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Optical coherence tomography (OCT)-based angiography (OCTA) provides in vivo, three-dimensional vascular information by the use of flowing red blood cells as intrinsic contrast agents, enabling the visualization of functional vessel networks within microcirculatory tissue beds non-invasively, without a need of dye injection. Because of these attributes, OCTA has been rapidly translated to clinical ophthalmology within a short period of time in the development. Various OCTA algorithms have been developed to detect the functional micro-vasculatures in vivo by utilizing different components of OCT signals, including phase-signal-based OCTA, intensity-signal-based OCTA and complex-signal-based OCTA. All these algorithms have shown, in one way or another, their clinical values in revealing micro-vasculatures in biological tissues in vivo, identifying abnormal vascular networks or vessel impairment zones in retinal and skin pathologies, detecting vessel patterns and angiogenesis in eyes with age-related macular degeneration and in skin and brain with tumors, and monitoring responses to hypoxia in the brain tissue. The purpose of this paper is to provide a technical oriented overview of the OCTA developments and their potential pre-clinical and clinical applications, and to shed some lights on its future perspectives. Because of its clinical translation to ophthalmology, this review intentionally places a slightly more weight on ophthalmic OCT angiography.
Optical coherence tomography (OCT) is a non-invasive and non-contact optical imaging technique [1, 2]. By detecting the interference formed between the reflected signals from reference mirror and from biological sample, it is capable of generating in-vivo cross-sectional volumetric images of the anatomical structures with microscopic resolution (1 to 10 µm) in real-time. Its non-invasive, non-contact, and high resolution nature has made OCT imaging become known as “optical biopsy.” With an ability to perform “optical biopsy” and provide microscopic structural information, OCT has made impact on our understanding of disease pathogenesis [3–5], as well as clinical diagnosis and management of various diseases [3–7].
Recent development of optical coherence tomography based angiography (OCTA) extends the OCT applications from pure structural imaging to functional imaging by enabling blood flow mapping of living subjects, pushing the OCT development into a new height. By measuring the differences in OCT signals caused by moving cells, OCTA utilizes the flowing red blood cells as the intrinsic contrast agent to generate blood flow signals, allowing the visualization of vascular networks without a need of dye injection.
Since the very first idea of using OCT to measure the blood flow (i.e. based on Doppler principle), the research and clinical investigations based on OCTA techniques have grown prosperously. A continuous increase in the number of publications year by year can be observed in Fig. 1, indicating how important this development is for research and clinical communities. In this review, we will first briefly discuss the OCT technique, then give a comprehensive historical review of the developments and evolution of OCTA techniques, followed by the discussions of artifacts, blood flow quantification, and its clinical applications and future perspectives.
OCT imaging generates cross-sectional (2D) or three-dimensional (3D) images by measuring the echo time delay and magnitude of backscattered light emerged from a sample through the principle of low coherence interferometry . The early OCT systems, also known as time-domain OCT (TD-OCT), consist of an interferometer with a low coherence and broad bandwidth light source. After passing through a beam splitter, the light is split into two beams, where one is sent to the reference arm or reference mirror, and the other beam is sent into the biological samples. The backscattered signal from the sample and the reflected signal from the reference mirror combine and generate an interference pattern with maximal intensity if the optical path lengths to the reference mirror and sample are matched to within the coherence length of the light source . By changing or scanning the position of the reference mirror, depth-resolved tissue reflectivity is then reconstructed from the interference pattern and recorded as an intensity profile along the axial direction, analogous to ultrasound A-scans. By moving and scanning the OCT beam on the sample in transverse direction, a sequence of A-scans are acquired to form an optical cross-section, which was demonstrated in 1991 . Such imaging protocol is analogous to ultrasound B-scan.
Instead of physically scanning a reference mirror, a later version of OCT detects the backscattering signals in frequency domain, which directly encodes the time delay information in spectral interferogram. This version is often referred to as Fourier-domain OCT (FD-OCT). Fourier-domain OCT includes two different forms in terms of system setup/configuration: spectral-domain OCT (SD-OCT) and swept-source OCT (SS-OCT), where SD-OCT is equipped with a broad-bandwidth light source and a spectrometer for detection, while SS-OCT acquires depth-resolved tissue information by sweeping a range of optical frequencies and the spectral interferograms are typically detected by photodiode detector [10–16]. Frequency information from all depths of one A-scan in tissue is acquired in parallel and converted into an intensity profile by a simple operation of the Fourier transformation of captured spectral interferogram. The implementation of the broadband light source with broader bandwidth enhances the axial resolution from 10 µm to 2 µm, and the introduction of the spectrometer or sweeping frequencies further improves the image acquisition speed from 400 A-scans/s to between 26,000 and 100,000 A-scans/s for commercial systems [6, 8, 17, 18], and to several MHz at research laboratories [19–23]. A higher signal-to-noise ratio (SNR) is also achieved . With the improvements of scanning speed, image resolution, and SNR in FD-OCT, it not only allows more information from the biological tissues to be acquired and visualized in a relatively short amount of time, but also makes the implementation of OCTA techniques become feasible.
The very first idea of using OCT technique to measure blood flow velocity started in the mid-1990s, following the invention of OCT. In 1997, Chen et al. developed an optical technique for non-invasive imaging of in vivo blood flow dynamics and tissue structures by combining Doppler velocimetry with TD-OCT . In the same year, Izatt et al. built a bidirectional color Doppler imaging system by employing coherence signal-acquisition electronics and joint time-frequency analysis algorithm for flow imaging in biological tissues while still keeping the conventional OCT functions . It is assumed that if an optical interface within sample, i.e., where an abrupt change in refractive index occurs, moves axially at a constant speed, , it will cause a frequency or phase shift, , on the backscattered OCT signals. The phase shift is also known as Doppler shift, and is additive to the carrier frequency associated with the reference arm. By demodulating the recorded OCT signal, the Doppler shift can be obtained and the blood flow velocity can be calculated based on the following equation
where is the central wavelength, n is the refractive index of the surrounding medium, and is the enclosed angle between the illumination direction of the incident beam and the moving direction of the interface. As a consequence, the first optical flow measurement technique is called Doppler OCT. In order to detect the Doppler shifted TD-OCT signal, a simple way is to record the full fringe signal and calculate the local frequency shift within a small window across each A-scan. However, in addition to a reduction of spatial resolution, this approach is computationally expensive and thus is difficult for realizing in vivo real-time flow measurements [26, 27].
