With existing optical imaging techniques three-dimensional (3-D) mapping of microvascular perfusion within tissue beds is severely limited by the efficient scattering and absorption of light by tissue. To overcome these limitations we have developed a method of optical angiography (OAG) that can generate 3-D angiograms within millimeter tissue depths by analyzing the endogenous optical scattering signal from an illuminated sample. The technique effectively separates the moving and static scattering elements within tissue to achieve high resolution images of blood flow, mapped into the 3-D optically sectioned tissue beds, at speeds that allow for perfusion assessment in vivo. Its development has its origin in Fourier domain optical coherence tomography. We used OAG to visualize the cerebral microcirculation, of adult living mice through the intact cranium, measurements which would be difficult, if not impossible, with other optical imaging techniques.
© 2007 Optical Society of America
Optical coherence tomography (OCT) [1, 2] is a non-invasive, three-dimensional (3-D) imaging technique, capable of optical ranging within a highly scattering sample, such as biological tissue, with visualization of microstructures at a resolution approaching that of conventional histology. The technique, based on the optical scattering properties of tissue, is feasible because most biological tissues have a sufficient number of complex microscopic scattering elements to produce good contrast for OCT images. Time-domain OCT (TDOCT) was the first version of OCT described in the early 1990s . As a result of improvements in the light source, the interferometer design, and the beam delivery systems, TDOCT is now being widely used to characterize tissue microstructures both in clinical studies and basic research laboratories [4–6]. It was later recognized that OCT imaging could be performed in the frequency domain (FD) without the requirement to scan the optical delays to perform the ranging as in TDOCT , thus allowed for faster imaging. Importantly, the detection sensitivity is also improved significantly . Such features are critical for the investigation of dynamic biological systems where the speed of data acquisition is vital. Over the past decade, particularly after the discovery of FDOCT, different modes of operation have emerged that enable the visualization and quantification of different tissue parameters in vivo, for example blood flow [9–11], birefringence [12–14], metabolic status [15,16], and elastic properties [17,18], among others. In this context, the in vivo blood flow assessment is accomplished by the phase-resolved Doppler OCT (DOCT) development [9–11] that explores the phase information of OCT signals which has seen promising clinical applications in characterization of dynamic blood flow, especially in human retina. Most recently, the phase-resolved DOCT has been used to perform the optical coherence angiography in human retina . However, because the technique is built on the phase assessment of OCT signals, DOCT is inherently sensitive to the phase stability caused by both the system and the measurement environments.
This paper reports the development of three dimensional optical angiography (OAG) that exploits the mathematical properties of Hilbert and Fourier transformations of real-valued interferometric signals for interpreting the light scattering properties of tissue. Specifically, we discuss the application of OAG for the non-invasive, high resolution, and high sensitivity mapping of blood flow within thick tissue layers in vivo. The technique developed does not rely on the phase information of the OCT signals to visualize and assess the dynamic blood flow, thus is not sensitive to the environmental phase stability.
