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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 4, Iss. 10 — Oct. 1, 2013
  • pp: 1909–1924
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Blood flow velocity quantification using split-spectrum amplitude-decorrelation angiography with optical coherence tomography

Jason Tokayer, Yali Jia, Al-Hafeez Dhalla, and David Huang  »View Author Affiliations


Biomedical Optics Express, Vol. 4, Issue 10, pp. 1909-1924 (2013)
http://dx.doi.org/10.1364/BOE.4.001909


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Abstract

The split-spectrum amplitude-decorrelation angiography (SSADA) algorithm was recently developed as a method for imaging blood flow in the human retina without the use of phase information. In order to enable absolute blood velocity quantification, in vitro phantom experiments are performed to correlate the SSADA signal at multiple time scales with various preset velocities. A linear model relating SSADA measurements to absolute flow velocities is derived using the phantom data. The operating range for the linear model is discussed along with its implication for velocity quantification with SSADA in a clinical setting.

© 2013 OSA

1. Introduction

Optical coherence tomography (OCT) is a high-resolution modality used for non-invasive depth-resolved imaging of biological tissue [1

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. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]

]. OCT has been used extensively in ophthalmology for imaging both structure and function in the human retina [2

2. M. R. Hee, J. A. Izatt, E. A. Swanson, D. Huang, J. S. Schuman, C. P. Lin, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography of the human retina,” Arch. Ophthalmol. 113(3), 325–332 (1995). [CrossRef] [PubMed]

4

4. B. White, M. Pierce, N. Nassif, B. Cense, B. Park, G. Tearney, B. Bouma, T. Chen, and J. de Boer, “In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical coherence tomography,” Opt. Express 11(25), 3490–3497 (2003). [CrossRef] [PubMed]

]. Of particular importance for studying various retinal pathologies is the measurement of retinal blood flow [5

5. 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]

,6

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

]. Doppler OCT is able to calculate absolute blood flow velocity by evaluating the phase differences between adjacent A-scans [7

7. Y. Zhao, Z. Chen, C. Saxer, S. Xiang, J. F. de Boer, and J. S. Nelson, “Phase-resolved optical coherence tomography and optical Doppler tomography for imaging blood flow in human skin with fast scanning speed and high velocity sensitivity,” Opt. Lett. 25(2), 114–116 (2000). [CrossRef] [PubMed]

11

11. 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]

]. The speed and sensitivity advantages that Fourier-domain systems, which includes both spectral-domain and swept-source systems, demonstrate relative to time-domain systems make them particularly suited for this purpose [12

12. R. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express 11(8), 889–894 (2003). [CrossRef] [PubMed]

]. Additionally, swept-source OCT has a larger Doppler dynamic range than spectral-domain OCT due to a higher fringe washout velocity and is thus suitable for measuring very fast flow speeds [13

13. 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]

]. However, Doppler OCT requires good phase stability for quantifying slow flow velocities [13

13. 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]

15

15. Y. J. Hong, S. Makita, F. Jaillon, M. J. Ju, E. J. Min, B. H. Lee, M. Itoh, M. Miura, and Y. Yasuno, “High-penetration swept source Doppler optical coherence angiography by fully numerical phase stabilization,” Opt. Express 20(3), 2740–2760 (2012). [CrossRef] [PubMed]

] and suffers from reduced sensitivity for small blood vessels [16

16. H. Ren and X. Li, “Clutter rejection filters for optical Doppler tomography,” Opt. Express 14(13), 6103–6112 (2006). [CrossRef] [PubMed]

,17

17. J. Tokayer and D. Huang, “Effect of blood vessel diameter on relative blood flow estimates in Doppler optical coherence tomography algorithms,” Proc. SPIE 7889, Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XV, 78892X, 78892X-8 (2011). [CrossRef]

]. Furthermore, the measured Doppler frequency shift in a blood vessel varies inversely with the cosine of the Doppler angle, or the angle between the incident beam and blood vessel [18

18. Y. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, “Retinal blood flow measurement by circumpapillary Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 13(6), 064003 (2008). [CrossRef] [PubMed]

]. Yet many blood vessels in the human retina are nearly perpendicular to the incident beam, so that the Doppler frequency shifts in these vessels are small and difficult to detect. Several techniques, including joint spectral and time domain OCT [19

19. M. Szkulmowski, A. Szkulmowska, T. Bajraszewski, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation using joint Spectral and Time domain Optical Coherence Tomography,” Opt. Express 16(9), 6008–6025 (2008). [CrossRef] [PubMed]

], use of a modified Hilbert transform [20

20. Y. K. Tao, A. M. Davis, and J. A. Izatt, “Single-pass volumetric bidirectional blood flow imaging spectral domain optical coherence tomography using a modified Hilbert transform,” Opt. Express 16(16), 12350–12361 (2008). [CrossRef] [PubMed]

] and smart scanning protocols [21

21. I. Grulkowski, I. Gorczynska, M. Szkulmowski, D. Szlag, A. Szkulmowska, R. A. Leitgeb, A. Kowalczyk, and M. Wojtkowski, “Scanning protocols dedicated to smart velocity ranging in spectral OCT,” Opt. Express 17(26), 23736–23754 (2009). [CrossRef] [PubMed]

], have been introduced to overcome some of the limitations of Doppler OCT. However, techniques that do not inherently depend on the Doppler angle may be particularly useful for visualizing blood vessels in the human retina.

