Ординатура / Офтальмология / Английские материалы / Handbook of Optical Coherence Tomography_Bouma, Tearney_2002

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followed using light from a lower power HeNe laser with a photomultiplier detector and an electronic correlator to measure blood flow in human retinal arteries and veins [2]. Subsequently, a number of investigators developed the methodology further to measure blood flow in a catheter [3] and skin pulsatile flow using a source-and- receiver geometry incorporating optical fibers [4]. One of the earliest reports describing the use of a light source with a broad spectral emission profile or short temporal coherence length for interferometric measurement of fluid flow was given by B. T. Meggitt and colleagues [5]. The power spectrum of light backscattered from a 200 m measurement volume in a test flow was measured using a Michelson configuration incorporating a low finesse Fabry–Perot recovery interferometer combined with differential detection. Using this technique, the authors measured the power spectrum of interference fringe intensity corresponding to light backscattered from discrete spatial locations in a test flow. More recently, development of high power amplified spontaneous emission (ASE) light sources that provide broad spectral emission profiles in a single transverse spatial mode have allowed high resolution ( 10 m) measurement of flow velocity in turbid media [6].

8.1.2Doppler Ultrasound

In Doppler ultrasound imaging, an acoustic transducer external to the tissue generates ultrasonic waves that are backscattered from moving red blood cells (RBCs) and shifted in frequency ( D) by an amount proportional to the velocity. In addition to being noninvasive, the chief advantage of Doppler ultrasound techniques is the ability to record images of the heart and relatively large diameter blood vessels. Although Doppler ultrasound imaging provides a means to resolve blood flow velocities at discrete spatial locations in tissue, the relatively long acoustic wavelengths required for deep tissue penetration limits spatial resolution to approximately 100 m. Application of Doppler ultrasound to the recording of tomographic images of microvasculature blood flow requires the use of high frequency acoustic waves that are strongly attenuated in tissue.

Differences in the spatial and velocity resolution between Doppler ultrasound and optical coherence tomography (OCT) are due to the large variance between characteristic wavelengths of corresponding optical and acoustic waves in tissue. The spatial resolution of Doppler OCT is an order of magnitude better than what can be achieved with ultrasound tomography [7]. Vessels positioned at depths to 1 mm beneath the tissue surface with diameters as small as 10 m can be imaged using Doppler OCT. Similarly, the velocity resolution of Doppler OCT is better than in ultrasound because of the difference in respective wavelengths ( ). For ultrasound,

acoustic depends on the wave frequency and mean velocity of sound through soft tissue (taken to be 1540 m/s). For 10 MHz ultrasound, acoustic ¼ 1540 ðm=sÞ=107 Hz ¼ 154 m compared to optic ¼ 0:85 m. Assuming equal measurement time ð tp) to record a single pixel in acoustic and optical Doppler imaging systems, the ratio of

minimum velocity (Vmin) resolutions is given by

Vacousticmin ¼ acoustic ¼ 154 ¼ 180

Vopticalmin optic 0:85

The two-order magnitude improvement in Vmin, together with a tenfold increase in Doppler OCT spatial resolution, allows very high resolution measurement of volu-

metric blood flow rates on the order of 10–100 pL/s. Notwithstanding the significant disparity in spatial resolution between ultrasound and OCT, the basic physics of the Doppler effect involving acoustic and electromagnetic waves is similar, and many of the signal processing techniques (hardware and software) used to estimate the Doppler shift D are analogous. Moreover, because the evolution of Doppler ultrasound predated OCT by more than a decade, signal processing and data estimation algorithms developed for ultrasound represent a valuable resource for Doppler OCT.