The introduction of FD-OCT systems significantly increases the scanning speed of OCT, presents higher signal sensitivity and image quality, leading to a dramatic improvement in Doppler OCT development. The first functional extension of FD-OCT for measuring blood flow was demonstrated by Leitgeb et al. in 2002 . By directly measuring the changes in the phase between adjacent A-scans, the axial velocity of the scatters can be calculated from
where and are the phase difference and the time interval between two A-scans, is the central wavelength of the light source, and n is the refractive index of the tissue or samples. With a high phase stability of the sample as well as the system, Leitgeb et al. showed that the system was able to detect a range of velocities from 10 µm/s to 2 mm/s using an in vitro phantom study.
Although Doppler OCT shows improved velocity sensitivity using FD-OCT system, giving promising results in the detection of a range of velocities in phantom studies, its application to biological tissues in vivo, thus potentially clinical translation, is unfortunately not very successful. This outcome may be due to several limitations. First, the known Doppler angle, the angle between the incident OCT beam and the sample tissues (or blood flow direction of interest), is required in priori in order to obtain accurate estimate of blood flow velocity; however, obtaining the accurate Doppler angle becomes a challenge for non-invasive in vivo imaging. In addition to the required Doppler angle, the incident OCT beams are almost perpendicular to the vessels in the tissue beds (particularly for retinal vessels), making it hard to generate sufficient phase shift in the backscattered signal that is measureable with confidence. As a consequence, DOCT measurement is less sensitive to the blood flows within microcirculatory tissue beds, e.g. capillary flows, which makes it only feasible to measure the flow velocity within relatively large blood vessels. Lastly, the phase difference is vulnerable to the sample motion, for example bulk motion or eye movements induced by saccades, and therefore, obstruct the acquisition of 3D imaging, for several seconds are often required for volumetric imaging.
Extending the notion of Doppler shift and noticing the changes in tissue reflectance when red blood cells (RBC) traveling through a vessel, a new technique, called OCT-based angiography (OCTA) has rapidly emerged in recent years, which images blood flow based on the variations of OCT signals. The basic concept of OCTA is to use the moving particles, for example the RBCs, in the biological tissues as an intrinsic contrast agent to image blood flow. Observing two OCT signals – one is backscattered from surrounding biological tissue and the other one is backscattered from a flowing vessel – over time, the OCT signal backscattered from tissue components remains steady for there is no movement in the tissue, while the OCT signal backscattered from vessel changes over time as the RBCs tumbling and moving while flowing through the vessel, as shown in Fig. 2, a simplified schematic figure. By calculating the differences in OCT signals acquired at the same location at different time points, OCTA distinguishes the moving particles from the static tissue, and therefore is able to generate flow signals and allows the visualization of microvascular networks in biological tissues without a need of intravenous dye injection.
OCT signal is naturally a complex function, consisting of amplitude and phase information, and can be written as the equation below:
where indicates the amplitude component and presents the phase component in an OCT signal. Various OCTA methods are developed to extract the flow signal based on different components of OCT signal. According to the information a method uses, OCTA techniques can be classified into three categories: phase-signal-based OCTA techniques, intensity-signal-based OCTA techniques, and complex-signal-based OCTA techniques.
Through reducing the effect of bulk motion from a sample, Makita et al. demonstrated the first in vivo non-invasive volumetric Doppler OCT on human retina . Makita et al. minimized the effects from sample motion by two approaches: (1) removing the axial shift between adjacent A-scans within one B-scan using histogram based bulk motion Doppler shift compensation, and (2) compensating the motion between neighboring B-scans using the cross-correlation of particular A-scans. After motion compensation, the flow signal from large vessels was obtained as the average of Doppler OCT between adjacent A-scans. In order to achieve a higher sensitivity and contrast in the smaller vessels, the power of the Doppler shift, defined as the power of the phase difference between adjacent A-scans, also was applied. Even though the bulk motion was significantly reduced that improved the quality of the flow images, the proposed optical coherence angiography was based on Doppler OCT, and thus was difficult, if not impossible, to visualize the microvascular networks within the tissue beds.
More recently, Kurokawa et al. improved the Doppler power imaging by combining the system with adaptive optics, so that the probe beam can be tightly focused onto the retina with minimal aberration . In this method, the flow signal intensity was determined by the squared power of Doppler shift. With the use of adaptive optics, an increased lateral resolution for vascular imaging was observed; however, the sensitivity to flow signal remained similar to the original Doppler approach.
The first quantitative 3D in vivo measurement of human retinal blood flow was demonstrated by Bachmann et al. using resonant Doppler OCT . Resonant Doppler OCT was based on the effect of interference fringe blurring that occurred when the path difference between structure and reference changed during camera integration. The method was able to extract in-vivo retinal blood flow in 3D by minimizing the blur signal resulted from sample movement, and demonstrated a scheme to measure flow velocity values based on the amplitude information without the need to extract the signal phase . Later, advanced spatial filtering methods were used to distinguish flow signatures from static background [32–36].
The phase information available within OCT signal allows for the computation of motion contrast . Doppler OCT was the first model utilizing this concept. Unlike Doppler OCT that directly calculates the phase difference (Doppler shift) between A-scans, a more phase sensitive approach by measuring the variance of phase changes was proposed so as to detect a larger dynamic range of flow velocities and be independent of vessel orientation, i.e. minimizing the dependence of Doppler angle in the measurement. Variance methods to contrast motion use either sequential pixel, A-scan [29, 38, 39], or consecutive B-scan measurements [40, 41] to calculate and contrast the flow signal, where the phase measurements between consecutive B-scans are not only able to acquire the imaging of an entire frame, but also allow a much longer separation time between two measurements to improve the detection sensitivity to the lower blood flow speeds [40, 41]. The phase variance measurement based on consecutive B-scans can be formulated as the following equation:
where N represents the repetition number of B-scans acquired at the same location, and indicate the phase value and phase difference in the i-th B-scans at lateral location x, depth position z, and time t, T is the time interval between two consecutive B-scans, and i is the index of the i-th B-scan.