2. OAG System setup
Figure 1 show the schematic diagram of the system used in this study to perform in vivo optical angiography. It is based on the Michelson optical interferometer and similar to an optical fiber based frequency domain optical coherence tomography (FDOCT) system previously reported . The system used a superluminescent diode with a central wavelength of 842 nm and FWHM bandwidth of 45 nm that yields a measured axial resolution of ∼8 μm in air. After passing through an isolator (not shown in the figure), the light was coupled into a fiber-based Michelson interferometer where the 2x2 fiber coupler acts as a beam splitter. The reference light was delivered onto a reference mirror that was either stationary or mounted on a piezo-translation stage (Physik Instrument, Germany) driven by a 10 Hz saw tooth waveform with amplitude of 50 μm. The sample light was coupled into a probe, consisting of a pair of X-Y galvanometer scanners and the optics to deliver the probing light onto and collect the light backscattered from the sample. The lateral imaging resolution was approximately 16μm determined by the objective lens that focused the sample light onto sample. The light power shone onto the sample was ∼1 mW. The light returning from the reference and sample arms was recombined and sent to a custom built high speed spectrometer, consisting of a 30mm focal length collimator, a 1200 lines/mm diffracting grating and an achromatic focusing lens with 150 mm focal length. The focused light spectrum was captured in parallel by a line scan charge coupled device (CCD) (Basler Vision Tech. Germany) consisting of 2048 pixels, each with 10X10 microns in size and 10 bits in digital depth, and capable of 29.2 kHz line rate. Polarization controllers were used in the reference, sampling and detection arms in order to maximize the spectral interference fringe contrast at the detector. The spectrometer has a designed spectral resolution of 0.055 nm, resulting in an optical ranging of approximately 6.4 mm in air, i.e. the full depth in the Fourier space, (z axis shown in the Fig. 1), where the positive frequency space (3.2 mm) was used for micro-structural imaging and the negative frequency space (3.2 mm) for flow imaging. The signal sensitivity of 95 dB was measured at z=+0.5 mm and dropped to 80 dB at z=+2.0 mm when the camera integration time was set at 34.1 μs.
The probe beam was scanned in the lateral direction (x axis shown in Fig. 1) by the X-scanner, driven by a 10 Hz saw-tooth waveform with an amplitude equivalent to 2.2 mm. The Y-scanner, driven at 0.02 Hz with amplitude of also 2.2 mm scanned the probe beam in the elevational direction (y axis). The camera integration time was set at 99 μs for imaging, allowing 1 μs for downloading the spectral data from CCD (2048 pixels, A scan) to the host computer via CameraLinkTM and a high-speed frame grabber board (PCI 1428, National Instruments, USA). This means that the CCD line scan rate was 10 kHz for the current study. In the x direction, there were 1000 discrete points measured that makes up a data matrix of 1000 by 2048 elements (slice, B scan). In the y direction, there were 500 discrete points over 2.2mm. Thus, a final volume data cube of 1000 by 500 by2048 (x-y-z) voxels was built from which the 3-dimensional structural and flow images, each with 1000 by 500 by 1024 voxels (C scan), were computed (see Section 4 below). It took 50 seconds to obtain such volume data cube using the current setup. The actions for probe scanning, piezo-stage translation (if needed), data acquisition, data storage and hand-shaking between them were controlled by a custom software package written in Labview® language.
The key difference between OAG and FDOCT is that the spectral interferogram in OAG is modulated by a constant Doppler frequency that makes it feasible to separate the moving and static scattering components within sample. In the current setup, this is achieved by mounting the reference mirror in the reference arm onto a linear Piezo-translation stage (Fig. 1) that moved the mirror at a constant velocity across the B scan (i.e. x direction scan). The modulation frequency introduced in the spectral interferograms was 1.25 kHz with the CCD line rate set at 10 kHz. Because the introduced modulation frequency is one eighth of the data acquisition rate, the phenomenon on the spectral interference fringe washout at the CCD camera can be neglected. The other methods to introduce this Doppler frequency modulation are straightforward, for example by means of phase modulator placed in either the reference or sample arms, or both like those used in full range complex imaging for FDOCT [21–23]. We note also that Yasuno et al  has in the past used the piezo-translation stage to dither the reference mirror to achieve the full range imaging in FDOCT, where the modulation frequency was, however, not constant.
3. Mathematical perspectives
Optical interferometry has long been used to detect movements such as red blood cell movements or background tissue movements. The mathematical analysis of the OAG method essentially maps velocities moving into the tissue away from the surface into one image and velocities moving out of the tissue toward the surface into a second image.
