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Adapted directivity approach for Photoacoustic Imaging
Reconstruction
Daniele Piras*a, Michelle Heijbloma,b, Wenfeng Xiaa, Ton G. van Leeuwenc, Wiendelt Steenbergena,
and Srirang Manohara
aBiomedical Photonic Imaging group, Mira, University of Twente, P.O. Box 217, 7500AE Enschede,
The Netherlands.
bCenter for Breast Care, Medisch Spectrum Twente hospital, P.O. Box 50000, 7500 KA, Enschede,
the Netherlands.
cBiomedical Engineering and Physics, Academic Medical Center, University of Amsterdam, P.O.
Box 2270, 1100 DE Amsterdam, the Netherlands.
ABSTRACT
In photoacoustic imaging, upon short laser pulse irradiation, absorbers generate N-shaped pulses which can be detected
by ultrasound transducers. Radio frequency signals from different spatial locations are then reconstructed taking into
account the ultrasound transducer angular response. Usually, the directivity is part of the "a priori" characterization of the
transducer and it is assumed to be constant in the reconstruction algorithm.
This approach is valid in both transmission and reflection ultrasound imaging, where any echo resembles the transducer
frequency response. Center frequency and bandwidth of any echo are almost the same, and the ultrasound transducer
collect signals with the same "fixed" acceptance angle. In photoacoustics, instead, absorbers generate echoes whose time
duration is proportional to the absorber size. Large absorbers generate low frequency echoes, whereas small absorber
echoes are centered at higher frequencies. Thus for different absorber sizes, different pulse frequencies are obtained and
different directivities need to be applied.
For this purpose once a radio-frequency signal is aquired, it is pre-processed with a sliding window: every segment is
Fourier transformed to extract the central frequency. Then, a proper directivity can be estimated for each segment.
Finally signals can be reconstructed via a backprojection algorithm, according to the system’s geometry. Echoes are
backprojected over spheres with the angular extension being adapted to the frequency content of the photoacoustic
sources.
Simulation and experimental validation of this approach are discussed showing promising results in terms of image
contrast and resolution.
Keywords: Photoacoustics, backprojection, directivity
1. INTRODUCTION
Breast cancer is a leading cause of women mortality with more than 240000 new cases in 2010 only in the United
States1. The need for sensitivity, specificity and non-ionizing diagnostic modalities pushes for new imaging techniques
to be developed.
Optical methods have raised interest2,3: but light is highly scattered in soft tissues and optical detection is limited by
depth of penetration4.
In photoacoustics the increased concentration of hemoglobin in malignancies provides the main source of contrast5,6, but
detection is performed with ultrasound which is low scattered in soft tissues. Malignancies, in particular, growing
*d.piras@tnw.utwente.nl; phone +31 53 489 3877; fax :+31 53 489 1105;
Photons Plus Ultrasound: Imaging and Sensing 2012, edited by Alexander A. Oraevsky, Lihong V. Wang,
Proc. of SPIE Vol. 8223, 82231Z · © 2012 SPIE · CCC code: 1605-7422/12/$18 · doi: 10.1117/12.907990
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beyond a few millimeters require angiogenesis to set up a feeding vascular network7: areas of enhanced vascularization
associated with cancer represent an ideal target under photoacoustics.
When short pulses of near-infrared laser light are used to illuminate a tissue, a fast heating is induced in absorbing
structures, followed by thermal expansion8-10: under thermal and stress confinement, a spherical absorber produces a
bipolar pressure wave transient which can be detected by ultrasound transducers. The peak to peak amplitude and the
time duration of the bipolar pulse would be proportional to the optical contrast and the size of the absorber, respectively.
Photoacoustic pulses are then collected at ultrasound detector surfaces: when the arrangement of the detectors is known,
pulses are reconstructed to retrieve the map of the original pressure distribution within the volume of interest. Usually
when a computerized tomography (CT) approach is used the reconstruction of the original pressure distribution is very
well achieved11-14. Furthermore in CT it is always possible to properly sample the volume of interest in the spatial
domain, despite of the ultrasound element size, by acting on the number of angular views to produce independent
realizations of the unknown medium. Unfortunately this is not possible when a linear (or planar) array configuration is
used15,16 where a limited view problem arises. In these cases, since the spatial arrangement of the detectors is fixed and
the spatial sampling is limited by the physical size of the elements, most of the image reconstruction quality depends on
the ability of the transducers to collect signals in a broad volume. This means that theoretically a large directivity would
be required for the single transducers: this can either be achieved by choosing a small element size with respect to the
center frequency or by artificially broadening the acceptance angle by means of acoustic lenses17. Unfortunately both
have pitfalls: small elements are expected to have low sensitivity because of the reduced active surface, and acoustic
lenses introduce further acoustic attenuation due to the lens thickness.