Several angiographic techniques have been introduced for imaging retinal blood flow. Some of these techniques are phase-based, while others are amplitude-based. Some of the phase-based techniques include optical coherence angiography [22

22. S. Makita, Y. Hong, M. Yamanari, T. Yatagai, and Y. Yasuno, “Optical coherence angiography,” Opt. Express 14(17), 7821–7840 (2006). [CrossRef] [PubMed]

], optical micro-angiography [23

23. L. An and R. K. Wang, “In vivo volumetric imaging of vascular perfusion within human retina and choroids with optical micro-angiography,” Opt. Express 16(15), 11438–11452 (2008). [CrossRef] [PubMed]

,24

24. R. K. Wang, L. An, P. Francis, and D. J. Wilson, “Depth-resolved imaging of capillary networks in retina and choroid using ultrahigh sensitive optical microangiography,” Opt. Lett. 35(9), 1467–1469 (2010). [CrossRef] [PubMed]

], Doppler variance [25

25. L. Yu and Z. Chen, “Doppler variance imaging for three-dimensional retina and choroid angiography,” J. Biomed. Opt. 15(1), 016029 (2010). [CrossRef] [PubMed]

,26

26. G. Liu, W. Qi, L. Yu, and Z. Chen, “Real-time bulk-motion-correction free Doppler variance optical coherence tomography for choroidal capillary vasculature imaging,” Opt. Express 19(4), 3657–3666 (2011). [CrossRef] [PubMed]

] and phase variance [27

27. J. Fingler, D. Schwartz, C. Yang, and S. E. Fraser, “Mobility and transverse flow visualization using phase variance contrast with spectral domain optical coherence tomography,” Opt. Express 15(20), 12636–12653 (2007). [CrossRef] [PubMed]

,28

28. B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, “Three-dimensional microscopy of the tumor microenvironment in vivo using optical frequency domain imaging,” Nat. Med. 15(10), 1219–1223 (2009). [CrossRef] [PubMed]

]. Some of the amplitude-based techniques include scattering optical coherence angiography [29

29. Y. Yasuno, Y. Hong, S. Makita, M. Yamanari, M. Akiba, M. Miura, and T. Yatagai, “In vivo high-contrast imaging of deep posterior eye by 1- um swept source optical coherence tomography and scattering optical coherence angiography,” Opt. Express 15(10), 6121–6139 (2007). [CrossRef] [PubMed]

,30

30. Y. Hong, S. Makita, M. Yamanari, M. Miura, S. Kim, T. Yatagai, and Y. Yasuno, “Three-dimensional visualization of choroidal vessels by using standard and ultra-high resolution scattering optical coherence angiography,” Opt. Express 15(12), 7538–7550 (2007). [CrossRef] [PubMed]

], speckle variance [31

31. A. Mariampillai, B. A. Standish, E. H. Moriyama, M. Khurana, N. R. Munce, M. K. K. Leung, J. Jiang, A. Cable, B. C. Wilson, I. A. Vitkin, and V. X. D. Yang, “Speckle variance detection of microvasculature using swept-source optical coherence tomography,” Opt. Lett. 33(13), 1530–1532 (2008). [CrossRef] [PubMed]

,32

32. H. C. Hendargo, R. Estrada, S. J. Chiu, C. Tomasi, S. Farsiu, and J. A. Izatt, “Automated non-rigid registration and mosaicing for robust imaging of distinct retinal capillary beds using speckle variance optical coherence tomography,” Biomed. Opt. Express 4(6), 803–821 (2013). [CrossRef] [PubMed]

], correlation mapping [33

33. E. Jonathan, J. Enfield, and M. J. Leahy, “Correlation mapping method for generating microcirculation morphology from optical coherence tomography (OCT) intensity images,” J Biophotonics 4(9), 583–587 (2011). [PubMed]

] and split-spectrum amplitude-decorrelation angiography [34

34. Y. Jia, O. Tan, J. Tokayer, B. Potsaid, Y. Wang, J. J. Liu, M. F. Kraus, H. Subhash, J. G. Fujimoto, J. Hornegger, and D. Huang, “Split-spectrum amplitude-decorrelation angiography with optical coherence tomography,” Opt. Express 20(4), 4710–4725 (2012). [CrossRef] [PubMed]

36

36. E. Wei, Y. Jia, O. Tan, B. Potsaid, J. J. Liu, W. Choi, J. G. Fujimoto, and D. Huang, “Parafoveal retinal vascular response to pattern visual stimulation assessed with OCT angiography,” PLoS ONE . submitted.

]. These methods have been implemented using both spectral-domain and swept-source OCT imaging systems. Most of these techniques can detect both transverse and axial flow, and have been successful in visualizing retinal and choroidal microvascular networks. While good qualitative imaging results have been shown for all of these methods, quantitative results that map angiograms to flow velocities are lacking. Decorrelation has been used for quantitative flow measurements in ultrasound [37

37. W. Li, C. T. Lancee, E. I. Cespedes, A. F. W. van der Steen, and N. Bom, “Decorrelation properties of intravascular echo signals: Potentials for blood velocity estimation,” J. Acoust. Soc. Am. 71(14), 70D–86D (1993).

