Ординатура / Офтальмология / Английские материалы / Handbook of Optical Coherence Tomography_Bouma, Tearney_2002
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Figure 17 Reconstruction of a beating Xenopus heart using the frame gating technique. Doppler processing is restricted to the region indicated by a rectangle. v, ventricle; a, atrium; ta, truncus arteriosus; p, pericardium; bv, branched vessels; d, diaphragm. The highly pulsatile flow of the truncus arteriosus appears only in the frame immediately after ventricular ejection. Meanwhile, flow through the branched vessels is observed in several frames due to its damped nature. (See color plate.)
8.4.6Applications in Ophthalmology
Evaluation of ocular hemodynamics is a challenging task whose performance has only recently become feasible with the advent of noninvasive and minimally invasive clinical tools. Although the exact effect of ocular disorders on blood flow is unclear, clinicians have noted vascular anomalies that are associated with several pathologies, including diabetic retinopathy, age-related muscular degeneration, glaucoma, and neurogenic optic atrophy [34]. Quantification of blood flow at discrete spatial locations in the retina may lead to a better understanding of the progression and treatment of these disorders.
System Implementation for Retinal Doppler OCT
For retinal imaging, the incident power on the cornea was less than 300 W, well within the maximum permissible exposure standards [35]. The sample arm, shown in
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Fig. 18, contained a standard slit lamp apparatus modified for viewing of the fundus simultaneously with OCT imaging. A CCD camera sensitive to low intensity and NIR light was used to determine the exact scan location of the fundus during Doppler OCT imaging. Transverse scanning of the OCT beam along the retina was performed using an XY-scanning galvanometric pair, enabling scans in any arbitrary linear or circular direction. The interferometric detector signal was coherently demodulated at the Doppler frequency r induced by the motion of the reference arm (78 kHz). The resulting signal was low-pass filtered at 20 kHz cutoff frequency, encompassing the range of Doppler shifts arising from blood flow in the retinal vessels. Dilation of the pupil was not necessary for these measurements.
To eliminate motion artifact, a registration algorithm [30] was used to align all A-scans. In this algorithm, it was determined at which pixel in the A-scan the backscattered amplitude is above a selected threshold, interactively chosen to isolate the surface of the retina. A profile of the retinal surface is obtained by tracking, as a function of transverse position, the index of the first axial pixel exceeding this threshold. An example of the unregistered profile of the retinal surface is shown in Fig. 17. Assuming that the high frequency components result from motion artifact and the low frequency components represent the topography of the retina, the raw profile was low-pass filtered (5 cycles/image) to indicate the desired profile. Each A-scan is shifted to align with the filtered profile of the retinal surface [36].
Human Retinal Vessels
Retinal imaging of structure and blood flow was performed in the undilated human eye. Figure 19 (see color plate) presents an in vivo Doppler OCT image capable of resolving sub-100 m diameter vessels within the retina. The conventional amplitude image clearly delineates several layers within the posterior eye. A fundus photograph indicating the location of the scan shows that the two vessels are overlapping. Nevertheless, Doppler OCT can distinguish Doppler shifts arising from the individual vessels.
Figure 18 Light path in Doppler OCT sample arm for retinal imaging. Ps, sample arm power; 0, source center wavelength.
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Figure 19 In vivo retinal Doppler OCT image (2048 axial by 100 lateral pixels, acquired in 10 s) of bidirectional flow in the human retina. The axial dimensions indicate the optical depth. Doppler OCT is able to distinguish various layers of tissue as well as quantify blood flow magnitude and direction. A fundus photograph (right) indicates that the linear scan was inferior to the optic nerve head. (See color plate.)
Figure 20 (see color plate) illustrates the effect of motion artifact on retinal imaging of structure and flow. Motion artifact appears in the unprocessed image as oscillations and discontinuities of the retinal surface. For example, the retinal pigmented epithelium (RPE) does not maintain its contiguity throughout the image. These artifactual features are superimposed on the natural retinal curvature, which is a more subtle variation as a function of transverse position. The registered image using the algorithm described earlier eliminates the motion artifact while maintaining the inherent topography of the retina. Figure 21 contains profiles of the retinal
Figure 20 Linear DOCT scan of the retina superior to the optic nerve head, comparing images before (left) and after (right) removal of motion artifact using A-scan registration. Fundus photograph (top) indicates location of image. (See color plate.)
