1. Introduction

Spectral domain optical coherence tomography (SDOCT) , including both spectrometer-based and swept-source systems, has demonstrated clinical potential for in vivo high-resolution and high-speed imaging of biological structures [1, 2]. Advances in Doppler SDOCT have demonstrated several image acquisition schemes that enabled real-time, high-resolution, volumetric display of blood flow maps [3–8]. These techniques, while able to provide 3D flow maps and velocimetry data, are inherently oversampled, and therefore have reduced imaging speed and are more susceptible to sample motion.

Current generation Doppler SDOCT techniques [3–8] use phase differences between sequential A-scans acquired at a single lateral position to calculate the velocity of moving scatterers through depth. These techniques relate the phase differences between sequential interferograms to a Doppler frequency-shift which, in turn, is related to the velocity of the moving scatterers. Recently, advances in Doppler SDOCT have led to a joint spectral and time domain acquisition scheme (STdOCT) which allows for near phase-noise limited velocity resolution in low signal conditions [9]. This technique is a variation of conventional Doppler, which functions by determining the velocity of moving scatterers using their temporal frequency shifts rather than the phase differences between sequential A-scans at a single lateral scan position. By taking a 2D Fourier transform of interference fringes temporally oversampled at the same A-scan position 20–40 times, STdOCT directly maps wavenumber to depth and time to Doppler frequency, thus creating a depth-resolved Doppler velocity map. This technique, while able to provide depth-resolved flow images and velocimetry data, is several times more oversampled than conventional Doppler, making it more susceptible to motion artifacts. Other techniques for identifying vessels involve injections of contrast agents such as FA [10] and ICGA [11], and/or manual segmentation of vessels.

Spatial frequency modulations across lateral scans have been introduced as a method for full range complex conjugate resolved imaging [12–17]. Similar to previously described complex conjugate resolving techniques using electro-optic phase modulators [18, 19] and acousto-optic frequency shifters [20–22], the spatial frequency modulation technique separates real and complex conjugate reflectivities by imposing a spatial carrier frequency laterally across a B-scan. The carrier frequency is generated by adding a phase delay to each A-scan using a moving reference arm or an off-pivot scanning beam. Similarly, a 3D optical angiography technique [23] has been demonstrated by using a modulated reference arm delay and by detecting scatterers not modulated at the carrier frequency as a result of flow-induced Doppler frequency-shifts. Resonant Doppler flow imaging [24] also uses reference arm modulations to detect flow, but instead of using a moving reference arm mirror, resonant Doppler uses an electro-optic modulator, driven at a flow detection frequency, to phase-match the reference signal to that of the moving scatterer. These techniques rely on precise synchronization of reference arm modulation and B-scan acquisition, require expensive or cumbersome modulators, and are unable to detect bidirectional flow in a single B-scan pass. Here we demonstrate an improvement on 3D optical angiography. Single-pass volumetric bidirectional blood flow imaging (SPFI) SDOCT detects moving scatterers using a modified Hilbert transform without the use of spatial frequency modulation. Since no frequency modulations are required and SPFI processing is applied to the spatial frequency content across a single B-scan, SPFI is applicable for both spectrometer-based and swept-source OCT systems, provided they have comparable B-scan acquisition rates. Unlike previously described techniques [23, 24], which require two separate B-scans to detect positive and negative flow, each with modulations tuned to the desired flow direction, SPFI is able to resolve bidirectional flow in a single B-scan pass across the sample.

2. Theory

The depth-encoded complex spectral interferometric signal from M discrete sample reflectors for an SDOCT system can be written as

where k is the wavenumber and A_m, Δz_m, and n represent the reflectivity, depth, and refractive index of each reflector, respectively. θ_m is a spatially-varying phase term related to the Doppler frequency-shift of the axial component of scatterer motion measured relative to the first lateral A-scan across each scatterer [6]. θ_h [x] represents the sum of phases arising from an optically heterogeneous sample and can be represented as a random variable with a mean of zero and a standard deviation, σ_h [x], that is related to the sampling spot-size. Previous work has demonstrated in vivo 3D blood flow mapping by imposing a known axial phase component across a lateral scanning dimension (B-scan) using a moving reference arm [23]. Similarly, modulation of this phase component has also been used for full range complex conjugate resolved SDOCT reconstruction [13, 14]. SPFI-SDOCT is a modification of these previous techniques where scatterers moving above a threshold velocity are imaged without the use of a modulation frequency.

