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High speed, wide velocity dynamic range Doppler optical coherence tomography (Part I): System design, signal processing, and performance

Victor X.D. Yang, Maggie L. Gordon, Bing Qi, Julius Pekar, Stuart Lo, Emily Seng-Yue, Alvin Mok, Brian C. Wilson, and I. Alex Vitkin

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Abstract

Improvements in real-time Doppler optical coherence tomography (DOCT), acquiring up to 32 frames per second at 250×512 pixels per image, are reported using signal processing techniques commonly employed in Doppler ultrasound imaging. The ability to measure a wide range of flow velocities, ranging from less than 20 µm/s to more than 10 cm/s, is demonstrated using an 1.3 µm DOCT system with flow phantoms in steady and pulsatile flow conditions. Based on full implementation of a coherent demodulator, four different modes of flow visualization are demonstrated: color Doppler, velocity variance, Doppler spectrum, and power Doppler. The performance of the former two, which are computationally suitable for real-time imaging, are analyzed in detail under various signal-to-noise and frame-rate conditions. The results serve as a guideline for choosing appropriate imaging parameters for detecting in vivo blood flow.

©2003 Optical Society of America

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Figures (17)
Fig. 1.
Fig. 1. (a) Schematic of the DOCT system. LS: light source. PC: polarization controller. OC: optical circulator. 3dB: 50-50 fiber coupler. PM: phase modulator. RSOD: rapid scanning optical delay line. BPD: balanced photo-detector. PMD: phase modulator driver. I&Q: inphase and quadrature demodulator. SD-1 & 2: scanner drivers. COMP: computer. (b) The hardware and software signal conditioning chain, particularly the I&Q demodulator. TIA: trans-impedance amplifier. HPF & LPF: high- and low-pass filters. DGC: depth-gain-compensation amplifier. DF: depth feedback signal. SIN & COS: 0° and 90° shifted carrier frequency, synchronized to the PMD. ADC: analog-to-digital converter. BGC: digital bias and gain compensation.

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Fig. 2.
Fig. 2. Signal and filter frequency response during coherent demodulation. Solid line: Calculated frequency response for 8.05 kHz RSOD when scanning 1.3 mm of depth. Dashed line: Frequency response of 12.95 kHz RSOD when scanning 1.0 mm of depth. After mixing with the 4.3 MHz carrier frequency, the signals are down-shifted to the base-band, and upshifted to 8.6 MHz. Blue line: Low pass filter response, approximating a matched filter for the base-band signals, and completely removing the up-shifted signal around 8.6 MHz.

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Fig. 3.
Fig. 3. (a) The mean phase shift can be calculated by evaluating the phase angle of the individual OCT signals and then computing the phase differences between axial scans. (b) The result is equivalent to computing the phase angle of the mean (〈X〉,〈Y〉) vector. The computation in (b) is numerically less complex than in (a), and so (b) is more suitable for real-time processing.

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Fig. 4.
Fig. 4. (a) Spatial averaging masks for improving the SNR in structural and flow images. Shaded areas indicate regions with shared computation between pixels. (b) Calculated axial velocity using two-quadrant arctan (red) and four-quadrant arctan (blue) functions, showing the aliasing effect and the color map used in color Doppler OCT. (c) Measured phase noise processed from different ensemble lengths (N=2 to 128, and M=1). Each data set (dots) represents the normalized distribution of phase noise measured from 20,000 pixels using a stationary diffuse reflectance target, with a Gaussian fit (line).

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Fig. 5.
Fig. 5. Schematic for generating audio output to accompany the Doppler spectrum display. The directional information is encoded in the stereo’s left and right channels. H: digital Hilbert transform performing 90° phase shift. DAC: digital-to-analog convertor.

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Fig. 6.
Fig. 6. (a) Structural, (b) color Doppler, and (c) normalized Doppler variance images of a 0.5% Intralipid stationary phantom, acquired at 2 fps. Scale bar=0.5 mm.

