Abstract

The spatial profiles of fluid flow velocity in transparent glass and turbid collagen conduits are measured by optical Doppler tomography (ODT). The flow velocity at a discrete user-specified spatial location in the conduit is determined by measurement of the Doppler shift of backscattered light from microspheres suspended in the flowing fluid. Experimental data and theoretical calculations are in excellent agreement. ODT is an accurate method for the characterization of high-resolution fluid flow velocity.

© 1995 Optical Society of America

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References

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  1. X. Clivaz, F. Marquis-Weible, R. P. Salathé, R. P. Novàk, H. H. Gilgen, Opt. Lett. 17, 4 (1992).
    [CrossRef] [PubMed]
  2. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, Science 254, 1178 (1991).
    [CrossRef] [PubMed]
  3. J. M. Schmitt, A. Knuttel, R. F. Bonner, Appl. Opt. 32, 6032 (1993).
    [CrossRef] [PubMed]
  4. X. J. Wang, T. E. Milner, R. P. Dhond, W. V. Sorin, S. A. Newton, J. S. Nelson, Opt. Lett. 20, 524 (1995).
    [CrossRef] [PubMed]
  5. W. V. Sorin, D. F. Gray, IEEE Photon. Technol. Lett. 4, 105 (1992).
    [CrossRef]
  6. M. R. Hee, D. Huang, E. A. Swanson, J. G. Fujimoto, J. Opt. Soc. Am. B 9, 903 (1992).
    [CrossRef]
  7. W. V. Sorin, D. M. Baney, IEEE Photon. Technol. Lett. 4, 1404 (1992).
    [CrossRef]
  8. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p.157.
  9. L. D. Landau, E. M. Lifshitz, Fluid Mechanics, 2nd ed. (Pergamon, Oxford, 1987), Chap. 2, pp. 52–57.
  10. M. Spiga, G. L. Morini, Int. Commun. Heat Mass Transf. 21, 469 (1994).
    [CrossRef]
  11. R. F. Bonner, R. Nossal, in Laser-Doppler Blood Flowmetry, A. P. Shepherd, P. A. Öberg, eds. (Kluwer, Dordrecht, The Netherlands, 1990), Chap. 2, p. 17.
  12. J. V. Chapman, in The Noninvasive Evaluation of Hemodynamics in Congenital Heart Disease, J. V. Chapman, G. R. Sutherland, eds. (Kluwer, Dordrecht, The Netherlands, 1990), Chap. 2, p. 57.
  13. P. A. J. Bascom, R. S. C. Cobbold, Ultrasound Med. Biol. 16, 279 (1990).
    [CrossRef] [PubMed]

1995 (1)

1994 (1)

M. Spiga, G. L. Morini, Int. Commun. Heat Mass Transf. 21, 469 (1994).
[CrossRef]

1993 (1)

1992 (4)

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

1990 (1)

P. A. J. Bascom, R. S. C. Cobbold, Ultrasound Med. Biol. 16, 279 (1990).
[CrossRef] [PubMed]

Baney, D. M.

W. V. Sorin, D. M. Baney, IEEE Photon. Technol. Lett. 4, 1404 (1992).
[CrossRef]

Bascom, P. A. J.

P. A. J. Bascom, R. S. C. Cobbold, Ultrasound Med. Biol. 16, 279 (1990).
[CrossRef] [PubMed]

Bonner, R. F.

J. M. Schmitt, A. Knuttel, R. F. Bonner, Appl. Opt. 32, 6032 (1993).
[CrossRef] [PubMed]

R. F. Bonner, R. Nossal, in Laser-Doppler Blood Flowmetry, A. P. Shepherd, P. A. Öberg, eds. (Kluwer, Dordrecht, The Netherlands, 1990), Chap. 2, p. 17.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Chapman, J. V.

J. V. Chapman, in The Noninvasive Evaluation of Hemodynamics in Congenital Heart Disease, J. V. Chapman, G. R. Sutherland, eds. (Kluwer, Dordrecht, The Netherlands, 1990), Chap. 2, p. 57.

Clivaz, X.

Cobbold, R. S. C.

P. A. J. Bascom, R. S. C. Cobbold, Ultrasound Med. Biol. 16, 279 (1990).
[CrossRef] [PubMed]

Dhond, R. P.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

M. R. Hee, D. Huang, E. A. Swanson, J. G. Fujimoto, J. Opt. Soc. Am. B 9, 903 (1992).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Gilgen, H. H.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p.157.

Gray, D. F.

W. V. Sorin, D. F. Gray, IEEE Photon. Technol. Lett. 4, 105 (1992).
[CrossRef]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Hee, M. R.

M. R. Hee, D. Huang, E. A. Swanson, J. G. Fujimoto, J. Opt. Soc. Am. B 9, 903 (1992).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Huang, D.

