Speed-of-sound and optical absorption reflect the structure and function of tissues from different aspects. A dual-mode microscopy system based on a concentric annular ultrasound array is proposed to simultaneously acquire the long depth-of-field images of speed-of-sound and optical absorption of inhomogeneous samples. First, speed-of-sound is decoded from the signal delay between each element of the annular array. The measured speed-of-sound could not only be used as an image contrast, but also improve the resolution and accuracy of spatial location of photoacoustic image in inhomogeneous acoustic media. Secondly, benefitting from dynamic focusing of annular array and the measured speed-of-sound, it is achieved an advanced acoustic-resolution photoacoustic microscopy with a precise position and a long depth-of-field. The performance of the dual-mode imaging system has been experimentally examined by using a custom-made annular array. The proposed dual-mode microscopy might have the significances in monitoring the biological physiological and pathological processes.
© 2017 Optical Society of America
Photoacoustic (PA) imaging is a promising noninvasive biomedical imaging technology and has been rapidly developed in recent years [1–11]. Acoustic-resolution photoacoustic microscopy (AR-PAM) is one major implementation of PA imaging . In PAM, the tissue is usually irradiated by a short-pulsed laser beam. Wideband ultrasound (US) waves are generated due to the absorption of laser energy and propagate in tissue. These US waves are detected outside the tissue by a focused US transducer. One-dimensional image along the transducer axis can be formed according to the distribution of optical absorbers, which is calculated from the time of flight (TOF) of PA waves and the priori knowledge of the speed-of-sound (SOS) of tissue. The lateral resolution depends on the focal diameter of the US transducer. Three-dimensional image is produced through a two-dimensional point-to-point transverse scanning. PA imaging has the high optical contrast. Simultaneously, taking advantages of lower acoustic scattering in tissue, it can provide penetration beyond the optical diffusion limit while maintaining an acoustic resolution. These merits promise PA imaging great potentials in tumor detection [12,13], in vivo brain monitoring [14–16], microvasculature imaging [17,18], tissue denaturation detection , and so on [19–24].
However, AR-PAM is often limited by its narrow depth-of-field and imprecise value of SOS. First, AR-PAM has a very narrow depth-of-field. AR-PAM has a good acoustic resolution only near its focal plane. If the imaging plane departs from the focal plane, the resolution will decrease significantly. For a classic AR-PAM, its depth-of-field is associated with the focal zone length 4λ(F/D)2 of the US transducer. D, F and λ are the diameter, focal length, and the wave length corresponding to the central frequency of the US transducer. Second, the accurate image recovery relies on the precise presetting of SOS of the tissue. During an image reconstruction process, SOS is a key to determine the exact positions of sound sources [25,26]. Usually, SOS is preset according to the priori knowledge of the tissue. However, the sound speed variation can be as large as 10% for various soft tissues. Even the change of temperature can also influence the SOS in tissues. Imprecise value of SOS will deteriorate the image by blurring and displacement.
Many methods have been proposed to improve an AR-PAM. Various US transducers, such as conical shape transducer , cylindrical transducer , double-ring shape transducer  and concentric ring array , have been investigated to broaden the narrow depth-of-field. Researchers have also developed some new algorithms and systems, such as the statistical PA image reconstruction algorithm [31,32], the finite-element reconstruction algorithm , the SOS optimization based on the coherent factor , an AR-PAM with a double-ring sensor , to reduce the influences of imprecise SOS. Especially, Passler et al. presented a piezoelectric detection system consisting of an annular array for large depth-of-field PA imaging . Dynamic focusing and coherence factor are used to extend the depth-of-field and suppress image artifacts.
In this study, we have inherited the advantage of a long depth-of-field of a concentric annular US array approach . Additionally, we have also extracted the SOS of the media according to the signal delay between each ring elements. Then, we propose a concentric annular US array to achieve an advanced AR-PAM as well as a SOS acoustic microscopy (SOS-AM). Compared to a focused US transducer in a traditional AR-PAM, the concentric annular US array allows us to alter the focal length dynamically by controlling time delay and weighting of each element. Then, it can provide a good lateral resolution as well as a long depth-of-field. In addition, SOS along the acoustic axis can be decoded from the signal delay between each element of the annular array. The obtained SOS could be used as the contrast of SOS images, and also be applied to rectify the image error of AR-PAM induced by the imprecise priori knowledge of SOS. A custom-made annular US array is produced to examine performance of the dual mode imaging in experiments.