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Fig. 7.
Fig. 7. SNR varied with depth; therefore, the image was divided into 5 horizontal regions of interest (ROI) to investigate velocity noise as a function of SNR. Each data point is the mean value within a ROI containing 25,000 pixels. (a) Background noise levels in the color Doppler mode at 2 – 32 fps and the corresponding structural image SNR conditions. (b) Background noise levels in the velocity variance mode at various frame rates and corresponding structural image SNR conditions. Note: 0 fps indicates no lateral scanning, i.e., analogous to M-mode ultrasound.

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Fig. 8.
Fig. 8. (a) Structural, (b) color Doppler, and (c) normalized velocity variance images of 0.5% Intralipid flow phantom, acquired at 0 fps. At 0 fps, the x-axis represents time, not distance. Flow rate=60 µL/min, corresponding to 0.68 mm/s peak velocity after accounting for Doppler angle. Vertical streaks in (b) are due to the discrete stepping motor motion on the infusion pump, prominent at low flow rates. Scale bar=0.5 sec.

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Fig. 9.
Fig. 9. (a) Structural, (b) color Doppler, and (c) normalized velocity variance images of 0.5% Intralipid flow phantom, acquired at 0 fps. At 0 fps, the x-axis represents time, not distance. Flow rate=1.5 mL/min, corresponding to 1.7 cm/s peak velocity after accounting for Doppler angle. Notice the aliasing pattern in (b), and the disappearance of the vertical streaks. Scale bar=0.5 sec.

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Fig. 10.
Fig. 10. Comparison of measured peak velocity in color Doppler mode (measuring the velocity vector along the optical axis) and the expected flow velocity, as set on the infusion pump. Each data point is the mean of 25,000 pixels at the center of the phantom. (a) Low flow rate conditions without aliasing. Solid line: Unity slope. Error bars: Standard deviation within the 25,000 pixels. (b) With flow velocities greater than 1.9 mm/s, aliasing occurs. Solid line: Expected relationship, following Fig. 4(b). Notice the increased scattering of data points with higher velocity, which forms the basis of velocity variance imaging.

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Fig. 11.
Fig. 11. Normalized velocity variance versus flow velocity (without Doppler angle correction). Each data point is the mean of 25,000 pixels. Solid line: Inverted Gaussian fit. Dashed vertical line: Aliasing velocity, measured at 81.4° Doppler angle.

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Fig. 12.
Fig. 12. (a) Structural, (b) color Doppler, and (c) normalized velocity variance images of a 0.5% Intralipid flow phantom, acquired at 0 fps. The x-axis is time and flow goes from right to left. The flow rate was adjusted to be pulsatile at ~ 9 Hz, with the peak velocity just below the aliasing velocity limit. Scale bar=250 ms.

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Fig. 13.
Fig. 13. (77, 172, 359, 737 and 1423 kB, respectively) Left to right: 2, 4, 8, 16, and 32 fps videos of the pulsatile flow phantom, each containing structural (top), color Doppler (mid), and velocity variance (bottom) images. Each video is 2 seconds long. The diameter of the tube is ~ 0.75 mm. Notice the peak velocity drifting laterally in the 2 and 4 fps videos, which is an artifact of low frame rates. The slow pulsatility (~ 1 Hz) observed in the 8 fps video is an aliasing artifact, since the actual pulse rate is ~ 9 Hz. At 16 fps, the pulsatility can be visualized properly. At 32 fps, although the temporal resolution is improved, the reduced velocity sensitivity degrades the image quality markedly.

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Fig. 14.
Fig. 14. Click to hear the associated audio output [33 kB]. (a) Doppler spectrum and (b) color Doppler images of the flow phantom driven at a steady flow rate of 150 µL/min, corresponding to 1.7 mm/s peak velocity after Doppler angle correction. The Doppler spectrum is obtained at the center of the phantom, along the white line shown in (b).

