Cardiac Motion estimation based on transverse oscillation and ultrafast diverging wave imaging

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Cardiac Motion Estimation based on Transverse
Oscillation and Ultrafast Diverging Wave Imaging
Philippe Joos, Sébastien Salles, Didier Vray, Barbara Nicolas and Her vé Liebgott
CREATIS ; CNRS UMR5220 ; Inserm U1044 ; INSA-Lyon ; Université Claude Bernard Lyon 1, France,
name@creatis.insa-lyon.fr
Abstract— Ultrafast ultrasound imaging using plane waves
(PW) has demonstrated its potential in assessing complicated
motion patterns in the blood or in the tissue. On the other hand,
the introduction of transverse oscillations (TO) combined with
Phase Based vector Motion estimation algorithms (PBM) has
shown to be a very promising technique to improve transverse
motion estimation. Cardiac imaging could greatly benefit of a
combination of ultrafast TO and PBM. Unfortunately, due to the
presence of the ribs, cardiac imaging has to be done with a
phased array. Consequently ultrafast imaging of the heart is
usually performed with diverging waves (DW) instead of PW. In
this paper, the objective is to extend our previously developed
ultrafast PW TO technique to ultrafast imaging of the heart
using DW. A validation of the method is proposed using
CREANUIS simulations with a realistic cardiac sequence.
Keywords— Ultrafast imaging, Phase motion estimation,
Transverse oscillations, Diverging Waves, Cardiac imaging
I. INTRODUCTION
Cardiovascular diseases are the first cause of death in
the world. According to the World Health Organisation, 17.5
million people died from cardiovascular diseases in 2012,
representing 31% of all global deaths [1]. People with
cardiovascular disease or who present a high cardiovascular
risk need early detection. Consequently it is fundamental to
develop imaging techniques to detect heart diseases.
Echocardiography is one of the most useful modality for
imaging the heart due to its high temporal resolution, its low
cost and because it is a safe diagnostic-imaging modality. The
quantification of the heart deformation, the strain, is relevant
information to qualify the good functioning of the heart [2].
We have previously developed motion estimation
techniques based on plane waves imaging, transverse
oscillations and phase-based motion estimators to assess the
displacement of the carotid artery wall [3]. The objective of
transverse oscillations is to produce a pattern in a direction
perpendicular to the wave propagation direction. Thanks to
these interference fringes patterns, the phase-based motion
(PBM) estimator [4] can quantify the displacement in both
axial and lateral directions with a high precision. These
motions have to be lower than the half-period of the
oscillations generated; this condition is guaranteed thanks to
ultrafast imaging.
In this context, we propose to combine ultrafast
transverse oscillations imaging and phase-based vector motion
estimation algorithms to determine the 2D cardiac motion.
Unfortunately, for cardiac ultrasound imaging, we need to use
phased array probes because of the ribs. Consequently
ultrafast imaging is performed using diverging waves instead
of plane waves [5]. Then we developed a polar beamforming
technique and applied a filter in the Fourier domain on polar
images to produce the TO images. This particular sectorial
beamforming allows us to filter the images in regard to the
Fraunhofer conditions [6] and to create transverse oscillations.
The PBM can finally be applied on these polar filtered images
to estimate the motion [7]. We validated this technique in
simulation thanks to a realistic cardiac sequence [8] and
CREANUIS [9], a software developed at CREATIS.
II. DIVERGING WAVE TRANSVERSE OSCILLATION
IMAGING
A. Diverging wave imaging for Fourier domain filtering
Diverging waves are used in order to perform ultrafast
imaging with a large enough field of view to observe the whole
cardiac muscle. From one diverging wave transmission, an
image of the heart can be built. We generate this diverging
wave assuming a virtual source behind the probe. Applying the
appropriate emission delays on each element on the probe, a
diverging wave focused on the virtual source is obtained.
Then, receiving the radio-frequency signals coming
back from the insonified media, there are several approaches to
perform beamforming: we opted for sectorial beamforming
considering the virtual source as the origin. The Fraunhofer
approximation is respected because the beamforming is made
in the focus plane of a converging wave [6]. The whole idea is
that in the focal plane, the spatial distribution of the amplitude
of the wave is proportional to the Fourier transform of the
distribution amplitude of the wave in the media.
Consequently the image is built with a delay and sum
sectorial beamforming considering the virtual source as the
origin of the polar coordinate system (Fig. 1.). Moreover, this
beamforming aims at avoiding the “sheared appearance” of the
point spread function in the images. Indeed with this
beamforming, we preserve the characteristic point spread
function pattern which is the same in the whole image.
978-1-4799-8182-3/15/$31.00 ©2015 IEEE 2015 IEEE International Ultrasonics Symposium Proceedings
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Fig. 1. Beamforming in a specific polar space represented
by analogy with the 4F optical system
B. TO imaging
Thanks to our specific [R-θ] beamforming, the
Fraunhofer approximation is respected. So we can apply a
filter in the Fourier domain and then take the inverse Fourier
transform to get back to the filtered image in the spatial
domain. The filter we choose works like Young’s slits: it is
like two diffracting sources which interfere in the image plane
to produce a diffraction pattern with transverse oscillations. So
the filter is weighting the amplitude distribution of the Fourier
spectrum with two peaks. This weighting function w(x) can be
expressed in Cartesian coordinates for one depth z and the
transverse oscillation wavelength obtained:
22
00
00
() ()
1
() (e e )
2
xx xx
wx





