Blumetti, C.

Carraresi, S.

Cheong, W. F.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Chernomordik, V.

Contini, D.

Cope, M.

S. R. Arridge, M. Cope, 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] [PubMed]

Coquoz, O.

Cubeddu, R.

Delpy, D. T.

S. R. Arridge, M. Cope, 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] [PubMed]

Dlugos, C.

A. Vogel, C. Dlugos, R. Nuffer, R. Birngruber, “Optical properties of human sclera, and their consequences for transscleral laser applications,” Lasers Surg. Med. 11, 331–340 (1991).
[CrossRef] [PubMed]

Farrel, T. J.

R. J. Hunter, M. S. Patterson, T. J. Farrel, J. E. Hayward, “Hemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of the top layer thickness,” Phys. Med. Biol. 47, 193–208 (2002).
[CrossRef] [PubMed]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1996), Vol. 1.

Frank, G. L.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Gandjbakhche, A. H.

Grossweiner, B.

Grossweiner, L. I.

Hattery, D.

Hayward, J. E.

R. J. Hunter, M. S. Patterson, T. J. Farrel, J. E. Hayward, “Hemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of the top layer thickness,” Phys. Med. Biol. 47, 193–208 (2002).
[CrossRef] [PubMed]

Hebden, J. C.

Hunter, R. J.

R. J. Hunter, M. S. Patterson, T. J. Farrel, J. E. Hayward, “Hemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of the top layer thickness,” Phys. Med. Biol. 47, 193–208 (2002).
[CrossRef] [PubMed]

Ismaelli, A.

Karagiannes, J. L.

Kienle, A.

Martelli, F.

Nossal, R.

Nuffer, R.

A. Vogel, C. Dlugos, R. Nuffer, R. Birngruber, “Optical properties of human sclera, and their consequences for transscleral laser applications,” Lasers Surg. Med. 11, 331–340 (1991).
[CrossRef] [PubMed]

Page, D. L.

T. L. Troy, D. L. Page, E. M. Sevick-Muraca, “Optical properties of normal and diseased breast tissues: prognosis for optical mammography,” J. Biomed. Opt. 3, 342–355 (1996).
[CrossRef]

Patterson, M. S.

R. J. Hunter, M. S. Patterson, T. J. Farrel, J. E. Hayward, “Hemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of the top layer thickness,” Phys. Med. Biol. 47, 193–208 (2002).
[CrossRef] [PubMed]

A. Kienle, M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A 14, 246–254 (1997).
[CrossRef]

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Peters, V. G.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Pifferi, A.

Prahl, S. A.

S. A. Prahl, M. J. C. van Gemert, A. J. Welch, “Determining the optical properties of turbid media by using the adding-doubling method,” Appl. Opt. 32, 559–568 (1993).
[CrossRef] [PubMed]

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1996), Vol. 1.

Sassaroli, A.

Sevick-Muraca, E. M.

T. L. Troy, D. L. Page, E. M. Sevick-Muraca, “Optical properties of normal and diseased breast tissues: prognosis for optical mammography,” J. Biomed. Opt. 3, 342–355 (1996).
[CrossRef]

Shatir, T. S. M.

Svaasand, L. O.

Taroni, P.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1996), Vol. 1.

Torricelli, A.

Tromberg, B. J.

Troy, T. L.

T. L. Troy, D. L. Page, E. M. Sevick-Muraca, “Optical properties of normal and diseased breast tissues: prognosis for optical mammography,” J. Biomed. Opt. 3, 342–355 (1996).
[CrossRef]

Valentini, G.

van Gemert, M. J. C.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1996), Vol. 1.

Vogel, A.

A. Vogel, C. Dlugos, R. Nuffer, R. Birngruber, “Optical properties of human sclera, and their consequences for transscleral laser applications,” Lasers Surg. Med. 11, 331–340 (1991).
[CrossRef] [PubMed]

Welch, A. J.

S. A. Prahl, M. J. C. van Gemert, A. J. Welch, “Determining the optical properties of turbid media by using the adding-doubling method,” Appl. Opt. 32, 559–568 (1993).
[CrossRef] [PubMed]

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Wyman, D. R.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Zaccanti, G.

Zangheri, L.

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, G. Zaccanti, “Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation,” Phys. Med. Biol. 45, 1359–1373 (2000).
[CrossRef] [PubMed]

Zhang, Z.

Appl. Opt.

IEEE J. Quantum Electron.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

J. Biomed. Opt.

T. L. Troy, D. L. Page, E. M. Sevick-Muraca, “Optical properties of normal and diseased breast tissues: prognosis for optical mammography,” J. Biomed. Opt. 3, 342–355 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Lasers Surg. Med.

A. Vogel, C. Dlugos, R. Nuffer, R. Birngruber, “Optical properties of human sclera, and their consequences for transscleral laser applications,” Lasers Surg. Med. 11, 331–340 (1991).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Med. Biol.

R. J. Hunter, M. S. Patterson, T. J. Farrel, J. E. Hayward, “Hemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of the top layer thickness,” Phys. Med. Biol. 47, 193–208 (2002).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope, 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] [PubMed]

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, G. Zaccanti, “Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation,” Phys. Med. Biol. 45, 1359–1373 (2000).
[CrossRef] [PubMed]

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Other

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1996), Vol. 1.