In photoacoustics, directivity is assessed18 by studying the angular response of the transducer to a broadband signal that
is generated by means of optical absorption at the interface of an optically transparent medium with a thin strongly
absorbing medium. Alternatively it can be assessed with an ultrasound transmission mode19 where the actual detector is
used as a receiver, and a known US source is used to scan angularly around the receiver transducer. In any case both
characterizations refer the angular behavior of the transducer to the frequency content of an ideal source.
The characterization of directivity so far is valid in pure ultrasound: the center frequency and bandwidth of a
radiofrequency signal from specular reflection in the insonified volume resembles the transducer’s impulse response,
and then the ultrasound transducer collects signals within the same "fixed" acceptance angle. Also elastic scattering20
behaves in a similar way. In photoacoustics, instead, absorbers generate echoes whose time durations are proportional to
the absorbers’s size21,22: this means that, within the transducer frequency bandwidth, large absorbers generate low
frequency echoes, whereas small absorber echoes are centered at higher frequencies. Thus for different absorber sizes,
different pulse frequencies are obtained and different directivities need to be applied.
In this manuscript an adaptive directivity approach is thus used to reconstruct photoacoustic signals. A planar
configuration with large elements is studied as it is the case for the Twente Photoacoustic Mammoscope16. Phantom
experiments and simulations have been carried out to support the adapted directivity hypothesis.
2. MATERIALS AND METHODS
The photoacoustic pressure p(r,t) is related to the absorbed optical energy via23:
'4
'
)'('),( 2
rr
c
rr
t
t
rArd
C
trp
p−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛−
−
∂
∂
=∫
π
δ
β
(1)
In case of a planar detection geometry, the reconstructed amplitude at the point (i,j) can be expressed as the superposition
of the conveniently delayed signals from the M available transducers24:
(
)
∑
=
+−= M
k
jikkpjiA
0
22
)(,),( (2)
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After RF-data from a specified region of interest have been collected, the signals are reconstructed with a 3D acoustic
back-projection algorithm25,26. By knowing the geometry of the detector and assuming a constant speed of sound in the
medium, the acquired signals are backprojected over spherical surfaces centered at the respective transducer element
positions. The directivity of the transducer should then be taken into account24,27 defined as the acceptance angle of the
array element. As explained in the introduction, this is fixed for backscattered ultrasound but is not for photoacoustics.
Figure 1. k-wave simulation on a 5mm x 5mm square element with center frequency of 1 MHz a) 1MHz source on axis; b) 1MHz
source 45 degrees off-axis; c) 200kHz source on axis; d) 200kHz source 45 degrees off-axis; e) detected signals from 1MHz source
at 0 and 45 degrees from a) and b); f) detected signals from 200kHz source at 0 and 45 degrees from c) and d) ; g) directivity of
1MHz and 200kHz sources.
The k-wave software28 was used to simulate the angular sensitivity of a 5mm x 5mm square element with center
frequency of 1MHz. Two spherical ultrasound sources were used: a 1.5mm and a 7.5mmm diameter sphere were
simulated and signals were collected at the surface of the transducer upon homogeneous illumination. Because of phase
interference, the on- and off-axis behavior is quite different (Figure 1.a-d): the low frequency signal experiences much
less destructive interference on the 5mm transducer surface than the high frequency signal does (Figure 1.e-f). As a
result, though the transducer’s characteristics have not been changed, the directivity profiles for these two frequencies
are dramatically different (Figure 1.g): roughly 30 degrees for 1MHz (1.5mm sphere) and 70 degrees for 0.2MHz
(7.5mm sphere). We believe that this difference needs to be taken into account for a proper reconstruction.
For this purpose once a radio-frequency signal is acquired, it is pre-processed with a sliding window: every segment is
Fourier transformed to extract the central frequency fm. Then a proper directivity D can be estimated for that segment29
with:
()
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
θ
π
θ
m
fc
L
D/
sinc (3)
where L is the transducer size and c is the assumed speed of sound in the medium. Finally, signals can be reconstructed
via backprojection algorithm with (2) according to the system’s geometry, but echoes are backprojected over spheres
with the angular extension being adapted to the frequency content of the photoacoustic sources based on (3).
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2.1 Simulations
The model was tested on a 3D synthetic phantom with the k-wave package28. A linear array of 21 square elements (5mm
x 5mm, central frequency 1MHz and 80% bandwidth, 1mm spacing between elements) is used to scan a homogeneous
medium. The medium had soft tissue optical and acoustic properties and included 3 spherical targets of 3, 5 and 10mm in
diameter. Since we were only interested in investigating the feasibility of the reconstruction approach, illumination was
supposed to be constant throughout the phantom. Reconstructions were performed with the fixed theoretical directivity
for such elements and with the adaptation for the frequency content.
