Abstract

We present an approach to measure pulsatile total retinal arterial blood flow in humans and rats using ultrahigh speed Doppler OCT. The axial blood velocity is measured in an en face plane by raster scanning and the flow is calculated by integrating over the vessel area, without the need to measure the Doppler angle. By measuring flow at the central retinal artery, the scan area can be very small. Combined with ultrahigh speed, this approach enables high volume acquisition rates necessary for pulsatile total flow measurement without modification in the OCT system optics. A spectral domain OCT system at 840nm with an axial scan rate of 244kHz was used for this study. At 244kHz the nominal axial velocity range that could be measured without phase wrapping was ±37.7mm/s. By repeatedly scanning a small area centered at the central retinal artery with high volume acquisition rates, pulsatile flow characteristics, such as systolic, diastolic, and mean total flow values, were measured. Real-time Doppler C-scan preview is proposed as a guidance tool to enable quick and easy alignment necessary for large scale studies. Data processing for flow calculation can be entirely automatic using this approach because of the simple and robust algorithm. Due to the rapid volume acquisition rate and the fact that the measurement is independent of Doppler angle, this approach is inherently less sensitive to involuntary eye motion. This method should be useful for investigation of small animal models of ocular diseases as well as total blood flow measurements in human patients in the clinic.

© 2012 OSA

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2011 (5)

2010 (3)

2009 (2)

Y. K. Tao, K. M. Kennedy, and J. A. Izatt, “Velocity-resolved 3D retinal microvessel imaging using single-pass flow imaging spectral domain optical coherence tomography,” Opt. Express 17(5), 4177–4188 (2009).
[Crossref] [PubMed]

Y. Wang, A. Lu, J. Gil-Flamer, O. Tan, J. A. Izatt, and D. Huang, “Measurement of total blood flow in the normal human retina using Doppler Fourier-domain optical coherence tomography,” Br. J. Ophthalmol. 93(5), 634–637 (2009).
[Crossref] [PubMed]

2008 (4)

2007 (2)

Y. M. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, “In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 12(4), 041215 (2007).
[Crossref] [PubMed]

H. Wehbe, M. Ruggeri, S. Jiao, G. Gregori, C. A. Puliafito, and W. Zhao, “Automatic retinal blood flow calculation using spectral domain optical coherence tomography,” Opt. Express 15(23), 15193–15206 (2007).
[Crossref] [PubMed]

2005 (1)

2004 (1)

2003 (2)

2002 (1)

J. Flammer, S. Orgül, V. P. Costa, N. Orzalesi, G. K. Krieglstein, L. M. Serra, J. P. Renard, and E. Stefánsson, “The impact of ocular blood flow in glaucoma,” Prog. Retin. Eye Res. 21(4), 359–393 (2002).
[Crossref] [PubMed]

1999 (2)

H. S. Chung, A. Harris, T. A. Ciulla, and L. Kagemann, “Progress in measurement of ocular blood flow and relevance to our understanding of glaucoma and age-related macular degeneration,” Prog. Retin. Eye Res. 18(5), 669–687 (1999).
[Crossref] [PubMed]

L. Schmetterer and M. Wolzt, “Ocular blood flow and associated functional deviations in diabetic retinopathy,” Diabetologia 42(4), 387–405 (1999).
[Crossref] [PubMed]

1997 (1)

E. Friedman, “A hemodynamic model of the pathogenesis of age-related macular degeneration,” Am. J. Ophthalmol. 124(5), 677–682 (1997).
[PubMed]

1992 (1)

V. Patel, S. Rassam, R. Newsom, J. Wiek, and E. Kohner, “Retinal blood flow in diabetic retinopathy,” BMJ 305(6855), 678–683 (1992).
[Crossref] [PubMed]

Bajraszewski, T.

Baumann, B.

Berisha, F.

Boas, D. A.

Bouma, B. E.

Bower, B. A.

Y. M. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, “In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 12(4), 041215 (2007).
[Crossref] [PubMed]

Cable, A. E.