,38

38. W. Li, A. F. W. van der Steen, C. T. Lancée, I. Céspedes, and N. Bom, “Blood flow imaging and volume flow quantitation with intravascular ultrasound,” Ultrasound Med. Biol. 24(2), 203–214 (1998). [CrossRef] [PubMed]

] and thus has the potential to be useful for measuring flow velocities in OCT. Recently, a decorrelation-based method termed intensity-based Doppler variance (IBDV) was introduced and its relationship with velocity was established [39

39. G. Liu, L. Chou, W. Jia, W. Qi, B. Choi, and Z. Chen, “Intensity-based modified Doppler variance algorithm: application to phase instable and phase stable optical coherence tomography systems,” Opt. Express 19(12), 11429–11440 (2011). [CrossRef] [PubMed]

41

41. G. Liu, A. J. Lin, B. J. Tromberg, and Z. Chen, “A comparison of Doppler optical coherence tomography methods,” Biomed. Opt. Express 3(10), 2669–2680 (2012). [CrossRef] [PubMed]

]. This method computes decorrelation using only the amplitude signal. The authors in [41

41. G. Liu, A. J. Lin, B. J. Tromberg, and Z. Chen, “A comparison of Doppler optical coherence tomography methods,” Biomed. Opt. Express 3(10), 2669–2680 (2012). [CrossRef] [PubMed]

] showed that the IBDV signal increased by 87.5% as the Doppler angle increased from 0° to 18°, indicating a significant Doppler angle dependence. One potential advantage of SSADA is that the algorithm first digitally creates an isotropic coherence volume, or resolution cell, prior to computing decorrelation. This could make the algorithm equally sensitive to axial and transverse motion so that SSADA may be used to quantify flow independent of Doppler angle.

The purpose of this paper is to determine a relationship between SSADA measurements and flow velocity. We hypothesize that this relationship is linear within a certain range of velocities and use in vitro blood flow phantom experiments to test this hypothesis. Whole blood was used in order to to closely mimic in vivo retinal imaging. The SSADA algorithm computes decorrelation between two OCT amplitudes that are taken at the same scanning position but are separated in time. We first examine the dependence of SSADA measurements on Doppler angle after splitting the source spectrum in wavenumber so that the axial resolution of the OCT imaging system is equal to its transverse resolution. The concept of multi-timescale SSADA is introduced, where the time separation between amplitude measurements is varied, and used to examine the time-dependence of decorrelation. We derive an equation that can be used to calculate the absolute flow velocity from a measured decorrelation value and particular time separation between OCT amplitude measurements. We then define the saturation velocity for which the decorrelation values saturate and the linear relationship is no longer valid.

2. Materials and methods

2.1 System setup

A detailed description of the experimental Fourier domain OCT system can be found in [20

20. Y. K. Tao, A. M. Davis, and J. A. Izatt, “Single-pass volumetric bidirectional blood flow imaging spectral domain optical coherence tomography using a modified Hilbert transform,” Opt. Express 16(16), 12350–12361 (2008). [CrossRef] [PubMed]

]. This system, originally designed for retinal imaging, was modified for capillary tube measurements by adding a focusing lens in the sample arm. Briefly, it contains a superluminescent diode source with a center wavelength of 840 μm and a bandwidth of 49 μm. The theoretical axial resolution of the system was 6.4 μm in air, while the measured axial resolution was 8.8 μm in air. The deviation from the theoretical value is likely due to the non-Gaussian spectrum profile as well as aberrations that reduce the spectral resolution of the spectrometer. A collimator was placed in the sample arm that produced a 1/e2 intensity diameter of approximately 1.0 mm, and was focused down to 20 μm spot size using a 20 mm focal length lens (Thorlabs LB/450-B Bi-convex lens with antireflection coating in 650 – 1050 nm range). The sample arm probe beam was focused onto a glass capillary tube (Wale Apparatus) with an outer diameter of 330 μm and an inner diameter of 200 μm. No anti-reflection material was used to coat the glass. The power incident on the capillary was 500 μW. The capillary was placed on top of a piece of paper and attached to a ball and socket mounting platform (Thorlabs). A syringe pump (Harvard Apparatus) was used to control the flow of human blood (coauthor J.T.) through the tube. The recombined field was spectrally dispersed by a spectrometer and detected by 1024 pixels on a line-scan camera. The wavelengths acquired by the spectrometer ranged from 806 nm to 876 nm in steps of 0.068 nm. The data from the camera was transferred to a computer for data processing. The time between two sequential A-scan acquisitions was 56 μs which corresponds to a 17 kHz repetition rate. A system schematic is show in Fig. 1
Fig. 1 Spectral domain OCT system schematic. SLD – superluminescent diode, FC – 2x2 fiber coupler, PC – personal computer, H20 – water cell, Galvos – scanning mirror galvanometers, BS beamsplitter. This system was originally designed for retinal imaging so that a water cell is in the reference arm for dispersion matching and a beamsplitter is in the sample arm to allow for slit lamp illumination of the retina. The retinal imaging system was modified by adding a focusing lens in the sample arm.
.

2.2 Scan protocol

Data was collected using both dual-plane [42

42. Y. 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]

] and M-mode protocols. The dual-plane protocol was implemented with two parallel B-scans that were separated by 100 μm and repeated eight times. The B-scans each consisted of 700 A-lines and covered 700 μm in the transverse dimension, resulting in a transverse step size of 1 μm. M-mode scans consisted of 2600 A-lines at the same transverse position inside the capillary. Measurements were taken for five different preset flow rates and five different Doppler angles. The Doppler angle was controlled using the ball and socket mount.

2.3 Data processing

The acquisition software was provided by Bioptigen Inc. (Durham, NC), and the custom processing and analysis software was coded in MATLAB. The custom processing software included methods for resampling to k-space via spline interpolation and dispersion compensation. Mirror reflections at two different sample depths were acquired and used for resampling to k-space as described in [43

43. S. Makita, T. Fabritius, and Y. Yasuno, “Full-range, high-speed, high-resolution 1 μm spectral-domain optical coherence tomography using BM-scan for volumetric imaging of the human posterior eye,” Opt. Express 16(12), 8406–8420 (2008). [CrossRef] [PubMed]

]. A dispersion mismatch between the reference and sample arms leads to a nonlinear phase dependence of the spectral interferogram in wavenumber [44

44. M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12(11), 2404–2422 (2004). [CrossRef] [PubMed]

]. To compensate dispersion, a linear function was fit to the unwrapped phase of one of the mirror reflections and the residual between the phase and the linear fit, representing the nolinear dependence, was used as a phase correction factor θc(k)=ϕ(k)ϕLINEAR(k). This phase correction factor was used to compensate each A-line for dispersion by multiplying each interferogram by exp(iθc(k)). After background subtraction, resampling to k-space, dispersion compensation and Fourier transformation we obtain complex OCT data. Sample OCT reflectance images are shown in Fig. 2
Fig. 2 Sample intensity images. Capillary was placed on top of a piece of paper. Left panel: B-scan; Right panel: M-mode scan.
.

