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

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Doppler OCT

221

8.4DOPPLER OCT BIOMEDICAL APPLICATIONS

The noninvasive nature and exceptionally high spatial resolution of Doppler OCT have distinct applications in the clinical management of patients in whom blood flow monitoring is essential. For example, with Doppler OCT it is possible to

Obtain an in situ three-dimensional tomographic image and velocity profiles of blood perfusion in tissue at discrete spatial locations in either the superficial or deep layers.

Determine burn depth; provide guidance regarding the optimal depth for burn debridement prior to definitive closure.

Determine tissue perfusion and viability immediately after injury, wound closure, replantation, or transposition of either rotational or free skin flaps.

Evaluate the vascular status of a buried muscle flap covered by a split thickness skin graft; perfusion in the superficial and deeper flap components can be monitored separately.

Distinguish between arterial or venous occlusion and determine the presence and/or extent of adjacent posttraumatic arterial or venous vascular injury by providing in situ tomographic image and velocity profile of blood flow.

Monitor the effects of pharmacological intervention on the microcirculation (e.g., effects of vasoactive compounds or inflammatory mediators); determine transcutaneous drug penetration kinetics; evaluate the potency of penetration enhancers, irritation of chemical compounds, patch-test allergens, and ultraviolet radiation; compare the reactivity of the skin microcirculation in different age and ethnic groups.

In human tissue, an important issue is the volume of tissue that may be interrogated and imaged using Doppler OCT. We describe two clinical entities designed to demonstrate how Doppler OCT can assist in the optimal management of patients where imaging blood flow in the skin’s most superficial layers (1–2 mm) is important:

(1) port wine stain (PWS)—the evaluation of laser therapy efficacy—and (2) superficial basal cell carcinoma—monitoring intratumoral blood flow during photodynamic therapy (PDT).

8.4.1Port Wine Stain

Port wine stain (PWS) is a congenital, progressive vascular malformation of the dermis; although PWS may occur anywhere on the body, most lesions appear on the face and neck. The pulsed dye laser can selectively coagulate PWS by inducing microthrombus formation within the targeted blood vessels. However, only a small proportion of patients obtain 100% fading of their PWS, even after undergoing multiple laser treatments. Histopathological studies of PWS show an abnormal plexus of layers of dilated blood vessels located 150–750 m below the skin surface in the upper dermis. These vessels have diameters varying on an individual patient basis and even from site to site on the same patient, over a range of 10–150 m. Barton et al. [24] reported application of Doppler OCT to investigate the relationship between irreversible photocoagulation of subsurface blood vessels and incident laser dosimetry (dose, pulse duration, and wavelength). Although these studies were completed using an in vivo animal model, application of Doppler OCT to provide a

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Milner and Izatt

fast semiquantitative evaluation of the efficacy of laser therapy in real time appears feasible.

8.4.2Superficial Basal Cell Carcinoma—Monitoring Intratumoral Blood Flow During Photodynamic Therapy

Superficial basal cell carcinoma (SBCC) is a malignant tumor arising from the basal cells at the epidermal-dermal junction located 50–500 m deep in the skin and is by far the most common form of skin cancer; in the United States 400,000–500,000 new cases are diagnosed each year. Existing treatments for these lesions include surgery, curettage with desiccation, and radiation, all of which may leave highly disfiguring scars. In recent years, photodynamic therapy (PDT) has been proposed as a treatment modality that may offer more cosmetically appealing results. Previous basic science studies have attempted to elucidate the mechanism of PDT-induced tumor destruction. Stoppage of tumor blood flow shortly after the initiation of PDT treatment has been demonstrated and also that complete cessation of tumor circulation was required to effect its complete eradication. Noncurative treatments frequently result in resumption of intratumoral blood flow. Taken together, these studies suggest that the vascular compartment represents an important target and that the progress of PDT could potentially be followed by monitoring intratumoral blood flow.

The rationale for using Doppler OCT in the clinical management of SBCC is that the technique offers a means of following the progress of PDT by monitoring intratumoral blood flow in real time. It is expected that blood flow reduction from preirradiation levels as measured by Doppler OCT will be proportional to the total light dosage delivered. At low total light dosage, there are relatively minor effects on the tumor vasculature; after the laser is turned off, reperfusion leads to a return in blood flow to preirradiation levels. Alternatively, high total light dosage effectively destroys the tumor vasculature, leading to complete and permanent reduction in blood flow. In this case, blood flow approaches zero during laser irradiation, and after the laser is turned off there is no return to preirradiation values observed with Doppler OCT. A correlation of tumor necrosis as a function of total light dosage can then be made.

