Wide dynamic range detection of bidirectional flow
in Doppler optical coherence tomography
using a two-dimensional Kasai estimator
Darren Morofke and Michael C. Kolios
Department of Physics, Ryerson University, Toronto, Canada
I. Alex Vitkin
Ontario Cancer Institute/University Health Network, Toronto, Canada
Victor X. D. Yang
Imaging Research, Sunnybrook Health Sciences Center, Toronto, Canada
Received August 30, 2006; accepted October 16, 2006;
posted October 27, 2006 (Doc. ID 74498); published January 12, 2007
We demonstrate extended axial flow velocity detection range in a time-domain Doppler optical coherence
tomography (DOCT) system using a modified Kasai velocity estimator with computations in both the axial
and transverse directions. For a DOCT system with an 8 kHz rapid-scanning optical delay line, bidirectional
flow experiments showed a maximum detectable speed of ?56 cm/s using the axial Kasai estimator without
the occurrence of aliasing, while the transverse Kasai estimator preserved the ?7 ?m/s minimum detect-
able velocity to slow flow. By using a combination of transverse Kasai and axial Kasai estimators, the ve-
locity detection dynamic range was over 100 dB. Through a fiber-optic endoscopic catheter, in vivo M-mode
transesophageal imaging of the pulsatile blood flow in rat aorta was demonstrated, for what is for the first
time to our knowledge, with measured peak systolic blood flow velocity of ?1 m/s, while maintaining good
sensitivity to detect aortic wall motion at ?2 mm/s, using this 2D Kasai technique. © 2007 Optical Society
OCIS codes: 170.3880, 170.4500, 110.4500, 170.3340, 170.2150, 100.2000.
Optical coherence tomography (OCT) can acquire of
high-resolution images of subsurface tissue structure
and function.1–4By use of autocorrelation,5,6phase
estimator,9,10Doppler frequency shifts can now be es-
timated in real time with Doppler OCT (DOCT). Flow
velocity can be determined via phase detection with
high sensitivity.6–10The transverse Kasai (TK) auto-
correlation estimator is suitable for imaging slow bi-
directional flows representative of microcirculation.
Aliasing due to the axial scan (a-scan) frequency,
however, limits the maximum TK detected nona-
liased axial flow speed to ?4 mm/s in OCT where
rapid scanning optical delay (RSOD) lines operate at
8 to 15 kHz.7,10,11This upper limit is increased to
?8 mm/s on spectral domain8or swept-source OCT
systems12with higher effective a-scan rates. New
swept-source systems13,14with effective a-scan rates
of 115 to 290 kHz can theoretically have an aliasing
limit of 7 cm/s. Phase-unwrapping techniques can
extend the velocity detection range; however, at high
flow rates, separation between aliasing rings can be-
come smaller than the spatial resolution of the imag-
ing system, making phase unwrapping unreliable.
Digital hardware autocorrelation with time delays
less than the a-scan period5and Hilbert transform
techniques15can provide higher aliasing limits up to
?35 cm/s with reduced sensitivity to low flow speed.
However, in applications such as coronary imaging,
flow velocity estimation in the range of meters per
second is required. In addition, blood flow velocity in
the microvasculature of atheroma can be orders of
magnitude lower than that in the lumen and both
can be present in the OCT field of view.
In this Letter we report Kasai autocorrelation per-
formed in both the axial and transverse directions, on
the same data set, which results in an extended axial
velocity estimation range. It is based on the 2D Kasai
algorithm proposed by Loupas et al.16for ultrasound
imaging. We previously reported TK estimation of
flow-induced frequency shift.10The aliasing limits
are ±1/2fa, the a-scan frequency, which is typically in
the kilohertz range. Sampling rate in the axial direc-
tion, however, is in the megahertz range. To take ad-
vantage of the larger bandwidth, we propose the
axial Kasai (AK) algorithm, computed as
where fsis the sampling rate and provides the alias-
ing limits at ±1/2fs. I and Q are in-phase and quadra-
ture components of the signal, and m and n are the
axial and transverse indices. When a stationary AK
result is subtracted from a moving source, the re-
maining signal is the Doppler shift induced by the
February 1, 2007 / Vol. 32, No. 3 / OPTICS LETTERS
0146-9592/07/030001-0/$15.00© 2007 Optical Society of America
motion of the scatterers. The change in frequency is
related to velocity by v=?0?f/2ntcos ?, where v is the
velocity at a specific point, ?0is the center wave-
length of the light, ntis the refractive index of the
sample, ? is the Doppler angle, and ?f is the change
in frequency due to Doppler shift estimated by TK or
moving AK subtracted from the stationary AK.
A flow phantom experiment was performed using
an infusion pump with calibrated flow rate control
and 1% Intralipid fluid pumped through a glass cap-
illary 0.5 mm inner diameter at a Doppler angle of
?=59°. Images were acquired using a previously de-
scribed time-domain DOCT system10containing a
5 mW broadband light source centered at 1.3 ?m
with 63 nm bandwidth with an 8 Hz a-scan frequency
?fa?. Transverse Kasai variance (TKV) processing,10
which computed the variance of the estimated mean
Doppler shift, provided segmentation between flow
and no-flow regions, similar to standard deviation
Doppler imaging.7Stationary background AK phase
change was then subtracted for AK flow visualiza-
tion. The fastest experimentally achievable peak flow
velocity was 2 m/s, with a Reynolds number of 730.
The calculated entrance length was 13 mm, shorter
than the capillary tube used. Laminar parabolic flow
was assumed for all flow rates in this experiment.