Starting from 2007, Fingler et al. developed a motion contrast technique based on phase variance approach to visualize the vasculature in zebrafish , in the retinal and choroid of the mouse , and then adapting the technique for human retinal imaging . Later on, Kim et al.  built a phase-variance OCT system with complementary metal oxide semiconductor (CMOS)  line detector, in which a superluminescent diode with an 855 nm central wavelength and a full width half maximum of 75 nm was used as the light source. The axial resolution was 4.5 µm in the retina, and the lateral resolution of the system at the retina was estimated at 10 to 15 µm. The image acquisition A-scan rate was at 125 kHz and therefore was capable of performing a larger field of view for imaging human retinal circulation. Furthermore, with the correction of bulk motion of the eye in lateral and axial directions, the phase noise in the low signal-to-noise region was markedly reduced. The angiograms from phase-variance OCTA of patients with dry age-related macular degeneration (AMD), with exudative AMD, and with non-proliferative diabetic retinopathy (PDR) were further demonstrated . Areas of geographic atrophy and choroidal neovascularization image by fluorescein angiography (FA) were also depicted by phase-variance OCTA as well as the regions of capillary non-perfusion from diabetic retinopathy, indicating the potential applications of phase-variance OCTA in ophthalmology . In addition to SD-OCT based phase-variance approach, swept-source based phase-variance OCTA system was also demonstrated by Motaghiannezam et al.  and Poddar et al. , enabling the visualization of vessel networks in the choroid. Using a high speed (100 kHz A-scan rate), 1 µm swept-source OCTA system equipped with a computationally efficient phase stabilization approach , the presented system showed higher sensitivity, reduced fringe wash-out for high blood flow speeds, deeper penetration in the choroid compared to its SD-OCT based counterpart, and allows generation of capillary perfusions in choriocapillaris and choroid (Sattler’s layer and Haller’s layer) in both normal and diseased eyes.
Phase-signal-based OCTA techniques described in Section 3.1 detect the flow signal by measuring the Doppler shift or the variance of phase signals caused by moving scatterers, e.g. moving red blood cells within patent vessels. Doppler OCT enables the detection and mapping of blood flow in various tissues noninvasively, however, the technique also suffers from an angular dependence of the measured blood flow and insensitive to the flow perpendicular to the scanning beam. Phase-variance OCT minimizes the angular dependence to the vessel orientation by measuring the variance of the detected phase shift, providing an opportunity to detect the blood flow perpendicular to the OCT scanning beam. Nevertheless, to reduce the phase noise and extract actual flow signal, a motion correction or phase compensation method is needed, which usually is computationally expensive. To overcome these disadvantages, researchers sought for solutions by exploring the other part of OCT signal – intensity or amplitude component.
In 2005, Barton and Stromski developed an alternative method to detect blood flow signal by measuring the speckle changes in OCT signal based on a TD-OCT system to mitigate the angular dependence issue of Doppler OCT . It is well-known that time-varying speckles due to particle motion within sample carry salt and pepper like noise that often degrades the quality of acquired images as well as actual information about tissue structure and flow . Derived by Goodman that the first order of laser speckle statistics describes speckle at a point while the second order statistics contains the joint statistical properties of speckle at two or more points as well as the information about the motion of scatterers [47, 49]. It has been found that the temporal speckle fluctuations at a point show a dependence on the mean velocity of the scatterers. Besides, the ratio of high to low frequency components of the power spectrum of speckle intensity has been shown to be a good indicator of average velocity of blood flow in skin . Coining this concept to OCT signals , Barton and Stromski hypothesized that the fluid flow in OCT images could be measured by treating sequential pixels as a sampling of time varying speckle pattern. Using the amplitude information in the OCT signal only, flow signals were obtained from four sequential axial pixel blocks that were averaged to mitigate the effects of noise and the single-pixel speckle caused by wide-angle multiple scattering. The authors successfully visualized the flow image in an in vitro tube phantom and in vivo hamster skin . This was the first application of using speckle analysis in OCT images to acquire a depth-resolved flow signals.
Not surprisingly, such speckle variance concept would be equally applicable to the SD-OCT signals. In 2008, Mariampillai et al. developed an SD-OCT based speckle variance imaging technique to visualize microcirculation and found that speckle variance OCTA was able to detect vessel size dependent vascular shutdown and transient vessel occlusion during photodynamic therapy .
The inter-frame speckle variance signal can be acquired by scanning the same transverse location multiple times and using following equation:
where N (equals 3 in Mariampillai’s study) represents the repetition number of B-scans at the same location, indicates the intensity value in i-th B-scans at lateral location x and depth position z, and is the average of the intensity value over the same set of pixels. An optimized method was later proposed by the same group that by adjusting the number of repetition at one location or the field of view, the image contrast and signal-to-noise ratio for visualizing microcirculation in tissue can be improved with both low and high bulk motion .
Motaghiannezam et al. further formulated a theory to contrast moving cells from static areas based on logarithmic intensity-based contrasts, variance, and differential logarithmic intensity variance . They validated their theory with a swept-source OCT based system (central wavelength at 1060 nm) and were able to visualize retinal capillary without compensation algorithms and extra optical modules . A simplified speckle-variance approach with two repetitions based on a 1060 nm Fourier domain mode locked (FDML) swept-source OCT was demonstrated by Blatter et al.  Flow signals were extracted by calculating the square of the intensity difference between successive B-scans. With the capability of reaching 1.68 MHz A-scan rate, the authors presented the vascular network centered at the fovea with a 48° wide field of view without the need of image stitching. Recently, a 1060 nm swept-source based speckle variance OCTA was proposed by Xu et al. . The system operated at an A-line rate of 100 kHz. The axial resolution was 6 µm in tissue, and 7.3 µm at the retina. Three repeated acquisitions at each B-scan location were acquired. The scan area was sampled in a 350 (A-scans) × 350 (transverse location) grid. With the help of graphics processing unit, the proposed system was able to display the blood flow in human retinal capillary networks in real time . The proposed device was used to detect the vessel networks around the foveal avascular zone (FAZ) and in the radial peripapillary capillaries in the peripheral region around the disc and the detected vessel networks were comparable to histological images [56, 57].