The potential application of Doppler OCT for in vivo blood flow monitoring during photodynamic therapy (PDT) was investigated in the rodent mesentery. Twenty minutes after injection of a 2 mg/kg solution of benzoporphyrin derivative

(BPD)

through the

rodent tail

vein, the effect of laser irradiation (

¼

690 nm,

2

 

tL ¼ 120 s)

 

 

D ¼ 12 J=cm

, and

on mesenteric blood flow was studied. Doppler

OCT images recorded before (Fig. 10A) and 16 min (Fig. 10B) and 71 min (Fig. 10C) after laser irradiation were obtained.

Sixteen minutes following laser irradiation, the diameter of the rodent artery had decreased from 320 m to 60 m; 71 min after laser irradiation, the diameter of the artery was 385 m. As expected and as described by other investigators [25], the artery went into vasospasm after laser exposure. Subsequently, in response to PDTinduced tissue hypoxia, compensatory vasodilation occurs within 1 h of laser irradiation.

Although these results suggest that the application of Doppler OCT to clinical problems of interest is feasible, the processing used to construct these images is based

Doppler OCT

223

Figure 10 (A) OCT structural and (A0) Doppler velocity images of rodent artery prior to laser irradiation. (B) OCT structural and (B0) Doppler velocity images of rodent artery 16 min after laser irradiation. (C) OCT structural and (C0) Doppler velocity images of rodent artery 71 min after laser irradiation.

on the spectrogram using an STFFT. Because the STFFT is computationally intensive, alternative approaches are required to obtain Doppler OCT imaging in real time.

8.4.3Alternative Implementations of the Short-Time Fourier Transform

To integrate Doppler OCT with clinical systems, processing must be performed rapidly, generating several flow images per second. Hardware methods for time– frequency analysis are desirable, because these implementations allow faster processing and analysis. This section describes alternative implementations for performing the short-time Fourier transform (STFT), allowing near-real-time acquisition of Doppler OCT images.

Filterbank Approach

As shown schematically in Fig. 11, the STFT can alternatively be implemented as the output of a filterbank [26]. Rather than measuring a spectrum for each window centered at time ti, the spectrogram can be formed by measuring the temporal response at each frequency i. Because the analysis window behaves as a low-pass filter [27], modulating it by expð j2 0n tsÞ results in a frequency-shifted version, or a bandpass filter (BPF). The summation in the STFFT may be viewed as a convolution summation between the Doppler signal and a BPF centered at frequency o:

Sd ðn ts; oÞ ¼ id ðn tsÞ wðn tsÞ expð j2 on tsÞ

ð25Þ

If several BPFs are employed, then the Doppler frequency at a given time can be taken as the center frequency of the BPF whose output contains the highest energy relative to all other filters [28].

Parallel Demodulation Approach

Alternatively, the filterbank approach to the STFT can be implemented by parallel demodulation [26,28,29] (i.e., demodulating at several frequencies concomitantly). In Eq. (25) grouping the exponential term with the Doppler signal current results in

Sd ðn ts; oÞ ¼ ½expð j2 on tsÞ&½id ðn tsÞ expð j2 on tsÞ wðn tsÞ& ð26Þ

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Milner and Izatt

Figure 11 A spectrogram can be implemented vertically or horizontally: by obtaining spectral information at times t1, t2, etc. or by arranging temporal information at frequencies f1, f2, etc. Currently, a velocity estimate in Doppler OCT is the centroid of the spectrum at some time ti. Alternatively, the local velocity can be estimated by selecting the filter fi that has the highest relative energy at that given time (depth).

Here the STFT is a convolution between the modulated detector current and the analysis window, or the operation performed by a quadrature detector at a single frequency. The output is then modulated by expðj2 o tsÞ. For Doppler OCT, this final step can be disregarded, because synthesis (reconstruction of the signal from the STFT) is not necessary and the amplitude is not altered by this omission. Hence, it has been demonstrated that time–frequency analysis in Doppler OCT can be implemented with parallel demodulation electronics. The output of each of the detection channels is nearly instantaneous, allowing real-time implementation of Doppler OCT. Hardware techniques avoid time-consuming computation of fast Fourier transforms used in Doppler processing of images presented above.