The dual-plane B-scans were used to compute the Doppler angle between the probe beam and the glass capillary, while the M-mode scans were used for velocity and decorrelation calculations. The velocities were calculated by first computing Doppler frequency shifts using the phase-resolved Doppler OCT algorithm [45

45. A. Szkulmowska, M. Szkulmowski, A. Kowalczyk, and M. Wojtkowski, “Phase-resolved Doppler optical coherence tomography--limitations and improvements,” Opt. Lett. 33(13), 1425–1427 (2008). [CrossRef] [PubMed]

] and then converting to absolute velocity using the measured Doppler angle. The capillary tube was automatically segmented in the M-mode scans using intensity thresholding and morphological operations. Figure 3
Fig. 3 Sample Doppler Frequency shifts
illustrates that there are significant projection artifacts in the paper underneath the glass capillary, which is likely due to multiple scattering by the moving blood cells. To avoid the influence of these artifacts on the measured Doppler frequency shifts, we chose a subregion in the upper half of the capillary to use for all subsequent calculations.

3. Theory

The OCT spectral interferogram can be written as [44

44. M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12(11), 2404–2422 (2004). [CrossRef] [PubMed]

]
I(k)Re{S(k)r(x,z)exp(4ln2(x2/ω02))exp(i2kz)dxdz}
(1)
where k=2π/λ denotes the wavenumber, Re{} denotes the real part operator,(x,z)denotes the coordinate of a reference frame fixed to the sample, S(k) is the source power spectral density, r(x,z) is the backscattering coefficient of the sample and ω0 is the full-width at half-maximum (FWHM) of the beam intensity profile. Note that Eq. (1) assumes that the zero path length difference in the interferometer is located at z=0 and that the beam is centered at transverse positionx=0. For a Gaussian spectral shape we can write
S(k)exp(4ln2(kk0)2/Δk2)
(2)
where k0=2π/λ0 is the center wavenumber of the source and Δk is its FWHM spectral width in wavenumber.

After Fourier transforming the spectral interferogram we obtain the complex OCT signal as a function of depthZ, which can be written as
I(Z)r(x,z)exp(i2k0(zZ))exp(4ln2(x2ω02+(zZ)2δz02))dxdz
(3)
whereδz0=4ln2/Δk denotes the FWHM axial resolution.

Each pixel in an OCT image is formed by a coherent sum of all of the light backscattered from a 3D coherence volume within a sample. The dimensions of the coherence volume are determined by ω0 andδz0, as can be seen by examining the rightmost exponential in Eq. (3). The explicit dependence on the FWHM ω0of the intensity profile, rather than the electric field profile has been explained in [46

46. S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, “Motion artifacts in optical coherence tomography with frequency-domain ranging,” Opt. Express 12(13), 2977–2998 (2004). [CrossRef] [PubMed]

]. Briefly, the sample arm fiber’s mode field modulates the illumination field, which the combines with the backscattering coefficient to produce the scattering field. The portion of the scattering field that couples back into the fiber is given by an overlap integral between the scattered field and the fiber mode field. Thus, the backscattering coefficients in the coherent sum are modulated by a function that is proportional to the square of the fiber mode field, which equals the intensity at the sample.

The SSADA algorithm computes decorrelation at a single voxel between OCT magnitudesA(Z)=|I(Z)| separated in time. In the original SSADA implementation in [34

34. Y. Jia, O. Tan, J. Tokayer, B. Potsaid, Y. Wang, J. J. Liu, M. F. Kraus, H. Subhash, J. G. Fujimoto, J. Hornegger, and D. Huang, “Split-spectrum amplitude-decorrelation angiography with optical coherence tomography,” Opt. Express 20(4), 4710–4725 (2012). [CrossRef] [PubMed]

], consecutive B-scans at the same slow axis scanning position (M-B scans) and separated by Δt=2.0ms are used to compute a decorrelation frame. In our current experiments, on the other hand, we use M-mode scans to compute the decorrelation of a single A-line. The main purpose of the switch to M-mode imaging is that it allows us to study the time course of decorrelation. We let Anm(Z) denote the mth split spectra from the nth A-line in our M-mode scan that is taken at timet=(n1)τ, where τ=56µs is the A-line rate of our system. Generalizing the average decorrelation equation given in [34

34. Y. Jia, O. Tan, J. Tokayer, B. Potsaid, Y. Wang, J. J. Liu, M. F. Kraus, H. Subhash, J. G. Fujimoto, J. Hornegger, and D. Huang, “Split-spectrum amplitude-decorrelation angiography with optical coherence tomography,” Opt. Express 20(4), 4710–4725 (2012). [CrossRef] [PubMed]

] to consider different time separations, the average decorrelation between 2 A-lines taken at the same transverse position can be written as
D¯(Z,Δt)=12N1 1Mn=1N1m=1MAnm(Z)An+Δt/τm(Z)Anm(Z)2+An+Δt/τm(Z)2 
(5)
where N=2000is the number of individual decorrelations that are being averaged, M=5 is the number of split-spectra/Gaussian filters that was previously described and Δt is an integer multiple of the line rate τ. Using our M-mode scans, we can compute a multi-timescale SSADA (MSSADA) image by computing the decorrelation at time separations ranging from τ throughNτ. A sample multi-timescale SSADA image is illustrated in Fig. 4
Fig. 4 Multi-timescale SSADA M-mode image of blood flow through capillary tube. Time separation indicates the time between the two A-lines used to compute the decorrelation.
.