8.1.3Laser Doppler Flowmetry

In laser Doppler flowmetry (LDF), incident highly coherent light at a single optical frequency (!) enters the tissue and is multiply scattered by static constituents and moving red blood cells (RBCs). A second fiber collects the backscattered light, a small fraction of which is Doppler shifted by moving RBCs; in comparison, light scattered exclusively by static constituents has little or no frequency change. Detection of the Doppler shift in LDF is founded on the heterodyne beating principle: shifted and nonshifted backscattered light amplitudes mix coherently on the surface of a photoreceiver to produce low frequency (< 10 kHz) intensity fluctuations. Power spectra of the intensity fluctuations are a function of the RBC velocity distribution and concentration in the microcirculatory network. An LDF blood perfusion signal is given by the first moment of the computed power spectrum of measured intensity fluctuations. Because the LDF signal is due to multiply scattered light with a large variation of optical pathlengths in the tissue, spatial resolution is poor (> 250 m) and information relevant to bloodflow at discrete positions is lost.

Many investigators have reported experimental and theoretical investigations to improve the LDF spatial resolution and demonstrate application to clinical diagnostic problems. Stern at Johns Hopkins University completed a detailed analysis of Doppler-shifted and multiply scattered light using a Feynman path integral formalism [8]. Obeid et al. [9] reported a two-wavelength LDF system to improve depth discrimination of tissue blood flow. In this technique, two coherent light sources with spectral emission in the visible and infrared are coupled into a multimode optical fiber and incident at a single position on the tissue. Light backscattered from the tissue is collected in a receiving fiber, and the first moment of the power spectrum of measured intensity fluctuations is computed at each wavelength. Because longer wavelength light is scattered less strongly in tissue than the visible wavelengths, penetration is deeper and the near-infrared LDF signal measures RBC velocity over a deeper range of depths. Comparison of visible and near-infrared LDF signals allows coarse depth discrimination of microvascular blood flow. Various investigators have reported application of LDF imaging instruments to clinical diagnostic problems [10]. In LDF imaging instruments, light emitted from a coherent laser source is scanned over a region of interest on the tissue surface. At each beam position on the tissue surface, intensity of backscattered light is measured and the first moment of the power spectrum of intensity fluctuations is computed. A blood perfusion image is produced by displaying the first moment of the power spectrum at each pixel. Because lateral spatial resolution of LDF is limited by the scattering properties of the probed tissue volume, pixel (250 m) and image (1–100 cm2) sizes are relatively large.

8.2DOPPLER OCT SYSTEM

We present a simple analysis of Doppler OCT by considering a turbid sample positioned in a Michelson interferometer. Spatially coherent light emitted from a source with broad spectral emission ½Soð!Þ& is coupled into the interferometer and split into reference and sample paths. At the interferometer output, interference fringe intensity may be detected using a single-element photoreceiver or an optical spectrum analyzer. In systems that measure interference fringe intensity using a single-element photoreceiver, optical time delay ( ) between light propagating in reference and sample paths is varied by using a delay line, and scanning of light in the turbid sample may be performed in two manners: (1) continuous scanning in depth followed by an incremental change in lateral position (longitudinal scanning) or (2) continuous scanning of lateral position followed by an incremental change in depth (lateral scanning). In scanning systems, interference fringe intensity is measured over a time delay approximately equal to the coherence time of source light ( c) to record position and velocity of static and moving constituents at a single pixel in the turbid sample; information at deeper positions is obtained by measuring fringe amplitude and phase at increased time delays ( ). A potential practical advantage of measuring fringe intensity in the optical spectral domain is that the requirement for a delay line in the reference path is removed and the optical time delay is scanned electronically by computing the amplitude of various harmonics of corresponding spectral oscillations. Despite the potential advantages in measuring fringe amplitude in the optical spectral domain, fabrication constraints in the detector array readout architectures have hindered practical application of electronic delay line scanning systems.