Apart from speckle-variance approach, Schmoll et al. imaged the parafoveal capillary network in human retina by extracting flow signals directly from the OCT tomogram based on the observation that blood flow generated higher backscattering signals compared to the surrounding retinal tissue . Motion artifacts were minimized and a dense sampling rate was achieved with a high speed SD-OCT system (A-line rate of 128 kHz). Since the flow signals were extracted directly from the OCT structural signals, the generated vascular enface images were free from shadow and projection artifacts (will be discussed in Section 4). However, it also suffered from low contrast and artifacts within tissue with stronger scattering characteristics.
Observing the phenomenon that vascular region and its vicinity showed stronger speckle signals compared to static tissue, in 2011, Jonathan et al. and Enfield et al. proposed a correlation mapping method that detects flow signal by calculating the correlation of OCT signals between adjacent B-scans [59, 60]. As flow regions showed lower correlation and the static tissues showed higher correlation, it is possible to distinguish micro-vasculatures from static tissues through estimating its correlation with a set threshold. The flow signal was acquired by cross-correlating a grid from frame A () to the same grid from frame B () acquired at the same transverse location using the following equation :
where M and N indicate the grid size and is the mean intensity value within the grid. The same notation as we showed before, indicates the intensity value in i-th B-scans at lateral location x and depth position z. Multiple B-scans were captured at the same transverse location (Jonathan et al. acquired 8 B-scans for mouse brain in vivo through a cranial window, while Enfield et al. adjusted to 2 B-scans for human volar forearm). The grid is then shifted across the entire B-scan and a two-dimensional (2D) map is generated. The correlation value ranges from −1 to 1, where 0 indicates weak correlation while −1 and 1 indicate strong correlation. The grid size used in the study was arbitrarily chosen for optimal image quality. Larger grid size leads to higher signal-to-noise ratio, but may also result in longer processing time, blurring effects, and loss of smaller vessels. In its first demonstration, correlation mapping showed the capillary pattern in a multi-layered capillary tube phantom and the capillary networks in mouse brain and human volar forearm.
Later, McNamara et al.  employed the same correlation mapping technique to a full-field OCT to perform non-scanning en face flow imaging from pairs of en face images. In contrast with most OCT approaches, full-field OCT directly takes 2D en face images with megapixel cameras . Since the large depth-of-field information is omitted, full-field OCT is able to provide 2D or 3D images with resolution of 1 µm, matching the cellular resolution . The study demonstrated the first application of correlation mapping to full-field OCT to provide in vivo functional imaging of blood vessels .
In 2012, Jia et al.  proposed a split-spectrum amplitude-decorrelation angiography (SSADA) algorithm to extract flow signal and distinguish functional vessels from static tissues based on the same concept of time-varying speckle effect. Opposite to the correlation mapping method, SSADA algorithm generates the flow signal by measuring the decorrelation signal between two consecutive B-scans. They first split the full OCT spectrum into several narrower bands. After splitting the spectrum, the data in each narrower bands were processed separately to generate several flow images for the same B-scan location. Finally, the decorrelation signal was calculated by subtracting the average of the narrower-band flow images from 1, as shown in the following equation:
where M is the number of split-spectrums, N indicates the repetition number of B-scans at the same location, and indicates the intensity value in i-th B-scans of m-th split-spectrum at lateral location x and depth position z.
Split spectrum method has been shown to improve the signal-to-noise ratio of flow detection [64, 65]. However, the resolution in the axial direction is reduced, typically ~3 times lower resolution compared with conventional decorrelation approach. On the other hand, with a reduction of axial resolution, it diminishes the sensitivity to pulsatile bulk motion in the axial direction. The same is also true to the sensitivity of detecting flow though. By increasing the number of split-spectrums, the decorrelation signal-to-noise ratio can be improved without increasing the scan acquisition time. The optimized number for split-spectrum was reported to be 9 [65, 66].
It has been demonstrated that SSADA algorithm is able to detect retinal vessels and capillary networks of human retina in the macular and optic disc regions, and used for differentiating diseased eyes from normal controls for AMD and glaucoma, and other retinal pathologies [67–74].
The representative of complex-signal-based OCTA technique is optical microangiography (OMAG), proposed first by Wang et al. in 2007  and then refined into the current implementation in 2010 [75, 76]. The rationale of including both phase and amplitude components in the OCT signal is to improve the sensitivity of flow detection. In order to be able to detect the flow signal where the induced change in optical signal only happens in the phase component meanwhile to be less vulnerable to the bulk motion, a phase compensation method was applied before to reduce the phase variation induced by pulsatile bulk motion [77, 78].
The flow signal based on OMAG algorithm is calculated by subtracting consecutive complex signals, as shown in the following equation:
where N indicates the repetition number of B-scans at the same transverse location, and indicates the complex signal (having both intensity and phase values) in i-th B-scans at lateral location x and depth position z. As indicated in the equation, the final flow intensity is obtained by calculating the average of the absolute values of the complex signal differences in each B-scan pair. In its first demonstration, the number of B-scans at each transverse location was set to 4, which was determined based on the trade-off between scanning time and number of B-scan repetitions (as averaging with more repetitions provides higher signal-to-noise ratio), and achieved high flow image quality. It was recently reported that 2 B-scans at the same location would also be able to detect capillary network with good image quality .
With the use of Hilbert transformation, OMAG is also able to discriminate the directions of the moving blood cells relative to the incident OCT beam direction , and therefore, OMAG can further provide the flow image either with or without directional information.
Optical microangiography has been shown capable of detecting microcirculation in mouse brain , human skin tissue beds , and human retina [76, 81, 82]. With its high sensitivity in detecting retinal capillaries, choroiocapillaries, and radial retinal capillaries, it was later demonstrated being capable of differentiating diseased eyes from normal eyes, and may add insightful information of disease developments [77, 83–87].
