Abstract

Bidirectional Doppler optical coherence tomography is a stable and accurate method to extract the absolute velocity of vessels close to perpendicular to the optical axis by illuminating the sample under two different angles. However it requires knowledge of the vessel angle in the en face plane. In this Letter, we demonstrate that a direct calculation of the flow out of bidirectional Doppler cross sections perpendicular to the illumination plane is independent of that angle and of the Doppler angle, thereby improving the accuracy and flexibility of that technique. We validate our approach with an in vitro experiment and in vivo measurements of a human retinal vessel and discuss the practical limitations of this approach. The method yields accurate flow values for most vascular plexuses without precise knowledge of the vessel orientation. The precision gradually decreases for larger en face angles.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. A. Leitgeb, in Advances in Imaging and Electron Physics, P. W. Hawkes, ed., Optics of Charged Particle Analyzers (Elsevier, 2011), Vol. 168, Chap. 3.
  2. R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, J. Biomed. Opt. 12, 041213 (2007).
    [CrossRef]
  3. S. Makita, T. Fabritius, and Y. Yasuno, Opt. Lett. 33, 836 (2008).
    [CrossRef]
  4. Y. M. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, J. Biomed. Opt. 13, 064003 (2008).
    [CrossRef]
  5. V. J. Srinivasan, S. Sakadzić, I. Gorczynska, S. Ruvinskaya, W. C. Wu, J. G. Fujimoto, and D. A. Boas, Opt. Express 18, 2477 (2010).
    [CrossRef]
  6. B. Baumann, B. Potsaid, M. Kraus, J. Liu, D. Huang, J. Hornegger, A. Cable, J. Duker, and J. Fujimoto, Biomed. Opt. Express 2, 1539 (2011).
    [CrossRef]
  7. T. Schmoll and R. A. Leitgeb, J. Biophotonics 6, 275 (2013).
    [CrossRef]
  8. W. Choi, B. Baumann, J. Liu, A. Clermont, E. Feener, J. Duker, and J. Fujimoto, Biomed. Opt. Express 3, 1047 (2012).
    [CrossRef]
  9. R. M. Werkmeister, N. Dragostinoff, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. A. Leitgeb, and L. Schmetterer, Opt. Lett. 33, 2967 (2008).
    [CrossRef]
  10. R. M. Werkmeister, N. Dragostinoff, S. Palkovits, R. Told, A. Boltz, R. A. Leitgeb, M. Gröschl, G. Garhöfer, and L. Schmetterer, Investig. Ophthalmol. Vis. Sci. 53, 6062 (2012).
    [CrossRef]
  11. C. Blatter, S. Coquoz, B. Grajciar, A. Singh, M. Bonesi, R. Werkmeister, L. Schmetterer, and R. Leitgeb, Biomed. Opt. Express 4, 1188 (2013).
    [CrossRef]
  12. A. Singh, C. Kolbitsch, T. Schmoll, and R. Leitgeb, Biomed. Opt. Express 1, 1047 (2010).
    [CrossRef]
  13. C. E. Riva, G. T. Feke, B. Eberli, and V. Bernary, Appl. Opt. 18, 2301 (1979).
    [CrossRef]
  14. A. Szkulmowska, M. Szkulmowski, A. Kowalczyk, and M. Wojtkowski, Opt. Lett. 33, 1425 (2008).
    [CrossRef]
  15. T. Schmoll, C. Kolbitsch, and R. Leitgeb, Opt. Express 17, 4166 (2009).
    [CrossRef]

2013

2012

W. Choi, B. Baumann, J. Liu, A. Clermont, E. Feener, J. Duker, and J. Fujimoto, Biomed. Opt. Express 3, 1047 (2012).
[CrossRef]

R. M. Werkmeister, N. Dragostinoff, S. Palkovits, R. Told, A. Boltz, R. A. Leitgeb, M. Gröschl, G. Garhöfer, and L. Schmetterer, Investig. Ophthalmol. Vis. Sci. 53, 6062 (2012).
[CrossRef]

2011

2010

2009

2008

2007

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, J. Biomed. Opt. 12, 041213 (2007).
[CrossRef]

1979

Bachmann, A. H.

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, J. Biomed. Opt. 12, 041213 (2007).
[CrossRef]

Baumann, B.

Bernary, V.

Blatter, C.