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Figure 21 Retinal surface profile before and after correction of motion artifact. Note that if all oscillations are removed (i.e., low-pass cutoff of 0 cycle/image) the processing will flatten the retinal profile.
surface, corresponding to the images in Fig. 20 before and after removal of motion artifact. The unprocessed profile contains low frequency terms attributed to the true topography as well as high frequency terms due to motion artifact. Filtering of the unprocessed profile at 5 cycles/image results in a smooth retinal profile. Another registration algorithm for retinal imaging has also been suggested using a crosscorrelation technique [37]. However, this technique fails in regions of the image where the RPE is not visible due to shadowing under vessels. Shadowing beneath the vessels is due to the increased scattering coefficient of blood [36] compared to the surrounding retinal tissue.
Discussion
Doppler OCT was applied for the first time to retinal flow mapping in the human eye. Quantification of retinal flow may have implications for better understanding of ocular hemodynamics and its role in several ocular disorders. Doppler OCT is the first technique to determine, with micrometer-scale resolution, the depth and diameter of vessels within the retina. In addition, this technique is capable of quantifying flow magnitude and direction simultaneously with imaging of the microanatomy of the posterior eye. Unlike fluorescein angiography, Doppler OCT is entirely noninvasive and does not require dilation of the pupil. Furthermore, Doppler OCT operates at longer wavelengths than laser Doppler velocimetry, so light exposure times can be safely increased [32]. In conclusion, Doppler OCT is a viable method for quantification of blood flow within the retina. This imaging technique is able to provide information that is unavailable or uncertain with other methods, such as LDV, fluorescein angiography, or color Doppler ultrasound. Doppler OCT is capable of imaging retinal structure and vasculature beyond the resolution of other techniques, without the need for pupil dilation. Blood flow speeds up to several
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millimeters per second were identified in sub-100 m vessels in the retina. Several layers in the posterior eye were clearly delineated, localizing retinal vessels within specific regions of the posterior eye. Accurate knowledge of retinal hemodynamics may prove helpful in understanding several ocular diseases, including diabetic retinopathy, glaucoma, and age-related macular degeneration.
REFERENCES
1.Riva C, Ross B, Benedek G. Laser Doppler measurements of blood flow in capillary tubes and retinal arteries. Invest Ophthalmol 11:936, 1972.
2.Tanaka T, Riva C, Ben-Sira B. Blood velocity measurements in human retinal vessels. Science 186(4166):830–831, 1974.
3.Tanaka T, Benedek GB. Measurement of the velocity of blood flow (in vivo) using a fiber optic catheter and optical mixing spectroscopy. Appl Opt 14:189, 1975.
4.Stern MD. In vivo evaluation of microcirculation by coherent light scattering. Nature (Lond) 254:56, 1975.
5.Meggit BT, Boyle WJO, Grattan KTV, Palmer AW, Ning YN. Fibre optic anemometry using an optical delay cavity technique. Proc SPIE 1314:321–326, 1990.
6.Wang X-J, Milner TE, Nelson JS, Fluid Flow velocity characterization using optical Doppler tomography. Opt. Lett 20:1337–9, 1995.
7.Angelsen BAJ. Waves, Signals and Signal Processing in Medical Ultrasonics, Vols 1 and 2. Trondheim: Norwegian Inst Sci Technol, Dept Physiol Biomed Eng, 1996.
8.Stern MD. Laser Doppler velocimetry in blood and multiply scattering fluids: Theory. Appl Opt 24:1968–1986, 1985.
9.Obeid AN, Bogget DM, Barnett NJ, Dougherty G, Rolfe P. Depth discrimination in laser Doppler skin blood flow measurements using different lasers. Med Biol Eng Comput 26:415–419, 1988.
10.Essex TJH, Byrne PO. A laser Doppler scanner for imaging blood flow in skin. J Biomed Eng 13:190–194, 1991.
11.Hlawatsch H, Boudreaux-Bartels. Linear and quadratic time-frequency signal representations. IEEE Signal Process Mag 9:21–67, 1992.
12.Izatt JA, Kulkarni MD, Yazdanfar S, Barton JK, Welch AJ. In vivo bidirectional color Doppler flow imaging of picoliter blood volumes using optical coherence tomography. Opt Lett 22:1439–1441, 1997.
13.Yazdanfar S, Kulkarni MD, Izatt JA. High resolution imaging of in vivo cardiac dynamics using color Doppler optical coherence tomography. Opt Express 1:424–431, 1997; www.osa.org.