Cense, B.

Cepurna, W.

Chen, T. C.

Chen, Z. P.

B. Rao, L. F. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. P. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
[Crossref] [PubMed]

Chiang, H. K.

B. Rao, L. F. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. P. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
[Crossref] [PubMed]

Chung, H. S.

H. S. Chung, A. Harris, T. A. Ciulla, and L. Kagemann, “Progress in measurement of ocular blood flow and relevance to our understanding of glaucoma and age-related macular degeneration,” Prog. Retin. Eye Res. 18(5), 669–687 (1999).
[Crossref] [PubMed]

Ciulla, T. A.

H. S. Chung, A. Harris, T. A. Ciulla, and L. Kagemann, “Progress in measurement of ocular blood flow and relevance to our understanding of glaucoma and age-related macular degeneration,” Prog. Retin. Eye Res. 18(5), 669–687 (1999).
[Crossref] [PubMed]

Costa, V. P.

J. Flammer, S. Orgül, V. P. Costa, N. Orzalesi, G. K. Krieglstein, L. M. Serra, J. P. Renard, and E. Stefánsson, “The impact of ocular blood flow in glaucoma,” Prog. Retin. Eye Res. 21(4), 359–393 (2002).
[Crossref] [PubMed]

de Boer, J. F.

Dhalla, A.-H.

Dragostinoff, N.

Drexler, W.

Duker, J. S.

Enfield, J.

Fabritius, T.

Fawzi, A. A.

Y. M. Wang, A. A. Fawzi, R. Varma, A. A. Sadun, X. B. Zhang, O. Tan, J. A. Izatt, and D. Huang, “Pilot study of optical coherence tomography measurement of retinal blood flow in retinal and optic nerve diseases,” Invest. Ophthalmol. Vis. Sci. 52(2), 840–845 (2011).
[Crossref] [PubMed]

Fercher, A. F.

Flammer, J.

J. Flammer, S. Orgül, V. P. Costa, N. Orzalesi, G. K. Krieglstein, L. M. Serra, J. P. Renard, and E. Stefánsson, “The impact of ocular blood flow in glaucoma,” Prog. Retin. Eye Res. 21(4), 359–393 (2002).
[Crossref] [PubMed]

Friedman, E.

E. Friedman, “A hemodynamic model of the pathogenesis of age-related macular degeneration,” Am. J. Ophthalmol. 124(5), 677–682 (1997).
[PubMed]

Fujimoto, J. G.

Gargesha, M.

M. W. Jenkins, L. Peterson, S. Gu, M. Gargesha, D. L. Wilson, M. Watanabe, and A. M. Rollins, “Measuring hemodynamics in the developing heart tube with four-dimensional gated Doppler optical coherence tomography,” J. Biomed. Opt. 15(6), 066022 (2010).
[Crossref] [PubMed]

Gil-Flamer, J.

Y. Wang, A. Lu, J. Gil-Flamer, O. Tan, J. A. Izatt, and D. Huang, “Measurement of total blood flow in the normal human retina using Doppler Fourier-domain optical coherence tomography,” Br. J. Ophthalmol. 93(5), 634–637 (2009).
[Crossref] [PubMed]

Gorczynska, I.

Götzinger, E.

Gregori, G.

Gu, S.

M. W. Jenkins, L. Peterson, S. Gu, M. Gargesha, D. L. Wilson, M. Watanabe, and A. M. Rollins, “Measuring hemodynamics in the developing heart tube with four-dimensional gated Doppler optical coherence tomography,” J. Biomed. Opt. 15(6), 066022 (2010).
[Crossref] [PubMed]

Harris, A.

H. S. Chung, A. Harris, T. A. Ciulla, and L. Kagemann, “Progress in measurement of ocular blood flow and relevance to our understanding of glaucoma and age-related macular degeneration,” Prog. Retin. Eye Res. 18(5), 669–687 (1999).
[Crossref] [PubMed]

Hendargo, H. C.