An eigen-decomposition-based method was demonstrated in 2011 by Yousefi et al.  in order to minimize the false-positive flow signals resulted from the tissue motion for complex-signal based OCTA techniques. As a model based statistical analysis approach, the OCT signal at each voxel was modeled as a superposition of three independent components: tissue signal (the clutter component, coming from the stationary and slowly moving tissue structures), hemodynamic signal (the blood component, mostly coming from moving red blood cells), and noise (additive white noise component, coming from system noise and shot noise). Due to its best mean-square approximation of the clutter, eigen-regression filters could theoretically provide maximum clutter suppression, and thus could successfully remove the bulk motion while preserving the flow information. The proposed method showed clear micro-vascular networks of in vivo human skins and mouse ears, and the results outperformed the flow images using phase-compensation method or static high-pass filtering to remove the bulk motion . This was the first demonstration that applied a model based statistical analysis of eigen-decomposition for flow signal extraction in optical imaging devices. The proposed eigen-decomposition method was later improved in 2014  – a multiple signal classification (MUSIC) method for flow signal detection. The MUSIC method was a super-resolution spectral estimation method based on the principle of orthogonality. By applying previously developed eigen-decomposition , the MUSIC method was capable of decomposing the backscattered OCT signal into orthogonal basis functions and distinguishing the flow signal caused by moving RBCs from static tissue and noise. The flow signal obtained using MUSIC approach enables the visualization of functional microvascular networks within skin tissue in vivo. Perhaps, the more important is that the extracted flow signals contain intact information of moving particles, therefore is amenable to provide quantifiable information about the dynamic flow, for example it has been shown that the extracted flow signal is correlated with flux information [89, 90].
As mentioned in the correlation mapping OCTA images, a larger correlation window size provides higher signal-to-noise ratio in the resulted OCTA images, however, it also creates a blurry flow image, i.e. the resolution is greatly reduced. In order to solve the blurry side effect due to increased correlation window size, Chen et al.  proposed in 2015 an imaginary part-based correlation mapping OCTA to reconstruct microcirculation maps with higher flow image quality and small vessel detection sensitivity. In the proposed method, a complex analytic signal in the space domain was obtained by performing Fourier transform in the wavenumber domain. The extracted imaginary part of an OCT signal was then correlated between consecutive B-scans to compute the flow signal. The flow signal was acquired using the following equation:
where M and N indicate the grid size and is the mean complex value within the grid. The same notation as we showed before, indicates the intensity value in i-th B-scans at lateral location x and depth position z. The same as intensity-based correlation mapping OCT, the grid was shifted across the entire image to obtain a 2D correlation map.
Similar concept to the OMAG technique, since the imaginary part-based correlation mapping method includes both intensity and phase, it is able to detect the phase changes caused by the displacements of curve shaped RBCs, which does not change the intensity. The imaginary part-based correlation mapping OCT is more sensitive to motion and can provide improved sensitivity for extracting blood flow information in small vessels compared with intensity-based correlation mapping OCT. The proposed method was tested with in vitro phantom and in vivo mouse ear. Their results detected more small blood vessels, which were missed by the conventional correlation mapping OCT method. This is the first study that introduced phase information into conventional intensity-based correlation mapping to increase the sensitivity for small vessels and signal-to-noise without increasing the grid size.
A phase gradient angiography (PGA) method was recently proposed in 2016 by Liu et al. in order to use the phase component in the OCT signal to map the microvasculature in tissue without the correction of bulk motion and laser trigger jitter induced phase artifacts and can be applied to both SD-OCTA and SS-OCTA systems . Similar to Doppler OCT, the phase difference () at location between two consecutive B-scans was calculated directly by subtraction:
where is the time interval between the two repeated B-scans. In order to extract the phase shift induced only by RBC movements, the calculated phase difference was modeled as the combination of RBC movement (), phase artifact originating from sample movement and equipment vibration (), and phase noise ():
As the major sources of phase artifacts () came from (1) the bulk motion from subjects’ involuntary movement (especially in SD-OCT), and (2) the phase artifacts caused by the mechanical scanning device used for wavelength sweeping (especially in SS-OCT), the bulk motion is not dependent on the axial direction while the trigger jitter induced phase shift is a linear function along the axial direction. Thus, its gradient will be a small constant value and can be neglected. The proposed PGA method detected the phase shift induced by RBC movements by taking gradient of the phase difference along the axial direction. Therefore, the flow signal calculated based on PGA method could be simplified as the following equation, eliminating the false phase difference induced by bulk motion:
The gradient of the phase difference could further be combined with other method to improve the flow contrast, for example combining with amplitude information or split-spectrum method.
The authors compared the proposed PGA method alone, PGA method combined with split-spectrum (SSPGA), PGA method combined with amplitude and split-spectrum (SSAPGA), and their previously developed SSADA algorithm by subjectively evaluating the generated angiograms and objectively measuring quality of the angiogram via a customized signal-to-noise ratio metric, which evaluated the flow image quality by measuring the ratio of the average of the signal intensity in the tissue region over the standard deviation of the noise region. Based on a phantom study and images from a normal eye, it was reported that SSAPGA gave better performance in terms of signal-to-noise ratio and contrast, where no significant difference was detected among SSPGA, SSADA, and SSAPGA. With the help of split-spectrum, the performance of PGA could be improved by more than 2 times.
OCTA generates 3D data sets containing microvasculature flow information. When it comes to flow image visualization and interpretation, it is usually presented as an en face angiogram. OCTA angiograms are obtained by performing maximum or mean flow intensity projection along the axial direction, where maximum projection retains the flow signal with the highest intensity value and mean projection calculates the average flow signal intensity within a specific range. With the help of segmentation software, OCTA angiograms can focus within certain range or within a specific tissue. Take retina for example. Boundaries of retinal layers can be identified via either auto- or semi-auto segmentation software, and with the identified boundary information: OCTA angiograms from superficial retinal layer, which is defined from the outer boundary of retinal nerve fiber layer (RNFL) to the outer boundary of inner plexiform layer (IPL); deep retinal layer, which is defined as the ocular tissue between the outer boundary of IPL and the outer boundary of outer plexiform layer (OPL); avascular layer, which is defined from the outer boundary of OPL to the outer boundary of the retinal pigment epithelium (RPE) and is the layer without vascular networks in normal subjects (as shown in Fig. 3). Being able to evaluate the vasculatures from an isolated depth-layer, OCTA angiograms will provide more visual information and better understanding of the changes in the vasculatures related to the diseases.
Projected OCTA flow en face images, i.e. OCTA angiograms, enable the visualization of vascular networks in individual retinal layer and tissues. However, when visualizing the angiograms from the deep retinal layer or from the choroid, it is observed that the vasculatures from the superficial retinal layer also appear, for example in Fig. 3(E) that in reality should be avascular. The false positive flow signals in the deep layers are called projection artifacts, which may limit our ability to visualize vasculature in the deeper tissue and mislead the interpretation or evaluation of the changes in the vascular networks, especially in the tissues are known to be avascular.
