raphy,â Optics Express 15(7), 4083â4097 (2007).  Wang, R., âThree-dimensional optical micro-angiography maps directional blood perfusion deep within.
Optical Angiography from Optical Coherence Tomograhy using a computational phase-shift Hanno Homann, Julia Walther, Gregor Mueller, and Edmund Koch Clinical Sensoring and Monitoring, Medical Faculty Carl Gustav Carus, Dresden University of Technology, Germany ABSTRACT We present a novel method to obtain optical angiographies (OAG) on a standard optical coherence tomography (OCT) system. The moving reference arm is simulated by introducing a phase-shift at the post-processing stage. The method can be applied bi-directionally from a single scan, one or more velocity-thresholds can be adjusted during post-processing. First in-vivo results are shown. Keywords: Optical coherence tomography, optical angiography,doppler imaging, ﬂow diagnosis
1. INTRODUCTION Optical coherence tomography (OCT) is an interferometric imaging technique that is capable to image biological tissues non-invasively at a resolution of a few micrometers. The original time-domain (TD-OCT) method uses short-coherent light to acquire a depth-scan by a rapidly moving reference mirror.1 In contrast to that, the more recent Fourier-domain (FD-OCT) method is based on spectral analysis of the interference signal and does not require a scanning reference mirror.2, 3 Moreover, it oﬀers a signiﬁcantly improved signal-to-noise ratio (SN R), allowing for higher scan rates.4, 5 In FD-OCT systems, the optical spectrum is either resolved spatially (Spectrometric OCT: SR-OCT) or time-encoded by a wavelength-tunable laser source (Swept-source OCT: SSOCT). In addition to structural information, OCT also allows for visualization and quantiﬁcation of spatially localized motion, such as blood ﬂow. The most common method, called Doppler OCT (DOCT) or phase-resolved OCT, is based on the linear relationship between velocity and the Doppler phase shift between two adjacent A-scans. DOCT has originally been demonstrated by Chen et al.6 using a TD-OCT. Zhao et al.7 improved the method by using the Hilbert transform to obtain a complex-valued TD-OCT signal, which yields an increased velocity sensitivity. Other researchers have presented variants of the DOCT approach for frequency domain systems (FD-OCT), for both spectrometric8 and swept-source9 OCT systems. Unfortunately, DOCT is highly susceptible to phase instabilities. Several researchers have extended the technique to overcome these sensitivities. Standard deviation imaging corrects the DOCT results based on the assumption that blood ﬂow varies due to turbulences or pulsation.10 Another recent approach to overcome phasesensitivity in low SN R conditions is the Joint-FD- and TD-OCT,11 however its need for repeated scanning at a constant transverse position reduces imaging speed and applicability for in vivo measurements. The Resonant Doppler method12 is an intensity-based technique, that requires an electro-optic phase modulator and cannot be applied for SS-OCT systems. Optical angiography (OAG) is an alternative technique recently proposed by Wang et al.13, 14 that separates moving from static scatterers in FD-OCT images by setting a velocity threshold by moving the reference mirror and exploiting mathematical properties of the Hilbert transform. The method is based on the phase-shift concept used for conjugate complex ambiguity suppression.15, 16 In contrast to DOCT, the method has been reported to be less sensitive to sample phase instabilities and OAG images are almost free of artifact-induced noise. Tao et al.17 modiﬁed the Hilbert transform, so that a bidirectional ﬂow information can be obtained from a single scan. In this contribution, we propose to simulate the physical mirror motion by a computationally introduced phase-shift. First in-vivo angiography images are presented. Further author information: Send correspondence to E. Koch: edmund.koch @ tu-dresden.de Optical Coherence Tomography and Coherence Techniques IV, edited by Peter E. Andersen, Brett E. Bouma, Proc. of SPIE-OSA Biomedical Optics, SPIE Vol. 7372, 737215 © 2009 SPIE-OSA · CCC code: 1605-7422/09/$18 · doi: 10.1117/12.831811 SPIE-OSA/ Vol. 7372 737215-1
2. METHODS 2.1 Principle of Optical Angiography (OAG) OAG provides velocity-thresholded grayscale angiographies based on phase information. The method separates moving scatterers from static tissue by exploiting mathematical properties of the Hilbert transform. The interference signal of a single moving scatterer, starting at z0 with a constant velocity vs , is given by: Pshif ted (k, tx ) = cos 2nk (z0 + (vs − vref )tx ) + φ˜ (1) where k is the wave number, tx is the time of the current A-scan, vref is an extra velocity shift that is originally introduced by moving the reference mirror, n is the refraction index, and φ˜ is a random phase ﬂuctuation term. All velocity terms used refer to the axial component of the velocity vector. From the measured real-valued signal, an analytic signal can be calculated using the Hilbert transform, provided that φ˜ is suﬃciently small. In case of OAG, the Hilbert transform is calculated for each B-scan row-by-row along the transverse parameter tx , where the vertical dimension is k. The corresponding transverse frequency is ωx = 2nk · (vs − vref ). The key point of OAG is that the Hilbert transform shifts positive frequencies by π/2 to give the imaginary part, but negative ones by −π/2. Hence, for ωx > 0 or vs > vref the resulting analytic function of Eq. 1 is: POAG (k, tx ) = exp j 2nk (z0 + (vs − vref )tx ) + φ˜
whereas for ωx < 0 or vs < vref it becomes: POAG (k, tx ) = exp −j 2nk (z0 + (vs − vref )tx ) + φ˜ .
