Novel optimization method for multi-dimensional breast photoacoustic tomography

Abstract

Photoacoustic tomography (PAT) is an effective optical biomedical imaging method which is characterized with noninonizing and noninvasive, presenting good soft tissue contrast with excellent spatial resolution. To build a multi-dimensional breast PAT image, more ultrasound sensors are needed, which brings difficulties to data acquisition. The time complexity for multi-dimensional breast PAT image reconstruction also rises tremendously. Compressive sensing (CS) theory breaks the restriction of Nyquist sampling theorem and is capable to rebuild signals with fewer measurements. In this contribution, we propose an effective optimization method for multi-dimensional breast PAT, which combines the theory of CS and an unevenly, adaptively distributing data acquisition algorithm. With this method, the quality of our reconstructed breast PAT images are better than those using existing multi-dimensional breast PAT system. To build breast PAT images with the same quality, the required number of ultrasound transducers is decreased by using our proposed method. We have verified our method on simulation data and achieved expected results in both two dimensional and three dimensional PAT image reconstruction. In the future, our method can be applied to various aspects of biomedical PAT imaging such as early stage tumor detection and in vivo imaging monitoring.

Full text

Novel Optimization Method for Multi-dimensional Breast
Photoacoustic Tomography
Meng Caoa, Ting Fenga, Jie Yuana*, Sidan Dua, Xiaojun Liuc, Xueding Wangb, Paul L Carsonb
a School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, China
b Department of Radiology, University of Michigan, Ann Arbor, MI 48109, USA
c School of Physics, Nanjing University, Nanjing 210093, China
*Email: yuanjie@nju.edu.cn
ABSTRACT
Photoacoustic tomography (PAT) is an effective optical biomedical imaging method which is characterized with
nonionizing and noninvasive, presenting good soft tissue contrast with excellent spatial resolution. To build a multi-
dimensional breast PAT image, more ultrasound sensors are needed, which brings difficulties to data acquisition. The
time complexity for multi-dimensional breast PAT image reconstruction also rises tremendously. Compressive sensing
(CS) theory breaks the restriction of Nyquist sampling theorem and is capable to rebuild signals with fewer
measurements. In this contribution, we propose an effective optimization method for multi-dimensional breast PAT,
which combines the theory of CS and an unevenly, adaptively distributing data acquisition algorithm. With this method,
the quality of our reconstructed breast PAT images are better than those using existing multi-dimensional breast PAT
system. To build breast PAT images with the same quality, the required number of ultrasound transducers is decreased
by using our proposed method. We have verified our method on simulation data and achieved expected results in both
two dimensional and three dimensional PAT image reconstruction. In the future, our method can be applied to various
aspects of biomedical PAT imaging such as early stage tumor detection and in vivo imaging and monitoring.
Keywords: photoacoustic tomography, compressive sensing, non-uniform data acquisition, breast imaging
1. INTRODUCTION
Photoacoustic tomography (PAT) is an effective optical biomedical imaging method which presents good soft tissue
contrast with high spatial resolution. Compared with traditional biomedical imaging techniques such as X-ray Computed
Tomography (XCT) and ultrasound imaging, PAT has the capability to image important physiological parameters such
as oxygen saturation and hemoglobin concentration, thus having broad application prospect in both clinic and basic
biomedical research.
As an emerging technology, PAT overcomes the high degree of scattering of optical photons in biological tissue by
making use of the photoacoustic effect. Light absorption by molecules creates a thermally induced pressure jump that
launches ultrasonic waves (typically with several tens or hundreds MHz bandwidth), which are received by ultrasonic
transducers to form images. The above process is the basic mechanism of PAT.[1]
Recent studies have found that the theorem of PAT can be applied to various biological medical fields such as brain
vessel imaging,[2] tumor angiogenesis imaging,[3] cardiovascular vulnerable plaque imaging,[4] blood hemoglobin and
oxygen saturation imaging,[5] and sentinel lymph nodes mapping,[6] etc. Besides, breast cancer detection is also an
important application of PAT. [7]
Breast cancer is one of the most terrifying illnesses which poses a great threat to women. Statistics have shown that it has
become the second leading cause of cancer death in the US, following lung cancer.[8] At present, x-ray mammography
and ultrasonography is the mainstream detecting method. However, studies have shown that the conventional method of
breast cancer detection provides low contrast of the abnormality.[9] Among 100 people claimed to have breast cancer by
x-ray mammography, only 20 to 30 people are real patients. In order to make accurate conclusions, a great number of
extra biopsies are needed, which is a huge burden both for patients and hospitals.