0
x
z
x


, where

is the wavelength of the
transmitted pulse and +/-
0
x
is the position of the peaks.
In the polar space we defined,
x




,
where +/-
x

is the position of the peaks in the
apodization function.
C. Transverse oscillations in polar space
The 2D Fourier transform of a polar transverse
oscillation image shows four regions which define the axial
and transverse oscillations frequencies. As the images are
beamformed in the [R-θ] coordinate system described above,
the filter operates in the [nu_R nu_θ] Fourier domain to
generate transverse oscillations. So the axial oscillation
frequency is a radial frequency and the transverse oscillation
frequency is an angular frequency. Consequently the cardiac
motion will be estimated in these two radial and angular
directions. It can be noticed that the polar transverse
oscillations images here can be achieved solely by filtering in
the Fourier domain.
III. SIMULATIONS VALIDATIONS
A. CREANUIS
CREANUIS is a software developed by our
laboratory CREATIS. It allows generating ultrasound radio
frequency (RF) images considering both linear and non-linear
propagation in the media. The non-linear propagation field
simulator and our sectorial TO image formation algorithm
were coupled to perform the images.
B. Simulations
In order to validate our approach we performed
simulations with the CREANUIS software described above
and different phantoms motion sequences: a simple numerical
squar e phan tom to validate the method and a realistic
numerical cardiac phantom. The virtual source was placed
17.6 mm behind the probe in order to insonify the media with
a π /2 sector. The images were then beamformed in the polar
space with 256 angles.
We first used simple square medium in which all the
scatterers describe the same constant motion in the angular
direction. This phantom was composed of 10
5
scatterers
distributed uniformly over a square of 60*20 mm
2
whose top
was positioned at 40 mm depth. The amplitude distribution of
the scatterers is a unit normal distribution. In order to be as
close as possible to the realistic sequences, we applied low
motions in the θ direction: from 0.01 pixels to 2 pixels, that is
to say from 0.0036° to 0.70°. Different approaches were used
to generate TO images. We first used a single lateral
frequency corresponding to a 5 pixel wavelength (1.78°) with
a lateral bandwidth characterized by the sigma value of the
filtering. The radial wavelength was equal to 0.308 mm. We
then tried another kind of filtering: mono-frequency filtering
with no angular or radial frequency bandwidth for each filter.
In this case the final motion estimation was obtained by
averaging the motion estimations based on different mono-
frequency filters placed over the whole initial 2D spectrum.
Finally we made simulation with a realistic cardiac
sequence. A simulated sequence was used, generated thanks to
a real sequence acquired from a healthy subject. The frame
rate of the initial simulated sequence was 33 frames per
second. Only the scatterers composing the myocardium were
kept and their positions were interpolated to increase the frame
rate up to 3301 frames per second. TO images were generated
with radial and angular wavelengths equal to 0.308 mm and
1.78°, respectively.
The motion was then estimated with the phase based
motion estimator on the entire images to obtain maps.
C. Results
The next figures, show the TO image and its spectrum for
the square phantom.