For all of the results presented in this work, the Doppler and SSADA signals were binned into four distinct equally space depth bins within the region of. The data within each bin was averaged so that each scan produced four Doppler measurements and four SSADA measurements.

4. Results

4.1 Doppler angle dependence

Since SSADA is an amplitude-based method and we create an isotropic voxel by splitting the source spectrum, we expect that the measured SSADA signal will exhibit similar sensitivities in the axial and transverse directions. In order to test this claim, we analyze the variation of the decorrelation signal with Doppler angle. To avoid both noise and saturation artifacts, we choose time separations Δt for which decorrelation values lie in a central region around 0.145 at zero Doppler angle. Specifically, time separations of Δt = 784, 280 and 168 μs for respective flow speeds of 0.37, 1.29 and 2.00 mm/s were used to plot SSADA measurements versus Doppler angle. Figure 5
Fig. 5 Dependence of measured SSADA decorrelation signal on Doppler angle. Spearman’s correlation coefficient between the decorrelation measurements and Doppler angle is ρ = 0.87. ρ is a nonparametric measure of how well the relationship between decorrelation and Doppler angle can be described using a monotonic function. In this case the function appears to be sigmoidal.
illustrates that while the decorrelation signal remains relatively constant for Doppler angles less than 10°, it increases above 10° and then appears to plateau above 20°. This indicates that while SSADA measurements are equally sensitive to axial and transverse flow for Doppler angles less than 10°, the measurements are more sensitive to axial flow for Doppler angles above 10°.

The change in decorrelation due to an angular variation can be used as an quantitative indicator of the sensitivity of the decorrelation signal to Doppler angle. Specifically, the decorrelation increases from approximated 0.144 at near perpendicular incidence to 0.159 at a Doppler angle of 30°. The change in decorrelation due to an angular deviation of 30°, is then computed as 100 x (0.159 - 0.144)/((0.159 + 0.144) / 2) = 9.9%, which indicates a small but significant dependence of decorrelation measurements on Doppler angle.

4.2 Saturation

SSADA effectively enumerates the dissimilarity between a pixel’s amplitude at two different time instances. If the interval between the two measurements is long enough, the respective amplitudes will be independent, and the decorrelation signal will be fully saturated. This defines a state of complete decorrelation, and any increase in the time interval will not alter the SSADA measurement. Thus, only decorrelation values that are below the saturation level are useful for distinguishing between varying flow speeds. By visually inspecting Fig. 6
Fig. 6 Multi-timescale decorrelation (Eq. (5)) for various flow speeds. The asymptotic decorrelation value for our experiments is 0.21.
, we can see that complete decorrelation occurs in approximately 500 μs for a flow speed equal to 2 mm/s. At this speed and time separation the red blood cells (RBCs) are displaced by only 1.0 μm, less than one-tenth of the coherence volume size. This suggests that the decorrelation reaches full saturation well before the RBCs move completely through the coherence volume, which indicates a high sensitivity to speckle variation caused by the RBCs moving through the coherence volume. Note that the curves in Fig. 6 asymptotically approach the complete decorrelation value of 0.21. This motivates us to define a threshold over which the decorrelation rate slows down considerably and the curves in Fig. 6. begin to flatten. We set this decorrelation saturation threshold to 85% of the asymptotic decorrelation value. The resulting threshold is 0.18, and all decorrelation values above this threshold are referred to as saturated.

4.3 Relationship between decorrelation and velocity

We summarize the fitting parameters in Table 1

Table 1. Summary of linear fit of decorrelation versus velocity

table-icon
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. From this table we see that the slope changes with time separation. On the other hand, the intercept values remain relatively constant with changing time separations. We thus establish the linear relationship
DΔt=mΔt(1)v+b(1)
(6)
whereDΔt is the measured decorrelation value at a particular time separationΔt, v is the flow velocity, mΔt(1) is the slope parameter that is a function of Δt andb(1)0.08 is the intercept parameter. The significance of this intercept parameter, which is equal to the decorrelation when the velocity is zero, is treated in the Discussion section.

Plugging this relationship into Eq. (6) gives us the decorrelation as a function velocity and time separation

D(v,Δt)=m(2)Δtv+b(1)=0.24Δtv+0.08
(7)

In practice, we measure the decorrelation at a particular time separation and wish to find the flow velocity. Thus, we can invert Eq. (7) to solve for velocity. Substituting m for 1/m(2) and b for b(1) we can write
v(D,Δt)=m(Db)Δt=4.17(D0.08)Δt
(8)
This model is only valid for a specific range of velocities and time separations, which define an operating range for our model. Using Eq. (8), we can compute the saturation velocityvSAT, which is defined as the velocity at which the decorrelation reaches the saturation cutoff value of 0.18, for various time separationsΔt. The linear model in Eq. (8) does not hold for velocities abovevSAT. Some time separation-saturation velocity pairs are illustrated in Table 2

Table 2. Operating range for linear model

table-icon
View This Table
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.