Hitzenberger, C. K.

Hornegger, J.

Huang, D.

B. Baumann, B. Potsaid, M. F. Kraus, J. J. Liu, D. Huang, J. Hornegger, A. E. Cable, J. S. Duker, and J. G. Fujimoto, “Total retinal blood flow measurement with ultrahigh speed swept source/Fourier domain OCT,” Biomed. Opt. Express 2(6), 1539–1552 (2011).
[Crossref] [PubMed]

Y. M. Wang, A. A. Fawzi, R. Varma, A. A. Sadun, X. B. Zhang, O. Tan, J. A. Izatt, and D. Huang, “Pilot study of optical coherence tomography measurement of retinal blood flow in retinal and optic nerve diseases,” Invest. Ophthalmol. Vis. Sci. 52(2), 840–845 (2011).
[Crossref] [PubMed]

Y. Wang, A. Lu, J. Gil-Flamer, O. Tan, J. A. Izatt, and D. Huang, “Measurement of total blood flow in the normal human retina using Doppler Fourier-domain optical coherence tomography,” Br. J. Ophthalmol. 93(5), 634–637 (2009).
[Crossref] [PubMed]

Y. M. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, “In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 12(4), 041215 (2007).
[Crossref] [PubMed]

Izatt, J. A.

Y. M. Wang, A. A. Fawzi, R. Varma, A. A. Sadun, X. B. Zhang, O. Tan, J. A. Izatt, and D. Huang, “Pilot study of optical coherence tomography measurement of retinal blood flow in retinal and optic nerve diseases,” Invest. Ophthalmol. Vis. Sci. 52(2), 840–845 (2011).
[Crossref] [PubMed]

H. C. Hendargo, R. P. McNabb, A.-H. Dhalla, N. Shepherd, and J. A. Izatt, “Doppler velocity detection limitations in spectrometer-based versus swept-source optical coherence tomography,” Biomed. Opt. Express 2(8), 2175–2188 (2011).
[Crossref] [PubMed]

Y. K. Tao, K. M. Kennedy, and J. A. Izatt, “Velocity-resolved 3D retinal microvessel imaging using single-pass flow imaging spectral domain optical coherence tomography,” Opt. Express 17(5), 4177–4188 (2009).
[Crossref] [PubMed]

Y. Wang, A. Lu, J. Gil-Flamer, O. Tan, J. A. Izatt, and D. Huang, “Measurement of total blood flow in the normal human retina using Doppler Fourier-domain optical coherence tomography,” Br. J. Ophthalmol. 93(5), 634–637 (2009).
[Crossref] [PubMed]

Y. M. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, “In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 12(4), 041215 (2007).
[Crossref] [PubMed]

Jenkins, M. W.

M. W. Jenkins, L. Peterson, S. Gu, M. Gargesha, D. L. Wilson, M. Watanabe, and A. M. Rollins, “Measuring hemodynamics in the developing heart tube with four-dimensional gated Doppler optical coherence tomography,” J. Biomed. Opt. 15(6), 066022 (2010).
[Crossref] [PubMed]

Jiao, S.

Johnson, E.

Jonathan, E.

Kagemann, L.

H. S. Chung, A. Harris, T. A. Ciulla, and L. Kagemann, “Progress in measurement of ocular blood flow and relevance to our understanding of glaucoma and age-related macular degeneration,” Prog. Retin. Eye Res. 18(5), 669–687 (1999).
[Crossref] [PubMed]

Kennedy, K. M.

Kohner, E.

V. Patel, S. Rassam, R. Newsom, J. Wiek, and E. Kohner, “Retinal blood flow in diabetic retinopathy,” BMJ 305(6855), 678–683 (1992).
[Crossref] [PubMed]

Kolbitsch, C. K.

Kraus, M. F.

Krieglstein, G. K.

