Doppler angler and flow velocity estimation using

Doppler angle and flow velocity estimation using conventional single-probing-beam optical Doppler tomography Daqing Piao, Quing Zhu Electrical & Computer Engineering Department, University of Connecticut, CT 06269-2157 Abstract Accurate flow velocity estimation requires measurement of the Doppler angle, which is not available in general clinical applications. We introduce a simple method of estimating Doppler angle and average flow velocity by using conventional single-probing-beam optical Doppler tomography. Both Doppler angle and flow velocity are estimated by combining Doppler shift and Doppler bandwidth measurements. Using two sets of intralipid experiments corresponding to fixed Doppler angle and fixed flow speed, we demonstrate that the estimated values of the Doppler angle and flow velocity are in good agreement with true values. The principle is further validated by in vivo measurements. Keywords: optical Doppler tomography, Doppler angle, flow velocity

1. Introduction

Optical Doppler tomography (ODT), [1-3] a functional extension of optical coherence tomography (OCT), [4] has found wide clinical applications in detection and estimation of subsurface blood flow velocity. Compared with ultrasonic Doppler flow mapping and laser Doppler velocimetry, ODT has advantages of high spatial resolution and high volumetric flow sensitivity. In ODT, Doppler frequency shift of interference signal between the light backscattered from the moving scatterers and light reflected from the reference arm is detected and it is proportional to mean flow velocity of the moving scatterers. For a scatterer that is moving perpendicular to the probing beam, Doppler shift vanishes; for a scatterer that is moving oblique to the probing beam, however, flow velocity cannot be accurately estimated from Doppler shift only without the knowledge of Doppler angle. The Doppler angle measurement with a double-beam technique in which two probing beams were oriented at a precisely known relative angle had been originally invented in Doppler ultrasound [5] and has also been extended to ODT. [6] The doublebeam technique in ODT, however, requires two optical beams with different polarizations to probe the target, which in addition must be supported with multi-channel detection electronics and polarization maintaining fiber optics. Moreover, the double-beam setup at the sample arm is apparently inconvenient for in vivo application. Doppler bandwidth is known in ultrasound and laser Doppler to be the effect of transit time broadening in which the output signal bandwidth is altered by moving scatterers crossing the probing beam. [7] In ODT, H. Ren, etc. reported detection of velocity component that is transverse to the optical probing beam with the Doppler bandwidth measurement. [8] As is reported, Doppler bandwidth is insensitive to the variation of Doppler angle when the angle is within ±15° perpendicular to the probing beam. However, inasmuch as a priori knowledge of Doppler angle is unavailable, the Doppler bandwidth only is not sufficient to accurately estimate the flow velocity either. In addition, Doppler bandwidth does not provide directional information of the flow. Doppler angle measurement, thus, ultimately limits the accuracy of flow velocity estimation. In this paper, we present to our knowledge a novel method for Doppler angle and flow velocity estimation using conventional single-beam ODT system. The Doppler angle is estimated by combining Doppler shift and Doppler bandwidth measurements, and flow velocity is calculated by using Doppler shift and the estimated Doppler angle. We conducted two sets of intralipid flow experiments corresponding to fixed Doppler angle and fixed flow speed, respectively, and demonstrate that the recovered Doppler angle and estimated flow velocity are in good agreement with true values for a range of Doppler angles from 58º to 90º and flow velocities from 18.5 mm/s to 141.9 mm/s, respectively. The capability of this method on flow direction identification, which is an outcome of Doppler angle measurement, and flow speed estimation is demonstrated with the imaging of in vivo human lip microvascularization. 2. Principle of Doppler angle and flow velocity estimation In ODT systems, at the distal end of the sample arm the light is focused to the sample. As indicated in Fig. 1, the

232

Coherence Domain Optical Methods and Optical Coherence Tomography in Biomedicine VII, Valery V. Tuchin, Joseph A. Izatt, James G. Fujimoto, Editors, Proceedings of SPIE Vol. 4956 (2003) © 2003 SPIE · 1605-7422/03/$15.00

Downloaded From: http://proceedings.spiedigitallibrary.org/ on 04/05/2017 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx

probing beam has a numerical aperture of NA = sin α before penetrating into the sample. The effective numerical aperture inside the sample is NAeff = sin α eff ≈ (sin α ) / n , where n is the refractive index. For an average flow velocity

Fig. 1. Sample arm probing geometry of a conventional single-beam ODT system. θ is the Doppler angle, υ is the average flow velocity, and α corresponds to the numerical aperture (NA) of light before penetrating into the sample ( NA = sin α ).