Consider a real function that varies with two variables, both of time coordinates, t1 and t2
where f0, fM and fD are the frequency components, respectively and ϕ is a random phase term. In connection with the discussion below, we here assume that f0 and fM are two modulation frequency components whereas fD is Doppler frequency component. We also assume that there is no correlation between t1 and t2, and when t1 varies t2 is constant and vice versa. The analytic function of Eq. (1) against t2 can be constructed through the well known Hilbert transformation if the Bedrosian theorem holds [25, 26] which states that if the modulation frequency fM – fD does not overlap the signal bandwidth caused by the random phase fluctuation term ϕ. Under this condition, the Hilbert transform of Eq. (1) is equal to its quadrature representation. Bear in mind that the function B(t1,t2) is modulated by the frequency fM - fD, and 2πf0t1 is a constant phase term. Therefore, if fM – fD > 0, the analytic function of Eq. (1) can be written as:
where ; whereas if fM – fD < 0, it is
From the mathematical point of view, Eq. (3) is clearly the complex conjugate of Eq. (2). Now we perform the Fourier transformation against the time variable t1 (Note that t2 is now constant). It is obvious that the frequency component f0 of Eq. (2) is placed in the positive space in the entire Fourier plane, while it sits on the negative space for Eq. (3). This is the key element that makes OAG to image the microvascular flow within tissue.
Consider the case of OAG (Fig. 1), if we assume that the reference mirror mounted on the piezo-stage moves at a velocity , with the probe beam proceeding in the B-scan (x-scan) at a velocity of vx (scalar), and we further assume that a reflecting particle that is detected by OAG also moves but with its directional velocity projecting onto the probe beam direction being , then for simplicity we can state the spectral interferogram in the wavelength λ domain as:
Note here that we use vector representations for velocities with the movement towards the incident beam being positive and that opposite being negative. The term zs is the initial depth-position of the reflecting particle (e.g., the red blood cell) at the lateral position x, and is the velocity of that reflecting particle, such that the pathlength difference between sample arm and reference arm is 2(zs + ( + )tx), where is the scanning time of the probe beam in the B scan, and the factor of 2 accounts for the round trip of the sampling light scattered from the sample back into the interferometer. The term φ(x, z, λ) is a random phase function that relates to the phases of the optical heterogeneous sample. The time tx = 0 would be the start of a B scan. Hence, B(1/λ,x) is a sinusoidal oscillation function versus x for each 1/λ value. It is clear that Eq. (1) and Eq. (4) are identical if the following substitutions are used:
Thus, the values of and determine whether the analytic function of Eq. (4) constructed through the Hilbert transformation is turned into Eq. (2) or Eq. (3). The analytic function is sequentially constructed through the Hilbert transformation to the B-scan along the x-axis at each 1/λ. During the operation, the factor 4πzs/λ is simply a constant phase since it does not vary with x.
If = 0 , positive velocities (vref) would modulate the signal with positive frequencies in x-space, and negative vref with negative frequencies. The Hilbert transformation converts the information of the modulated signal versus x into a complex number , but now any subsequent Fast Fourier Transform (FFT) towards , , of the Hilbert-encoded information would map positive frequency components into the positive-frequency space and map negative frequency components into the negative-frequency space of the FFT result, leading to that the full range frequency space can be utilized for imaging . This is in contrast to simply taking , which always maps both positive and negative frequencies into both the positive- and negative-frequency spaces of the transform, resulting in only half of the space being useful for imaging.
Now, consider the effect of a moving particle, vs ≠ 0. The particle movement will modify the modulation frequency through the velocity mixing, + , similar to the frequency mixing in the signal processing discipline. An opposite movement of the particle, e.g. blood cells, relative to the movement of the reference mirror results in a decrease of the difference in photon pathlength between sample and reference arm and decreases the effective frequency of the modulation. If the value of vs is sufficiently large, the value + will change its sign. Consequently, after the operations of Hilbert and Fourier transforms, the corresponding signal due to the particle movement will map into the frequency space opposite to that with vs = 0. However, any small particle movement that is not strong enough to change the sign of the value of + vs will still map to the frequency space of when vs = 0. Hence, the signals from the perfused blood cells and the bulk static tissue can be separated in the frequency space of FFT, with the background noise due to small tissue movements rejected in the space that represents the image of blood perfusion.