The projection artifacts result from the multiple scattering effects after the incident OCT beam interacts with functional blood vessels. When the incident OCT beam hits moving RBCs, the light beam can be reflected, refracted, absorbed, or passes the vessel. The reflected OCT beam will be captured by the detector and forms the OCT and OCTA signal. On the other hand, the light being refracted or passing through moving blood cells can further encounter tissue components below the vessels. When the underlying tissue is hyper-reflective, such as the retinal pigment epithelium (RPE), the light (that passes through the overlaying vessels already) will be backscattered, and inevitably generates false or ghost blood flow signals on the deeper tissue, as mentioned by Spaide et al.  Besides the multiple scattering effect, with the three-dimensional nature of OCT, the fluctuating shadows from flowing blood cells in the superficial vessels also will cast extra flow signals to the deeper vascular networks, and therefore generates false vessel networks.
In order to minimize the projection artifacts and reveal the actual vasculatures in the outer retinal avascular space (ORAS) for choroidal neovascularization analysis, Zhang et al.  proposed a model to mimic the angiogram in the ORAS, which was defined as a space between the outer boundary of plexiform layer (OPL) to the Bruch’s membrane. Their hypothesis was that the angiogram of ORAS can be viewed as a combination of the actual flow signal in the ORAS and the projection artifacts from the superficial retinal vasculature, as expressed in the following equation:
where indicates the angiogram constructed from the detected flow signals in the ORAS, indicated the true flow signal in the ORAS, indicates the flow signal in the retina, and is a scaling factor to properly scale the level of retinal flow signals. Applying a logarithm operation, the equation can be rewritten as:
As a consequence, the true flow signals in the ORAS can be acquired by subtracting the retinal flow signals from the detected flow signal in the ORAS with a proper scaling. For most pathological retinal cases, the structural pathological change may precede the development of neovascular growth, and therefore, the retinal structural information should also be taken into account in order to improve the accuracy of projection artifact removal. Hence, the final equation is displayed below:
where denotes normalization operation, which normalizes the retinal image into a range between 0 and 1. The proposed method successfully removed the projection artifacts in the ORAS, demonstrated the avascular layer in a normal eye, and revealed the outer retinal neovascularization in an eye with Type 1 choroidal neovascularization (CNV). Similar method was also reported by Liu et al.  The authors removed the projection artifacts in the deeper retinal layer by directly subtracting the inner retinal angiogram (from inner limiting membrane to OPL) from the outer retinal avascular layer without intensity value scaling, and a saliency algorithm was applied after the subtraction to detect the CNV region for further neovascularization quantification.
Different from the angiogram subtraction methods, Zhang et al. proposed a projection-resolved algorithm to remove the projection artifacts in OCTA by directly dealing with individual A-scans . The authors observed from individual A-scan and noticed that the intensity of the false flow signals are almost always weaker than the actual flow signals. Based on this observation, they developed a method to search successive higher peaks in the normalized decorrelation value from the end of each peak toward to the deep tissue along the axial direction. Unlike the angiogram subtraction methods, the projection-resolved algorithm eliminated the projected signals in the cross-sectional images less aggressively, and thus was able to preserve vessels hidden under big retinal vessels; besides, it did not require the angiogram from the superficial retinal layer in priori. It was demonstrated that projection-resolved OCTA was able to preserve the continuity of vessel networks and capillary plexuses after saliency algorithm processing.
Optical coherence tomography angiography enables the visualization of microvasculature in tissue beds in vivo in a non-invasive fashion, and has demonstrated its ability to detect morphological changes in vasculatures related to disease progression and provide functional vessel information with finer resolution compared with conventional methods, such as fluorescein angiography (FA) and indocyanine green angiography (ICGA). OCTA has shown promising results in qualitative assessment, however, when it comes to quantitative analysis, the relationships between flow signal intensity and actual flow volume, velocity, flux, or perfusion still remain unclear, despite the effort has been paid recently. Based on Doppler principle, several studies were conducted to determine the relationship between OCT signal intensity and flow speed [97–99]. Liu et al. showed that even though the Doppler OCT signal intensity showed a strong dependence to the Doppler angle, it was able to quantify flow speed when the flow rate was within a certain range, dependent on the adjacent A-scan time interval . Szkulmowski et al. proposed Joint Spectral and Time domain OCT to estimate flow velocities more accurately by incorporating information from both time and optical frequency domains, and found a linear relationship between OCT signal and theoretical velocity within detectable velocity range [100–102]. Nevertheless, in order to extract the actual blood flow quantity (either flow volume, velocity, flux, or perfusion in tissues) from OCTA techniques, the acquired OCTA signals need to retain the complete blood flow information. For this reason, variance-based approaches (phase-variance and speckle-variance OCT) may not be suitable for this purpose, therefore are less amenable to provide the quantifiable information as to flow dynamics.
Tokayer et al.  tested the relationship between SSADA decorrelation signal and blood flow velocity using an in vitro phantom experiments. Whole blood was used in this study to mimic in vivo retinal imaging. It was found that SSADA decorrelation signal had a linear relationship with flow velocity when the time interval between two consecutive A-scans ranged from 56 µs to 280 µs (translating to a frame rate from ~3,750 fps to ~17,857 fps). When the flow velocity equaled 2 mm/s, the SSADA decorrelation signal was saturated, meaning that the SSADA decorrelation signal value would be independent to the velocity with A-scan time interval below around 500 µs (i.e. < 2,000 fps). Clearly, the commercial grade OCTA systems currently available are not capable of such frame rate during imaging.
Recently, Choi et al.  used an in vitro microfluidic flow phantom to investigate the relationship between OMAG signal and flow parameters. Intralipid with concentration varying from 1% to 4% was used to mimic blood flow with various concentrations with velocity ranged from 1 mm/s to 4 mm/s with 1 mm/s increment each time. A simplified analytic model was proposed to simulate the OMAG signal that the difference of complex OCT signal could be viewed as the product of concentration (i.e. how many particles within one scanning voxel) and flow velocity (from amplitude decorrelation), and therefore the value of the calculated OMAG flow signal represented the concept of flux – number of particles passing through over a unit cross-section within a unit time. From both the simulation and experimental results, two conclusions were drawn (as shown in Fig. 4): (1) OMAG signal magnitude has a linear relationship with flow velocity within a certain velocity range which is dependent on the OCT B-scan rate. When the time interval between consecutive B-scans is 50 µs, the OMAG signal is approximately linear with flow velocity ranging from 0.3 to 4 mm/s, and (2) OMAG signal magnitude increases as the Intralipid concentration increases.