υ and Doppler angle θ , which is defined as the angle between the flow velocity vector and the beam axis, the

average Doppler frequency shift f is given as 2υ cos θ f =

λ

(1)

0

where λ 0 is the center wavelength. For a Gaussian optical beam, the full-width at half-maximum (FWHM) Doppler bandwidth ∆f is calculated as [8]

∆f =

π ln 2 υ NAeff sin θ +b 2 λ0

(2)

where NAeff is the effective numerical aperture of the probing light inside the sample, and b accounts for a systemspecified spectrum bandwidth background that is independent of the macroscopic flow velocity. Equations (1) and (2) indicate that, when b and NAeff are known, the Doppler angle θ can be obtained by combining Doppler shift and spectrum bandwidth measurements as

θ = tan −1 (

1 ∆f − b ) f π ln 2 NAeff 4

(3)

and the flow velocity can be calculated by

υ=

fλ 0

(4)

2 cosθ

Equations (3) and (4) estimate θ and υ only for a non-zero Doppler shift f , however, this poses no problem to a zero Doppler shift case. In this situation the Doppler angle is considered to be 90º, and the flow velocity can be calculated directly from equation (2) by

υ=

2

λ0

π ln 2 NAeff

( ∆f − b )

(5)

3. Algorithms for Doppler shift and Doppler bandwidth measurements

In our previous work, [9] we presented a quantitative comparison of three categories of Doppler shift estimation algorithms, including centroid techniques (adaptive centroid technique and weighted centroid technique), slidingwindow filtering technique, and correlation techniques (autocorrelation and cross-correlation). Among these 5 methods, the weighted centroid and sliding-window filtering algorithms were, to our knowledge, first introduced. Simulations and in vivo blood flow data were used to assess the Doppler shift estimation accuracies of these algorithms. Our study demonstrated that the sliding-window filtering technique is superior to other techniques in terms of estimation accuracy and robustness to noise. Consequently, we employed this technique to the Doppler shift measurement in this paper for Doppler angle and flow velocity estimation. The sliding-window filtering

Proc. of SPIE Vol. 4956


233

technique can also be extended to the spectrum bandwidth measurement, and the detailed discussion is given in this paper. We will demonstrate that this sliding-window filtering technique outperforms existing correlation method and STFT method in terms of estimation accuracy and robustness to noise in spectrum bandwidth measurement. In ODT, by taking into account the averaging necessary to improve SNR, the detected two-dimensional (2-D) interference signal after Hilbert transform can be expressed by [9] ~ (6) z k , i (t ) =| ~ z k , i (t ) | e jω t where, t is the time argument along the depth scanning direction, k represents the lateral dimension of the k th Aline, i is the index of the repeated A-line measurements, and ω = 2π f is the angular frequency of signals reflected from the target. If we use STFTk , i (t n , ω ) to represent the discrete STFT of the sampled interferometric signal ~ z k , i (t n ) , where t n = n t s and t s is the sampling interval, the local power spectrum is given by

P n k , i (ω ) = STFTk , i (t n , ω ) STFTk , i (t n , ω ) where (•) represents complex conjugate. The FWHM bandwidth of P described as follows.

(7) n

k,i

(ω ) can be measured by three techniques

3.1 Short time Fourier transform method When the power spectrum P n k , i (ω ) of a sampled interferometric signal ~z k , i (t n ) is known, the FWHM spectrum bandwidth ∆ω k , i ( n) = 2π∆f can be estimated by simply following the definition of FWHM. 3.2 Autocorrelation method It is reported by Ren et al. that the standard deviation σ of the local power spectrum with respect to the mean angular frequency is determined by the Doppler bandwidth Bd as [8] σ=

π Bd 32

(8)

where σ is extracted from the cross-correlation function between sequential A-scan lines. In our ODT system, due to the limitation of scanning speed, we could not directly use this cross-correlation method because of the aliasing inherent in the 2π phase ambiguity. [8, 9] Instead, we used the autocorrelation function of individual A-lines to obtain the standard deviation of the local power spectrum and our method is explained as follows. Mathematically, the complex cross-correlation function between sequential A-lines is given by C n k , i (T ) = ∫

tn

t n − NT

~ ~ Z k , i (t + T ) × Z k , i +1 (t ) dt

(9)

where T is the time interval between sequential A-scans, while the complex autocorrelation function R n k , i (τ ) of ~ z k , i (t n ) is expressed as R n k , i (τ ) = ∫

tn tn − N ′ ts

~ z k , i (t + τ ) × ~ z k , i (t ) dt

(10)

where N ′ t s is the time duration of integration. When the cross-correlation function of sequential A-lines is used, the standard deviation σ is given by [10, 11]

[σ

]

2

≈ k , i (n)

n 2  C k , i (T )    1 − T2  Rkn, i (0)   

As the auto-correlation of individual A-lines is interested, the standard deviation n 2  Rk , i (∆T )  2   1− n σ k , i (n) ≈ (∆T ) 2  Rk , i (0)   

[

234

]

(11)

σ

can be approximated by (12)



where ∆T denotes the temporal lag of autocorrelation. Since ∆T can be user-defined, the aliasing is readily avoided if ∆T is chosen to be much less than the interval T between sequential A-scans. The lower limit of ∆T is the sampling interval t s .When the standard deviation σ is known, the FWHM spectrum bandwidth is calculated by:

(13)

∆ω k , i (n) = 4 ln 2σ

3.3 Sliding-window filtering method The sliding-window filtering technique was introduced to directly map the frequency shift at each pixel using digital band-pass filtering. We assume that the local power spectrum P n k , i (ω ) of the detected signal ~z k , i (t n ) has a peak at ω p = ω 0 + ω s , where ω 0 corresponds to the fundamental modulation frequency and ω s represents the frequency shift. If ~z k , i (t n ) is digitally band-pass filtered within a sliding narrow filter window (ω l , ω h ) , the filtered ~z k , i (t n )

will have a maximum power when the condition ω l < ω p < ω h satisfies or, in other words, the spectrum distributed around the peak falls in the filtering window. The relative position of the sliding filter window to the fundamental frequency, (ω l + ω h ) / 2 − ω 0 , represents the Doppler shift of the local scatterers.