M. R. Hee, D. Huang, E. A. Swanson, J. G. Fujimoto, J. Opt. Soc. Am. B 9, 903 (1992).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Knuttel, A.

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Fluid Mechanics, 2nd ed. (Pergamon, Oxford, 1987), Chap. 2, pp. 52–57.

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Fluid Mechanics, 2nd ed. (Pergamon, Oxford, 1987), Chap. 2, pp. 52–57.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Marquis-Weible, F.

Milner, T. E.

Morini, G. L.

M. Spiga, G. L. Morini, Int. Commun. Heat Mass Transf. 21, 469 (1994).
[CrossRef]

Nelson, J. S.

Newton, S. A.

Nossal, R.

R. F. Bonner, R. Nossal, in Laser-Doppler Blood Flowmetry, A. P. Shepherd, P. A. Öberg, eds. (Kluwer, Dordrecht, The Netherlands, 1990), Chap. 2, p. 17.

Novàk, R. P.

Puliafato, C.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Salathé, R. P.

Schmitt, J. M.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Sorin, W. V.

X. J. Wang, T. E. Milner, R. P. Dhond, W. V. Sorin, S. A. Newton, J. S. Nelson, Opt. Lett. 20, 524 (1995).
[CrossRef] [PubMed]

W. V. Sorin, D. F. Gray, IEEE Photon. Technol. Lett. 4, 105 (1992).
[CrossRef]

W. V. Sorin, D. M. Baney, IEEE Photon. Technol. Lett. 4, 1404 (1992).
[CrossRef]

Spiga, M.

M. Spiga, G. L. Morini, Int. Commun. Heat Mass Transf. 21, 469 (1994).
[CrossRef]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

M. R. Hee, D. Huang, E. A. Swanson, J. G. Fujimoto, J. Opt. Soc. Am. B 9, 903 (1992).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Wang, X. J.

Appl. Opt. (1)

IEEE Photon. Technol. Lett. (2)

W. V. Sorin, D. F. Gray, IEEE Photon. Technol. Lett. 4, 105 (1992).
[CrossRef]

W. V. Sorin, D. M. Baney, IEEE Photon. Technol. Lett. 4, 1404 (1992).
[CrossRef]

Int. Commun. Heat Mass Transf. (1)

M. Spiga, G. L. Morini, Int. Commun. Heat Mass Transf. 21, 469 (1994).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Ultrasound Med. Biol. (1)

P. A. J. Bascom, R. S. C. Cobbold, Ultrasound Med. Biol. 16, 279 (1990).
[CrossRef] [PubMed]

Other (4)

R. F. Bonner, R. Nossal, in Laser-Doppler Blood Flowmetry, A. P. Shepherd, P. A. Öberg, eds. (Kluwer, Dordrecht, The Netherlands, 1990), Chap. 2, p. 17.

J. V. Chapman, in The Noninvasive Evaluation of Hemodynamics in Congenital Heart Disease, J. V. Chapman, G. R. Sutherland, eds. (Kluwer, Dordrecht, The Netherlands, 1990), Chap. 2, p. 57.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p.157.

L. D. Landau, E. M. Lifshitz, Fluid Mechanics, 2nd ed. (Pergamon, Oxford, 1987), Chap. 2, pp. 52–57.

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Figures (5)

Fig. 1
Fig. 1

Schematic of ODT instrumentation.

Fig. 2
Fig. 2

OLCR scans of static (upper curve) and flowing (lower curve) microspheres suspended in a glass conduit (curves offset by 60 dB). The four principal peaks (air– glass, glass–fluid, fluid–glass, and glass–air) are labeled A, B, C, and D, respectively.

Fig. 3
Fig. 3

Power spectra of four flow velocities (A, 188; B, 287; C, 423; D, 620 μm/s) at a discrete spatial location in a glass conduit (curves offset by 20 dB).

Fig. 4
Fig. 4

Experimental (circles) and theoretical (solid curve) velocity profiles and corresponding Doppler shifts in a glass conduit of square cross section (velocity uncertainty ΔV/V = 3%).

Fig. 5
Fig. 5

Experimental (circles and squares) and theoretical (solid curves) velocity profiles in a turbid cylindrical collagen conduit of inner diameter d = 940 μm (velocity uncertainty ΔV/V = 7%).

Equations (4)

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D = T sin ( ϕ ) / n g ,
V ( x ) = Δ f ( x ) λ 0 / 2 cos ( ϕ ) ,
V ( x , y = D / 2 ) = 16 D 2 Δ p π 4 μ Δ L × n = 2 i + 1 m = 2 j + 1 sin ( n π / 2 ) sin ( m π x / D ) m n ( n 2 + m 2 ) ,             i , j = 0 , 1 , 2 , 3 ,
V ( r ) = d 2 Δ p 16 μ Δ L [ 1 - ( 2 r d ) 2 ] .

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