In the current study, the reference mirror moved away from the beam splitter at 500 μm/s. With such a moving reference mirror, a stationary red blood cell appears to be moving into the tissue away from the surface. Any small movements less than 500 μm/s, such as small background movements and low blood perfusion rate, can modulate this velocity, but the red blood cell still appears to be moving into the tissue. Hence, these red blood cells will map into the first image, which we call the static image. Only red blood cells moving toward the surface in excess of 500 μm/s will exceed the reference mirror movement and appear to be moving toward the surface. Hence, those red blood cells will map into the second image, which we call the perfusion image.
To image the perfusion into the tissue, the reference mirror needs to be moved toward the beam splitter rather than away from the beam splitter. Otherwise, the method is the same. The choice of 500 μm/s can be varied, such that the threshold for detection of low perfusion velocities can be adjusted. The effect of the moving reference mirror is a frequency modulation that can be achieved in several ways. The moving mirror is one method which is useful for the purpose of explanation.
4. Data processing outline
The X-Y scanner in Fig. 1 enabled the collection of the 3-D spectral interferogram data set from which the 3-D OAG image was computed. A typical 3-D data cube in this work consists of 1000 by 500 by 2048 voxels. The data processing was based on the slice (B scan) by slice basis. Each B scan contains 1000 (positions) by 2048 (wavelengths) pixels of the spectral interferogram data. The data processing stages to obtain the final 3-D OAG image are:
In this step, all the spectral interferograms in each slice along the x-direction are ensemble-averaged at each wavelength to obtain a reference spectrum, which is then subtracted from each A scans. This operation effectively removes/minimizes autocorrelation, self-cross correlation, and camera noise artifacts presented in the final OAG images  that considerably improves the image quality. The subtracted spectral interferograms are then converted into the equal frequency space by use of the spline interpolation method as usually done in the FDOCT . This is because the spectral interferogram data matrix captured by the CCD camera are functions of wavelength, however the Fourier transform relationship is between time (distance) and frequency (wavenumber).
- Hilbert and Fourier transformations
This is the essential step to obtain the final OAG images. The pre-processed spectral data matrix is Hilbert-transformed row by row to form the discrete analytic functions, i.e. operation is done for each wavenumber along the positions separately. This Hilbert-transformed data matrix was then Fourier transformed column by column (i.e. performed at each position along the wavenumbers) to convert the data matrix from the spectral domain into the time domain that results in the positive and negative time-coordinates in the output separated by the zero-phase delay line. The resulted data matrix is then multiplied by the speed of light in the sample to give the distance information. The speed of light in the sample is taken as the speed of light in the vacuum (2.99*108m/s) divided by the refractive index of typical biological tissue which is approximately 1.4 [29, 30].
The data matrix is then split along the zero delay line into two equal parts. The positive part gives the microstructure information of the sample that is essentially the same as that of the conventional OCT image. The negative part gives only the signals pertinent to the moving particles within sample, such as the moving blood cells in the blood vessel, which is flipped to coincide with the microstructural image obtained in the positive part. Both images are of 1000 by 1024 pixels.
Return to (a) to process the next slice until the last slice was completed in the 3-D data cube. Finally, two volume images are obtained, both of which are of 1000 by 500 by 1024 voxels.
- Fusion (optional)
This step performs the data fusion to fuse the microstructural image and flow image into a single image to give us a better view on how the blood flow in vessels is orientated in the tissue. The flow signal is normally coded with a color while the structural image coded with the grey scale.
Due to the computer memory limitations, the volume image was cropped to remove the bottom portion of the volume that does not contain useful imaging information, and then re-sampled and scaled down to 500x500x400 voxels, equivalent to a physical volume dimension of 2.2 by 2.2 by 1.7 mm3. The 3-D image was log-compressed and displayed as grayscale (color if necessary) coded over 50 decibels (dB) where the minimum was set at 25 dB and the maximum at 75 dB.