J. Flammer, S. Orgül, V. P. Costa, N. Orzalesi, G. K. Krieglstein, L. M. Serra, J. P. Renard, and E. Stefánsson, “The impact of ocular blood flow in glaucoma,” Prog. Retin. Eye Res. 21(4), 359–393 (2002).
[Crossref] [PubMed]

Kuppermann, B. D.

B. Rao, L. F. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. P. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
[Crossref] [PubMed]

Kurtz, R. M.

B. Rao, L. F. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. P. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
[Crossref] [PubMed]

Leahy, M.

Leitgeb, R. A.

Liu, J. J.

Lu, A.

Y. Wang, A. Lu, J. Gil-Flamer, O. Tan, J. A. Izatt, and D. Huang, “Measurement of total blood flow in the normal human retina using Doppler Fourier-domain optical coherence tomography,” Br. J. Ophthalmol. 93(5), 634–637 (2009).
[Crossref] [PubMed]

Makita, S.

McNabb, R. P.

Morrison, J.

Nassif, N.

Newsom, R.

V. Patel, S. Rassam, R. Newsom, J. Wiek, and E. Kohner, “Retinal blood flow in diabetic retinopathy,” BMJ 305(6855), 678–683 (1992).
[Crossref] [PubMed]

Orgül, S.

J. Flammer, S. Orgül, V. P. Costa, N. Orzalesi, G. K. Krieglstein, L. M. Serra, J. P. Renard, and E. Stefánsson, “The impact of ocular blood flow in glaucoma,” Prog. Retin. Eye Res. 21(4), 359–393 (2002).
[Crossref] [PubMed]

Orzalesi, N.

J. Flammer, S. Orgül, V. P. Costa, N. Orzalesi, G. K. Krieglstein, L. M. Serra, J. P. Renard, and E. Stefánsson, “The impact of ocular blood flow in glaucoma,” Prog. Retin. Eye Res. 21(4), 359–393 (2002).
[Crossref] [PubMed]

Park, B. H.

Patel, V.

V. Patel, S. Rassam, R. Newsom, J. Wiek, and E. Kohner, “Retinal blood flow in diabetic retinopathy,” BMJ 305(6855), 678–683 (1992).
[Crossref] [PubMed]

Peterson, L.

M. W. Jenkins, L. Peterson, S. Gu, M. Gargesha, D. L. Wilson, M. Watanabe, and A. M. Rollins, “Measuring hemodynamics in the developing heart tube with four-dimensional gated Doppler optical coherence tomography,” J. Biomed. Opt. 15(6), 066022 (2010).
[Crossref] [PubMed]

Pierce, M. C.

Pircher, M.

Potsaid, B.

Puliafito, C. A.

Rao, B.

B. Rao, L. F. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. P. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
[Crossref] [PubMed]

Rassam, S.

V. Patel, S. Rassam, R. Newsom, J. Wiek, and E. Kohner, “Retinal blood flow in diabetic retinopathy,” BMJ 305(6855), 678–683 (1992).
[Crossref] [PubMed]

Renard, J. P.

J. Flammer, S. Orgül, V. P. Costa, N. Orzalesi, G. K. Krieglstein, L. M. Serra, J. P. Renard, and E. Stefánsson, “The impact of ocular blood flow in glaucoma,” Prog. Retin. Eye Res. 21(4), 359–393 (2002).
[Crossref] [PubMed]

Rollins, A. M.

M. W. Jenkins, L. Peterson, S. Gu, M. Gargesha, D. L. Wilson, M. Watanabe, and A. M. Rollins, “Measuring hemodynamics in the developing heart tube with four-dimensional gated Doppler optical coherence tomography,” J. Biomed. Opt. 15(6), 066022 (2010).
[Crossref] [PubMed]

Ruggeri, M.

Ruvinskaya, S.

Sadun, A. A.

Y. M. Wang, A. A. Fawzi, R. Varma, A. A. Sadun, X. B. Zhang, O. Tan, J. A. Izatt, and D. Huang, “Pilot study of optical coherence tomography measurement of retinal blood flow in retinal and optic nerve diseases,” Invest. Ophthalmol. Vis. Sci. 52(2), 840–845 (2011).
[Crossref] [PubMed]

Sakadzic, S.