C. Blatter, S. Coquoz, B. Grajciar, A. Singh, M. Bonesi, R. Werkmeister, L. Schmetterer, and R. Leitgeb, Biomed. Opt. Express 4, 1188 (2013).
[CrossRef]

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, J. Biomed. Opt. 12, 041213 (2007).
[CrossRef]

Boas, D. A.

Boltz, A.

R. M. Werkmeister, N. Dragostinoff, S. Palkovits, R. Told, A. Boltz, R. A. Leitgeb, M. Gröschl, G. Garhöfer, and L. Schmetterer, Investig. Ophthalmol. Vis. Sci. 53, 6062 (2012).
[CrossRef]

Bonesi, M.

Bower, B. A.

Y. M. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, J. Biomed. Opt. 13, 064003 (2008).
[CrossRef]

Cable, A.

Choi, W.

Clermont, A.

Coquoz, S.

Dragostinoff, N.

R. M. Werkmeister, N. Dragostinoff, S. Palkovits, R. Told, A. Boltz, R. A. Leitgeb, M. Gröschl, G. Garhöfer, and L. Schmetterer, Investig. Ophthalmol. Vis. Sci. 53, 6062 (2012).
[CrossRef]

R. M. Werkmeister, N. Dragostinoff, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. A. Leitgeb, and L. Schmetterer, Opt. Lett. 33, 2967 (2008).
[CrossRef]

Duker, J.

Eberli, B.

Fabritius, T.

Feener, E.

Feke, G. T.

Fujimoto, J.

Fujimoto, J. G.

Garhöfer, G.

R. M. Werkmeister, N. Dragostinoff, S. Palkovits, R. Told, A. Boltz, R. A. Leitgeb, M. Gröschl, G. Garhöfer, and L. Schmetterer, Investig. Ophthalmol. Vis. Sci. 53, 6062 (2012).
[CrossRef]

Gorczynska, I.

Götzinger, E.

Grajciar, B.

Gröschl, M.

R. M. Werkmeister, N. Dragostinoff, S. Palkovits, R. Told, A. Boltz, R. A. Leitgeb, M. Gröschl, G. Garhöfer, and L. Schmetterer, Investig. Ophthalmol. Vis. Sci. 53, 6062 (2012).
[CrossRef]

Hitzenberger, C. K.

Hornegger, J.

Huang, D.

Izatt, J. A.

Y. M. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, J. Biomed. Opt. 13, 064003 (2008).
[CrossRef]

Kolbitsch, C.

Kowalczyk, A.

Kraus, M.

Lasser, T.

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, J. Biomed. Opt. 12, 041213 (2007).
[CrossRef]

Leitgeb, R.

Leitgeb, R. A.

T. Schmoll and R. A. Leitgeb, J. Biophotonics 6, 275 (2013).
[CrossRef]

R. M. Werkmeister, N. Dragostinoff, S. Palkovits, R. Told, A. Boltz, R. A. Leitgeb, M. Gröschl, G. Garhöfer, and L. Schmetterer, Investig. Ophthalmol. Vis. Sci. 53, 6062 (2012).
[CrossRef]

R. M. Werkmeister, N. Dragostinoff, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. A. Leitgeb, and L. Schmetterer, Opt. Lett. 33, 2967 (2008).
[CrossRef]

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, J. Biomed. Opt. 12, 041213 (2007).
[CrossRef]

R. A. Leitgeb, in Advances in Imaging and Electron Physics, P. W. Hawkes, ed., Optics of Charged Particle Analyzers (Elsevier, 2011), Vol. 168, Chap. 3.

Liu, J.

Makita, S.

Michaely, R.

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, J. Biomed. Opt. 12, 041213 (2007).
[CrossRef]

Palkovits, S.

R. M. Werkmeister, N. Dragostinoff, S. Palkovits, R. Told, A. Boltz, R. A. Leitgeb, M. Gröschl, G. Garhöfer, and L. Schmetterer, Investig. Ophthalmol. Vis. Sci. 53, 6062 (2012).
[CrossRef]

Pircher, M.

Potsaid, B.

Riva, C. E.

Ruvinskaya, S.

Sakadzic, S.

Schmetterer, L.

Schmoll, T.

Singh, A.

Srinivasan, V. J.

Szkulmowska, A.

Szkulmowski, M.

Tan, O.

Y. M. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, J. Biomed. Opt. 13, 064003 (2008).
[CrossRef]

Told, R.

R. M. Werkmeister, N. Dragostinoff, S. Palkovits, R. Told, A. Boltz, R. A. Leitgeb, M. Gröschl, G. Garhöfer, and L. Schmetterer, Investig. Ophthalmol. Vis. Sci. 53, 6062 (2012).
[CrossRef]

Villiger, M. L.