 

Fig. 1. Flow chart of SDOCT spectral datacube processing. (a) Spectral inverse Fourier transform of B-scan yields (b,c) conventional SDOCT depth-resolved reflectivity map and lateral Fourier transform yields (d,e) sample spatial frequency information.

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The recorded interferometric signal represents the real-part of a summation of signals from M discrete reflectors (Eq. (1)) in a coherence volume (i.e. spot-size x coherence-length) and thus the phase term, θ_m [x], can be represented as

where v_m and v_x are the axial components of scatterer velocities and lateral scan speed, respectively. ∏ is the boxcar function defined by ${\prod }_{\frac{w_0}{2}}\left[x-\frac{\mathrm{dL}}{D}\right]=H\left[x-\frac{\mathrm{dl}}{D}+\frac{w_0}{2}\right]-H\left[x-\frac{\mathrm{dL}}{D}-\frac{w_0}{2}\right]$ and restricts the measured phase to moving scatterers within the spot-size, w ₀. d represents the A-scan location of the moving scatterer across a lateral scan of length L, sampled with a density of D A-scans. Combining Eq. (1) and Eq. (2), the sampled interferometric signal can be represented as the conventional SDOCT signal with a velocity-associated phase modulation

where g[x] and h[x] are the interferometric components associated with the optical heterogeneity and moving scatterers, respectively.

The recorded spectral datacube, I[k, x, y], in SDOCT is comprised of the real-parts of the interferometric signals (Eq. (3)) accumulated during a 2D raster scan and can be separated into a series of B-scan, I[k,x], data slices (Fig. 1(a)). The inverse Fourier transform in the spectral dimension, ${\mathrm{FT}}_{k\to z}^{-1}\left[I\left[k,x\right]\right]=R\left[z,x\right]+\bar{R}\left[z,x\right]$, represents the depth-resolved reflectivity map in conventional SDOCT (Fig. 1(b),(c)). Fourier transforming the lateral dimension (B-scan) yields the spatial frequency content

H[u] is the spatial frequency content of the phase associated with moving scatterers integrated across a spot size

where κ is a constant scaling factor. Eq. (4) can be represented in the form of ${\mathrm{FT}}_{x\to u}\left[I\right[u,k\left]\right]=\mathrm{R\prime }\left[u,k\right]+\overline{\mathrm{R\prime }}\left[u,k\right]+V_{\pm }\left[k,u+f_{D,\pm }\right]+{\bar{V}}_{\pm }\left[k,u-f_{D,\pm }\right]$. Here both moving, $V_{\pm }\left[k,u+F_{D,\pm }\right]$, and non-moving, R’[u,k], scatterers in the sample are imaged (Fig. 1(d),(e)), where f _D,± represents the Doppler frequency shift associated with the axial components of positive and negative scatterer motion. Note that all scatterer motion and associated flow refer to the axial components of motion (e.g. negative flow refers to the axial component of velocity for scatterers moving away from the sample beam). The Doppler frequency shift is related to Eqs. (2) and (3) by f_D = nkv_m/π and can be considered a sum of frequency shifts, representing all moving scatterers within a coherence volume, convolved with their respective reflectivities, in the spatial Fourier domain. Non-moving scatterers, in this case, are centered around DC (Fig. 1(d),(e)). The spatial frequency bandwidths of both moving and non-moving scatterers across a B-scan are related to the spatial frequency standard deviation of the heterogeneity term, G[u], where the standard deviation results from a summation of independent random variables [25]

and is representative of the spatial correlation between sequentially sampled A-scans with a high correlation lower limit associated with the optical heterogeneity of scatterers within a coherence volume, θ_h [x], and a Nyquist sampling upper limit.

 

Fig. 2. Flow chart of SPFI-SDOCT processing. (a) Lateral Fourier transform of B-scan yields (b) spatial frequency of sample centered around DC and spatial frequency of moving scatterers shifted by their respective Doppler frequencies. (c) Applying a frequency-shifted Heaviside step function and inverse Fourier transform of spatial frequencies recreates (d) the analytic interferometric signal (modified Hilbert transf'rm). (e) Spectral inverse Fourier transform of the analytic interferometric signal maps depth-solved reflectivities of bidirectionally moving scatterers on opposite image half-planes which can then be (f) overlaid for vessel identification.