Schmetterer, L.

Schmoll, T.

Serra, L. M.

J. Flammer, S. Orgül, V. P. Costa, N. Orzalesi, G. K. Krieglstein, L. M. Serra, J. P. Renard, and E. Stefánsson, “The impact of ocular blood flow in glaucoma,” Prog. Retin. Eye Res. 21(4), 359–393 (2002).
[Crossref] [PubMed]

Shen, T.

Shepherd, N.

Singh, A. S. G.

Srinivasan, V. J.

Stefánsson, E.

J. Flammer, S. Orgül, V. P. Costa, N. Orzalesi, G. K. Krieglstein, L. M. Serra, J. P. Renard, and E. Stefánsson, “The impact of ocular blood flow in glaucoma,” Prog. Retin. Eye Res. 21(4), 359–393 (2002).
[Crossref] [PubMed]

Tan, O.

Y. M. Wang, A. A. Fawzi, R. Varma, A. A. Sadun, X. B. Zhang, O. Tan, J. A. Izatt, and D. Huang, “Pilot study of optical coherence tomography measurement of retinal blood flow in retinal and optic nerve diseases,” Invest. Ophthalmol. Vis. Sci. 52(2), 840–845 (2011).
[Crossref] [PubMed]

Y. Wang, A. Lu, J. Gil-Flamer, O. Tan, J. A. Izatt, and D. Huang, “Measurement of total blood flow in the normal human retina using Doppler Fourier-domain optical coherence tomography,” Br. J. Ophthalmol. 93(5), 634–637 (2009).
[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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[PubMed]

Biomed. Opt. Express (5)

BMJ (1)

V. Patel, S. Rassam, R. Newsom, J. Wiek, and E. Kohner, “Retinal blood flow in diabetic retinopathy,” BMJ 305(6855), 678–683 (1992).
[Crossref] [PubMed]

Br. J. Ophthalmol. (1)

Y. Wang, A. Lu, J. Gil-Flamer, O. Tan, J. A. Izatt, and D. Huang, “Measurement of total blood flow in the normal human retina using Doppler Fourier-domain optical coherence tomography,” Br. J. Ophthalmol. 93(5), 634–637 (2009).
[Crossref] [PubMed]

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L. Schmetterer and M. Wolzt, “Ocular blood flow and associated functional deviations in diabetic retinopathy,” Diabetologia 42(4), 387–405 (1999).
[Crossref] [PubMed]

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Y. M. Wang, A. A. Fawzi, R. Varma, A. A. Sadun, X. B. Zhang, O. Tan, J. A. Izatt, and D. Huang, “Pilot study of optical coherence tomography measurement of retinal blood flow in retinal and optic nerve diseases,” Invest. Ophthalmol. Vis. Sci. 52(2), 840–845 (2011).
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B. Rao, L. F. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. P. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
[Crossref] [PubMed]

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[Crossref] [PubMed]

Y. M. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, “In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 12(4), 041215 (2007).
[Crossref] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

Schematic of the ultrahigh speed spectral domain OCT system. PC: polarization controller, DC: dispersion compensation glass, RM: reference mirror, GS: galvanometer scanner pair, DG: diffraction grating, SLD: superluminescent diode, CMOS: line scan camera. A similar OCT system with reduced power at the cornea was used for human imaging.

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Fig. 2
Fig. 2

(A) In conventional Doppler methods, calculation of blood flow involves extraction of the Doppler angle θ, which is the angle between the probe beam and blood vessel. (B) In en face Doppler, simply integrating the axial velocity components over an en face cross-section that intercepts the vessel provides blood flow.

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Fig. 3
Fig. 3

(A) Flow chart for alignment/acquisition procedure for pulsatile total retinal blood flow imaging. (B) An example of a Doppler C-scan preview image. The red square denotes the scan area of interest, which can be adjusted by moving the crosshair. Velocity wrapping can be observed at the center of the central retinal artery, which can be unwrapped for flow calculation during post-processing.