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, J. Biomed. Opt. 12, 041213 (2007).
[CrossRef]

Wang, Y. M.

Y. M. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, J. Biomed. Opt. 13, 064003 (2008).
[CrossRef]

Werkmeister, R.

Werkmeister, R. M.

R. M. Werkmeister, N. Dragostinoff, S. Palkovits, R. Told, A. Boltz, R. A. Leitgeb, M. Gröschl, G. Garhöfer, and L. Schmetterer, Investig. Ophthalmol. Vis. Sci. 53, 6062 (2012).
[CrossRef]

R. M. Werkmeister, N. Dragostinoff, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. A. Leitgeb, and L. Schmetterer, Opt. Lett. 33, 2967 (2008).
[CrossRef]

Wojtkowski, M.

Wu, W. C.

Yasuno, Y.

Appl. Opt.

Biomed. Opt. Express

Investig. Ophthalmol. Vis. Sci.

R. M. Werkmeister, N. Dragostinoff, S. Palkovits, R. Told, A. Boltz, R. A. Leitgeb, M. Gröschl, G. Garhöfer, and L. Schmetterer, Investig. Ophthalmol. Vis. Sci. 53, 6062 (2012).
[CrossRef]

J. Biomed. Opt.

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, J. Biomed. Opt. 12, 041213 (2007).
[CrossRef]

Y. M. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, J. Biomed. Opt. 13, 064003 (2008).
[CrossRef]

J. Biophotonics

T. Schmoll and R. A. Leitgeb, J. Biophotonics 6, 275 (2013).
[CrossRef]

Opt. Express

Opt. Lett.

Other

R. A. Leitgeb, in Advances in Imaging and Electron Physics, P. W. Hawkes, ed., Optics of Charged Particle Analyzers (Elsevier, 2011), Vol. 168, Chap. 3.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Coordinates of the vessel and illumination plane (yz plane, spanned by vectors e⃗A and e⃗B) relative to the scanning (x,y) and optical (z) axes.

Fig. 2.
Fig. 2.

Schematic of the optical setup. Red, beam A; blue, beam B; SS, swept source; FC, fiber coupler; PC, polarization control; L1–L5, lenses; M, mirror; Prism, dove prism; Galvo, scanning mirrors; D, dichroic mirror; F, fixation screen; DM, dispersion matching; DBD, dual-balanced detector [11].

Fig. 3.
Fig. 3.

In vitro validation with a perfused capillary. Circle, square, and diamond markers indicate the measured velocity, the corrected velocity according to the cosine of the varied angle, and the measured flow, respectively. If not indicated, the size of the markers denotes the standard deviation. The dashed lines indicate the set velocities and flow as well as the theoretical reduction of the velocity. (a) Variation of β for α0°. The cross sections are plotted for β=0°, 30°, and 60°. (b) Variation of α for β0 and β50° in black and gray, respectively. For better visibility the flow was set slightly different.

Fig. 4.
Fig. 4.

In vivo validation on a retinal artery of a healthy volunteer. (a) 5° field of view OCT en face view indicating the measurement area 7° inferior to the ONH. B-scan time series of 3° (white lines) were acquired at different y locations crossing the artery with different β. (b) Result of the quantitative evaluation of the different locations, 1 to 8 from left to right. The flow (cross marker) remains constant with a relative standard deviation (RSD) of 3%. The measured velocity (circle marker) is reduced for larger β. With known β the absolute velocity can be determined (+ marker). The correction did not account for the Doppler angle α.

Equations (11)

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

v⃗(x,y,z)=(vxvyvz)=v(sinβsinαcosβsinαcosα).
e⃗A=(0sinΔα2cosΔα2),e⃗B=(0sinΔα2cosΔα2).
vA=v,e⃗A=vysinΔα2+vzcosΔα2,
vB=v,e⃗B=vysinΔα2+vzcosΔα2,
vA,B=ΔφA,B2knT,
Δv=vAvB=2vysinΔα2vyΔα,
v=vycosβsinαΔvΔαcosβsinα.
F=Sv⃗·n⃗dS=xzv⃗·e⃗ydS=xzvydS,
F=1ΔαxzΔvdS=Δv¯ΔαS,
F=v¯Av¯BΔαxzΔSv¯Av¯B2Δα(SA+SB),
v¯A,B=12knT(mA,BeiΔϕA,B(m)).

Metrics