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Since the recorded spectral datacube is real-valued, the previously described spatial Fourier transforms include both real and complex conjugate peaks. Previous works [13–15, 17, 23] have shown that by imposing a constant phase shift between A-scans along a single lateral scan direction, a carrier frequency can be added to the phase term and thus isolating real and complex conjugate peaks to opposite spatial frequency spaces. Windowing out the conjugate peaks, inverse transforming back to k-space (Hilbert transform), and then applying conventional spectral Fourier transforms on the data allowed for separation of moving (flow) and non-moving (structure) scatterers to opposite image half-planes. Imaging of bidirectional flow required applying positive and negative carrier frequencies and processing each datacube separately. In SPFI-SDOCT, we recognize that without the use of carrier frequencies, the spatial frequencies of moving and non-moving scatterers do not overlap at spatial frequencies above the non-moving scatterer bandwidth (Fig. 2(b)). An analytic signal for the spectral interferogram can be obtained by applying a Heaviside function (H[u–f_T]), frequency-shifted outside of the structural bandwidth (Fig. 2(c)), and then inverse Fourier transforming the result (Fig. 2(d)). Application of this modified Hilbert transform (HT*) enables bidirectional flow imaging by windowing Eq. (4) to yield

where α represents the fractional portion of bidirectional flow with Doppler frequencies outside of the spatial frequency bandwidth of non-moving scatterers (Fig. 2(c)). This threshold frequency (f_T) defines the minimum detectable velocity in SPFI-SDOCT and is related to the spatial correlation of sequential A-scans. Therefore, lateral oversampling of A-scans allows for a reduced threshold frequency and thus, slower minimum detectable velocities. All spatial frequencies above f_T can be detected given that their associated accumulated phases are above the system phase-noise floor.

Spatial oversampling and velocity resolution can be related by combing the velocity-related Doppler frequency shift with the spatial frequency resolution, which can be represented as

where λ ₀ is the center wavelength, τ is the integration time, and θ_D is the Doppler angle between the scanning beam and the direction of scatterer motion. n is the index of refraction, L is the lateral scan length, D is the number of A-scans acquired across the lateral scan, and w_o is the scanning beam spot size. Eq. (8) shows that velocity resolution in SPFI increases and the maximum detectable velocity decreases linearly with increased spatial oversampling.

Since the resulting complex interferometric signal is a sum of positive moving scatterers and the conjugate of negative moving scatterers, application of conventional SDOCT processing yields a flow image where bidirectional flow is imaged to opposite sides of DC (Fig. 2(e)). Finally, application of the Heaviside function to isolate moving scatterers also acts to reduce the overall noise of the velocity map. In a similar analysis for complex conjugate removal [17], it was demonstrated that spatial frequency windowing provides an SNR gain related to the window function. Similarly in SPFI, the resulting vessel map should benefit from a signal gain as a result of rejection of noise components outside of the velocity detection band.

 

Fig. 3. SPFI-SDOCT microscope. 2-dimensional scanning was implemented using a galvanometer scanning pair and f/8.5 microscope optics were optimized for a 9μm spot-size. The reference arm was blocked to allow for commonpath imaging.

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3. Methods

SPFI-SDOCT was implemented on a high-speed SDOCT microscope (Fig. 3) with the central wavelength at 859nm and a FWHM bandwidth of 99nm. The sample arm was a custom-built f/8.5 microscope equipped with scanning galvanometers and imaging optics optimized for a 9μm spot-size. SPFI data was demonstrated using both conventional and commonpath SDOCT configurations by blocking the reference arm of a typical SDOCT interferometer to implement a self-referenced [26] imaging scheme to reduce phase-noise such that f_T is dominated by lateral sampling. Phase-noise between sequential A-scans in a homogeneous phantom was measured to be 127mrad and 4.2mrad in conventional and commonpath configurations, respectively. Since the lower limit of the resolving power in SPFI is proportional to the phase-noise, the commonpath configuration was used for animal model imaging. Interferometric signals were captured using a 2048 pixel line-scan camera (e2v, Ltd.). Custom software (Bioptigen, Inc.) performed real-time data acquisition, processing, archiving, and display. Using a 1.3mW sample beam, the SNR measured near DC was 108dB with an axial resolution of 3.29μm in tissue and a 6dB falloff at 0.8mm. DC removal, k-space resampling, and flow imaging using the modified Hilbert transform algorithm [14, 15, 23] were computed during post-processing using Matlab (MathWorks, Inc.). Vessel and structure were visualized using Amira (Visage Imaging, Inc.).