Fig. 2. Schematic of sliding-window filtering technique. The slidingwindow filtering bank is applied to measure the components of each interference signal that change at a rate corresponding to the passband of the filters.

Using this approach, the detected signal ~z k , i (t n ) at each sampling point t n is processed by a filter bank consisting of M filters, ω1 , ω 2 , …, ω M , yielding one signal at the output of each filter as illustrated in Fig. 2. This procedure produces M output signals O~m (t n ) , m = {1, 2, ..., M } for each detected signal such that ~ Om (tn ) = ~ zk , i (tn ) ⊗ F −1 (ωm )

(14)

where the pass band of ω m is [(2m − 1)π 2M − ∆ω / 2, (2m − 1)π 2M + ∆ω / 2] with ∆ω being the filter bandwidth. The output signals represent components of input signal that change at a rate corresponding to the passband of the filters. Low frequency (or less shift from ω 0 ) passband will select slow moving component, and high frequency (or more shift from ω 0 ) passband will select fast moving component of the intereference signal. Then, at each t n , the energy in each filter, ε m (t n ) , is estimated by [12]

ε m (t n ) =

tn + ∆ t / 2

∑

[O~

t ′= t n −∆ t / 2

m

(t ′)

]

2

(15)

where ∆t represents a short range window centered at t n . At any given t n , the filter window ω mˆ , of which ε mˆ (t n ) = ε max (t n ) = max imum of [ε m (t n )], represents the most significant frequency component of flow signal. The Doppler shift is then calculated by



235

ω k , i ( n) =

2mˆ − 1 π − ω0 2M

(16)

This method can be further applied to spectrum bandwidth measurement.

At each t n , the average energy in each

filter is expressed by ε (t n ) =

1 M

M

∑ε m =1

m

(17)

(t n )

The number of filters of which the energy ε m (t n ) is greater than the average energy ε (t n ) can be considered as a relative spectrum bandwidth, which is denoted by ∆ω (t n ) . For a Gaussian spectrum, knowing ε (t n ) , ε max (t n ) , and ∆ω (t n ) , the FWHM spectrum bandwidth can be calculated by ∆ω k , i (n) = ∆ω (t n )

ln 2 ln[ε max (t n ) ε (t n )]

(18)

It is to be demonstrated in this paper that for spectrum bandwidth detection, this sliding–window filtering technique is more accurate and robust to noise compared with the autocorrelation and STFT methods. We will then use this method to calculate Doppler bandwidth as well as Doppler shift.

4. A laminar flow simulation model for evaluation of Doppler bandwidth estimation algorithms To quantitatively assess the performance of above-mentioned three Doppler bandwidth estimation algorithms, we have simulated laminar blood flow signals with different SNRs. The simulation model illustrated in Fig. 3(a) is represented by ~ ~ ~ n, k (19) Z k , i (t n ) = S k (t n , t i ) ⊗ F −1[ Fa (ω ,ω )] + N k (t n , t i ) where t n = n t s as previous defined, and t i = i t s . In equation (19), S~k (t n , t i ) is a 2D Gaussian function to simulate random scatters, N~ k (t n , t i ) is zero mean white noise, Fa n,k (ω , ω ) is a spatially symmetric function of

Fa

n ,k

(ω ) = u (ω )[ F n k (ω ) + jFˆ n k (ω )]

(20)

where u (ω ) root of P n k (ω ) expressed by

is a unit-step function, Fˆ n k (ω ) represents the Hilbert transform of F n k (ω ) , and F n k (ω ) is the square  [ω − ω p (t n )]2  P n k (ω ) = exp−   ∆ω1/ 2 (t n ) 2 ln 2

[

(

  2  

)]

(21)

At the first step of simulation, we generate a Gaussian random signal S~k (t n , t i ) , which has a uniform spectrum. At the second step, a Gaussian distribution function P n k (ω ) = exp{− [ω − ω p (t n )]2 [∆ω1 / 2 (t n ) /(2 ln 2 )]2 } is generated to simulate the desired power spectrum with ω p and ∆ω 1 / 2 representing the center frequency and spectrum bandwidth of flow signal, respectively. At the third step, the square root of P n k (ω ) is taken to generate u (ω ) F n k (ω ) , which simulates the positive frequency part of Fourier transform of the desired signal, where u (ω ) is a unit-step function. At the fourth step, a function is formed as Fa n,k (ω ) = u(ω )[ F n k (ω ) + jFˆ n k (ω )] , where Fˆ n k (ω ) is the Hilbert transform of F n k (ω ) . Fa n, k (ω ) is used to simulate the Fourier transform of an analytic signal whose real part is the desired flow signal. The spatially symmetric function of Fa n, k (ω ) will form a 2D spectrum profile Fa n,k (ω , ω ) . At the fifth step, the

inverse Fourier transform of Fa n,k (ω , ω ) is convolved with S~k (t n , t i ) to simulate a flow signal that carries the desired spectrum information. Finally, a zero mean white noise N~ k (t n , t i ) is added to the generated signal and the SNR of ~ Z k , i (t n )

will be controlled to facilitate the evaluation of Doppler bandwidth estimation. By definition, the power

spectrum represents the energy of each frequency component, and the area within the spectrum bandwidth accounts