Fig. 3. TO image B-mode, with λ=5px (1.78°), σ=9px (3.20°)
Fig. 4. TO image spectrum, with λ=5px (1.78°), σ=9px (3.20°)
Then, the angular motion can be estimated using the
PBM described in [4] on the entire image with our sequence
from 0.01 pixels to 2 pixels motion. The errors are shown in
pixels (Fig. 5.). Big standard deviations of motions estimated
are observed here (Fig. 6.). We think this is due to the width
of the spectrum which generates random interference patterns
with oscillation wavelengths different from the one used in the
estimator.
So we had the idea to make motion estimation with
an average the estimations obtained with one frequency filter.
The comparison of the map obtained is convincing enough to
recommend this second approach (Fig. 7.). Very little standard
deviations and good estimations can also be observed. Indeed
the angular motion error was first 0.057 +/- 0.1[pixels], and
with the second method the angular motion error is 0.029 +/-
0.0001 [pixels].
The figure 8 shows our initial result on the realistic
cardiac simulation. Here only the approach without filtering
could be used. The effect of the width of the spectrum is
critical here and we cannot consider that the generated motion
map is satisfactory (Fig. 8.). The mono-frequency approach
could not be applied yet because a segmentation of the
phantom has to be performed first to apply this specific filter
on particular region of the phantom.
Fig. 5. Angular motion estimation errors: real motion Ο and
estimated motion Χ. The plot at the top left represents all
motions from 0.01 to 2 pixels, the next plots shows zoom from
0.01 to 0.1 pixels, from 0.1 to 1 pixel and from 1 to 2 pixels
Fig. 6. Angular motion standard deviations. The plot at the
top left represents all motions from 0.01 to 2 pixels, the next
plots shows zoom from 0.01 to 0.1 pixels, from 0.1 to 1 pixel
and from 1 to 2 pixels

Fig. 7. Motion estimation map comparison (frequency
bandwidth on the left, monofrequency + average on the right)
Fig. 8. Angular Motion: Reference (left) and Estimation
(right)
IV. DISCUSSION
The specific sectorial beamforming technique we
propose allows generating images in a polar space without
“sheared appearance” of the PSF. The filtering approach in the
Fourier domain, based on the Fraunhofer diffraction theory,
provides transverse oscillation patterns with wavelengths
which can be controlled. The wavelength issue is essential
because it is the key of the phase based motion estimator. If a
bandwidth of the spectrum, centered around a central
frequency, is kept the motion estimated can be wrong. Indeed
we observe oscillations corresponding to this central frequency
but also other random oscillation patterns due to the other
frequencies of the spectrum. The consequence of this
bandwidth is a big standard deviation in the motion estimated.
This effect can be corrected for homogeneous motion by
applying filters with only one frequency and averaging
estimations with different frequencies spread over the full
spectrum. The advantage of this approach is the use of the
whole spectrum instead of choosing one central frequency.
Moreover with this method the motion estimated standard
deviation is much reduced. We have to notice that this
approach is more time consuming than the “bandwidth
approach” but it should also be easily parallelized.
For the cardiac application, the motion of the muscle
is not homogeneous and the method has to be improved. The
model of the square doing only translation in the radial or
transversal direction is too simple to be reproducible for the
heart motion. So th e next stage to validate the model will be an
intermediate situation and should consist in applying our
method to phantom with complex circular motions.
Finally, for the cardiac application the method will
have to be implemented in 3 dimensions because the heart
motion is not constant in a 2D plan.
V. CONCLUSION
In this paper we presented a new approach to combine
transverse oscillation and ultrafast imaging using diverging
waves. We performed a specific sectorial beamforming which
allows filtering in the Fourier domain. The transverse
oscillations are generated in an angular direction and the
motion estimation is performed in the polar space. The
simulations showed good results for simple translations in the
angular transverse direction. Realistic heart motion models are
for now too complex to take advantage of our method. But
there are some ideas of better use of the spectrum of the image
to improve the method. It is now important to pursue
simulations with more complex motions and to apply the
technique on real phantom with control motions.
ACKNOWLEDGMENT
This study was conducted within the Laboratoire
d’Excellence (LABEX) Centre Lyonnais d’Acoustique
(CeLyA) (ANR-10-LABX-0060) and Physique, Radiobiogie,
Imagerie Medicale et Simulation (PRIMES) (ANR-10-LABX-
0063) programs of Université de Lyon, within the
Investissements d’Avenir program (ANR-11-IDEX-0007)
operated by the French National Research Agency (ANR). H.
Liebgott and S. Salles received financial support from the
Région Rhône-Alpes (Explora’Pro and Explora’Doc Grants).
The authors want to acknowledge Martino Alessandrini and
François Varray for their important input regarding the cadiac
simulation with CREANUIS.
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