As shown in Fig. 1, a pulse laser beam illuminates the sample and generates PA signals. An annular US transducer consisting of N concentric ring elements picks up the PA signals. Each of these rings can be described by its radius rn and width wn, with the inner diameter of rn – 0.5wn and outer diameter to be rn + 0.5wn (n = 1, 2,…, N). Conversely, the distribution of optical absorption and SOS along the axis of the transducer could be reconstructed from the PA waves. By scanning the sample point-by-point along the x-direction, we can get sectional imaging of this sample.
2.1 Reconstruction of Photoacoustic Images
PA signals picked up by the n-th ring at the position r = (x, y) is recorded as pn (r, t). Then, the PA image can be reconstructed by ,
where the image pixel value A is proportional to the optical absorption in sample. β = |ΣnH[pn(r,tn)]|2/NΣn|H[pn(r,tn)]|2 is a weighting correlation coefficient to suppress the side lobes and enhance the lateral resolution further more [30, 36], where H[•] represents Hilbert transform. C(r; z) is the average SOS from the depth z to the US transducer. tn is the TOF of PA signals from the absorbers located at the depth z to the n-th ring element.
By manipulating the delay time of the multi-channel signal pn, the focus can be dynamically shifted along the axial direction to the target position at different depth z. Multi-sliced windows around different depths are used to capture signals which are well-focused to synthesize an AR-PAM image. Because the focus is dynamically shifted at different depth through post-processing of the detected signals, the assembled image with multiple focal zones will maintain a good resolution within a long axial range. It is said that the image has a long depth-of-field.
The sensitivity of the annular array is related to its entire sensing area, although the sensing area of each transducer in the annular transducer array is much less than the entire sensing area of a focused transducer. For a focused transducer with a focal length F and sensing area Sf, its sensitivity is proportional to Sf/F. For the concentric annular array, the sensitivity is proportional to Σn[cosφn·Sn/(z/cosφn)], where cos2φn = z2/(z2 + rn2) and Sn is the area of the n-th element of annular array. If the annular array and focused transducer have the similar entire sensing areas and focal length, i.e., Sf = Σn[Sn] and z = F, the sensitivity of the annular array is lower than that of a focused transducer, because of the term cosφn. When the numerical aperture of transducer is small and cosφn approaches 1, their sensitivity is closed.
2.2 Images of SOS
In Eq. (1), the average SOS C(r; z) plays the key role in determining the position of optical absorption and reconstructing high quality PA images. Previous studies usually neglected the distribution of SOS and preset the value of C(r; z) according to the priori knowledge of biological tissue. Actually, SOS in different tissue has different value and it can also be changed by disparate environment. The sound speed increases as the environment temperature rises. The deviation between the actual SOS and the preset SOS will reduce the quality of PA imaging.
Using the annular US transducer, SOS could be directly extracted from the PA signals pn(r, t). According to the relationship,
Practically, tn can be estimated as follows: for any given t1, it has tn = t1 + τn. τn is the signal delay between the first and the n-th ring due to their different distance to the same PA source region. τn can be estimated by maximizing the cross-correlation between pn and p1,
With the known average SOS from the depth z to the transducer, the SOS at any depth can be recovered by using a recursive method. The medium has M layers with different SOS. The average SOS from the m-th layer to transducer is obtained and written as C(r; zm). The SOS at the depth zm, named as cm, can be evaluated by:
The obtained SOS could be utilized to construct the image with a contrast of SOS, as well as to enhance the image quality of AR-PAM. In Eq. (1), the real-time obtained SOS can be used instead of the priori value of SOS in tissue, which will avoid the excursion of SOS taken by different tissue and environmental factor.