Time Domain Autocorrelation Implementation

The Wiener–Khinchin theorem relates the power spectral density of a wide-sense

stationary process to its autocorrelation via the Fourier transform:

ð1

Rð Þ ¼

 

Pð Þei2 d

ð27Þ

1

 

 

The center frequency, given by

 

1

P d

 

¼

Ð 11 P ð

Þd

ð28Þ

1

ð

Þ

 

can thus beÐ directly calculated using the signal autocorrelation

 

ð

Þ

 

 

_

 

 

 

 

 

R

 

 

 

¼ i

Rð Þ

 

 

ð29Þ

 

 

 

 

 

 

 

 

 

 

 

 

¼0

Doppler OCT

225

_

where Rð Þ is the derivative of Rð Þ with respect to . Because the autocorrelation is typically calculated using a fast Fourier transform algorithm, direct calculation of Eq. (29) may be time-consuming. To simplify the computation, the autocorrelation can be evaluated in terms of the amplitude and phase. Define

Rð Þ Að Þei ð Þ

ð30Þ

and

 

R_ð Þ ¼ A_ð Þ þ iAð Þ _ð Þ ei ð Þ

ð31Þ

Equation (29) can now be estimated by taking the derivative of the phase of the autocorrelation [14]:

 

¼

_

0

Þ

ðTÞ ð0Þ

¼

ðTÞ

ð

32

Þ

 

 

ð

T

T

 

where T is the time delay of the detected signal. Implemented in software, the autocorrelation technique reduces computation time by greater than tenfold.

Experiments to detect flow in an Intralipid phantom in real time using a variation of the autocorrelation technique was recently implemented in hardware [18] as described schematically in Fig. 12. A high dynamic range limiter removes the amplitude dependence of the interferogram, which is then low-pass filtered and split into two paths. One of these paths is electronically delayed with respect to the other by a time . A phase detector then measures the difference in phase between the

Figure 12 Flow diagram of real-time Doppler OCT using autocorrelation implementation. The interferogram is bandpass filtered (BFP) to reduce noise, then input into a high dynamic range limiter, which removes the envelope, or amplitude dependence, of the Doppler signal. A low-pass filter (LPF) then removes the higher harmonics introduced by the limiter. The signal is split into two paths, one of which is electronically delayed with respect to the other. The two paths are multiplied and low-pass filtered, thus implementing the autocorrelation in hardware. Because the enevolpe has been removed, this process results in a sinusoidal function of the phase of the autocorrelation, which is related to the sample arm Doppler frequency by Eq. (34).

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Milner and Izatt

signals from the two paths. The output of the phase detector (i.e., the autocorrelation) is a sinusoidal function of the phase difference between the two paths, given by

~

ð33Þ

Rð Þ ¼ sin½2 ð r þ sÞ &

which is, equivalently, the autocorrelation of the detector current without the envelope.

~

By choosing r and appropriately such that Rð Þ ¼ 0 when s ¼ 0, the autocorrelation reduces to

~

ð34Þ

Rð Þ ¼ sinð2 s Þ

Therefore, because s is related to flow velocity, positive values of the autocorrelation encode flow in one direction, and negative values encode flow in the other direction (Fig. 13). Implemented in hardware, this technique was used to measure flows representative of larger blood vessels at 6 fps [18].

8.4.4Perfusion and Turbulent Flow Characterization

In Sections 8.3.1 and 8.3.2, multiple scattering of light was observed to broaden the Doppler signal power spectra. When direction of the incident and backscattered light is constrained so that ks ¼ ki, turbulent motion or spatial variation in the velocity of moving constituents, V, creates a distribution of detected Doppler frequencies characteristic of the sample under investigation. Turbulent flow, although generally not present in the micrometer-scale vasculature, also leads to Doppler broadening. In this case an estimate of local tissue perfusion or turbulent flow, spectral broad-

Figure 13 (a) Sinusoidal output of phase detector in Fig. 12, chosen such that zero Doppler shift in the sample corresponds to zero output. Positive and negative Doppler shifts are then represented by red and blue, respectively. (b) Choosing a shorter time delay results in a longer monotonic response range but lower velocity sensitivity. (c) A longer delay improves the sensitivity, but over a smaller response range.