236



for the strength of flow signal. Accordingly, the maximum of P n k (ω ) is normalized to the corresponding value of ∆ω 1 / 2 , such that the simulated flow signal has a relatively uniform strength across the flowing portion. A uniform SNR in the flow region is important for the evaluation of algorithms. Figure 3(b) represents a structural image of simulated 2D flow signal, and Fig. 3 (d) shows one A-line profile from the image in Fig. 3 (b) to manifest the uniformity of signal amplitude across the flow region. The generated 1D spectrum bandwidth and corresponding 0.95

10

Lateral dimension

0.9 20

0.85 0.8

30

0.75 40

0.7 0.65

50

0.6

60 20

40 60 80 Axial dimension

100

0.55

120

(b)

0.7 0.6

Doppler shift profile Spectrum bandwidth profile

Relative value

0.5 0.4 0.3 0.2 0.1 0

20

40

60 80 Axial dimension

100

120

(c)

100

120

(d)

5 0

(a) Signal: dB

Fig. 3. A laminar flow simulation model incorporating both Doppler shift and Doppler bandwidth. (a) Schematic of the simulation model, (b) amplitude image of simulated 2-D flow signal, (c) 1-D spectrum bandwidth and corresponding Doppler shift profiles of the simulated signal, (d) 1-D profile of the simulated signal, manifesting the uniformity of signal strength across the flow region.

-5 -10

Flow region

-15 -20 -25 -30

20

40


Doppler shift profiles extracted from simulated 2D flow signal at the same location are shown in Fig. 3(c). The generated Z~k , i (t n ) has a dimension of 2048×512 and is segmented to 2048×8×64, which corresponds to 2048 points in one A-line (axial direction), 8 sequential A-lines for averaging at one lateral step, and 64 lateral steps. These data dimensions of max(n) = 2048 , max(i ) = 8 , and max( k ) = 64 are comparable to those used in experiments. For each A-line signal 16 data points correspond to one image pixel, which results in an image dimension of 128 (axial) × 64 (lateral). In the actual Doppler shift and Doppler bandwidth calculation, a typical 50% overlapping is implemented, so for each pixel, 32 data points are actually processed. Using this model, we have simulated flow signals of 90mm/s speed and 80o Doppler angle with SNRs from 5 dB to 20 dB. The control parameters are λ = 1300nm , NAeff = 0.13 , and ω = π corresponds to f = 128 KHz . These parameters are very close to those used in experiments. Due to a finite number of data points involved in the simulation for each Z~k , i (t n ) , a minimum spectrum bandwidth of 22.9KHz is available, and the spectrum broadening is added on top of it.

5. Methods 5.1 Experiments on intralipid flow The same ODT system that was described in Ref. 9 is used for Doppler shift and spectrum bandwidth measurements. Briefly, this ODT system is a typical balanced setup configured with one 1×2 and one 2×2 fiber couplers. A superluminescent diode with 1300nm center wavelength, 40nm spectral width, and 2.4mW output power is used as the low coherence source. In the reference arm, a scanning optical delay line based on Littrowmounting of diffraction grating is used to generate range scanning and a phase modulation for carrier frequency as



237

well. The delay line is configured to generate 3.125mm scanning range in free space and 35.5KHz carrier frequency. In the sample arm, a GRIN lens is driven by a motorized stage at a maximum speed of 300µm/s for lateral scanning. In the detection arm, the signal is detected differentially using an auto-balanced receiver, with which the source intensity noise is rejected. The signal is then amplified, band-pass filtered in a range of 16.4KHz to 125KHz and digitized with a 16-bit analog-to-digital converter at a sampling rate of 262KHz. The number of data points for each A-line is 2048. A cross-sectional (B-scan) image consists of 1024 A-lines is taken in 16 seconds. Eight sequential A-lines are averaged at one lateral pixel, and 16 data points are averaged along the axial direction. The pixel dimension of final B-scan images is 128×128. Figure 4 shows the schematic of the intralipid flow setup in our experiment. The ODT probing-beam is focused to the axis of a glass capillary tubing with 1.0mm inner diameter, 1.2mm outside diameter and 100mm in length. A 0.25% intralipid solution is used as the turbid medium. The glass capillary is mounted to a rotation stage, and connected to a 2-meter long 3/32″ plastic tubing. A peristaltic tubing pump is used to drive the intralipid through the capillary tubing and circulate it in the tubing loop. A damper is inserted before the glass capillary tubing to suppress the pulsation induced by peristaltic pumping. The mean flow velocity of intralipid through the glass capillary tubing is converted from the time interval of liquid traveling 1 meter distance in the 3/32″ plastic tubing that is placed straightly on a horizontal plane. The tubing pump has a minimum rotation of 28 rpm and a maximum rotation of 225rpm with 5% speed control repeatability.