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Fig. 4
Fig. 4

Flow chart for automatic flow calculation. Because of the robustness of the algorithm, essentially no user input is necessary and entirely automatic processing becomes feasible. The plot shows flow as a function of depth is generated from a data set acquired from a normal rat.

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Fig. 5
Fig. 5

(A) An OCT cross-sectional image acquired at 244,000 A-scans per second centered at the optic nerve head (ONH). An average of 10 neighboring B-scans from a volumetric data of 700 × 700 A-scans over 1.5mm × 1.5mm is shown. (B) Visualization of the capillary network. (C) An OCT fundus projection view over an area of 0.5mm × 0.5mm at ONH. (D) A Doppler B-scan image showing vasculature located at the red dotted line in the fundus projection view. (E) A Doppler B-scan image showing the vasculature located at the blue dotted line in the fundus projection view. The blue arrow indicates the central retinal artery cross-section. The axial velocity range of ±15mm/s was chosen for display purposes in order to optimize image contrast. Scale bar: 100µm in all images.

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Fig. 6
Fig. 6

(A) Pulsatile total retinal arterial blood flow measured at the central retinal artery of a Sprague Dawley rat anesthetized with isoflurane/xylazine. (B) Simultaneously acquired plethysmographic pulse waveform from a pulse oximeter. (C) En face Doppler images at time points indicated by the red arrows in (A). The arrows from left to right in (A) correspond to Doppler images 1 to 4 in (C). 200μm × 200μm.

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Fig. 7
Fig. 7

(A) Pulsatile total flow measured at the central artery of a Sprague Dawley rat anesthetized with ketamine/xylazine and simultaneous acquisition of plethysmographic pulse waveform from a pulse oximeter. (B) En face Doppler images at time points indicated by the red arrows in (A). The arrows from left to right in (A) correspond to Doppler images 1 to 4 in (B). 150μm × 150μm. (C) Systolic, diastolic and mean total flow values. PI: pulsatility index, RI: resistance index. Numbers in parentheses are coefficients of variation.

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Fig. 8
Fig. 8

(A) An intensity en face projection image of the human optic nerve head of a normal subject. The yellow square indicates the size and approximate location of the area of scanning used for repeated volumetric acquisition for pulsatile total blood flow measurements. 600 × 600 A-scans over 6mm × 6mm acquired within 1.7 seconds. Scale bar: 500μm. (B, C) Intensity B-scan images extracted from the locations indicated by the blue and tan dotted lines in (A). Averages of 4 neighboring B-scans displayed in logarithmic scale. Scale bar: 250μm.

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Fig. 9
Fig. 9

(A) An intensity B-scan image of the human retina of a normal subject. (B) A Doppler B-scan image corresponding to (A) showing the vasculature. (C) Pulsatile total retinal arterial blood flow measured at near the center of the optic nerve head. (D) An example of intensity fundus projection of a volumetric scan. (E) En face Doppler images at time points indicated by red the arrows in (C). The arrows from left to right in (C) correspond to Doppler images 1 to 4 in (E). 800μm × 800μm.

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Tables (2)

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Table 1 Pulsatile total blood flow characteristics in a normal rat

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Table 2 Pulsatile total blood flow characteristics in a normal human subject.

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Equations (5)

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v z = λ c ΔΦ 4πTn
F= ∫ S v⋅dA = ∫ S vcosθdA
X[k]≡ ∑ n=0 N−1 x[n] e −jkn(2π/N) = ∑ n=0 N−1 x[n]{ cos(2πkn/N)−jsin(2πkn/N) } = ∑ n=0 N/2−1 [ { x[n]+x[N−n] }cos(2πkn/N)−j{ x[n]−x[N−n] }sin(2πkn/N) ]
PI=( F sys − F dias )/ F mean
RI=( F sys − F dias )/ F sys

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