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Figures (7)

Fig. 1
Fig. 1

Geometric scheme used. A cw light beam illuminates a cell containing a diffusive medium of known optical properties. A small inclusion with unknown optical properties is immersed in the cell. Measurements of relative transmittance are repeated as a function of the distance of the inclusion from the light beam.

Fig. 2
Fig. 2

Examples of relative cw perturbation that is due to scattering and absorption evaluated with the analytical model. The inclusion, with μ si ′ = 1.4 mm-1 and V = 0.5 ml, is centered in a 40-mm-thick cell with μ s0′ = 1 mm-1. Three values of μ a0 have been considered: μ a0 = 0, 0.01, and 0.03 mm-1. The corresponding values of μ ai (0.0011, 0.0152, and 0.0432 mm-1) have been chosen in order to have the same contrast as for the scattering inclusion.

Fig. 3
Fig. 3

Relative cw perturbation obtained from MC simulations for a spherical inclusion immersed in a cell with μ s0′ = 0.5 mm-1 and μ a0 = 0.01 mm-1. The inclusion has a radius of 5 mm and (circle) μ si ′ = 0.35 mm-1 and μ ai = 0.002 mm-1, (diamond) μ ai = μ a0 and μ si ′ = 0.35 mm-1, and (cross) μ si ′ = μ s0′ and μ ai = 0.002 mm-1. The continuous curves report the results obtained from the fit.

Fig. 4
Fig. 4

Examples of relative cw perturbation introduced by the wire for different concentrations of Intralipid. The perturbation significantly enhances when μ s0′ increases. The continuous curves report the results of the fit.

Fig. 5
Fig. 5

Examples of relative cw perturbation measured on samples of gel and of Teflon. The curves that best fit the results and the corresponding perturbations that are due to scattering, δT s /T hom, and to absorption, δT a /T hom, are also reported. (a) Gel with μ ai = 0.0015 mm-1 and μ si ′ = 0.83 mm-1, (b) gel with μ ai = 0.01 mm-1 and μ si ′ = 0.87 mm-1, (c) Teflon with μ ai = 0.0008 mm-1 and μ si ′ = 2.52 mm-1.

Fig. 6
Fig. 6

Measurements on gels. The results of measurements carried out with different concentrations of Intralipid are reported as a function of μ s0′.

Fig. 7
Fig. 7

Measurements on Teflon. The results of measurements carried out with different concentrations of Intralipid are reported as a function of μ s0′.

Tables (1)

Tables Icon

Table 1 Summary of the Results for the Optical Properties of Samples of Gel and of Teflon

Equations (6)

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Tpertρ=Thomρ+δTsρ+δTaρ,
Thomρ=14πn=-+zn+1+σρn+ρn+3exp-σρn+-zn-1+σρn-ρn-3exp-σρn-,
δTsρ=μsi-μs0μsi14π2m=-+η=-+Vdr2z12,m+×hρ12,m+, ρ23,η++hρ12,m+, ρ23,η--z12,m-hρ12,m-, ρ23,η++hρ12,m-, ρ23,η-+z23,η+2ρ12,m+·2ρ23,η+wρ12,m+, ρ23,η+-2ρ12,m-·2ρ23,η+wρ12,m-, ρ23,η+-z23,η-2ρ12,m+·2ρ23,η-wρ12,m+, ρ23,η--2ρ12,m-·2ρ23,η-wρ12,m-, ρ23,η-,
δTaρ=-Thomρμai-μa0lintμai=μa0, ρ×exp-μai-μa0lintμai=μa0, ρ,
lintμai=μa0, ρ=1Thomρ3μs04π2m=-+η=-+Vdr2×z23,η+1+σρ23,η+ρ23,η+3exp-σρ12,m++ρ23,η+ρ12,m+-exp-σρ12,m-+ρ23,η+ρ12,m--z23,η-1+σρ23,η-ρ23,η-3exp-σρ12,m++ρ23,η-ρ12,m+-exp-σρ12,m-+ρ23,η-ρ12,m-
σ=3μa0μs01/2,ρn+=ρ2+zn+21/2,ρn-=ρ2+zn-21/2,wx, y=1+σxx23+3σy+σ2y2y4exp-σx+y,hx, y=1+σxx31+σyy3exp-σx+y,zn+=2nd+4nze+z0,zn-=2nd+4n-2ze-z0,z23,η+=2ηd+4ηze+z2,z23,η-=2ηd+4η-2ze-z2,z12,m+=z2-2md+2ze-z0,z12,m-=z2-2md+2ze+2ze+z0,ρ12,m+=x2-x02+y2-y02+z12,m+21/2,ρ12,m-=x2-x02+y2-y02+z12,m-21/2,ρ23,η+=x3-x22+y3-y22+z23,η+21/2,ρ23,η-=x3-x22+y3-y22+z23,η-21/2,2ρ12,m+=1ρ12,m+x2-x0, y2-y0, z12,m+,2ρ12,m-=1ρ12,m-x2-x0, y2-y0, z12,m-,2ρ23,η+=1ρ23,η+x2-x3, y2-y3, -z23,η+,2ρ23,η-=1ρ23,η-x2-x3, y2-y3, +z23,η-,ze=2A/3μs0.

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