14.Kulkarni MD, v. Leeuwen TG, Yazdanfar S, Izatt JA. Velocity estimation accuracy and frame rate limitations in color Doppler optical coherence tomography. Opt Lett 23:1057– 1059, 1998.
15.Kremkaul FW. Principles and pitfalls of real-time color flow imaging. In: Vascular Diagnosis. 4th ed. EF Bernstein, ed. Mosby Year Book, 1993.
16.Chen Z, Milner TE, Dave D, Nelson JS. Optical Doppler tomographic imaging of fluid flow velocity in highly scattering media. Opt Lett 22:64–66, 1997.
17.Chen Z, Milner TE, Srinivas S, Wang X, Malekafzali A, van Gemert MJC, Nelson JS. Noninvasive imaging of in vivo blood flow velocity using optical Doppler tomography. Opt Lett 22:1119–1121, 1997.
18.Rollins AM, Yazdanfar S, Ung-arunyawee R, Izatt JA. Real time color Doppler optical coherence tomography using an autocorrelation technique. Proc SPIE 3598, San Jose, CA, 1999.
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Milner and Izatt |
19.Kasai C, Namekawa K, Koyano A, Omoto R. Real-time two-dimensional blood flow imaging using an autocorrelation technique. IEEE Trans Sonics Ultrasonics SU-32:458– 464, 1985.
20.Lindmo T, Smithies DJ, Chen Z, Nelson JS, Milner TE. Accuracy and noise in optical Doppler tomography studied by Monte Carlo simulation. Phys Med Biol 43:3045–3064, 1998.
21.Siegman AE. The antenna properties of optical heterodyne receivers. Appl Opt 5:1588– 1594, 1966.
22.Schmitt JM, Knu¨ttel A, Yadlowsky M. Interferometric versus confocal techniques for imaging microstructures in turbid biological media. SPIE Proc 2135:251–262, 1994.
23.Smithies DJ, Lindmo T, Chen Z, Nelson JS, Milner TE. Signal attenuation and localization in optical coherence tomography studied by Monte Carlo simulation. Phys Med Biol 43:3025–3044, 1998.
24.Barton JK, Welch AJ, Izatt JA. Investigating pulsed dye laser–blood vessel interaction with color Doppler optical coherence tomography. Opt Express 3:251–256, 1998; www.osa.org.
25.Fingar VH, Wieman TJ, Wiehle SA, Cerrito PB. The role of microvascular damage in photodynamic therapy: The effect of treatment on vessel constriction, permeability, and leukocyte adhesion. Cancer Res 52:4914–4921, 1992.
26.Nawab SH, Quatieri TF. Short-time Fourier transform. In: Advanced Topics in Signal Processing. JS Lim, AV Oppenheim, eds. Englewood Cliffs, NJ: Prentice-Hall, 1989, pp 289–327.
27.Oppenheim AV, Schafer RW. Discrete-Time Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989.
28.Yazdanfar S. High resolution in vivo blood flow imaging using color Doppler optical coherence tomography. MS Thesis, Department of Biomedical Engineering, Case Western Reserve Univ, 1998.
29.van Leeuwen TG, Kulkarni MD, Yazdanfar S, Rollins AM, Izatt JA. High flow velocity imaging using color Doppler optical coherence tomography. Adv Opt Imag Photon Migration 21:364–366, 1998.
30.Yazdanfar S, Rollins AM, Izatt JA. In vivo imaging of blood flow in human retinal vessels using color Doppler optical coherence tomography. Proc SPIE 3598, San Jose, 1999.
31.Nieuwkoop PD, Faber J. Normal Table of Xenopus laevis (Daudin). New York: Garland, 1994.
32.Izatt JA, Kulkarni MD, Yazdanfar S, Barton JK, Welch AJ. In vivo bidirectional color Doppler flow imaging of picoliter blood volumes using optical coherence tomography. Opt Lett 22:1439–1441, 1997.
33.Boppart SA, Tearney GJ, Bouma BE, Southern JF, Brezinski ME, Fujimoto JG. Noninvasive assessment of the developing Xenopus cardiovascular system using optical coherence tomography. Proc Natl Acad Sci USA 94:4256–4261, 1997.
34.Alm A. Ocular circulation. In: Adler’s Physiology of the Eye: Clinical Application. 9th ed. JWM Hart, ed. St. Louis, MO: Mosby Year Book, Inc, 1992.
35.ANSI. Safe Use of Lasers. ANSIZ136.1. New York: Am Nat Stand Inst, 1993.