For processing of the images presented in this work, the above algorithm was implemented in Matlab 7, running on a 1.8 GHz Windows XP based personal computer. The total processing time required to produce the final 3-D OAG image shown in Fig. 3 was ∼ 35 minutes. However, the processing time can be shortened considerably if the algorithm was implemented in an optimized, compiled computer language and run on a more powerful computer. The 3-D data representations and movie making from the final OAG data set obtained from the above algorithm that are presented in this work were rendered by separate Amira 3-D visualization software (Mercury Computer System, Inc., San Diego, USA).
5. In vivo Testing of OAG
For demonstrating the potential of OAG in the non-invasive assessment of microvascular blood flow, we obtained transcranial images of the cerebrovascular circulation in mice. The experimental protocol was in compliance with the Federal guidelines for care and handling of small rodents and approved by the Institutional Animal Care and Use Committee. Three-month-old male C57BL/6J mice were purchased from commercial breeders (Charles River Laboratories) and kept in our rodent colony until use. The mice, each weighing 23 to 28 g, were prepared for OAG one day before the experiments by shaving the heads followed by a depilatory cream to remove all remaining hair from the top of the skull. Anesthesia was induced by subcutaneous injection of a “Rodent cocktail” containing ketamine hydrochloride (30 mg/kg), xylazine hydrochloride (2 mg/kg) and acepromazine (1 mg/kg) in 100 μL total volume. Anesthesia was maintained by half of the induction dose, typically administered 45 to 60 min after induction. The right common carotid artery (CCA) was exposed, a loose 6-0 silk suture loop was placed around the vessel, and the edges of the wound were pulled together with both ends of the suture hanging out approximately 15 cm. The animal was then transferred to a custom stereotaxic imaging stage, positioned on its ventral side, and the head was secured with a tape to minimize its movement due to breathing. An incision of ∼10 mm was made along the sagittal suture; the skin was pulled to the sides exposing the frontal, parietal and interparietal bones. The exposed skull bones were washed with saline, and a drop of mineral oil was used to keep the window hydrated. The animal was then positioned under the OAG scanning probe as described in Section 2. Following the first full surface scan, the right CCA was narrowed by tightening the loose suture, and a second scan was performed to determine whether the cortical blood flow pattern was affected by the temporary stenosis. The animal was sacrificed and photographs of the scanned surface were obtained. The bone and meninges were then carefully removed, and the cerebral cortex was photographed for matching the visible superficial vessels with the OAG images.
The experiments performed in this study confirmed that OAG can evaluate transcranial blood perfusion at the capillary level of resolution. The cortical blood perfusion in mice was reproducibly visualized over several days with the cranium intact. In the current OAG system (Fig. 1), a near-infrared broadband light centered at 842nm was used to progressively slice the mouse brain with the skull intact so that a 3-D raw spectral interferogram dataset is collected. Figure 2(B) shows the image obtained from the raw spectral interferograms [Fig. 2(A)] representing one slice within the 3-D dataset using OAG, where the entire Fourier space is separated into two equal regions. The bottom region is the positive frequency space containing the normal OCT cross-sectional image within which the histologically important layers such as cranium and cortex may be clearly demarcated, but it is almost impossible to identify the blood vessels. Because red blood cells flow through all blood vessels, including capillaries, these moving components can be precisely localized in the negative space [upper region, Fig. 2(B)] in OAG. As the positive and negative spaces are exactly mirrored, they can be folded to fuse a single image to localize with high precision the blood vessels within the tissue (Fig. 2C). Similar to OCT, OAG is capable of resolving the cortical structures and blood perfusion at depths of ∼1.5 mm through the cranium, a penetration depth that can not be achieved with confocal microcopy. This depth, primarily limited by the high scattering properties of the brain, can be extended further if a light having a longer wavelength is used for imaging, as opposed to 842nm used here. The axial resolution for resolving blood vessel dimensions in OAG is determined by the bandwidth of the light source used; for the configuration shown in Fig. 1, it was ∼6μm within the biological tissue, which is capable of resolving the capillaries that are of an average size of 10 μm . Lateral resolution was ∼16μm which is determined by the objective lens that focused the light into the tissue.
