1Pb5-2
A Preliminary Study to Extend Nyquist Flow Speed of
Echocardiography using a Dual-PRF Dealiasing Method
Yuki Okada1‡, Naoya Kanno1, Takuro Ishii1, 2, Yoshifumi Saijo1 (1Grad. School of
Biomed. Eng., Tohoku Univ., 2FRIS, Tohoku Univ.)
1. Introduction
Blood flow measurement in the heart is one of
the most important diagnostic indicators inevaluating cardiac function. To assess and quantify
the blood flow measurement, color Doppler
ultrasound imaging is an essential imaging modality.
While conventional color Doppler imaging is realtime and noninvasive, it is limited to measuring only
a component of the blood flow velocity component
along the ultrasound beam. Our research group hasreported an imaging framework1) that estimates 2D
velocities based on trigonometric relationships
between two 1D velocities obtained by transmitting
diverging waves in two different directions.
Nevertheless, one problem with this method was that,as the number of transmission directions increases,
the pulse repetition frequency (PRF) in the same
direction becomes smaller, resulting in reduced
robustness against aliasing artifacts. To achieve morerobust 2D flow vector estimation, this study aimed topropose a method to extend the Nyquist speed using
two PRFs, leveraging the staggered multiple-PRF
ultrafast color Doppler2) and investigate the optimal
imaging scheme for echocardiography. On this topic,
this paper specifically presents the preliminary trials
to test the new framework using a straight constantflow model and to compare the performance of the
proposed method with that of conventional “singlePRF” color Doppler method.
2. Method
2.1 Dual-PRF dealiasing method
The Nyquist velocity 𝑉𝑁 in the color Doppler
method is given by
𝑃𝑅𝐹 × 𝜆(1),𝑉𝑁 =4where 𝜆 is the wavelength of the acoustic pluses.
In the dual-PRF method, two different PRFs (𝑃𝑅𝐹1and 𝑃𝑅𝐹2 )were first selected. 𝑃𝑅𝐹1 was defined
based on the imaging depth and the expected
maximum flow velocity, and the other PRF was set
in the following relationship.
𝑝(2),𝑃𝑅𝐹2 = 𝑃𝑅𝐹1
𝑞
where 𝑝 and 𝑞 are mutually prime natural
yuki.okada.t1@dc.tohoku.ac.jp

numbers and 𝑝 < 𝑞. Also, the relationship between
the Nyquist speeds 𝑉𝑁1 and 𝑉𝑁2 can be written as,𝑝(3).
𝑉𝑁2 = 𝑉𝑁1𝑞To illustrate the principle of the Nyquist
velocity being extended, Fig.1 depicts therelationship between actual and measured velocities
when 𝑝 = 2 and 𝑞 = 3 . As shown Fig.1, eachcolor-coded region has a unique difference between
flow speed value measured by 𝑃𝑅𝐹1 and 𝑃𝑅𝐹2 ,respectively. This difference can be used to extend
the Nyquist speed up to twice the 𝑉𝑁1 .
Measured velocity

RealvelocityFig.1

Relationship between speeds at two PRFs.

Each unique region in Fig.1 can be identified
by calculating,
𝑉𝐷 − 𝑉𝐷1(4),nint (𝑞 2)
2𝑉𝑁1
here nint is the function to calculate the closest
integer value.
Based on the integer number acquired in eq.
(4), the speed correction in the dual-PRF dealiasing
method was performed. The combination of Nyquist
numbers 𝑛𝑁𝑖 was derived from the integer number
and Table I. The derived Nyquist number 𝑛𝑁𝑖 aresubstituted into the following equation to finallycalculate the dealiased Doppler velocity 𝑉𝐷𝑢 ,𝑞(𝑉𝐷1 + 2𝑛𝑁1 𝑉𝑁1 ) + (𝑉𝐷2 + 2𝑛𝑁2 𝑉𝑁2 )𝑝𝑢(5).
𝑉𝐷 =𝑞1+𝑝B-mode
15 Tx

Doppler
17 Tx
×2 directions

Doppler
17 Tx
×2 directions

Doppler
17 Tx
×2 directions

Doppler
17 Tx
×2 directions

time

Fig.2 Transmission sequence for acquiring one frame.