Different flow speeds were analyzed using Eq. (1),
and the AK frequency results were shown in Fig. 1A.
Bidirectional velocity was obtained by subtraction of
the stationary signal, shown in Fig. 1B. The esti-
mated peak velocities from theAK and TK (mean and
standard deviation over 1000 lines) were plotted in
Fig. 2, which showed good agreement between the
measured and expected velocities. We separated the
flow regimes into Zone I, with velocities estimated by
TK; Zone II, where the spatial dimensions of the
aliasing rings are larger than the spatial resolution
of the system and phase unwrapping can be reliably
applied; and Zone III, where TK aliasing rings are
smaller than the axial resolution and the TKV ap-
proaches fa; so phase unwrapping cannot be reliably
performed, and the velocity estimation relies on AK,
as shown in Fig. 3. In Zones I and II, the TK exhib-
ited better velocity resolution than AK. Beyond them,
the phase unwrapped TK underestimated the true
velocities, where the AK was still able to estimate ve-
locities with good agreement with set flow rates.
Hence it is possible to use the full 2D Kasai estimator
(TK and AK) to accurately measure across a wide
(7 ?m/s to ±57 cm/s, which is over 100 dB.
In vivo transesophageal M-mode DOCT imaging of
a rat aorta was performed using an endoscopic
catheter.17Motion artifacts were removed by a-scan
alignment using the aortic wall to blood interface.
The heart rate to be 230 beats per min or 0.26 s per
beat. A temporal smoothing filter set at 0.025 s in
length (?10% of the cardiac cycle), was used to im-
prove the signal-to-noise ratio (SNR) while still pre-
serving the temporal resolution and allowing visual-
ization of the cardiac cycle. The Doppler angle was
through the aorta was estimated to be ?1 m/s (Fig.
4C), in good agreement with literature.18Comparing
Figs. 4A and 4B, it is evident that the TK is sensitive
to a slower flow, detecting the pulsating motion of the
aortic wall (velocity ?2 mm/s), while the AK is ca-
pable of estimating high flow velocities ??1 m/s?
without aliasing. We are exploring the use of TKV to
aid merging of the TK andAK results to yield a single
wide dynamic range velocity image.
The physical limiting factor in the maximum de-
tectable Doppler shift using AK in our system is the
bandwidth of the hardware demodulation circuit,
which is ±1.6 MHz (−3 dB point) around the carrier
frequency. Since this is much smaller than the sam-
of flowvelocities, spanning from
function of flow velocities from −57 to 34 cm/s in capillary
tube. B, When the no-flow AK result is subtracted from the
flowing conditions, parabolic profiles are obtained.
A, Change in the AK estimated frequency as a
SD) are compared to expected flow velocities. A, Peak ve-
locities derived from TK and AK algorithms recorded over a
large range of velocities. B, detailed view of TK (with phase
unwrapping) and AK estimated velocities for lower flow ve-
locities. See text for Zone I, II, and III definitions.
TK and AK estimated peak velocities (mean and
tion zones showing structural, TK, and AK color maps after
flow segmentation. In (I), TK accurately measures velocity,
and the aliasing rings in (II) can be unwrapped reliably. In
(III), the aliasing rings cannot be accurately unwrapped.
The AK is able to accurately measure flow in (III), but not
in (I) and (II). Aggregation of Intralipid produced artifacts,
especially at low shear rate regions.
(Color online) M-mode images of the three detec-
OPTICS LETTERS / Vol. 32, No. 3 / February 1, 2007
pling frequency of the system, the AK velocity esti-
mator does not experience aliasing before the OCT
signal diminishes. This corresponds to a maximum
detectable velocity limit of ±0.78 m/s in the axial di-
rection (±5.6 m/s at 82° with our endoscopic cath-
eter), which can be further increased by widening the
demodulation bandwidth, with a trade-off in SNR of
the OCT signal. The computational complexity of AK
is of the same order as TK and can be implemented
for real-time operation in software.10Compared with
previous autocorrelation methods,5,6the Kasai esti-
mation output is linear with the flow velocity. We
note that misalignments in the RSOD, wavelength-
dependent scattering and absorption, and nonlineari-
ties in the demodulation process contributed to the
background AK phase changes, which need to be sub-
tracted for visualizing the true flow induced phase
changes. The TK and TKV processed from the same
data set are sensitive to slow flow conditions, and the
results can serve as segmentation maps for distin-
guishing stationary versus flow regions in subse-
quent AK calculations. Conversely, we are also ex-
ploring the AK as a tool for estimating the centroid
shift due to wavelength-dependent scattering and ab-
sorption in spectroscopic OCT after the segmentation
In conclusion, we described the AK algorithm as a
method for extending the velocity estimation range
on high-speed DOCT systems, to include higher flow
velocities. Using the Kasai autocorrelation technique
in two dimensions by combining the AK with TK, one
can obtain sensitivity from extremely slow to fast
flow velocities on the same data set. For what is for
the first time to our knowledge, we demonstrated in
vivo transesophageal imaging of the rat aortic blood
flow using the 2D Kasai technique.
Support from the Canada Research Chairs pro-
gram, Photonics Research Ontario and Canadian In-
stitutes of Health Research is acknowledged. We
thank A. Mariampillai and B. Standish for their
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sophageal DOCT of rate aortic blood flow. A, TK results
overlaid on structural image. Doppler signals indicate aor-
tic wall motion ???, systolic rush of high-speed blood flow
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arrows). B, AK results overlaid on the same structural im-
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(Color online) In vivo M-mode images of transe-
February 1, 2007 / Vol. 32, No. 3 / OPTICS LETTERS