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Fig. 15.
Fig. 15. Click to hear the associated audio output [33 kB]. (a) Doppler spectrum and (b) color Doppler images of the flow phantom driven under pulsatile conditions. The ~ 9 Hz pulses had peak flow rates ~ 2 mm/s. Notice the small reflection observed in (a), likely due to bias and gain mismatch in the I and Q channels.

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Fig. 16.
Fig. 16. (a) Structural, (b) color-Doppler, and (c) normalized power Doppler OCT images of a glass channel flow phantom of 0.25% Intralipid with peak velocity ~ 6 mm/s. Note the aliasing effect in (b) due to phase wrap-around, and the loss of flow directionality in (c).

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Fig. 17.
Fig. 17. (a) Structural, (b) color-Doppler, and (c) normalized velocity variance images of a similar glass channel flow phantom of 0.5 % Intralipid. Notice the different appearance of (c) comparing to that in Fig. 16(c). Scale bar: 250 µm.

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Tables (3)

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Table 1. Requirements of axial scan frequency and analog-to-digital sampling rates for 500×500 pixels per frame.

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Table 2. Computation complexity for velocity estimation for a single pixel

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Table 3. Ensemble length and overlap values for various frame rates.

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Equations (16)

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Δ f OCT ( t ) = 2 π D Δ λ λ 0 2 f a cos ⁡ ( 2 π f a t ) ,
S = I + j Q .
〈 S 2 〉 = 1 M N ∑ m = 1 M ∑ n = 1 N [ I m , n 2 + Q m , n 2 ] .
〈 v 〉 = λ 0 f D 2 n t cos ⁡ ( θ ) , and
f D = f a 2 π arctan ⁡ { 1 M ( N − 1 ) ∑ m = 1 M ∑ n = 1 N − 1 ( I m , n + 1 Q m , n − Q m , n + 1 I m , n ) 1 M ( N − 1 ) ∑ m = 1 M ∑ n = 1 N − 1 ( Q m , n + 1 Q m , n + I m , n + 1 I m , n ) } = f a 2 π arctan ⁡ { 〈 Y 〉 〈 X 〉 }
F r = f a ( 1 − β ) N K X , 0 ≤ β < 1 ,
V z = λ 0 f a 2 n t ,
Δ 〈 v z 〉 = λ 0 f a 2 n t · Δ ϕ 2 π ,
VDR [ dB ] = 20 log ⁡ ( V z Δ 〈 v z 〉 ) ,
H ( i ) = h i = n h ( i Δ v h ) K z , for v min < i Δ v h < v max ,
Δ v h = ( v max − v min ) B h ≈ Δ 〈 v z 〉 .
V btm = i btm Δ v h , where i btm = H − 1 ( max ( h i ) ) .
〈 v ̂ 〉 z = { 〈 v 〉 z − V btm , { V btm > 0 , V btm − 1 2 V z < 〈 v 〉 z ≤ + 1 2 V z V btm < 0 , − 1 2 V z ≤ 〈 v 〉 z < 1 2 V z + V btm 〈 v 〉 z − V btm + V z , V btm > 0 , − 1 2 V z ≤ 〈 v 〉 z ≤ V btm − 1 2 V z . 〈 v 〉 z − V btm − V z , V btm < 0 , 1 2 V z + V btm ≤ 〈 v 〉 z ≤ + 1 2 V z
σ v 2 f a 2 = ( 1 − MN ∣ ∑ m = 1 M ∑ n = 1 N − 1 S m , n S m , n + 1 * ∣ M ( N − 1 ) ∑ m = 1 M ∑ n = 1 N S m , n S m , n * ) = ( 1 − 〈 X 〉 2 + 〈 Y 〉 2 〈 S 2 〉 ) .
P D = 1 MN ∑ m = 1 M ∑ n = 1 N ( I ' m , n 2 + Q ' m , n 2 ) ,
∣ S ̂ ( f D ) n T a , M ∣ = 1 M ∑ m = 1 M ∣ FFT { W [ S ( t ) n − N FFT , n , m ] } ∣ ,
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