 

Fig. 4. Phantom and in vivo flow models.(a) Two micro-capillaries were connected and oriented such that fluid flowed in opposite directions in a B-scan cross-section (line indicates B-scan orientation).(b) Chicken embryo preparation showing live embryo and peripheral vessels on both amnion and yolk surfaces (arrow).(c) Mouse window chamber preparation showing skin fold vasculature and tumor.

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Bidirectional flow imaging was demonstrated on a flow phantom using the conventional SDOCT configuration. Two glass micro-capillary tubes (1.5mm outer diameter, 0.6mm inner diameter) were connected using silastic tubing and pumped with 1% liposyn at 0.01mL/min (Harvard Apparatus). The micro-capillaries were then positioned adjacent to each other on an angled stage such that fluid in the tubes flowed in opposite directions in a B-scan cross-section (Fig. 4(a)), simulating bidirectional flow.

Vessel imaging was demonstrated on chicken embryo and mouse tumor window chamber models (Fig. 4(b),(c)). Fertilized Hubert Ross chicken eggs were incubated at 38°C and 97% humidity in a forced-draft incubation chamber [27]. At Hamburger-Hamilton (HH)-stages 23–25 [28], a window was created through the outer shell and the chorionic membrane was removed. Peripheral yolk vasculature (Fig. 4(b)) was then imaged using the commonpath configuration with the top amnion surface as the reference reflector. Vessels away from the embryo were imaged to avoid pulsatile flow as a result of heart beat. Embryo temperatures were maintained using a heat-lamp during the course of imaging.

Mouse in vivo experiments were conducted under protocols approved by the Duke University Institutional Animal Care and Use Committee. Mouse tumor models were prepared by surgically implanting a titanium window chamber on the back of anthymic (nu/nu) nude mice under anesthesia (ketamine 100mg/kg and xylazine 10mg/kg intraperitoneal). 4T1 metastatic mouse mammary adenocarcinoma cells were used. During window implantation, 10μL of a cell suspension of 5×10³ cells was injected into the dorsal skin flap and covered with a 12mm diameter #2 round glass coverslip over the exposed skin (Fig. 4(c)) [29].

Animals were housed in an environmental chamber with free access to food and water and standard 12hr light and dark cycles. Mice tumors were imaged two weeks after implantation using the window chamber surface as a reference reflector. The mice were anesthetized during imaging using isoflurane (1.5–2.5%) in medical air. Mice were imaged using the commonpath configuration, self-referenced using the surface of the window chamber as the reference reflector.

 

Fig. 5. Flow phantom imaging showing (a) conventional SDOCT depth image with complex conjugate mirror image,(b) SPFI processed flow image showing bidirectional flow, and (c) overlaid flow and structure image. Negative flow (blue), positive flow (red), and non-moving structure (orange) are identified.

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4. Results and Discussion

Bidirectional flow imaging was demonstrated on a liposyn-pumped flow phantom (Fig. 5). The phantom was angled such that components of flow were oriented in the axis of the imaging beam to enable SPFI detection. We assume a standard minimum B-scan size of 1000 A-scans/frame for a 3mm lateral scan at an integration time of 50μs. Faster lateral scan velocities result in galvanometer jitter, and therefore poor image quality and phase stability. Spatial oversampling for SPFI is defined based on these scan parameters in the following. A 3mm B-scan was acquired with 1800A-scans/frame with an A-scan integration period of 50μs, a factor of 1.8 increase in lateral oversampling. Conventional SDOCT processing (Fig. 5(a)) showed depth-ranged reflectivity of scatterers including structure, flow, and their complex conjugate mirror images. The directionality of flow in each tube is not readily discernable using conventional processing steps (Fig. 5(a) – red/blue arrows). After applying the modified Hilbert transform algorithm (Fig. 5(b)), all non-moving scatterer reflectivities (structure) and mirror images of flow are resolved leaving only positive and negative flow on opposite image half-planes. The phantom structural heterogeneity was bandlimited as a result of lateral oversampling, allowing the frequency-shifted Heaviside function to window out only moving scatterers (Eq. (6)). Similarly, the mirror images of moving scatterers were also eliminated by application of the modified Hilbert transform, leaving only the real-valued positive flow and complex conjugate negative flow, which are imaged to opposite sides of DC (Fig. 5(b)). Using the SPFI processed image, positive and negative flow are separated and overlaid onto the structural image for visualization (Fig. 5(c)). Given the oversampling parameters and the threshold frequency determined experimentally from the phantom data, the magnitude of the detectable positive and negative flow velocities was 0.39–1.12mm/s.