5. Discussion

5.1 Model parameters

In order to study the parameters of our model, we first rewrite Eq. (8) as
vΔt=Δx=m(Db)=4.17(D0.08)
(9)
where Δx is the distance that the RBCs move between scans separated by time interval Δt and all other terms have been previously defined. The two parameters in this model are the slope m and the decorrelation interceptb. Since decorrelation is dimensionless, the parameter b must be dimensionless as well. Furthermore, we see from Eq. (9) that when the RBC displacement equals zero, the decorrelation equalsb. Thus the parameter bis equal to the decorrelation in non-flow pixels, or the bulk decorrelation. It equals the minimum measurable decorrelation value and can be defined as the decorrelation noise floor. We expect that this parameter will vary inversely with the system signal-to-noise ratio, similar to the way that the phase noise floor does for Doppler OCT [49

49. S. Yazdanfar, C. Yang, M. V. Sarunic, and J. A. Izatt, “Frequency estimation precision in Doppler optical coherence tomography using the Cramer-Rao lower bound,” Opt. Express 13(2), 410–416 (2005). [CrossRef] [PubMed]

]. Further experiments are required to verify if and how this parameter relates to the signal-to-noise ratio of a particular OCT imaging system.

5.2 Model limitations

There are a number of limitations of the linear model in Eq. (8). First, in order to establish the linear relationship between decorrelation and velocity we had to exclude saturated points from our analysis. In practice, this establishes an upper limit on a velocity-time separation pairing for quantitative SSADA using our linear model. Furthermore, as we can see in Fig. 6, for very slow flow speeds (e.g. 0.37 mm/s) the curve looks more s-shaped than linear. We expect that for slower speeds the curve will look even more s-shaped. It seems then that a more accurate model for the decorrelation to velocity relationship might be sigmoidal. Both of these models would also naturally handle the saturated data points.

5.3 Comparison with previous work on intensity-based Doppler variance angiography

Liu and colleagues also performed similar flow phantom experiments [40

40. G. Liu, W. Jia, V. Sun, B. Choi, and Z. Chen, “High-resolution imaging of microvasculature in human skin in-vivo with optical coherence tomography,” Opt. Express 20(7), 7694–7705 (2012). [CrossRef] [PubMed]

,41

41. G. Liu, A. J. Lin, B. J. Tromberg, and Z. Chen, “A comparison of Doppler optical coherence tomography methods,” Biomed. Opt. Express 3(10), 2669–2680 (2012). [CrossRef] [PubMed]

] and found similar results for both intensity-based Doppler variance (IBDV) and Doppler phase variance. Note that they used IBDV which is similar to SSADA but does not apply spectrum splitting and uses a difference averaging procedure. Many of the results of the two works are similar, including establishing decorrelation saturation values and a linear range relating the calculated signal to velocity that depends on the time separation between measurements. However, there are a couple of important differences between the results in that work and those shown here. First, there is a significant difference regarding the dependence on Doppler angle. In order to compare the variation with Doppler angle, we first normalize our SSADA measurements by subtracting the background decorrelation of 0.08 found at zero flow. Because the IBDV background values were negligibly small compared to flow signal in [41

41. G. Liu, A. J. Lin, B. J. Tromberg, and Z. Chen, “A comparison of Doppler optical coherence tomography methods,” Biomed. Opt. Express 3(10), 2669–2680 (2012). [CrossRef] [PubMed]

] background subtraction was not necessary for IBDV. We compare the variation in the measurements over a Doppler angular range of approximately 18° (the largest angle tested by Liu et al.). Specifically, after background subtraction, the SSADA signal increases from 0.065 at perpendicular incidence to approximately 0.080 at a Doppler angle of 18° for the data presented in Fig. 5. Thus, our results in this work indicate that the SSADA signal increases by approximately 23% over an angular range of 18°. On the other hand, the IBDV signal in [41

41. G. Liu, A. J. Lin, B. J. Tromberg, and Z. Chen, “A comparison of Doppler optical coherence tomography methods,” Biomed. Opt. Express 3(10), 2669–2680 (2012). [CrossRef] [PubMed]

] increases from 80 at perpendicular incidence to approximately 150 at 18°, an 87.5% increase over the same angular range. Thus, the Doppler angle dependence of IBDV [41

41. G. Liu, A. J. Lin, B. J. Tromberg, and Z. Chen, “A comparison of Doppler optical coherence tomography methods,” Biomed. Opt. Express 3(10), 2669–2680 (2012). [CrossRef] [PubMed]

] was significantly higher than the angle dependence of SSADA reported here. Another important difference between this work and that found in [40

40. G. Liu, W. Jia, V. Sun, B. Choi, and Z. Chen, “High-resolution imaging of microvasculature in human skin in-vivo with optical coherence tomography,” Opt. Express 20(7), 7694–7705 (2012). [CrossRef] [PubMed]

] is that in [40

40. G. Liu, W. Jia, V. Sun, B. Choi, and Z. Chen, “High-resolution imaging of microvasculature in human skin in-vivo with optical coherence tomography,” Opt. Express 20(7), 7694–7705 (2012). [CrossRef] [PubMed]

] the authors showed a saturation velocity over 100 mm/s for a time separation of 0.02 ms, whereas our model predicts a saturation velocity of approximately 20 mm/s for that time scale.