In a second step, the Fourier transform is calculated along the spectral parameter k column by column as usual in FD-OCT. The resulting image is not symmetric to the virtual reference plane, but the sign of the frequency ωx determines whether a point is mapped to the positive or the negative Fourier space. For vref > 0 all particles moving away from the reference plane at a velocity vs > vref are mapped into the positive Fourier space, which is called the ﬂow image whereas the negative space is referred to as the static image. For vref < 0 the eﬀect is reversed. This technique eﬀectively separates particles moving faster than the reference mirror from slower ones.
2.2 OAG with computed phase shift Mathematically, it is essential that the phase shift 2nkvref tx is present in the signal. It is originally introduced by moving the reference mirror but may likewise be introduced computationally. Our basic idea is to simulate the physical mirror motion during post-processing (cf. Fig. 1). First, a B-scan is acquired as usual, k-space linearization is performed and we obtain the raw data matrix POCT (k, tx ) where every column contains an A-scan and every row is of constant wave number k. Fourier transform gives the complex OCT image A(z, tx ). Then we calculate the phase shift for every pixel in the raw
flow > static
phase shifted OCT image
B(z,t) Binary flow image
Static image OAG image
Figure 1. Flowchart of OAG with computed phase shift: Whereas the original algorithm measured Pshif ted , we simulate the moving reference mirror by incorporating the phase shift φref into a standard OCT measurement.
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data matrix that would be expected if the reference mirror had been moved at an arbitrary constant velocity vref during scan time: φref (z, tx ) = 2nk0 tx vref · sgn(z).
The result is then Inverse-Fourier-transformed to give the phase shifted interference signal Pshif ted (k, tx ) which is known from the original OAG algorithm in Eq. 1. We continue data processing according to the original algorithm: The Hilbert transform Hx is applied row-by-row along tx which gives the analytic signal POAG (k, tx ). The result is then again Fourier-transformed column-by-column along k. The resulting image is then split at the reference plane to get the ﬂow image and the static image. Finally, we compare both images on a pixel-by-pixel basis to create a binary ﬂow image from those pixels where the intensity in the ﬂow image exceeds the intensity in the OCT image. Our computed phase shift method does not require a physically moved mirror. Apart from avoiding extra hardware, this method also allows to vary the velocity threshold vref for a single data acquisition. The velocity threshold can be applied bidirectionally. Instead of using the gray scale ﬂow image itself,13, 17 we propose to extract the thresholded velocity information binarily. As far as noise is concerned, the phase ﬂuctuations term in Eqs. 2 and 3 adds linearly to the sample velocity vs , so that no SN R advantage can be expected when compared to Doppler OCT.
2.3 System configuration We use a swept source type OCT system for ﬂow measurements, as it achieves scan rates of several tens of kHz 18, 19 and axial motion does not induce fringe washout.20 The system uses a commercially available swept source laser (Santec HSL-2000) with a mean wavelength λ0 = 1320 nm, a full scanning range of Δλ = 120 nm, and operates at an A-scan rate of fA = 20 kHz. The system conﬁguration is shown in Fig. 2. The interferometer is integrated in a handheld scanner. A custom-made phase-optimized 80/20 beam splitter provides increased optical power in the sample arm. The ﬁberless interferometer design avoids stress-induced deterioration of the interference signals and enables ﬂexible handling. An 8 M Hz anti-aliasing ﬁlter is applied to limit the signal bandwidth to a frequency that corresponds to a measuring range of 2 mm. The interference signal is digitized at a 25 M Hz sampling rate. The maximal signal-to-noise ratio was measured to be SN R = 95 dB with a depth dependent loss of −6 dB at the end of the measuring range. Axial and transverse resolution in the optical focus were measured to be approximately 13 μm in air. The numeric aperture of the object lens was N A = 0.0433. The focal spot 1/e2 -diameter was 19.4 μm. To overcome trigger-to-sample-clock jitter, we use the time-stamp function of our digitizer (NI PCI-5122) to measure the time delay between the A-scan trigger of the swept-source laser and the ﬁrst sample. To achieve phase stability, this random time delay (0 . . . 40 ns) is then compensated in the k-space linearization interpolation routine.