Numerical simulation is used to validate the proposed dual mode microscopy. PA signals are detected by a seven-element annular array with a central frequency of 5 MHz. Each ring of the annular array holds the equal area. Their radius are rn = 1.89 mm, 4.56mm, 5.95 mm, 7.05 mm, 8.01 mm, 8.85 mm, and 9.63 mm, respectively. The widths are wn = 3.78 mm, 1.57 mm, 1.2 mm, 1.01 m, 0.89 mm, 0.81 mm, and 0.74 mm respectively. A spherical optical absorber with a radius of 20 µm lies in a depth of 20 mm from the scanning plane. The SOS of the surround media is 1400m/s, which is closed to the SOS in fat.
Figure 2 gives the simulation results. Figure 2(a) illustrates the PA signals detected by each ring. Since different distance between each ring and the optical absorber, the signals have different TOF from the source to different elements. The delay time τn between the central element and the other rings can be extracted according to the maximum of the cross-correlation curve, as shown in Fig. 2(b). With the known radius of each ring, the relationship between rn2 and tn2 can be plotted with blue dots as shown in Fig. 2(c). The black line in Fig. 2(c) is a linear fitting of rn2-tn2 relationship with the least square estimation. Then, we can extract the slope of rn2-tn2 curve and obtain C = 1400.2 m/s, which is very close to the actual value of 1400 m/s. Finally, the PA image is reconstructed by Eq. (1) with the obtained SOS, as shown in the right of Fig. 2(d). For sake of comparison, the PA image is also obtained by using a focused US transducer with a fixed focal point at a depth of 20 mm, as shown in the left of Fig. 2(d). Here, it is supposed that the accurate SOS is not yet known. A priori SOS of 1600 m/s in muscular tissue is used for the image recovery. Clearly, for the focused transducer, the image of optical absorber deviated from its actual position since the lack of accurate SOS. Moreover, the lateral resolution is poor. In contrast, the optical absorber has accurate position and good lateral resolution in the image obtained by the annular transducer as shown in Fig. 2(d).
The proposed scheme is still effective even when SOS distribution is inhomogeneous. It is supposed that the media has six layers with different SOS from 1400 m/s to 1650 m/s, and the optical absorbers are placed at different depth from 20 mm to 45 mm with a step of 5 mm. Figure 3(a) gives the SOS at different depth obtained by using the annular array and Eqs. (2-4). The obtained SOS agrees with the accurate value very well. Figures 3(b) and 3(c) compare the PA images obtained by a focused transducer and the annular array. For results of the focused transducer, the focus is fixed at a depth of 30 mm and the SOS is preset as 1500 m/s. Positions of optical absorbers are quantified in Fig. 4(a). As shown, the image obtained by a focused transducer [Fig. 3(b) and the blue squares in Fig. 4(a)] has a large excursion due to the inaccuracy of preset SOS. Moreover, in comparison to the absorber located at the fixed focal point z = 30 mm, the image intensity of the first optical absorber is too weak to be shown clearly in the same image. However, the proposed dual mode scheme can estimate the accurate SOS in each layer and decrease the position offset, as shown in Fig. 3(c) and the red dots in Fig. 4(a). Lateral resolution is also quantified by the full width at half maximum (FWHM) in the x direction, as shown in Fig. 4(b). Since the focal point of the transducer used in Fig. 3(b) is set at z = 30 mm, the lateral resolution of a focused transducer is optimal in the focal point [Fig. 3(b) and the blue squares in Fig. 4(b)]. The FWHM increases observably outside of the focal zone. However, by dynamic focusing and SOS correction, the FWHM of the image obtained by the proposed scheme keeps optimal value in a long depth-of-field [Fig. 3(c) and the red dots in Fig. 4(b)]. Given a desired lateral resolution, the depth-of-field can be estimated from the FWHM at the focus of the ultrasound filed. If the desired lateral resolution is 1.0 mm, the depth-of-field can reach about 50 mm. If the desired lateral resolution is 0.6 mm, the depth-of-field is about 29 mm. The image obtained by the proposed method has correct position in different depth and keeps a good resolution in a long depth-of-field. However, for the image obtained by a focused transducer, the images of optical absorbers deviate from their correct positions and the resolution is decreased rapidly outside of the focal plane.