8.2.1Doppler OCT Signal

We calculate the Doppler signal current id =ðdÞ measured by a single-element photoreceiver (e.g., photodiode) by determining the correlation between light amplitudes in the reference and sample paths of the interferometer. When the sample contains moving constituents (e.g., RBCs), optical time delay ( ) is due to scanning in the reference path ( s) and possible delays due to Doppler motion of scattering centers parallel to the optical axis in the sample path ð D). The amplitude of light emitted by the source and coupled into the interferometer ½UðtÞ& at time t is written as a

harmonic superposition,

ð1

UðtÞ ¼ 7ð!Þei!td! ð1Þ

0

where UðtÞ is a complex-valued analytic signal representing the field amplitude emitted by the light source; 7ð!Þ is the corresponding spectral amplitude at optical frequency !. Cross-spectral density of 7ð!) satisfies

7 ð!Þ7ð! 0Þ ¼ Soð!Þ ð! ! 0Þ ð2Þ

here, h i is a time average over various realizations of 7ð!Þ; Soð!) is the optical source power spectral density in watts per hertz (W/Hz); and ð!Þ is the Dirac delta function. Light emitted by the source is coupled into the interferometer and split equally into reference and sample spectral amplitudes, each denoted by 7oð!Þ. After splitting, spectral amplitude of light in the reference path propagates forward to the

delay line, is reflected, and is coupled back into the interferometer. After return to the 2 2 splitter, the reference spectral amplitude is

Here, s is the variable delay time between light propagating in the sample and reference paths established by the scanning delay line; Kr is the amplitude reflection coefficient of light returning from the delay line. In writing Eq. (3), we have assumed that the delay line is dispersion-free and does not limit the source spectrum. After splitting, spectral amplitude of light in the interferometer sample path propagates forward to the turbid sample, is backscattered, and is coupled back to the splitter.

After return to the 2 2 splitter, the sample spectral amplitude is

X

7sð!Þ ¼ 7oð!Þ Ksð sÞei! D ð4Þ

where the sum is taken over all backscattering centers in the sample. Ksð sÞ is the complex amplitude reflection coefficient of light backscattered from a center position in the sample with time delay s established by the delay line in the reference path (for simplicity we assume no spectral modulation of light propagating in the sample); when light backscatters from a moving particle, the phase of light in the sample path varies according to ! D, where D is the Doppler time delay of light backscattered from moving constituents. Using expressions for the spectral amplitude of light in the reference [Eq. (3)] and sample [Eq. (4)] paths, we derive the temporal coherence function ½ OCTð Þ& for the interference fringe intensity. Combining harmonic expansions [Eq. (1)] for 7sð!Þ and 7rð!Þ and applying Eq. (2) when computing a time average, the temporal coherence function is

Because the Doppler signal current is the measured quantity of interest, we write the expression for id at time delay s D as

Here, ð!Þ is the quantum efficiency of the detector and h is Planck’s constant. When the sample is nondispersive, the source photon spectral density is Gaussian with center frequency !o and total power Po, and the quantum efficiency ( ) of the detector is constant over the source bandwidth, the Doppler signal is

to ‘‘short-time’’ (i.e., localized or windowed) segments of the Doppler signal current. Each local Fourier transform provides the spectral information for that particular time segment, and the window is then shifted to a slightly later time to generate another local spectrum. Following this approach, the properties of the signal can be simultaneously analyzed in the temporal and frequency domains. Although a number of algorithmic approaches can be used to estimate the spectrogram of a timevarying signal, a simple approach is to compute the fast Fourier transform (FFT) of the Doppler signal current id ðtÞ for each time delay interval. The value of the spectrogram ½Sd ðti; jÞ, Eq. (11)] at frequency j is given by the squared magnitude of the short-time fast Fourier transform (STFFT) of the Doppler signal current in the ith time-delay interval, ðti; ti þ tp),

The gray-scale value at the ith pixel in a Doppler OCT structural image

½SOCTðiÞ, Eq. (12)] is given by the logarithm of the spectrogram value, Sd ðti; jÞ, at the carrier frequency o established by the delay line in the reference path,

The gray-scale value at the ith pixel in a Doppler OCT velocity image ½VOCTðiÞ, Eq. (13)] is given by the Doppler shift ( D) of the recorded signal

We have assumed that ks ¼ ki and that is the angle between ki and V and nm is the mean refractive index of the medium. Velocity resolution is dependent on pixel acquisition time ( tp) and the angle ( ) between flow velocity (V) and the incoming and backscattered light directions (ks and ki) in the turbid sample; velocity resolution may be improved by reducing the angle ( ) or increasing the pixel acquisition time ( tp). The detected velocity is color coded to indicate the magnitude and direction of flow and may be overlaid on the OCT structural image or displayed separately (see subsection on color coding of structure, flow, and variance).