3-D OAG imaging can be performed by evaluating the spectrogram data slice by slice, then re-combining to yield the 3-D volume dataset (x-y-z), from which high quality information regarding vasculature, blood flow and microstructures can be extracted. A detailed 2-D vasculature mapping is obtained by projecting the 3-D flow image available in the negative space into the x-y plane [Fig. 3(A)]. Because OAG also gives the 3-D microstructure of the sample in the positive space, the 3-D localized moving scattering elements in the negative space can be folded to combine with the 3-D structural image to give us a complete view of how the blood vessels are orientated within the tissue [see Fig. 3(B), and associated videos]. In the current configuration of Fig. 1, the imaging speed was 10 frames per second; the entire image acquisition time of Fig. 3 was ∼50s. This imaging time can be shortened by employing a higher power light source and a higher speed of piezo-translation stage. The computation time for post processing of images was ∼4.2 s per slice on a personal computer, or about 35 min for a full 3D image. This computational load can be reduced significantly with parallel processing on a more powerful computer.
The detailed cerebro-vascular perfusion that can be visualized in 3-D using OAG, combined with the quantification of blood flow within individual blood vessels and tissue volumes, holds considerable appeal for the investigation of neurological diseases in small animal models. For example, ischemic thrombotic stroke is widely studied in small animal models such as the genetically altered mouse. Thus a detailed view of cerebro-vascular blood flow phenomena and its regulation across the entire cerebral cortex – at the level of individual blood vessels down to the capillary – will be important to better understand the pathophysiology of cerebrovascular diseases and the potential benefits of pharmacological interventions. To document that OAG can serve as a tool in the study of cerebro-vascular blood flow, multiple 3-D images of the mice brain were collected over different regions of the skull. Images from different regions of brain were then combined as a mosaic. Figure 4(A) shows the blood flow in the cerebral cortex of a mouse with the skull intact. Occlusion of one carotid artery does not cause cerebral infarction or neurological deficits in the mouse. The image of Fig. 4(B) was taken from the same animal while the right carotid artery was blocked for 5 minutes. It is apparent that the blood flow in the cortex, rather than in the right hemisphere only, is reduced as compared to Fig. 4(A). This is consistent with the well-known collateral circulation between brain hemispheres leading to a total reduction in cortical blood volume due to the occlusion of one common carotid artery. The capacity of OAG to achieve such high resolution imaging of the cerebral cortex – within minutes and without the need for dye injections, contrast agents or surgical craniotomy, - makes it an extremely valuable tool for studying the hemodynamics of the brain.
6. Discussion on OAG system sensitivity
Theoretically, according to Eq. (2) and Eq. (3), the system sensitivity of OAG to image the flow can be high, close to the zero flow velocity. Although the moving speed of the reference mirror sets a threshold for flow velocity detection, practically, the lower limit of flow imaging is determined by the bandwidth of spectral interference signals that resulted from the lateral scanning of the probe beam due to the heterogeneous property of sample. This in turn is determined by the overlapping degree of probe beam spot between adjacent A scans. It is trivial to show that the bandwidth of spatial interference signal is infinitely narrow if the signals at different positions along the x scanning direction are totally correlated (e.g. repeated A scans). The efficient separation between the signals from the static and moving elements also requires that the modulation frequency and the signal bandwidth are not overlapped. Thus, the minimum blood flow velocity that can be practically detected by the OAG system is half of the spectral interference signal bandwidth. We observed that the interference signal bandwidth was typically ∼800Hz from the in vivo animal experiments with the system configurations described in Fig. 1 where we used the separation distance between the adjacent A scans about one fifth of the diameter of the probe beam focus. Therefore, the minimum flow velocity achievable by the current OAG system was ∼ 170μm/s for in vivo imaging. For detecting the flow that has lower speed, one solution could be to increase the A-scan sampling density relative to the probe beam spot. This however will inevitablely increase computational load to obtain meaningful OAG images.