Table I Relationships between the integer number
given in eq. (4) and the number of aliasing wrapping for
Doppler measurement at each PRF.

𝐧𝐢𝐧𝐭 (𝒒𝟐𝑽𝑫 𝟐 − 𝑽𝑫 𝟏)
𝟐𝑽𝑵𝟏
210-1-2𝒏𝑵𝟏

𝒏𝑵𝟐010-10-1
10-1
1

Doppler images is shown in Fig.3 (c), and the mean
absolute error (MAE) was 25.9 mm/s. Up to thedepth of 65 mm, the dual-PRF dealiasing method
was observed to show the same results as the singlePRF method, but for the deeper region (> 65 mm),the error was found to be larger. This might be due tothe missing color Doppler data of 𝑃𝑅𝐹2 at deeper
than 65 mm depth, which can be seen in Fig.3 (d).
This finding suggested that, when using the dualPRF dealiasing method, color Doppler images ofboth PRFs need to be highly accuracy. In the future
study, the devised framework will be furtherevaluated under other flow conditions such aspulsating flow.

2.2 Experimental Setup

3. Results and Discussion
Color Doppler images for the Tx angle of+30° respectively derived from the dual-PRF
dealiasing method and single-PRF are shown inFig.3. The absolute error of the two dealiased color[mm/s]
600(a)

50(b)400
200600-20070

Depth [mm]Depth [mm]506070-40080
50010Width [mm]-60080[mm/s]
3005020(c)10070-1000-10010Width [mm]20010Width [mm]

20(d)

200

60

Depth [mm]-10Depth [mm]Phantom experiments were performed toevaluate the performance of the dual-PRF dealiasing
method on a sector probe imaging setting. A
research-purpose ultrasound system (Vantage 256system, Verasonics) equipped with a sector probe (64channels, fc: 2.5 MHz) was used to image a Doppler
403 flow phantom with a flow tract of 5 mm indiameter and tilted at 40°. The flow rate was set as
constant at 8.0 ml/s.
A transmission sequence to generate a pair ofa B-mode image and a flow vector map wasconfigured as shown in Fig.2. First, B-mode images
frame was acquired by emitting 15 diverging
were pulses (Tx angles range: ±42°). Subsequently,
the dual-PRF Doppler measurement sequence
consisted of four blocks shown in Fig.2 was run.
Each block emitted 34 diverging waves from ±30°alternatively. 𝑃𝑅𝐹1 was set for the first and third
blocks, while 𝑃𝑅𝐹2 was used for the rest of blocks.
In each experiment, 10 frames of data were acquired.
The echo data of Doppler measurement at each PRF
was processed with the SVD clutter filtering and lag1 autocorrelator to estimate 𝑉𝐷1 and 𝑉𝐷2 that canbe used to estimate an aliasing-free velocity map.
Later, the estimated velocity maps were averaged
over 9 frames. For comparison, the conventional
single-PRF color Doppler imaging was performed
with data taken at 𝑃𝑅𝐹1 only and the aliasing
artifacts were removed by the phase unwrapping.

6070-200
80-300-10010Width [mm]2080-10Fig.3 Color Doppler images with (a) dual-PRF
dealiasing method, and (b) single-PRF, (c) absolute errorof (a) and (b), (d) color Doppler of 𝑃𝑅𝐹2 used in dualPRF dealiasing method.

3. Conclusion
In this study, the performance of the dual-PRF
dealiasng method for a sector probe imaging wasevaluated by a straight tube phantom experiment.
The results showed that if the color Doppler of each
PRF used in the dual-PRF dealiasing method wasaccurately acquired, the performance was as good asthat of color Doppler using the single-PRF method.
References
1. M. Maeda et al.: Jpn. J. Appl. Phys. 57 (2018)
07LF02-1.
2. D.Posada et al.: IEEE Trans. Med. Imaging 35(2016) 1510.