A dual-mode microscopy could be established by using the annular US array. On the one hand, a SOS-AM can be achieved by using the optical absorbers as labels. On the other hand, an advanced AR-PAM with a long depth-of-field can be realized by using the annular array and the achieved SOS. Figure 5 demonstrates the dual-mode microscopy in a more realistic situation, where many optical absorbers are placed randomly in the sample. In Figs. 5(a)-5(c), SOS is setting as 1400 m/s in the left and 1600 m/s in the right. Figure 5(a) is the PA image obtained by a focused transducer with a radius of 10 mm and a focal length of 20 mm. Due to the imprecise SOS (1500 m/s) used for the image recovery, the positions are out of right places. Using the optical absorbers as labels, the SOS-AM recovers the image of SOS, as shown in Fig. 5(c). Then, the estimated SOS can help Eq. (1) to reconstruct PA images with correct position, as shown in Fig. 5(b). Also, the annular array promises an improved lateral resolution in a long depth-of-field. In Figs. 5(d)-5(f), SOS in the medium is layered as 1400 m/s, 1500 m/s, 1600 m/s from the top to the bottom. As shown in Fig. 5(d), where a focused transducer with a focal length of 35 mm is used, the image has a narrow depth-of-field, significant position deviation and poor image quality out of the focal plane. Whereas, the dual mode image scheme can simultaneously obtain the SOS image [Fig. 5(f)] and the PA image with a precise position and a good resolution within a long depth-of-field [Fig. 5(e)].
Finally, the performance of the PA-SOS dual-mode microscopy is validated in experiments by using a custom-made annular US array. Figure 6(a) illustrates the schematic diagram of the experimental system. The custom-made array, as shown in Fig. 6(b), has seven equal-area elements with a central frequency of 5 MHz and a bandwidth of 3.8 MHz at −6 dB. The radius rn (n = 1, 2, …7) of each element is 1.89 mm, 4.56mm, 5.94 mm, 7.05 mm, 8.01 mm, 8.85 mm, and 9.63 mm, respectively. And the width wn of each element is 3.78 mm, 1.57 mm, 1.2 mm, 1.01 mm, 0.89 mm, 0.81 mm, and 0.74 mm, respectively.
A phantom made of agar, 1-propanol and water was prepared for the experiment. This phantom had three layers. In the top layer, the agar to water ratio was 0.5%. The SOS in this layer was about 1497 m/s, which was closed to SOS in water (about 1496 m/s at 25 °C). In the middle layer, 1-propanol was added to raise its SOS to about 1588 m/s. In the bottom layer, the agar to water ratio was about 1.2% and the SOS was measured as 1460 m/s at 25 °C. Hairs were embedded in phantom at different layers.
The sample was illuminated by a Q-switched Nd:YAG laser with a wavelength of 532 nm, a pulse width of 8 ns, a pulse energy of 80 mJ, and a pulse repetition rate of 10 Hz. The generated PA signals were picked up by the custom-made annular array [Fig. 6(b)], amplified by the custom-made preamplifiers with a gain of 40 dB [Fig. 6(c)], sampled by a data acquired card (NI, PCI-5105) with a sampling frequency of 60 MHz, and stored in computer for the later analysis. The sample was scanned along the x-direction under the control a linear stage, which allows us to acquire the x-z section images.
Figure 7 gives the experimental results. For the sake of comparison, the focal length of the annular array is fixed at 15 mm, which is similar to a focused US transducer. Then the image is obtained with a preset SOS of 1500 m/s, as shown in Fig. 7(a). Since the inaccurate SOS setting and acoustic inhomogeneous of the sample, the image has poor quality. Next, the proposed method was used to obtain the SOS image and PA image of the sample. Using the hairs as labels, we have the SOS distribution in phantom, as shown in Fig. 7(c). The SOS from the top to the bottom are measured as 1496.7 ± 16.9 m/s, 1645.9 ± 17.3 m/s and 1432.9 ± 27.0 m/s respectively, which are close to their actual values. Then, substituting the obtained SOS into Eq. (1), the PA image of the sample is obtained, as shown in Fig. 7(b). Benefitting the accurate SOS and dynamic focusing of annular array, the image shows a good resolution in a long depth-of-field and more accurate positions. The experiment demonstrates that the proposed imaging scheme can provide an accurate SOS image and a high quality PA image of an inhomogeneous tissue, simultaneously.