A typical Doppler OCT depth scan (A-scan) is analyzed using a rectangular window (N points) shifted by a decimation factor (d points) along the entire A-scan (L points), resulting in k Doppler spectra, where

For typical parameters (L ¼ 512, N ¼ 32, and d ¼ 1), k corresponds to 480 localized complex fast Fourier transforms per A-scan. Inasmuch as STFFT calculations are computationally intensive (e.g., the processing time for an image with 100 A-scans using a 266 MHz Pentium personal computer is approximately 10 s), real-time acquisition of Doppler OCT images is problematic. Improved algorithms for real-time processing of Doppler signals recorded in vivo are discussed in Sections 8.4.2–8.4.4.

Velocity Resolution and Frame Rate Limitations

The velocity resolution in Doppler OCT, defined as the minimum resolvable velocity, Vsmin, is directly proportional to the minimum detectable Doppler shift given by

mins ¼ 1=N ts, which is determined by the STFFT window size N and the sampling

increment, ts. Substituting mins into Eq. (13) [12],

the velocity resolution can be expressed in terms of the image acquisition or frame rate Rf as [13,14]

where is the axial scanning duty cycle and K is the number of A-scans per image with L pixels. For a given set of system parameters, an inverse relationship exists between the desired frame rate (Rf ) and the minimum detectable velocity, Vsmin. Faster frame rates increase Vsmin and reduce Doppler velocity resolution; conversely, increasing precision of the velocity resolution requires a reduced frame rate.

The width of the Doppler spectrum and modulation by speckle in turbid media [ s in Eq. (10)] also give rise to a trade-off between the velocity estimation precision and frame rate [13,14]. In practice, precision of the estimated Doppler shift is also limited by the Doppler signal bandwidth [14], which is proportional to the optical

source spectral width !. Thus the practical velocity resolution, Vsp, is worse than Eq. (16) and is given by the product of Vsmin and the number of frequency samples

M ð2 ND=cLÞ spanned by :

The velocity resolution limits, determined by Eq. (16), for typical design parameters ( ¼ 1:3 m, nm ¼ 1:4, ¼ 45 , K ¼ 100, L ¼ 512, N ¼ 32, ¼ 0:8) are 0.13 mm/s at a slow image acquisition time of 10 s. High speed imaging (8 fps) results in a

theoretical velocity resolution of 10.5 mm/s.

Color Coding of Structure, Flow and Variance

Two color coding formats for Doppler OCT have been reported. One format [14] is consistent with color Doppler ultrasound [15], in which backscatter amplitude is logarithmically assigned a gray-scale value [Eq. (12)], white indicating the highest reflectivity. Flow direction is encoded red or blue, and the flow magnitude is determined by the red or blue saturation. The Doppler velocity image [Eq. (13)] is thresholded to remove velocity noise and superimposed on the amplitude image [Eq. (12)], simultaneously delineating tissue microstructure and blood flow. In the literature, this format is referred to as color Doppler OCT (CD-OCT). A format that uses false color coding has also been used to display Doppler OCT images [16,17]. In this format, backscatter amplitude is displayed with red and green representing high and low backscatter amplitude, respectively. Flow is encoded in a separate image, with black indicating no flow and red indicating saturation proportional to blood flow velocity. In the literature, this format is referred to as optical Doppler tomography (ODT).

Turbulence (or more appropriately, depth-resolved spectral broadening) has been designated [18] (refer to Section 8.4.3) by using green to indicate regions of increased variance, with intensity indicating the extent of spectral broadening. In color Doppler ultrasound, increasing variance adds green to red or blue (producing