Fortunately, PAT presents a good solution to the above problem. According to experimental research results of the
Biomedical Optics Laboratory of Twente University, in all malignant cases, the PA contrast of the abnormality was
Optics in Health Care and Biomedical Optics VI, edited by Qingming Luo, Xingde Li,
Ying Gu, Yuguo Tang, Proc. of SPIE Vol. 9268, 92681H · © 2014 SPIE
CCC code: 1605-7422/14/$18 · doi: 10.1117/12.2070977
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higher than the contrast on x-ray mammography.[9] Moreover, the PA contrast appeared to be independent of the
mammographically estimated breast density and was absent in the case of cysts. To date many efforts have been made to
improve the technique of PAT. For instance, OptoSonics have developed a three-dimensional breast vascular imaging
system,[10] which has succeeded in achieving a maximum imaging depth of 4cm with the spatial resolution of about
0.25mm. Besides, a dual system developed by TomoWave Laboratories Inc. has been able to analyze the US and OA
clinical images.[11] So does an integrated ultrasound, photoacoustic, and thermoacoustic imaging system developed by
Haixin Ke.[12]
However, despite all of the progress made by former research, when building multi-dimensional breast PAT images,
more ultrasound transducers are needed, which adds hardware cost and time complexity. In order to make full use of the
acquired data, we have proposed a new method by incorporating compressive sensing theory into PA image
reconstruction process. On this basis, so as to further improve the reconstructed image quality, we have employed a new
mechanism of data acquisition which is different from current methods. This method have been verified via simulation
and achieved expected results in PAT image reconstruction.
In this paper, the overall imaging system architecture and the data acquiring mechanism are described in Section 2. Both
images and numeric results for the original and the improved computer simulations are reported in Section 3, as well as
the work summarize with discussion in Section 4.
2. METHODS
2.1 Compressive Sensing
Generally speaking, the PA signals are usually sparse or contain little information. In order to achieve better
reconstruction results out of the sparse signals, we have proposed a method that incorporates Compressive Sensing
theory in the process of photoacoustic imaging.
Candès and Donoho first proposed The Compressive Sensing Theory in 2006.[13] As an emerging technique of efficient
data compression and processing, it is built upon the assumption that the signal is sparse (we define a signal is K-Sparse
if it is a linear combination of only K basis vectors). Before accurately reconstruct the original signal from a small
amount of compressed data, we need to perform two steps. In the first step, we design a stable measurement matrix to
perform a coefficient projection from a high-dimensional space to a low-dimensional space. In the second step, we
develop a reconstruction algorithm which solves a sparse optimization problem as well as recovering the original signal
from the measurements. With this method, it is possible to rebuild signals with fewer measurements.
In our study, instead of directly perform reconstruction with the collected PA signals, we intend to add an extra step of
CS reconstruction after the preliminary process of PA reconstruction. Specifically, first we sparse the signals by
performing a wavelet transformation, then we adopt an appropriate CS algorithm to accurately reconstruct the input
signals. After this extra step, the outcome is sent to continue the rest process of PA reconstruction. Theoretically, the
reconstructed image quality will get improved.