Doppler OCT

227

ening can be measured by using the variance of the spectrum. The variance of the local spectrum Sðn ts; Þ for an N-point STFT window is given by

 

 

 

 

 

Þ ¼ P

i¼þN=2

½ i ðn ts

2

Sd ðn ts; iÞ

 

2 n t

s

i¼ N=2

Þ&

35

 

ð

 

 

 

 

i

 

N=2

Sd

 

 

ts; i

 

ð Þ

 

 

 

 

P

i¼þN=2

n

 

where

 

 

 

 

 

 

 

 

¼

ð

 

 

 

 

Þ

 

 

 

 

 

 

 

i¼þN=2

 

 

 

 

 

 

 

 

 

 

 

n t

s

 

 

 

i¼ N=2 iSd ðn ts; i

Þ

 

 

36

ð

 

Þ ¼

 

i

N=2

Sd

n ts; i

 

 

 

 

ð Þ

 

 

P i¼þN=2

Þ

 

 

 

 

 

 

 

 

 

P

 

¼

 

 

ð

 

 

 

 

 

 

 

is the corresponding centroid used in the Doppler OCT images.

Spectral broadening was measured [30] in depth-resolved backscattered spectra in the cardiovascular system of a stage 51 [31] Xenopus laevis tadpole, shown in Fig. 14 (see color plate). The images were processed using the STFT algorithm described in Section 8.2.2. On the left are velocity images during systole and diastole, and on the right are the corresponding variance images. Note that in the velocity images, motion on the ventricular tissue induced Doppler shifts in the sample arm that were detected using Doppler OCT. This artifactual signal, referred to as clutter [15], is also observed in clinical Doppler ultrasonography. Motion of the ventricle is uniform and thus is not composed of large velocity gradients that lead to spectral broadening. However, blood flow in the ventricle, atrium, and truncus arteriosus contains sufficient velocity gradients to generate uncorrelated random shifts of light backscattered

Figure 14 Comparison of velocity (left) and variance (right) images in a stage 51 Xenopus tadpole heart [13] during systole (top) and diastole (bottom). Motion of the ventricle induces a uniform Doppler shift that generates cluttered images. Variance images eliminate clutter by identifying regions containing large flow gradients, such as within the ventricle, atrium, and truncus arteriosus. (See color plate.)

228 Milner and Izatt

from these regions, broadening the Doppler spectrum considerably. Variance within these regions exceeds that induced by the ventricular wall.

In addition to detecting the center Doppler frequency of the signal spectrum, the autocorrelation formulation can be used to approximate the variance of the

spectrum as a measure of turbulence in the flow [14]. The variance is given by

 

 

 

 

 

 

1

 

 

 

 

2P

d

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 ¼

Ð1ð1 P Þ

Þ

dð Þ

¼ 2 2

ð37Þ

 

 

 

 

 

 

 

1

ð

 

 

 

 

 

 

 

 

Here, the

second derivative of the autocorrelation is also necessary, because

 

 

 

 

 

 

 

Ð

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_

 

 

 

2

 

 

 

 

 

 

 

 

 

 

2

 

 

 

Rð0Þ

 

 

 

Rð0Þ

 

 

 

 

38

 

¼

 

Rð0Þ

Rð0Þ

 

 

 

ð

Þ

 

 

 

 

 

 

which can be approximated by

 

 

 

2

 

 

2

 

 

1

 

 

Rð Þj

 

 

 

 

39

 

 

T2

 

jRð0Þ

 

 

 

ð

Þ

 

 

 

 

 

 

 

Within the sampling volume of the STFT window, a distribution of scatterers with various velocity vectors (i.e., a velocity gradient within the window) will lead to Doppler broadening of the measured frequency spectrum. Quantification of broadening is particularly useful for estimating tissue perfusion when the dimensions of the vessels are smaller than the dimensions of the STFT window. Depth-resolved spectral broadening was used in Fig. 14 to distinguish regions of the Xenopus ventricle with large velocity gradients. This technique may also be useful for removal of image clutter, such as that induced by the motion of the ventricular tissue.

8.4.5High Precision Velocity Image Reconstruction in Periodic Flows

The minimum resolvable velocity in Doppler OCT is proportional to the image acquisition rate [13,14,17,32]. Images must be acquired relatively slowly ( 1 s/ image) in order to obtain high velocity resolution (< 0:5 mm/s). This prevents imaging of dynamic structures due to motion artifact in living subjects, a task that will be necessary in clinical environments. Thus the problem arises of overcoming motion artifact while retaining the capability of measuring flow in the microcirculation, where velocities approaching the resolution of Doppler OCT may be encountered. In this section, a technique is presented for motion arti- fact–free reconstruction of flow [13] in a beating Xenopus heart. This technique is illustrated with reconstructed Doppler OCT frames displaying the dynamics of the cardiovascular system simultaneously with high velocity resolution Doppler flow mapping. Movies arranged from the reconstructed frames have been published and are available for viewing on-line [13].