Fig. 4. Schematic of experimental intralipid flow loop.

Two sets of experimental data were taken from the intralipid sample. In the first set, the flow velocity was fixed at 53.6mm/s and the Doppler angle was varied from 56o to 90o with a uniform 1o step. The 90o Doppler angle orientation was carefully adjusted and monitored beforehand by checking the zero Doppler shift at maximum available flow velocity. In the second set, the Doppler angle was fixed at 80o and the flow velocity was varied from minimum available 18.5mm/s to maximum available 141.9mm/s with non-uniform steps. At each Doppler angle or flow velocity setup, a B-scan image that covers the entire cross-section of the glass capillary tubing was taken, and the Doppler shift and spectrum bandwidth were calculated. For the first and second sets of experiments, a total of 35 and 30 B-scans were taken, respectively. 5.2 In vivo study The in vivo blood flow was taken at the upper lip of a female volunteer. The volunteer was asked to hold her lip position while pushing her chin against a custom designed bracket during the ODT scanning. The probing-beam from GRIN lens was oriented close to 90° with respect to the surface of the imaging spot. The spot of ODT scan was taken at pars villosa (PV) of the lip, which has the most extensive subsurface blood supply. It is reported that in PV of the lip, the papillary loop network is the most characteristic. [13] PV contains two types of loops: short loops and long loops (see Fig. 5 for PV microvascularization). The short loops (250 µm) are papillary networks in contact with the deep aspect of the epidermis. The long loops (700 µm), which are more numerous, penetrate deep into the papillary layer of the dermis. They are arranged perpendicular to the periphery of the lip. Both short loop and long loop contain a centrol arteriol, peripheral capillaries and a postcapillary venule. The papillary network connects with the reticular network. The reticular network is composed of two distinct parts: a superficial part and a deep part. The superficial part essentially receives the short loops and has the appearance of fine, irregular meshes arranged parallel to the surface. The deep part drains the superficial part of the reticular network and the long loops of the papillary network.

238



Fig. 5. A literature picture of microvascularisation of the PV (taken from Ref. 10, ×55), where 1=a short loop; 2=a long loop, both 1 and 2 containing an arteriole, peripheral capillaries and a postcapillary venule; 3=superficial part of the reticular network, 4=deep part of the reticular network.

6. Results 6.1 Evaluation of spectrum bandwidth estimation algorithms 1 Sliding-window filtering Autocorrelation STFT

0.9

60

Spectrum bandwidth

Estimaiton accuracy

0.95

0.85 0.8 0.75 0.7 0.65 0.6

Top: Sliding-window filtering Middle: Autocorrelation Bottom: STFT

40

20

0

-20 5

10

15 SNR: dB

20

20

40


100

120

(a) (b) Fig. 6. A comparison of the spectrum bandwidth estimation using three techniques, namely STFT method, autocorrelation method, and sliding-window filtering method. (a) The estimation accuracy as a function of SNR of simulated data. (b) An example of 1-D spectrum bandwidth profiles estimated by the three methods on a typical experimental flow data.

The Doppler shift and Doppler bandwidth measurements are needed for the Doppler angle and flow velocity estimation. The Doppler shift measurement was in favor of the sliding-window filtering technique as previously investigated, however, there was no available guidance for choosing the Doppler bandwidth estimation algorithms. We thus studied the performance of three above-mentioned spectrum bandwidth estimation methods, namely STFT technique, autocorrelation technique, and sliding-window filtering technique. All algorithms are tested using simulated and experimental data without/with flow to verify that they can retrieve the correct background spectrum bandwidth ( b in equation (2)) and flow profiles. Then the simulated data with different SNRs are used to assess the spectrum bandwidth detection accuracy of these three algorithms. The accuracy of each algorithm is evaluated using the correlation coefficient between the estimated 2D spectrum bandwidth profile and the actual profile that is available in simulation study. Fig. 6(a) shows the estimation accuracy of each algorithm on simulated data as a function of SNR from 5 dB to 20 dB. The result for each algorithm at each SNR is an average of 5 data sets calculated using independent additive white noises. It is clear that at the entire SNR range that we have investigated, the sliding-window filtering method is superior to other algorithms. To visualize the performance of these algorithms, we present in Fig. 6(b) typical 1D plots of spectrum bandwidth estimation using each algorithm on the same experimental data. It is shown that in most of the flow region, the performance of autocorrelation method is slightly more noisy than that of sliding-window filtering method, however, at very low flow region, the autocorrelation method overestimates the spectrum bandwidth. It is also observed from the experimental data, where the SNR of the flow region is not uniform, that the autocorrelation method is noisy at low SNR region. The noisy performance of spectrum bandwidth detection by autocorrelation technique at lower flow speed and/or lower SNR region is consistent with that of Doppler shift detection by the same technique. Again, the reason is that correlation techniques are more sensitive to local decorrelation of the flow field resulting from low SNR or high velocity gradient that is present at low flow velocity region. [9, 14] The STFT technique is known to be noisy for