36.Roggan A, Friebel M, Dorschel K, Hahn A, Muller G. Optical properties of circulating human blood in the wavelength range 400–2500 nm. J Biomed Opt 4:36–46, 1999.
37.Swanson EA, Izatt JA, Hee MR, Huang D, Lin CP, Schuman JS, Puliafito CA, Fujimoto JG. In vivo retinal imaging by optical coherence tomography. Opt Lett 18:1864–1866, 1993.
9
Polarization-Sensitive
Optical Coherence Tomography
JOHANNES F. DE BOER*, SHYAM M. SRINIVAS, and J. STUART NELSON
University of California at Irvine, Irvine, California
THOMAS E. MILNER and MATHIEU G. DUCROS
University of Texas at Austin, Austin, Texas
9.1INTRODUCTION
9.1.1OCT and Polarization-Sensitive OCT
In the previous chapters, light was treated as a scalar wave. However, light is described by a transverse electromagnetic wave that is markedly different from a longitudinal wave such as sound. The extra degrees of freedom due to the transverse character are described by the polarization state of light. Polarization-sensitive OCT (PS-OCT) uses the information carried by the polarization state to extract extra information from the sample under study. PS-OCT provides high resolution spatial information on the polarization state of light reflected from tissue that is not discernible using existing diagnostic optical methods. This chapter will be devoted to PS-OCT and its application in biomedical imaging.
9.1.2Optical Properties of Tissue That Influence Polarization
Two mechanisms dominate the changes in the polarization state of light propagating through biological tissue: scattering and birefringence. Scattering changes the polarization of light mainly in a random manner, as will be demonstrated by the following examples. Let us assume circular polarized light incident on an isotropic scatterer (i.e., a spherical particle much smaller than the wavelength). The forward-scattered
Current affiliation: Harvard Medical School and Wellman Laboratories of Photomedicine, Massachusetts General Hospital, Boston, Massachusetts
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light has the same circular polarization state, but the helicity of the backscattered light is reversed, and light scattered at an angle of 90 from the incident direction is linearly polarized. This example illustrates that a single scattering event can dramatically scramble the incident polarization state. As particle size increases (the scattering becomes more anisotropic), the incident polarization is preserved better [1]. For linearly polarized light, the incident polarization is better preserved by isotropic scattering than by anisotropic scattering [1–3]. For spherical particles and cylinders, exact solutions to the Maxwell equations can be computed by Mie theory [4]. For nonspherical particles, Mishchenko and Hovenier [5] calculated the polarization scrambling, concluding that the difference in polarization scrambling of circularly and linearly polarized light cannot be considered a universal measure of the departure of particle shape from that of a sphere. As the light scatters multiple times, the scrambling effect of single scattering events accumulates, until finally, the polarization state is completely random (i.e., not correlated with the incident polarization state). Assuming a random orientation and arbitrary shape of scattering structures in tissue, the polarization state will be changed in a random manner.
One exception is organized linear structures, such as fibrous tissues, that can exhibit birefringence. Birefringence changes the polarization state of light by a difference ( n) in the refractive index for light polarized along, and perpendicular to, the optic axis of a material. The difference in refractive index introduces a phase retardation, , between orthogonal light components that is proportional to the distance x traveled through the birefringent medium,
¼ 2 n x ð1Þ
Birefringence in biological tissues can have two components: Form birefringence results from ordered linear structures surrounded by a ground substance with a different refractive index [6]; intrinsic birefringence results from molecules with different optical retardance arranged in an ordered configuration. Birefringence changes the polarization state in a predictable manner, described by, for instance, the Mueller or Jones matrix of a linear retarder. Many biological tissues, such as tendons, muscle, nerve, bone, cartilage and teeth, exhibit birefringence. The advantage of PS-OCT is the enhanced contrast and specificity in identifying structures in OCT images by detecting induced changes in the polarization state of light reflected from the sample. Moreover, changes in birefringence may, for instance, indicate changes in functionality, structure, or viability of tissues.
9.2THEORY
9.2.1Historical Overview
The emphasis in optical coherence tomography (OCT) has been on the reconstruction of two-dimensional maps of changes in tissue reflectivity, and the polarization state of light was of minor importance. However, in 1992, Hee et al. [7] reported the first OCT system able to measure the changes in the polarization state of light reflected from a sample. They demonstrated birefringence-sensitive ranging in a wave plate, an electro-optic modulator, and calf coronary artery. In 1997, the first two-dimensional images of birefringence in bovine tendon were presented, and the effect of laser-induced thermal damage on the birefringence of collagen was demon-
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strated [8], followed in 1998 by a demonstration of the birefringence in porcine myocardium [9]. To date, polarization-sensitive OCT measurements have attracted active interest from several research groups.