We hypothesize that these significant differences are likely caused by the choice of the algorithms and the difference in the flowing phantom. Specifically, by creating an isotropic voxel after splitting the source spectrum, SSADA aims to reduce flow directional sensitivity over IBDV. This could explain the reduced directional dependence of SSADA over IBDV, which did not split the OCT signal spectrum and therefore had much finer axial resolution compared to transverse spot size. Additionally, intralipid solution composed of spherical particles of 0.356 μm diameter was used as the flowing phantom in [40

40. G. Liu, W. Jia, V. Sun, B. Choi, and Z. Chen, “High-resolution imaging of microvasculature in human skin in-vivo with optical coherence tomography,” Opt. Express 20(7), 7694–7705 (2012). [CrossRef] [PubMed]

,41

41. G. Liu, A. J. Lin, B. J. Tromberg, and Z. Chen, “A comparison of Doppler optical coherence tomography methods,” Biomed. Opt. Express 3(10), 2669–2680 (2012). [CrossRef] [PubMed]

]. In contrast our flow phantom used whole blood where the predominant scattering particles are red blood cells that have an average diameter of 7.2 μm and a disc-like shape [50

50. M. L. Turgeon, Clinical Hematology: Theory and Procedures (Lippincott, Williams and Wilkins 2005). Chap. 6.

]. Because Doppler variance decreases with increasing particle size [51

51. C. S. Kim, W. Qi, J. Zhang, Y. J. Kwon, and Z. Chen, “Imaging and quantifying Brownian motion of micro- and nanoparticles using phase-resolved Doppler variance optical coherence tomography,” J. Biomed. Opt. 18(3), 030504 (2013). [CrossRef] [PubMed]

], we expect that the saturation velocity decreases as well. Another difference between this work and the work in [40

40. G. Liu, W. Jia, V. Sun, B. Choi, and Z. Chen, “High-resolution imaging of microvasculature in human skin in-vivo with optical coherence tomography,” Opt. Express 20(7), 7694–7705 (2012). [CrossRef] [PubMed]

] and [41

41. G. Liu, A. J. Lin, B. J. Tromberg, and Z. Chen, “A comparison of Doppler optical coherence tomography methods,” Biomed. Opt. Express 3(10), 2669–2680 (2012). [CrossRef] [PubMed]

] is that a swept-source OCT system was used for the experiments in [40

40. G. Liu, W. Jia, V. Sun, B. Choi, and Z. Chen, “High-resolution imaging of microvasculature in human skin in-vivo with optical coherence tomography,” Opt. Express 20(7), 7694–7705 (2012). [CrossRef] [PubMed]

] and [41

41. G. Liu, A. J. Lin, B. J. Tromberg, and Z. Chen, “A comparison of Doppler optical coherence tomography methods,” Biomed. Opt. Express 3(10), 2669–2680 (2012). [CrossRef] [PubMed]

] but a spectral domain OCT system was used here. For the same A-line rate, the integration time in the spectrometer OCT system is longer than that in a swept-source system. The difference in integration time may also affect the saturation velocity. Additional effects of blood such as tumbling and high viscosity could cause these observed differences as well.

5.4 Clinical SSADA

The flow phantom experiments presented in this work have a number of implications for clinical SSADA. We have shown that SSADA measurements have little dependence on Doppler angle for Doppler angles less than 10 degrees. So for retinal imaging where the OCT beam is nearly perpendicular to retinal vessels, clinical SSADA may be effectively angle independent. The clinical SSADA scans previously published by our research group [34

34. Y. Jia, O. Tan, J. Tokayer, B. Potsaid, Y. Wang, J. J. Liu, M. F. Kraus, H. Subhash, J. G. Fujimoto, J. Hornegger, and D. Huang, “Split-spectrum amplitude-decorrelation angiography with optical coherence tomography,” Opt. Express 20(4), 4710–4725 (2012). [CrossRef] [PubMed]

36

36. E. Wei, Y. Jia, O. Tan, B. Potsaid, J. J. Liu, W. Choi, J. G. Fujimoto, and D. Huang, “Parafoveal retinal vascular response to pattern visual stimulation assessed with OCT angiography,” PLoS ONE . submitted.

] used an interframe time separation Δt=2.0 ms, which is on the long side of the time scale investigated in this article. Referring back to Eq. (8) we see that for this time scale the saturation velocity is vSAT=0.2 mm/s (0.3 mm/sec if adjusted for the longer wavelength of 1050 nm). Since human retinal capillary flow speeds have been estimated to be in the range of 0.4-3.0 mm/s [52

52. C. E. Riva and B. Petrig, “Blue field entoptic phenomenon and blood velocity in the retinal capillaries,” J. Opt. Soc. Am. 70(10), 1234–1238 (1980). [CrossRef] [PubMed]

54

54. J. Tam, P. Tiruveedhula, and A. Roorda, “Characterization of single-file flow through human retinal parafoveal capillaries using an adaptive optics scanning laser ophthalmoscope,” Biomed. Opt. Express 2(4), 781–793 (2011). [CrossRef] [PubMed]

], this suggests that SSADA is well suited for detailed angiography down to the capillary level. However, decorrelation signal should be saturated even at the capillary level according to our phantom calibration. This does not entirely agree with the clinical retinal angiograms that we have observed, where there is a gradation of flow signals at the smallest retinal vessels as visualized by a false color scale [34

34. Y. Jia, O. Tan, J. Tokayer, B. Potsaid, Y. Wang, J. J. Liu, M. F. Kraus, H. Subhash, J. G. Fujimoto, J. Hornegger, and D. Huang, “Split-spectrum amplitude-decorrelation angiography with optical coherence tomography,” Opt. Express 20(4), 4710–4725 (2012). [CrossRef] [PubMed]

,35

35. Y. Jia, J. C. Morrison, J. Tokayer, O. Tan, L. Lombardi, B. Baumann, C. D. Lu, W. Choi, J. G. Fujimoto, and D. Huang, “Quantitative OCT angiography of optic nerve head blood flow,” Biomed. Opt. Express 3(12), 3127–3137 (2012). [CrossRef] [PubMed]

], and this graduated flow signal increased with visual stimulation [36

36. E. Wei, Y. Jia, O. Tan, B. Potsaid, J. J. Liu, W. Choi, J. G. Fujimoto, and D. Huang, “Parafoveal retinal vascular response to pattern visual stimulation assessed with OCT angiography,” PLoS ONE . submitted.