239

Doppler shift measurement, [9] and it is again shown to give highly noisy estimation for the spectrum bandwidth detection. From this study, the sliding-window filtering technique is shown to outperform other two techniques in terms of estimation accuracy and robustness to noise. Accordingly, we will use the sliding-window filtering technique for spectrum bandwidth measurement and Doppler shift estimation. 6.2 Doppler angle and flow velocity estimations based on experimental data 200

70 60 Calculated value Experimental setup

50 40 30 20 10 0

55

60

65 70 75 80 Doppler angle setup: degree

85

90

140 120 100 80 60 40

0

(a)

Estimation accuracy: 94.3% 55

60

65 70 75 80 Doppler angle setup: degree

85

90

(b)

200 Calculated with estimated Doppler angle Calculated with actual Doppler angle Experimental setup

180

80

Flow velocity estimation: mm/s

Doppler angle estimation: degree

160

20

Estimation accuracy: 97.6%

90

70 60 Calculated value Experimental setup

50 40 30 20 10 0

Calculated with estimated Doppler angle Calculated with actual Doppler angle Experimental setup

180

80

Flow velocity estimation: mm/s

Doppler angle estimation: degree

90

40

60 80 100 Flow velocity setup: mm/s

120

140

140 120 100 80 60 40 20


160

0

(c)


40

60 80 100 Flow velocity setup: mm/s

120

140

(d)

Fig. 7. The performance of Doppler angle and flow velocity estimation on intralipid flow data. The first experimental setup is with fixed flow velocity and changing Doppler angle. The second experimental setup is with fixed Doppler angle and changing flow velocity. (a) Doppler angle estimation profile for the first setup. The actual Doppler angle is from 56° to 90° with 1° increment. (b) Flow velocity estimation profiles based on calculated Doppler angle and actual Doppler angle for the first setup. The actual flow velocity is 53.6mm/s. (c) Doppler angle estimation profile for the second setup. The actual Doppler angle is 80 degree. (d) Flow velocity estimation profiles based on calculated Doppler angle and actual Doppler angle for the second setup. The actual flow velocity is from 18.5mm/s to 141.9mm/s with non-uniform steps.

In the estimation of Doppler angle a system-specified background spectrum width b and the effective numerical aperture of light inside the sample must be determined in advance. We calculated the spectrum bandwidth for a noflow intralipid sample, resulting an average of 6.0 KHz that is also the background level in the spectrum bandwidth profile of flowing intralipid. Based on the geometry of the GRIN lens specified by the provider (18.5mm in length, 2.4mm in diameter, 3mm working distance, 1 magnification factor), and knowing the refractive index of intralipid to be around 1.4, [15] the effective numerical aperture of the light inside the sample is calculated to be 0.08. The estimated Doppler angles and actual setup values for the first experimental test at fixed average velocity of 53.6mm/s are shown in Fig. 7(a). The estimated values are in good agreement with actual Doppler angles from 58o to 90o. In our experiment, limited by hardware, primarily the band-pass filtering range, the Doppler angle smaller than 57o can not be reasonably estimated at this 53.6mm/s flow velocity setup since the Doppler shift is getting close to the filter cutoff frequency and the spectrum bandwidth information is greatly distorted. Nevertheless, the overall Doppler angle estimation accuracy is as high as 97.6%. The calculated flow velocity based on the estimated Doppler

240



angle is shown in Fig. 7(b). The overall flow velocity estimation accuracy is calculated to be 94.3%. If the actual Doppler angles are used, the calculated flow velocities show slightly better performance at Doppler angles smaller than 85o, however, at Doppler angles close to 90o, the flow velocity quantification based on estimated Doppler angle is more reliable. The reason is that the measured Doppler angles are lower than actual values for close to 90 o setup, so the calculated flow velocities are not approaching to infinity as they are when the actual Doppler angles are used. The estimated Doppler angles for the second experimental test at fixed 80o Doppler angle are shown in Fig. 7(c). The overall Doppler angle estimation accuracy is 98.2%, which is very close to that of the first experimental set. The calculated flow velocity values based on the estimated Doppler angle are shown in Fig. 7(d). The overall flow velocity estimation accuracy is calculated to be 90.4%, which is lower than that of the first experimental set. At this test, if the flow velocity is calculated with the actual Doppler angle, the estimation has better performance at entire flow velocity range compared with the calculation based on estimated Doppler angle. Nevertheless, an overall evaluation of the two experimental results shows reliable performance of the proposed principle at the full Doppler angle and flow velocity ranges that are manageable in our system. C. Doppler angle and flow velocity estimations based on in vivo data

(a)

(b)

(c)

(d)

Fig. 8. (a) is a Doppler shift image superimposed on B-scan structure imaging taken from PV of the upper lip of a female volunteer. In spot 1, two regions of blood flow are in apposite directions. (b) is the Doppler bandwidth image superimposed on structure image. The smaller flow spot 2 in Doppler bandwidth image is not detected by Doppler shift shown in (a). (c) is the Doppler angle mapping depicted based on the estimated value from equation (6), where the three flow regions in Spot 1 and 2 are represented with arrows of different orientations. (d) is the local velocity mapping calculated by Doppler shift and estimated Doppler angle. Three flow regions in Spot 1 and 2 are clearly identified with corresponding flow directions.