2.2 Data Acquisition Method
Currently, PAT has a variety of detecting methods, such as linear plane scanning, probe rotating scanning, sample
rotating scanning, etc. Most of the PAT systems adopt single or multiple unit ultrasound transducers to detect the PA
signals. The transducers or the sample often need to rotate so as to obtain a complete picture. As a result, the application
of PAT was limited because such a process usually takes up to several tens of minutes.[14] Besides, currently the imaging
area is restricted, usually to the millimeter level. However, in clinical applications, we also hope to obtain images of
larger targets. Under this background, the study of more efficient large-sized target imaging has become an important
research topic.
In this paper, we proposed an effective optimization PAT method which combines the theory of CS and a non-uniformly
data acquisition algorithm. Generally speaking, the number of data acquiring channels that work at the same time is
limited, therefore we cannot open all the transducers to receive PA signals. For example, the maximum number of
transducers around the target is 1024, but only 128 transducers can receive signal at the same time. Experience has
shown that when the distance between neighboring working channels is 1mm to 3mm, the image quality reaches the
optimum value. For uniformly selected 128 channels in a circular system, this rule restricts the radius of imaging area to
the value between 4cm and 12cm. If we want to add the radius to image larger objects, the distance between neighboring
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channels rises while reconstructed image quality drops. So it is important to choose a channel selecting mechanism that
can produce relatively good image out of 128 channels.
As a solution, we proposed a method to take better use of the working channels, which consists two steps. The first step
is pre-imaging, during this process the channels are uniformly distributed around the target, which is also a commonly
used method to perform PA reconstruction at present. The second step is re-imaging, as shown in Fig. 1, we change the
position of selected channels according to the pre-imaging result.
Fig. 1 Data acquisition method during the process of PAT imaging with CS theory.
Specifically, for the target region (usually the diseased area with more detailed features and structure varieties due to its
optical absorption properties), we add more working channels to collect more data for reconstruction, while for the area
of unconcern (non-diseased area such as the healthy part of tissue), as its imaging result is usually chunks of single color
(e.g. pure black or grey), such parts have little value of medical research, so we arrange less working channels for this
area. In this way, with the total number of working channels unchanged, more channels are arranged to valuable regions,
consequently, the image quality may get improved.
Figures and tables concerned will be presented in Section 3.
3. RESULTS AND ANALYSIS
Our results consists of two parts: (1) images and data comparison of breast PAT reconstruction simulation before and
after CS technique is implemented, and (2) multi-dimensional reconstruction images of four different groups of
biological targets as well as the numerical contrasts between existing method and our optimized method.
3.1 PA reconstruction with CS
First, we will use computer simulated data to perform the process of PA reconstruction. Simulated PA signals
were generated using MATLAB K-Wave Toolbox.[15] From the K-Wave Toolbox function, PA signal generating and
capturing can be modeled. We have adopted a novel CS algorithm named Stagewise Orthogonal Matching Pursuit
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Fig. 2 Simulated images. (a)PAT without CS (b) PAT with CS
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(StOMP) [16] to improve image quality. For the first group of experiment, our subject was an image of breast cancer
(288*288 pixels). In order to display the differences before and after the implementation of CS algorithm, Fig.2
and Table 1 are presented below. (Table indexes: Corr: Correlation Coefficient; Q: Quality Index; MSE: Mean
Square Error.)
Table 1. Simulated results.
Corr Q MSE
PAT without CS 0.8041 0.3070 0.1140
PAT with CS 0.8179 0.3329 0.1056
As can be seen from Fig.2(a), more grids and noise appeared in the reconstruction image of PAT without CS, while
for its counterpart in Fig.2 (b), with CS algorithm added to the process of PAT, the image quality was improved in
both the visual effect and the numeric results. The result indicates that the quality of our reconstructed breast
PAT image was better than that of current breast PAT system. As a novel method, this technique can be applied to
various aspects of biomedical imaging.
3.2 Improving Multi-dimensional Reconstruction Results
Next, four groups of various biological parts were adopted as targets. For each group, a multiple of simulations were
implemented under different selections of non-uniform channels with a control group of 128 uniformly selected
receiving channels. We chose a best result from all the non-uniform selections to verify our viewpoint that uneven
selection of channels according to the target region distribution produces better result than conventional uniform
selection method.