2.2 Phantom experiments
The Twente Photoacoustic Mammoscope16 was then used to experimentally validate the model. An IntraLipid (Fresenius
Kabi) solution, having a reduced scattering coefficient of 0.1 mm-1, was used as a background medium embedding PVA
absorbing spheres (μa = 0.07 mm-1 )30-32. The spheres diameter were 5 and 2mm and the spacing between them was set to
0, 1 and 1.5mm (corresponding to centers inter-distances of d1=3.5mm, d2=4.5mm, d3=5mm respectively). We used a
broad and steady illumination (300mJ on 30cm2, 1064 nm) scheme, and targets were at 1cm in depth with respect to the
illuminated surface of the phantom. The acquired ROI was about 4cm x 4cm. Also in this case, signals were
reconstructed with and without the adapted directivity.
3. RESULTS AND DISCUSSION
3.1 Phantom experiments
With the k-wave package28, a set of synthetic RF data was obtained and this is shown in Figure 2.a. The reconstruction
with a fixed directivity for those elements (10 degrees) shows that the final imaging (Figure 2.b) is comparable with the
original set of RF data, since the overlapping between circles of reconstruction of the elements is very limited. When
adapted directivity is used (Figure 2.c), instead, the spreading of the beams can be relatively higher: the small target has
roughly 30 degrees spreading , the medium target is at about 40 degrees and the large target reaches up to 80 degrees. In
this case the overlapping of reconstruction circles leads indeed to a much better reconstruction as shown in Figure 2.c.
Figure 2. a) RF signals; b) reconstruction with fixed directivity; c) reconstruction with adapted directivity
3.2 Phantom experiments
With the Twente Photoacoustic Mammoscope we also obtained good results. Figure 3.a-b show two isosurface levels of
the reconstructed volumes for the two approaches. In general we found an improvement in the resolution of the system
with a 0.5mm and 0.8mm reduction in size, i.e. a better size estimation, for the large and small sphere respectively. The
signal to noise ratio was also improved from 3.2 to 3.6 for the large sphere and from 2.3 to 2.5 for the small sphere (these
differences were significantly different). The fixed directivity reconstructions were also considerably affected by artifacts
caused by the resolution limit proximity of the two inclusions: Figure 3.b-c show that in the “fixed” reconstructions the
second high amplitude object is not the expected target but an artifact which is located roughly 10mm away from the
large sphere: as a consequence the true small sphere is barely visible. In the adapted directivity reconstruction this
artifact is not present and, with the exception of d1 measurement (spheres spacing is 0mm, corresponding to an inter-
distance of 3.5mm), the measured inter-distances between the spheres are in good agreement with the setup distances.
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The element size for PAM is 2mm x 2mm which causes that the natural directivity is larger than in the simulation (18
degrees vs. 10 degrees) where elements were 5mm x 5 mm. Moreover the lateral sampling of PAM is higher (3.175mm
pitch vs. 6mm pitch). Therefore, the effect of adapting the directivity with frequency content was expected to be less
prominent in PAM than in the simulation. Nevertheless we obtained improvements in terms of artifact reduction, better
size estimation and higher signal to noise ratio (Figure 3.c).
Figure 3.For fixed and adapted directivity: a) high threshold isosurface (200/255) with only the large sphere visible; b) medium
threshold isosurface (110/255) with also the small sphere visible; c) profiles throughout the large and small spheres.
4. CONCLUSIONS
In this paper we proposed to investigate the effect of the frequency content of photoacoustic signals and how this affects
the capability of an ultrasound transducer to collect signals from on- and off-axis.
Since the time duration of a photoacoustic pulse generated from an absorbing structure is proportional to the structure
size, different absorber sizes necessarily generate different signals in the frequency domain. We took this into account to
refine the reconstruction algorithm and we found promising results both in simulations and in phantom experiments. We
could get better resolution (0.5mm reduction) and higher signal to noise ratio. Artifacts were also diminished. Even if
this method is especially thought for limited view detection geometries, we believe it can also be helpful in CT
geometries. Though the spatial sampling in CT is already high because of the possibility to take multiple projections, if a
“fixed” directivity is used to design a CT setup, the overall dimensions might be overestimated in order to fit the object
of interest in the ultrasound array field of view. With this method, instead, the acceptance angle of an ultrasound element
is no longer dependent only on its central frequency, and as a consequence the total acceptance angle of the array can be
broader than that for the designed center frequency and the systems can be made more compact.
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