The in vivo structural image taken from human lip is shown in Fig. 8 as the gray scale background. The apparent distortion of the image is due to the respiratory motion at a period of approximately 4.6 seconds. Nevertheless, this respiratory motion is out of the range that could introduce artifacts to Doppler shift and Doppler bandwidth images. In Fig. 8(a) the Doppler shift image is superimposed on structure image, which reveals a flow region (spot 1) in the



241

middle-left of the image. Figure 8(b) shows the Doppler bandwidth image. Compared with Doppler shift image in Fig. 8(a), there is one smaller flow region (spot 2) shown up in addition to spot 1 in Doppler bandwidth image. The flow spot 2 has Doppler angle very close to 90° and it is not identifiable in Doppler shift image. The spot 1 in Doppler bandwidth image appears as one large flow region, however, in Doppler shift image it shows up as two regions with opposite flow directions. Figure 8(c) is the local Doppler angle mapping of Spot 1 and Spot 2 calculated from equation (7) and superimposed on structure image for better visualization. The down-tilted arrows inside the solid circle in Spot 1 represent Doppler angle greater than 90°, while the up-tilted arrows inside the dashed circle represent Doppler angle smaller than 90°. The horizontal arrows in Spot 2 represent flow that is perpendicular to the probing beam. With local Doppler angle information, the calculated flow velocity vector image is shown in Fig. 8(d). Both Spot 1 and Spot 2 show up in velocity mapping, and the small negative flow region (blue color) in Spot 1 is clearly identified. The flow areas in spot 1 and 2 are approximately 700µm in depth, 600µm in length and have maximum flow velocity about 100mm/s. To our knowledge, there is no literature information regarding the flow speed of human lip blood supply, however, the blood vessel sizes we measured agree well with those reported in anatomic studies. [13] Based on the location and size, we believe that the larger flow region in Spot 1 and the flow area in Spot 2 are all long loops. In the velocity image, there is a discrete strip of flow region that is parallel to the surface (depicted by the neighboring white strip), which is also shown in Doppler angle mapping. Based on the depth and orientation, we believe that this is the superficial part of the reticular network.

7. Discussions The Doppler angle estimation shows higher accuracy than the flow velocity estimation from both experimental setups. The higher accuracy of Doppler angle estimation can be understood by comparing equations (3) and (4). It is easy to show that dυ dθ = dυ θ = θ tan θ . For Doppler angle greater than 50°, θ tan θ > 1 , which υ θ dθ υ indicates that in our experiments flow velocity estimation is less accurate than that of Doppler angle. In the first experimental setup where the Doppler angle is changed at a fixed flow velocity, the Doppler angle and flow velocity can be well recovered even when the Doppler angle is very close to 90°. The flow velocity estimation using calculated Doppler angle is even more robust than using the actual Doppler angle. In the actual imaging scenario, the Doppler spectrum is modified by stochastic scatterer distributions in the flow filed. [16] The stochastic modification of the Doppler spectrum implies possibly detectable Doppler shift estimation even for almost-90o Doppler angle. This indicates that Doppler shift and Doppler bandwidth combination can be used to close-to-90 o flow orientation without worrying about the infinite denominator in the Doppler angle estimation. It is shown from the in vivo study that the Doppler bandwidth detection is more robust than Doppler shift imaging, particularly in detecting close-to-90° blood flows. This is not a surprise because for Doppler angle in the neighboring of 90° Doppler bandwidth is angle–insensitive, while the Doppler shift is highly dependent on the angle. The angle-insensitivity of Doppler bandwidth, however, limits the sensitivity of flow velocity estimation if it is based solely on Doppler bandwidth. Furthermore, the Doppler bandwidth-only imaging does not provide flow direction information. Doppler shift, on the other hand, is direction-dependent. By combining Doppler shift and Doppler bandwidth measurements, we can form local Doppler angle and flow velocity vector mapping, which preserves the robustness of Doppler bandwidth detection while maintains the velocity sensitivity and flow direction information of Doppler shift imaging. As is shown, the new ODT imaging method introduced in this letter is capable of identifying more blood vessels and blood volumes as well as the directions of the flow. The average SNR of the flow areas shown is found to be approximately 10dB. Although this SNR of in vivo tissue is less than 13dB of intralipid in experiments, simulations have shown that at this SNR greater than 90% accuracy for Doppler angle and 85% accuracy for flow velocity estimations can be expected. One deficiency of flow velocity mapping is the lack of color-code discrimination between 90° flow and positive flows, however, this can be easily overcome by integration with Doppler angle mapping.