The raster scanning protocol in the current commercial SD-OCTA systems acquires the repeated B-scan after finishing the entire B-scan. Therefore, the time interval between two consecutive B-scans, or between two A-scans from the same location, is around 2 to 4 ms with an A-scan rate of 70 kHz and 300 sampling points in one B-scan. At this time scale, the relationship between OCTA signals and flow velocity reaches a plateau, and therefore the detected OCTA signal value is not sensitive to the change in flow velocity regardless of which OCTA technique is used. Although the flow signal is independent to flow velocity, OMAG flow signal may still be related to the concentration of red blood cells as mentioned above. The saturated relationship between OCTA flow signal and flow velocity may be improved by using an M-mode scan protocol, which repeatedly captures multiple A-scans at one location before the probe moves to the next sampling location, or using an ultrafast OCT system that can provide a shorter inter-frame time interval.
In addition to correlating OCTA signal value with the actual flow parameters, other quantitative parameters to indirectly assess blood flow changes from OCTA angiograms were also developed. For example, flow index and vessel density were proposed by Jia et al. [68, 105] to objectively measure the average decorrelation values (as claimed to correlate with blood flow velocity ) and the percentage area occupied by vessels in the region of interest based on SSADA angiograms. Similarly, Chen et al.  used flux index, vessel area density, and normalized flux to quantify OMAG flow signals. Chu et al.  developed a comprehensive metrics to quantitatively assess and describe OCTA angiograms based on vessel morphology. The five metrics are: vessel area density, vessel skeleton density (assessing the functional vascular networks by calculating the percentage of area occupied by vessel but not being biased by vessel diameter), vessel diameter index, vessel perimeter index, and vessel complexity index (assessing tortuosity of the vessels). All the parameters have been demonstrated to be correlated with lesion and defected regions in retina, which may provide further information and help understanding the disease mechanisms [68, 87, 106–108].
As a functional extension of OCT technology, OCTA has rapidly translated to clinical ophthalmology since its first demonstration. Fluorescein angiography (FA) and indocyanine green angiography (ICGA) have been the mainstays for evaluating functional blood flow involved in various retinal and choroidal diseases by providing a series of 2D en face image captured at various time points . Because all the functional vascular information is projected onto a 2D image, FA and ICGA are not able to provide depth information and require sufficient experience to interpret the angiograms and distinguish the location of vessels. Besides, the need of intravenous dye injection, the long acquisition and waiting times, and the potential side-effects of the dyes make traditional FA and ICGA less desirable and less practical in the busy clinical settings. In contrast, OCTA is fast, safe, non-invasive and cost-effective to provide high-resolution and depth-resolved retinal blood flow information in only a few seconds. With the aid of retinal layer segmentation and post-processing, OCT angiograms at various depths can be properly extracted and displayed.
With a short period of clinical translation, OCTA has shown its ability to present vascular defects comparable to and correlated with the defects imaged by FA and ICGA in diabetic retinopathy (e.g., Fig. 5 top row) [69, 72, 74, 110], retinal vein occlusion [84, 111–114], retinitis pigmentosa [84, 115], as well as to detect the changes in the choriocapillaries and choroid by polypoidal choroidal vasculopathy (e.g., Fig. 5 bottom row) , choroidal neovascularization caused by age-related macular degeneration [69, 85, 116], or the changes in vascular distribution before and after anti-VEGF injection [117, 118], and to differentiate vascular dysfunction between normal and glaucomatous eyes [70, 86, 87, 119, 120]. Its quantitative parameters, for example vessel area density, also showed significant associations with visual field defects and disease severity in glaucoma. Recently, wide-field OCTA imaging has been developed either via a real-time auxiliary line scan ophthalmoscope (LSO)  or via montaging in the post-processing stage. Wide-field imaging will provide more detailed microvasculature in the peripheral regions, where it is believed to have some early defects taking place before hitting the central vision . Even though OCTA is not able to detect leakage in the retina, OCTA may still provide further insightful information to help understand the pathophysiology of retinal diseases. Having OCTA as one of the clinical standard routine may help clinicians and physicians monitor the progression of diseases and guide therapeutic treatment at its earliest possible time point.
In dermatology, OCT was first applied to skin imaging in 1997 , and has demonstrated its potential to identify skin structures such as the dermal-epidermal junction (DEJ) and sweat ducts in its early images. Later on, OCT was applied to the diagnosis of non-melanoma skin cancer and has been shown to improve the diagnostic accuracy of basal cell carcinoma . Recently, with the development of OCTA, it allows the visualization of in vivo blood vessels and their distribution with specific lesions and provides additional functional information within dermis for up to a depth of 1.5 – 2 mm (Fig. 6) [124–126]. OCTA is capable of demonstrating the vascular networks of two distinct horizontal plexuses in the dermis in normal skin [80, 124]; detecting the angiogenesis, finding arborizing vessels and a loose and more vascularized dermis between tumor nests in basal cell carcinoma (BCC), which are important for providing diagnostic clue to BCC [124, 127–129]; visualizing a variable vascular pattern and the densely clustered red dots in the superficial dermis in melanoma ; identifying the changes of the blood flow caused by inflammatory skin diseases, monitoring the chronic wounds and scars formation, and assessing of burn injury [131–134]. Themstrup et al. further validated the use of OCTA for imaging of skin blood flow by comparing with clinically accepted technologies, chromametry and laser speckle contrast imager (LSCI), and showed that OCTA was able to reliably image and identify morphologic changes in the vascular network consistent with the induced physiological changes of blood flow . OCTA may improve the diagnostic accuracy of skin diseases, be helpful to identify the individual tumor risk, and aid in the early diagnosis of skin cancer.