The maximum flow that can be detected by the OAG system is influenced by the integration time set by CCD camera. Because the increase of flow velocity would increase the modulation frequency in the interferograms captured by the CCD camera, too fast the flow will cause the interference fringe washout at the camera due to the well known Nyquist sampling theorem . Therefore, for the current system setup with the integration time set at 99μs, the maximum flow velocity that can be detected is ∼±2.1 mm/s, or equivalent to ±5kHz Doppler frequency. Note that this maximum velocity is quoted for the velocity projecting onto the probe beam direction. To further increase the up-range of flow imaging, one would simply increase the speed of CCD camera used.
It is worth mentioning that OAG method as described here is capable of detecting the directional flows, which is important for many cases of biological applications. From Section 3, one straightforward approach to imaging of directional flow is to drive the reference mirror back and forth at a constant speed, so that it detects the blood flow running towards the incident beam when the mirror moves away from the probe beam, otherwise it detects the opposite flow. The detailed discussion and demonstration for this will be discussed in a separate publication.
7. Comparison between OAG and phase-resolved Doppler OCT
Over the past few years, phase-resolved Doppler OCT (DOCT) based on the time-domain OCT (9, 33, 34) and later on the Fourier domain OCT (10,35-38) has been reported to make high-resolution and high-velocity sensitivity imaging of blood flow. Briefly, the technique was developed based on the phase measurement between successive axial (A) scans. If the sample moves by an instantaneous distance Δd during a time interval τ between two successive A-scans, the measured phase changes by an amount of Δϕ=2n 0 k¯δd due to the well-known Doppler effect, where n 0 is the average refractive index of the sample and k¯ is the average wavenumber of the light source used. This phase change is related to the Doppler frequency by fD = Δϕ(2πτ)-1. Evaluating Δϕ at each depth z yields depth-resolved measurements of both the magnitude and direction of the flow velocity under the assumption that this change is solely caused by the moving scatterers within the sample. Assuming that the probe beam intersects the flow velocity vector at an angle β (Doppler angle), the flow velocity is given by v = Δϕ(2n 0 k¯τcosβ)-1. This method was originally demonstrated in time-domain OCT  and later in Fourier-domain OCT , and is the method that is commonly used in OCT nowadays to assess the localized blood flow in tissue. Such technique has seen successful and promising in vivo applications, particularly for the characterization of dynamic blood flow in human retina, by use of both the time-domain [39, 40] and frequency domain [10,11,19] approaches.
Theoretically, the sensitivity of phase resolved DOCT to measure the blood flow is in the order of micrometers per second, largely limited by the OCT system noise floor (38). However, in practical in vivo applications, the assumption of the phase change between the adjacent A scans solely caused by the moving scatterers within sample will be difficult to meet. This is because 1) DOCT essentially measures the relative motion which represents as the Doppler shift in the light frequency between the light it emits and that it receives. This shift is imparted when the light strikes an object which is moving, relative to the probe. Therefore, the inevitable sample movement will give artifacts on the blood flow measurement that is difficult to manage because the assessment is based on phase information of OCT signals in DOCT. 2) The tissue sample is naturally of optical heterogeneity. This optical heterogeneity property of the sample will impose a texture background noise floor on the flow images obtained from the phase-resolved DOCT technique . Although practically one can employ dense sampling approach in the lateral direction (B scan), i.e. taking more A scans than it is necessary, to minimize this noise floor. The disadvantage is that it reduces the imaging speed and also increases the computational load to obtain the meaningful flow images. 3) The phases are mathematically limited to the interval (-π π] corresponding to the principal value of the arctangent function. Theoretically, one can use the phase un-wrapping technique to correct the phases, however it is un-practical to implement this under the in vivo situations because of the reasons 1) and 2) above, in addition to that the phases are strongly dependent on the OCT signal strength  and the system noise level. Therefore, the phase resolved DOCT images are quite noisy. Nevertheless, in vivo mapping of vasculature networks in the retina has been most recently reported based on the phase-resolved DOCT technique  by use of sophisticated algorithms to minimize the noise artifacts.