]. This difference could be caused in part by the fact that the work in [34

34. Y. Jia, O. Tan, J. Tokayer, B. Potsaid, Y. Wang, J. J. Liu, M. F. Kraus, H. Subhash, J. G. Fujimoto, J. Hornegger, and D. Huang, “Split-spectrum amplitude-decorrelation angiography with optical coherence tomography,” Opt. Express 20(4), 4710–4725 (2012). [CrossRef] [PubMed]

36

36. E. Wei, Y. Jia, O. Tan, B. Potsaid, J. J. Liu, W. Choi, J. G. Fujimoto, and D. Huang, “Parafoveal retinal vascular response to pattern visual stimulation assessed with OCT angiography,” PLoS ONE . submitted.

] used a swept-source OCT system while this work utilized a spectral domain OCT system. As described previously, the difference in integration time may affect the saturation velocity and consequently the flow signal gradation. Another explanation for the graduated decorrelation signal that we see in clinical SSADA is that there is a long sigmoidal tail above what we set a the saturation point (top of the linear region) where the decorrelation still increased with velocity, albeit at a shallow slope. We further hypothesize that the gradation could also be due to the fact that real blood capillaries are smaller than the diameter of the OCT probe beam, therefore both flow and stationary tissue existed within the same interrogation volume for SSADA, which has an expanded axial resolution due to spectral splitting. These factors may account for the proportional SSADA signal to capillary flow that is a response to either capillary diameter or velocity. Our flow phantom used a capillary tube that is much larger than the OCT beam diameter. This is one aspect in which our phantom setup differs significantly from real human capillaries. In other aspects such as the beam diameter, the use of whole blood, and the SSADA algorithm, the phantom results should simulate the clinical parameters well.

For the purpose of measuring flow velocity, a faster OCT system with a shorter inter-frame time scale would be better suited. Specifically, in order to bring the saturation velocity above 3.0 mm/s and thus enable capillary velocity quantification within the linear range, a time separation less than Δt=139 μs is suitable, according to Eq. (8). If our M-B mode imaging protocol calls for 200 A-lines per B-scan, then an imaging speed of 1.4 million A-lines per second (1.4 MHz) is needed. Thus, megahertz OCT systems [55

55. T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express 19(4), 3044–3062 (2011). [CrossRef] [PubMed]

,56

56. B. Potsaid, V. Jayaraman, J. G. Fujimoto, J. Jiang, P. J. S. Heim, and A. E. Cable, “MEMS tunable VCSEL light source for ultrahigh speed 60kHz – 1MHz axial scan rate and long range centimeter class OCT imaging,” Proc. SPIE 8213, Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XVI, 82130M, 82130M-8 (2012). [CrossRef]

] may be useful for blood flow velocity quantification within the linear range of SSADA.

6. Conclusion

Financial interests

Jason Tokayer, Yali Jia and David Huang have a significant financial interest in Optovue, a company that may have a commercial interest in the results of this research and technology. These potential conflicts of interest have been reviewed and managed by Oregon Health & Science University. Al-Hafeez Dhalla has no financial interest in the subject of this article.

Acknowledgment

This publication was supported by NIH grants R01 EY013516, P30EY010572 and an unrestricted grant from Research to Prevent Blindness. We gratefully acknowledge the assistance of Garth Tormoen.

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M. L. Turgeon, Clinical Hematology: Theory and Procedures (Lippincott, Williams and Wilkins 2005). Chap. 6.

51.

C. S. Kim, W. Qi, J. Zhang, Y. J. Kwon, and Z. Chen, “Imaging and quantifying Brownian motion of micro- and nanoparticles using phase-resolved Doppler variance optical coherence tomography,” J. Biomed. Opt. 18(3), 030504 (2013). [CrossRef] [PubMed]

52.

C. E. Riva and B. Petrig, “Blue field entoptic phenomenon and blood velocity in the retinal capillaries,” J. Opt. Soc. Am. 70(10), 1234–1238 (1980). [CrossRef] [PubMed]

53.

R. Flower, E. Peiretti, M. Magnani, L. Rossi, S. Serafini, Z. Gryczynski, and I. Gryczynski, “Observation of erythrocyte dynamics in the retinal capillaries and choriocapillaris using ICG-loaded erythrocyte ghost cells,” Invest. Ophthalmol. Vis. Sci. 49(12), 5510–5516 (2008). [CrossRef] [PubMed]

54.

J. Tam, P. Tiruveedhula, and A. Roorda, “Characterization of single-file flow through human retinal parafoveal capillaries using an adaptive optics scanning laser ophthalmoscope,” Biomed. Opt. Express 2(4), 781–793 (2011). [CrossRef] [PubMed]

55.

T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express 19(4), 3044–3062 (2011). [CrossRef] [PubMed]

56.

B. Potsaid, V. Jayaraman, J. G. Fujimoto, J. Jiang, P. J. S. Heim, and A. E. Cable, “MEMS tunable VCSEL light source for ultrahigh speed 60kHz – 1MHz axial scan rate and long range centimeter class OCT imaging,” Proc. SPIE 8213, Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XVI, 82130M, 82130M-8 (2012). [CrossRef]

OCIS Codes
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.4470) Medical optics and biotechnology : Ophthalmology
(170.4500) Medical optics and biotechnology : Optical coherence tomography

ToC Category:
Optical Coherence Tomography

History
Original Manuscript: July 17, 2013
Revised Manuscript: August 22, 2013
Manuscript Accepted: August 27, 2013
Published: September 3, 2013

Citation
Jason Tokayer, Yali Jia, Al-Hafeez Dhalla, and David Huang, "Blood flow velocity quantification using split-spectrum amplitude-decorrelation angiography with optical coherence tomography," Biomed. Opt. Express 4, 1909-1924 (2013)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-4-10-1909


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