8. Conclusion To conclude, we introduced a convenient technique for estimating Doppler angle and flow velocity with

242



conventional single-beam ODT setup. In this technique, both Doppler angle and flow velocity are estimated by combining Doppler shift and Doppler bandwidth measurements. With intralipid experiments we demonstrated that the Doppler angle can be estimated with high accuracy; and for the flow velocity, although the estimation error is greater than that of Doppler angle, a reliable recovery can be readily achieved even at close-to-90° flow orientation. The in vivo imaging of human lip microvascularisation showed the capability of this method on quantifying blood flow direction and velocity vector.

Acknowledgement This work is partially supported by research grant from the National Institutes of Health (NIH 1R01 DE11154-03) and a pre-doctoral training grant from Department of Defense (DAMD17-02-1-0358). D. Piao and Q. Zhu’s e-mail addresses are [email protected] and [email protected], respectively.

References [1]. X.J. Wang, T.E. Milner, and J.S. Nelson, “Characterization of fluid flow velocity by optical Doppler tomography,” Optics Letters, Vol. 20, No. 11, pp. 1337-1339, June, 1995. [2]. Z.P. Chen, Y.H. Zhao, S.M. Srinivas, J.S. Nelson, N. Prakash, and R.D. Frostig, “Optical Doppler tomography,” IEEE Jounal of Selected Topics in Quantum Electronics, Vol. 5, No. 4, pp. 1134-1142, July/August, 1999. [3]. J.A. Izatt, M.D. Kulkarni, S. Yazdanfar, J.K. Barton and A.J. Welch, “In vivo bi-directional color Doppler flow imaging of picoliter blood volumes using optical coherence tomography,” Optics Letters, Vol. 22, No. 18, pp. 1439-1441, September, 1997. [4]. D. Huang, E.A. Swanson, C.P. Lin, J.S. Schuman, W.G. Stinson, W. Chang, M.R. Hee, T. Flotte, K. Gregory, C.A. Puliafito, and J.G. Fujimoto, “Optical coherence tomography,” Science, Vol. 254, 1178-1181, 1991. [5]. M.D. Fox, “Multiple crossed beam ultrasound Doppler velocimetry,” IEEE Transactions on Sonics and Ultrasonics, Vol. SU-25, pp. 281-286, 1978. [6]. D.P. Davè and T.E. Milner, “Doppler-angle measurement in highly scattering media,” Optics Letters, Vol. 25, No. 20, pp. 1523-1525, October, 2002. [7]. V.L. Newhouse, E.S. Furgason, .G.F. Johnson, and D.A. Wolf, “The Dependence of Ultrasound Doppler Bandwidth on Beam Geometry,” IEEE Transactions on Sonics and Ultrasonics, Vol. SU-27, No. 2, pp. 50-59, March, 1980. [8]. H. Ren, K. M. Brecke, Z. Ding, Y. Zhao, J.S. Nelson, and Z. Chen, “Imaging and quantifying transverse flow velocity with the Doppler bandwidth in a phase-resolved functional optical coherence tomography,” Optics Letters, Vol. 27, No. 6, pp. 409-411, March, 2002. [9]. D. Piao, L. Otis, N.K. Dutta, Q. Zhu, “Quantitative assessment of flow velocity estimation algorithms for optical Doppler tomography imaging,” Applied Optics, Vol. 41, No. 29, pp. 6118-6127, October, 2002. [10]. Y.H. Zhao, Z.P. Chen, C. Saxer, Q.M. Shen, S.H. Xiang, J.F. de Boer, and J.S. Nelson, “Doppler standard deviation imaging for clinical monitoring of in vivo human skin blood flow,” Optics Letters, Vol. 25, No. 18, pp. 1358-1360, September, 2000. [11]. C. Kasai, K. Namekawa, A. Koyano, and R. Omoto, “Real-time two-dimensional blood flow imaging using an autocorrelation technique,” IEEE Transactions on Sonics and Ultrasonics, Vol. SU-32, No. 3, pp. 458-463, May, 1985. [12]. J.R. Crowe, B.M. Shapo, D.N. Stephens, D. Bleam, M.J. Eberle, E.I. Cèspedes, C.C. Wu, D.W.M. Muller, J.A. Kovach, R.J. Lederman, and M. O’Donnell, “Blood speed imaging with an intraluminal array,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 47, No. 3, pp. 672-681, May, 2000. [13]. R. Wolfram-Gabel, and H.Sick, “Microvascularisation of the lips in the fetus and neonate,” Cells Tissues Organs, Vol. 164, No. 2, pp.102-111, 1999. [14]. P.C. Li, C.J. Cheng, and C.K. Yeh, “On velocity estimation using speckle decorrelation,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 48, No. 4, pp. 1084-1091, July, 2001. [15]. T.L. Troy, and S.N. Thennadil, “Optical properties of Human skin in the NIR wavelength range of 10002200nm,” Instrumentation Metrics, Inc. [16]. M.D. Kulkarni, T.G. van Leeuwen, S. Yazdanfar, A.J. Welch, and J.A. Izatt, “Velocity-estimation accuracy and frame-rate limitations in color Doppler optical coherence tomography,” Optics Letters, Vol. 23, No. 13, pp. 1057-1059, July, 1998. Proc. of SPIE Vol. 4956


243