In contrast, OAG rejects the small scale sample movement and the noise signals originated from the optical heterogeneity of the sample. Note that large scale of sample movement is not rejected in OAG. In addition, only OAG flow signals appear in the negative space of the output plane which makes the flow image almost free of artifact-induced noises. Furthermore, the calculations are straightforward and do not involve sophisticated algorithms that considerably reduce the computational effort in obtaining the 3-D angiograms as compared to that using the phase resolved DOCT .
In Fig. 5, we illustrate the difference between OAG and phase-resolved DOCT imaging of blood vessel network over the mouse brain using the same data set. In obtaining the DOCT flow image, we followed the algorithms published in  where the algorithms for minimization of the sample motion artifacts, segmentation of regions of interest and correction of phase-wrapping errors were implemented, and then the resulted phase shifts between the adjacent A scans were squared (i.e. power Doppler imaging approach) to obtain the map of vasculatures. From Fig.5, the advantages of OAG in mapping the detailed vasculature network are apparent. The dramatic contrast between the two approaches is currently still not clear. It maybe due to that the phase-resolved DOCT algorithm was optimized for the vascular network visualization in human retina, while the current approach is optimized for the cerebral circulations in mice. Clearly, the dynamics for cerebral blood flow in mice and blood circulations in human retina is different. Therefore, a further systematic study is needed.
However, the advantages of phase-resolved DOCT over OAG are that it can provide us with the magnitude of velocity about the blood flow from the calculated phase shifts with much less imaging time and computational efforts. Fortunately, the difference of the post-data processing between OAG and phase-resolved DOCT lies purely in the algorithms. Here, the modulated spectral interferograms during the imaging in OAG can be easily dealt with in the software. Therefore, although the phase-resolved DOCT is difficult to identify the capillaries in tissue, it can be combined with OAG to provide the flow velocity in the major blood vessels. Figure 6 gives such an example shown in video format. In addition, it should mention that because OAG requires a relatively cost piezo-translation stage or phase-modulator to modulate the spatial OCT spectral interferograms so that the scattering elements from static and moving components can be separated, this nevertheless adds a complexity to the system implementation in comparison to the current phase-resolved DOCT system.
We have presented an optical angiography technique capable of high resolution imaging of blood perfusion within localized blood vessel embedded within highly scattering tissue. By exploiting the inherent properties of the OCT signals, the moving and static scattering elements within tissue can be efficiently separated by the OAG method, thereby enabling precise localization of blood perfusion in 3-dimensional microstructures. This is achieved by modulating the spatial OCT spectral interferograms at a constant modulation frequency while the probe beam is scanned across the B scan. The modulation frequency introduced is similar to setting a velocity threshold for OAG to detect the dynamic blood flow above the threshold. The use of contrast agents and newer imaging agents administered into blood, for example nanoparticles and microbubbles (41), might enhance even more the light backscattered from the moving elements, thus enhancing further the sensitivity of 3-D OAG. The system is compact, fast, optically stable, and easily implemented in both the hospital and research laboratory environments.
Although the present report demonstrates the usefulness of OAG in transcranial cerebrovascular imaging in mice models, it is also well suited for performing 3-D angiograms on thick tissues in other basic and clinical settings, where the visualization and quantification the microcirculation are important for understanding mechanisms and treatments, e.g. tumor angiogenesis, wound healing. Other examples of prospective applications include neuroscience, where changes in cortical blood flow are coupled to certain types of neuropathology, such as dementia; ophthalmology, where ocular and retinal circulatory beds are very important in the diagnosis and management of disorders such as glaucoma, diabetic retinophathy and age-related macular degeneration. As OAG and the associated computation are developed into a rapid imaging system, we will be able to assess tissue perfusion at the resolution level of capillary flow in real time without interfering with the sample in a significant way.
This research was made possible with generous support from Department of Biomedical Engineering, Oregon Health & Science University.
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