 

Fig. 6. 3D reconstruction of bidirectional volumetric flow magnitude in chicken embryo model. 3mm × 3mm volume is comprised of nine 1mm × 1mm volumes sampled with 1ms integration time. Vessel sizes of 40μm (purple) to 270μm (orange) were within detection limits. Amionic vessel (blue), amionic vessel branch point (green), and motion artifact (red) are indentified.

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Fig. 7. (7.73MB) Movie of 3D rendering of bidirectional flow magnitude in chicken embryo model. [Media 1]

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In vivo volumetric blood flow imaging was demonstrated on Hubert Ross chicken embryos and mice window chamber models. A 3mm × 3mm volume mosaic was created by acquiring nine 1mm × 1mm volumes imaged with 1800A-scans/frame and 100frames/volume, a factor of 5.4 increase in lateral oversampling. Each SPFI-SDOCT reconstructed frame was separated into two halves and combined to create bidirectional flow maps with intensities corresponding to the reflectivity of scatterers moving into or out of the A-scan axis.

 

Fig. 8. 3D reconstruction of bidirectional volumetric flow magnitude in mouse window chamber model. 3mm × 3mm volume is comprised of nine 1mm × 1mm volumes sampled with 2ms integration time. Vessel sizes of 20μm (purple) to 110μm (green) were within detection limits. Tumor region vasculature (blue) and motion artifact (red) are indicated.

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The peripheral yolk vascular network (Fig. 6) is clearly visible in the chicken embryo model. SPFI-SDOCT imaged vessels are tubular, as expected, and appear to be confined to a 500μm layer (Fig. 7). The large and partially imaged vessel across the volume mosaic (Fig. 6 – blue arrow) is a shadow artifact arising from imaging through a large vessel in the amionic (reference reflector) layer. The well defined portion of this vessel (Fig 6 – green arrow) represents areas where the vessel branches from the yolk surface up towards the surface of the amnion. The faded regions (Fig. 6 – blue arrow) are areas where the vessel is on top of the amion surface and out of the imaging depth range. Yolk surface vessels follow the curvature of the yolk sac and are shown gradually descending away from the reference surface (Fig. 7). Detected vessel sizes ranged from 40μm (Fig 6 – purple arrow) to 270μm (Fig 6 – orange arrow). “Hazy" sections (Fig. 6 – red arrow) are indicative of sample bulk motion which resulted in non-moving structural scatterers being resolved along with flow. Chicken embryo volumes were acquired using 1ms A-scan integration time in order to detect small vessels with minimal flow velocities. The magnitude of the detectable positive and negative flow velocities for the embryo model was 65.6-168.6μm/s.

Normal and tumor vasculature (Fig. 8) were imaged in the mouse window chamber model. Tumor regions were indentified prior to imaging (Fig. 8 – blue arrow) and show highly tortuous vessels indicative of neoplastic angiogenesis. Surrounding vasculature indicate normal skin fold vessels. Detected vessel sizes ranged from 20μm (Fig 8 – purple arrow), which approaches the sampling limit of the microscope, to 110μm (Fig 8 – green arrow). The volumes were acquired using 2ms A-scan integration time in order to detect small vessels however these volumes were more sensitive to bulk motion artifacts (Fig. 8 – red arrow). The magnitude of the detectable positive and negative flow velocities for the mouse tumor model was 32.8–84.3μm/s. Small noise signals throughout the volumes indicate areas of reference reflector saturation due to small optical reflectivity heterogeneities across the reference window chamber surface.

5. Conclusions

We have demonstrated a new noninvasive in vivo volumetric bidirectional flow imaging technique. SPFI-SDOCT allows for flow imaging without acquiring multiple A-scans at a single lateral position. Using a modified Hilbert transform algorithm, reflectivities of the components of moving scatterers flowing into and out of the axis of each A-scan are mapped to opposite sides of the image plane, thus allowing for volumetric visualization of flow without the need for manual segmentation.