The reconstruction images and results of original PAT under uniformly selected channels (left) and improved PAT with
CS under non-uniformly selected channels (right) of four groups of simulations are presented below in Fig. 3 and Table 2.
(a)
(b)
(c)
(d)
Fig. 3 Reconstruction images of original PAT under uniform transducers (left) and improved PAT with CS under non-
uniform transducers (right). (a) breast cancer ; (b) stomach ; (c) intestine ; (d) hip bone.
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As can be seen from Fig. 3, the image quality of original PAT reconstruction was low in that much noise could be seen
inside the target areas, especially in Fig. 3 (d), where much dotted artifacts appeared around the image of hip bone. While
for the reconstructed images of our proposed method, as presented in Fig. 3, the image quality was significantly improved
and the visual effect was much clearer than the former result, as the amount of noise dropped in the same area.
Also, in Table 2, all the indexes have been improved under the improved PAT+CS scheme, which indicates that for a
particular target, it is possible to find a non-uniform channel selecting method to produce better reconstruction PAT
results than the uniform scheme can produce. In other words, there exists such a probability that, by using our proposed
method, we could build PAT images of the same quality with the number of ultrasound transducers decreased. In the
following research process, we plan to cut down on the number of channels to see whether our method can provide
images of the same quality and how much time complexity can be reduced due to the decrease of channels. Furthermore,
more work can be done to improve the image quality of PAT reconstruction.
Table 2. Reconstruction results of original PAT under uniform transducers (left) and improved PAT with CS under non-
uniform transducers (right).
Corr Q MSE
breast cancer
original PAT 0.8041 0.3070 0.1140
improved PAT+CS 0.8172 0.3392 0.1053
stomach
original PAT 0.7839 0.4020 0.0815
improved PAT+CS 0.7945 0.4314 0.0747
intestine
original PAT 0.7316 0.3280 0.1093
improved PAT+CS 0.7415 0.3775 0.1003
hip bone
original PAT 0.8803 0.3511 0.0648
improved PAT+CS 0.8877 0.4106 0.0568
4. CONCLUSION AND DISCUSSION
The images presented in Fig.2 and Fig.3 indicate that, although existing method of PAT reconstruction has
produced good results, our technique can be applied to circumstances when target areas are relatively large and
image quality needs to be further improved. By comparing the images in Fig. 3, we observed that the quality of
images has improved and less noise can be seen in the reconstruction result of our method than the existing
method. For instance, in Fig. 3 (b) (The reconstruction images of the stomach), we could see less dots in the right
part of the improved image, which may reduce the possibility of misdiagnosis. In addition, numeric comparison of
quality evaluation index had clearly shown the difference in Table 1 and Table 2, in which some improvement were
relatively evident, such as the Quality Index, which had a maximum rise of 17 per cent.
It has been verified that the simulation results mentioned above are consistent with our assumption, which demonstrates
the feasibility of our proposed method. Although the channel selecting scheme of our method differs with different
targets, it has succeeded in providing an appropriate mechanism of data acquisition which could improve the image
quality of PAT reconstruction with the amount of acquired data unchanged.
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This paper theoretically explained a new method combining PAT and CS technology, as well as an adaptive data
acquisition algorithm, with the aim to improve the image quality of PAT. As presented above, analytic reconstruction
methods were developed and applied to a considerable amount of simulations. Both visual and numerical results agreed
perfectly with the theoretical conclusions. As a novel method, it can be practically applied to multi-dimensional early
stage breast cancer detection, in vivo imaging and monitoring, and other types of tumor detection which are suitable for
PAT imaging.
5. ACKNOWLEDGEMENT
Work supported by National Natural Science Foundation of China under grants number 61201425, Natural Science
Foundation of Jinagsu Province under grants number BK20131280 and a project funded by the Priority Academic
Program Development of Jiangsu Higher Education Institutions.
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