OpU Ca I
Stetic referecce mirror
Figure 2. Configuration of the Swept-Source OCT system used in this study
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3. EXPERIMENTS AND RESULTS 3.1 Velocity measurement at a flow phantom For veriﬁcation of the velocity threshold in OAG, a ﬂow phantom was used. The model consisted of a glass capillary (Paul Marienfeld GmbH & Co. KG) with 0.31 mm inner diameter and an infusion pump (Injectomat MC Agilia, Fresenius Kabi AG) delivering a 1% Intralipid emulsion (Intralipid 20, Baxter GmbH) at a constant ﬂow rate. Assuming laminar ﬂow, the expected ﬂow proﬁle is parabolic: r2 vs (r) = vcenter · sin β · 1 − 2 R
where vcenter is the peak velocity, β is the angle between the capillary and the reference plane, r is the radius coordinate relative to the capillary center, and R is the inner capillary radius. The ﬂow rate was set to Q = 3.0 ml/h, corresponding to an approximate maximum velocity in the center of vcenter = 4.5 mm/s. The angle β was measured to equal 11.6◦ from a 3D scan. To achieve a suﬃcient phase correlation between successive A-scans, the transverse step width of the scanner was set to Δx = 1 μm. This corresponds to approximately 13-fold lateral oversampling. We then acquired a single B-scan (Fig. 3, left) and processed the data as described above. In the OAG image, static structures and particles slower than the velocity threshold vref are suppressed in the ﬂow image (center) and vice versa. However, suppression is not complete, especially the bright back surface of the capillary is still visible in the ﬂow image. The computation of the binary ﬂow image (right) allows for a clear velocity thresholded distinction. The procedure is repeated for several diﬀerent reference velocities vref equally seperated by Δvref := 0.5 mm/s. For comparison, DOCT images are obtained by multiplying each A-scan with its conjugate-complex successor21 and smoothing the complex result with a mean ﬁlter. Furthermore, both images, OAG and DOCT, were thresholded based on intensity in the OCT image slightly above the background noise level. A median ﬁlter was applied to all images to reduce speckle induced noise. The resulting ﬂow proﬁles for OAG and DOCT are shown in Fig. 4(a,b). The central cross-section in Fig. 4 on the right shows that velocities obtained from OAG are comparable to DOCT. This is as expected, since both methods are based on the sample motion induced phase shift. However, OAG slightly underestimates velocities, for the algorithm works based on the minimum velocity threshold vref with a digitization error Δvref .
Figure 3. The OCT image (a) shows a cross-section through the Intralipid-filled capillary. The OAG image (b) contains the flow image (top) and the static image (bottom). For velocity thresholded distinction, a binary flow image is created (c).
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z I mm
Figure 4. Flow profiles obtained by both methods: a) Optical Angiography (OAG), b) conventional Doppler OCT (DOCT), and a comparison of a cross-sectional profile.
3.2 In-vivo angiographies For in-vivo validation, we examined the saphenous vasculature of a wild type mouse (C57BL/6). Before examination, the mouse was narcotized and the skin covering the area of interest was removed. One 3D OCT image was acquired at the distal branching area of the saphenous vessels. The procedure was approved by the Institutional Ethic Commission for Animal Experiments of the medical faculty at Dresden University of Technology and the government of Saxony. Two velocity thresholds vref of 3 mm/s and −3 mm/s were used to obtain a bi-directional angiography. This threshold is reasonable as typical ﬂow velocities in the major saphenous vessels are about 30 − 100 mm/s and the incident angle was measured as 24◦ . The resulting angiography is shown in Fig. 5. The diameters of the central artery (light gray) and the veins (dark gray) were measured from the OCT image to be approximately 230 μm and 210 μm, respectively, under physiological conditions.
Figure 5. In-vivo experiment: In the two processed datasets were combined to a bi-directional 3D rendering, the bifurcation network of the saphenous vessel becomes visible.
4. CONCLUSIONS We have demonstrated a novel method for optical angiography that simulates the moving reference arm by introducing phase-shift in the lateral spatial frequency domain at the post-processing stage. Experiments with our ﬂow model showed that velocity measurements are comparable, but ﬂow rates are underestimated in OAG due to ﬁnite velocity discretization. Since random phase ﬂuctuations add linearly to the sample velocity, a sensitivity advantage of OAG over Doppler OCT was not apparent in this study. In-vivo experiments demonstrated that the technique can bi-directionally separate moving scatterers from static tissues. Further studies will include research on the variation of the simulated reference velocity and on the robustness against phase noise.
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