Gated Reconstruction Algorithm

With the sample beam incident on the ventral side of each specimen, oblique (45 from sagittal to coronal) sections of the beating heart were acquired with Doppler OCT and analyzed for flow. The heartbeat of the specimen was measured under a microscope, using OCT ‘‘optical cardiograms’’ [33]. Reconstruction of the beating

Doppler OCT

229

heart was performed by obtaining a 1000 A-scan OCT image that was oversampled in the lateral direction, ensuring that at least five A-scans were acquired per heartbeat while the sample was translated laterally by one focused sample probe beam spot size (14 m). From this image, separate time-gated cardiac image frames were extracted. Each of the frames was composed of A-scans occurring at the same segment of the cardiac cycle. Therefore, if the number of A-scans per beat was T, sequential frames were composed of 1000=T lateral pixels each. Gating of the image data according to the heartbeat was performed by estimating the value of T retrospectively, by selecting that value that completely eliminated motion artifact in the reconstructed frames.

Reconstruction of Cardiac Flow Dynamics

An OCT image through the ventral surface of the specimen is shown in Fig. 15. Although stationary structures are clearly delineated in the OCT image, the motion artifact, indicated by alternating dark and light vertical bands in the center of the image, blurs the image data within the pericardium. The general shape of the heart is apparent, but large structures such as the distinct chambers are not resolvable.

Figure 16 isolates a selected smaller time segment from the OCT image in Fig. 15, demonstrating the repetitive expansion and contraction of the heart that result in motion artifact. This figure illustrates that each heart beat (measured between consecutive and diastolic dimensions) comprised approximately five A-scans. Therefore,

Figure 15 Oblique (45 from sagittal to coronal) optical section of Xenopus heart through ventral surface of body. The abscissa is the equivalent time of acquisition for the image. This image is composed of 1000 lateral and 256 axial pixels, spanning 2.0 mm across and 1.07 mm deep (assuming a mean index of refraction of 1.4). Whereas some structures are visible with high resolution, image clarity is drastically reduced in moving structures (i.e., heart and diaphragm). White bars indicate the region magnified in Fig. 14. st, stomach; l, liver; p, pericardium; bv, branched vessels.

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Milner and Izatt

Figure 16 A-scans extracted from Fig. 15 between the vertical white bars within the ventricle. One period of the cardiac cycle required exactly five (T ¼ 5:00 0:01) A-scans.

approximately every fifth A-scan was recorded at the same segment of the cardiac cycle, during which the sample beam was translated laterally 10 m, less than one focused sample probe beam spot size. This reconstruction method effectively imitates heart beat gated image acquisition without requiring the insertion of electrodes or otherwise independent monitoring of the heart rate.

Figure 17 (see color plate) is a gated Doppler OCT reconstruction of the beating Xenopus heart performed using the five sequential time frames extracted from Fig. 15. Using optical cardiograms it was determined that the heart rate was 1.6 beats/s and the number of A-scans per beat T ¼ 5:00 0:01. Color Doppler flow processing was performed solely on the region of interest indicated by the rectangle enclosing the counterpropagating vessels. The appearance of flow in each vessel during the cardiac cycle correlates to its corresponding role in systole or diastole. The contraction of the heart during systole is followed immediately by maximum pulsatile flow in the truncus arteriosus. Also, flow into the heart through the vein occurs preceding and during expansion of the ventricle (diastole). Owing to its pulsatile nature, flow within the truncus arteriosus appears briefly; however, flow through the vein is detected for a longer duration, because blood flow is damped when returning to the heart.

Motion of the vessel walls also results in Doppler shifts in the backscattered light in addition to flow within the truncus arteriosus. In Fig. 17, the upper region of the arterial wall expands during systole, generating negative (blue) Doppler shifts that can be misinterpreted as flow.

This technique requires no additional hardware with current Doppler OCT instrumentation. Because gating assumes that the dynamic process under analysis is periodic throughout acquisition of the image, a potential use for this reconstruction algorithm is for measurement of flow in clinical environments, in which periodic, pulsatile flow is commonly encountered, such as flow in large retinal vessels. Gated reconstruction diminishes motion artifact yet preserves velocity resolution in Doppler OCT.