In addition to ophthalmology and dermatology, OCTA also showed its ability in neuroscience and brain imaging (Fig. 7) . The first demonstration of FD-OCT based OCTA technique was made in 2007 on a rodent cerebrovascular model using OMAG technique . With light sources of 1300 nm central wavelength , the OMAG technique successfully visualized pial vessels with the scalp left intact although capillaries were not distinguished clearly because of the sensitivity limitation. With the improvement of the system and the utility of high-pass filtering of time series of OCT signals, real-time imaging became available, which further enabled the longitudinal measurements of meningeal vascular responses to an insult and the responses in the cortex , observations of the changes in vessel diameters and connections in the cerebral cortex during hypercapnia through a cranial window  and monitoring microcirculation responses during hypoxia through an intact skull . OCTA was also used to quantify cerebral blood flow (CBF), to measure velocity changes in the rat cortex [141–144], and to assess the red blood cell flux in capillaries [145, 146]. Besides monitoring and measuring vasculature in brain, OCTA techniques were able to monitor vasodynamics after stroke [147, 148], detect ischemia regions, and capture the capillary response to a traumatic brain injury (TBI) in the cortex . Although most of the experiments and validations in neuroscience using OCTA techniques are based on rodent so far, the results are still promising that OCTA may be able to visualize the microvasculature and hemodynamic responses in the brain and may aid in the understanding, diagnosis, and monitoring of brain injury.
The development of OCTA has extended, and enriched the potential applications of OCT technique. The capacity of OCTA for visualizing the micro-vascular networks within tissue beds in vivo non-invasively and for providing insights into the changes in blood flow related to disease progression like AMD, glaucoma, and melanoma have been demonstrated. However, further advancements of the OCTA are still needed to equip the technique with more functions to broaden its scope for clinical practice.
Current version of OCTA is developed based on FD-OCT, either using SD-OCT or SS-OCT. With an acquisition rate ranging between 70,000 A-scans/s to 100,000 A-scans/s, 3D OCTA images are achievable in clinic. The scanning protocol of OCTA image is determined by the acquisition time a subject can tolerate not to blink or move, which is typically around 3 – 6 seconds. To strike a balance between sampling density and number of B-scan repetition, 300 and 500 A-scans are acquired in one B-scan with 4 repeats and 2 repeats for 3 × 3 mm2 or 6 × 6 mm2 scanning area, respectively, in the commercial systems. An OCTA system with faster acquisition speed is needed in order to be able to scan over a wider area while keeping the similar sampling density and B-scan repetition, or retaining the same sampling density but increasing the B-scan repetition – which allows a longer time interval between B-scan pairs so that the detection of slower flow signal becomes feasible. Although faster imaging speed of 400 kHz SS-OCTA has been demonstrated that may meet the requirements of improved imaging FOV and detecting the slower blood flows, such prototype device is only available in specific research laboratory at the current stage of development [116, 152, 153].
In addition to the faster acquisition speed, a clinical OCTA system using the light source centered at a longer wavelength of 1050 nm, as opposed to 800 nm range wavelength for ophthalmology applications, is also required. Incident light beam with longer wavelength can penetrate deeper, reach deeper tissue, and therefore may be able to provide flow information in the deeper tissue, such as the choriocapillaris and choroid . The same is true for dermatology applications where a central wavelength range of 1,680 nm as opposed to the current use of 1300 nm wavelength should provide more opportunity for the light to penetrate deeper into the dermis. Therefore, the future development of the systems that implement application-dependent optimal wavelengths is required, leading to more insightful information to aid in the early diagnosis, monitoring and therapeutic treatment of various diseases that have vascular involvement.
Motion correction is another active area of research in OCTA in order to eliminate false-positive flow signal caused by tissue’s bulk motion and reveal actual flow information. Motion correction can either be done during the image acquisition with active motion tracking system  or be achieved using post-processing to exactly align and register each A-scan or B-scan pairs when calculating the flow signals by cross-correlation, phase-correlation, or quantitative 3D-OCT motion correction method . Although imaging with an active motion tracking system generates almost motion-free OCTA images, the scanning probe has to redo or resume the scan if blink or tissue movement is detected, and as a consequence it results in a longer imaging time, which may have an impact on the patient compliance. On the other hand, post-image processing to remove tissue motion may create additional unwanted artifacts. A motion correction method that is able to successfully remove tissue bulk motion and generate motion-free image data without increasing image acquisition time or adding potential artifacts is clearly necessary, in terms of both clinical and pre-clinical applications. In addition to motion correction methods, an improved projection artifact removal method to extract actual flow information hidden in the projected artifacts will also help provide more information of the changes in the tissues.
The quantification of OCTA flow signal remains a big challenge. A few studies investigated the correlation between the calculated flow signal intensity and blood flow quantities were discussed in this review paper, however, none found a satisfactory relationship between the actual dynamic flow and the practical measurements. As mentioned in Section 6, in order to be able to infer the flow signal intensity to actual blood flow measurement, the derived OCTA flow signal has to carry intact blood flow information. As a model based statistical approach, Eigen-decomposition method models the composition of the detected flow signal based on statistical analysis, and therefore has potential to obtain the flux information of red blood cells. A detailed and more systematic investigation is needed to prove the correlation.
Last but not the least, the field of view of OCTA with desired A-scan sampling density and B-scan repetition is currently severely limited. In diabetic retinopathy, more evidence has shown that the early changes in blood flow or vessel morphology happen in the peripheral region, and may not be noticed if the scanning area only covers 6 × 6 mm2 (approximately ) area of central fovea. A wide field of view imaging system or a robust vascular image montaging algorithm is critical to enable the visualization of functional vascular networks in the peripheral region (with a viewing angle of at least ~100°).
Scientists and engineers dedicate themselves to search for solutions that are capable of observing blood flow dynamics in the human body tissue non-invasively. OCTA provides 3D vascular networks within microcirculatory tissue beds in vivo with microscopic resolution through detecting the changes in OCT signals due to moving red blood cells without the need of intravenous dye injection or biopsy. With the ability to evaluate dynamic changes in the tissue bed over time and without interfering with the tissue, OCTA has shown its potential in ophthalmology, dermatology, neuroscience, and many other realms for the detection of early changes in vessel distributions in tissue, identifying differences in blood flow caused by diseases, and monitoring the effects and responses before and after treatments. OCTA may give us additional and insightful information of the pathophysiology as well as the dynamic progression or regression of disease development. It will not only help in a better understanding of the pathology, but also in the development of new therapeutic treatment strategies, ultimately benefiting the health care system.
National Institutes of Health contracts NEI R01-EY024158 and NHLBI R01-HL093140, and Carl Zeiss Meditec Inc.