9.2.2Experimental Configuration
The theory of PS-OCT will be offered based on the experimental configuration first presented by Hee et al. [7]. Figure 1 shows a schematic of this PS-OCT system, which was used for all images presented in this chapter except for Figs 9–12. Light with a short coherence length passes through a polarizer P to select a pure linear horizontal input state and is split into reference and sample arms by a polarization-insensitive beamsplitter (BS). Light in the reference arm passes through a zero-order quarterwave plate (QWP) oriented at a 22:5 angle to the incident horizontal polarization. Following reflection from a mirror or retroreflector and a return pass through the QWP, light in the reference arm has a linear polarization at a 45 angle with respect to the horizontal. Light in the sample arm passes through a QWP oriented at a 458 angle to the incident horizontal polarization and through focusing optics, producing circularly polarized light incident on the sample. Reflected light from the sample, in an arbitrary (elliptical) polarization state determined by the optical properties of the sample, returns through the focusing optics and the QWP. After recombination in the detection arm, the light is split into its horizontal and vertical components by a polarizing beamsplitter (PBS) and focused on pinholes or single-mode fibers to detect a single polarization state and spatial mode.
Figure 1 Schematic of the PS-OCT system. SLD: superluminescent diode, 0.8 mW output power, central wavelength ¼ 856 nm, and spectral FWHM ¼ 25 nm. L, lens; P, polarizer; BS, beamsplitter; QWP, quarter-wave plate; NDF, neutral density filter; PBS, polarizing beamsplitter; PZT, piezoelectric transducer. Two-dimensional images were formed by either axial movement of the sample with constant velocity v ¼ 1 mm/s (z direction), repeated after each 10 m lateral displacement (x direction), or lateral movement of the sample with constant velocity v ¼ 1 mm/s (x direction), repeated after each 10 m axial displacement (z direction). The latter allows for focus tracking in the sample.
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Two-dimensional images can be formed by lateral or axial movement of the sample at constant velocity v, repeated after each axial or lateral displacement, respectively. The carrier or interference fringe frequency can be generated by axial movement of the sample or the reference mirror, by translating the reference mirror mounted on the piezoelectric transducer over a few wavelengths, or by a combination of both. Transverse and axial image resolutions are determined by, respectively, the beam waist at the focal point and the coherence length of the source.
9.2.3Jones Matrix Formalism
The polarization state in each arm of the interferometer is computed using the Jones matrix formalism. The intensity detected in each polarization channel can be described by a two-dimensional intensity vector I, where the two components describe the horizontal (x) and vertical (y) polarized intensities, respectively. The
intensities at the detectors |
are given by |
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Ið zÞ ¼ Ir þ Is þ |
ErxEsx z |
þ |
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ErxEsx z |
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ð2Þ |
EryEsyðð zÞÞ |
EryEsyðð zÞÞ |
|||||
where E, E are the electric field component and its complex conjugate, z is the pathlength difference between the two arms of the interferometer, and subscripts r and s denote the reference and sample arms, respectively. The angular brackets denote time averaging. The last two terms of Eq. (2) correspond to the interference between reference and sample arm light. After the polarizer, horizontally polarized
source light is described by the Jones vector,
EðzÞ ¼ EðzÞ |
1 |
ð3Þ |
0 |
In our analysis, the electric field amplitude is represented by a complex analytic
function EðzÞ [10], with
ð
EðzÞ ¼ e~ðkÞ expð ikzÞ dk |
ð4Þ |
where e~ðkÞ is the field amplitude as a function of free-space wavenumber k ¼ 2= with
e~ðkÞ ¼ 0 |
if k < 0 |
ð5Þ |
From the Wiener–Khinchin theorem, it follows that |
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e~ðkÞe~ðk 0Þ ¼ SðkÞ ðk k0Þ |
ð6Þ |
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which defines e~ðkÞ in terms of the source power spectral density SðkÞ. The beamsplitter splits the light evenly between both arms of the interferometer, and the Jones
vector describing the light that enters the sample and reference arm is given by
E z |
E z |
EðzÞ |
1 |
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sið Þ ¼ |
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ð Þ |
rið Þ ¼ p2 |
0 |
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First, the polarization state of light reflected from the reference arm is calculated. The Jones matrix for a QWP with fast and slow axes aligned along the horizontal and vertical axes is given by