In this study, a concentric annular US array is proposed to acquire a SOS image, as well as an advanced AR-PAM. On the one hand, SOS distribution is directly decoded from PA signals according to their delay between each element of the annular array. The obtained SOS could not only provide a SOS image, but also rectify the image error of AR-PAM induced by the imprecise preset SOS. On the other hand, benefitting from the accurate SOS and multiple focuses of the annular array, the AR-PAM can provide a high quality image with a precise position and good lateral resolution with a long depth-of-field. In this study, our method is based on the PA signals generated by optical absorbers. The optical absorbers label the average SOS of its surround tissue. Essentially, the existence of optical absorbers, which can generate strong PA effect, is the precondition of its applications. If there are no optical absorbers in samples or optical absorption is weak, the performance of the proposed method could be degraded. This technique could be used for tissue imaging. However, in real situation, the complexity of biological tissue could reduce the signal and noise ratio of the detected PA signals. In addition, the annular array has a relative low sensitivity in comparison to a focused transducer. These factors could restrict the proposed method. In practical biomedicine application, we could utilize the strong optical absorbers, e.g. blood vessels or the injected PA contrast agent, to generate PA signals with a good signal and noise ratio. These strong optical absorbers could play a similar role as the small point in our experiments.
In summary, SOS and optical absorption reflect the structure and function of tissues from different aspects. Moreover, the image quality of AR-PAM is significantly improved. Therefore, the proposed scheme of dual-mode imaging could be found valuable biomedical applications in monitoring the biological physiological and pathological processes.
This work was supported by the National Basic Research Program of China (2016YFC0102300); National Natural Science Foundation of China (NSFC) (11422439, 11274167, 11274171).
References and links
3. H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging,” Nat. Biotechnol. 24(7), 848–851 (2006). [CrossRef] [PubMed]
4. Z. Yang, J. Chen, J. Yao, R. Lin, J. Meng, C. Liu, J. Yang, X. Li, L. Wang, and L. Song, “Multi-parametric quantitative microvascular imaging with optical-resolution photoacoustic microscopy in vivo,” Opt. Express 22(2), 1500–1511 (2014). [CrossRef] [PubMed]
6. B. Ning, M. J. Kennedy, A. J. Dixon, N. Sun, R. Cao, B. T. Soetikno, R. Chen, Q. Zhou, K. Kirk Shung, J. A. Hossack, and S. Hu, “Simultaneous photoacoustic microscopy of microvascular anatomy, oxygen saturation, and blood flow,” Opt. Lett. 40(6), 910–913 (2015). [CrossRef] [PubMed]
7. L. Li, C. Dai, Q. Li, Q. Zhao, X. Jiang, X. Chai, and C. Zhou, “Fast subcellular optical coherence photoacoustic microscopy for pigment cell imaging,” Opt. Lett. 40(19), 4448–4451 (2015). [CrossRef] [PubMed]
8. P. Hajireza, J. Sorge, M. Brett, and R. Zemp, “In vivo optical resolution photoacoustic microscopy using glancing angle-deposited nanostructured Fabry-Perot etalons,” Opt. Lett. 40(7), 1350–1353 (2015). [CrossRef] [PubMed]
9. C. Tian, Z. Xie, M. L. Fabiilli, and X. Wang, “Imaging and sensing based on dual-pulse nonlinear photoacoustic contrast: a preliminary study on fatty liver,” Opt. Lett. 40(10), 2253–2256 (2015). [CrossRef] [PubMed]
10. Y. Sun and B. O’Neill, “Imaging high-intensity focused ultrasound-induced tissue denaturation by multispectral photoacoustic method: an ex vivo study,” Appl. Opt. 52(8), 1764–1770 (2013). [CrossRef] [PubMed]
12. J. Staley, P. Grogan, A. K. Samadi, H. Cui, M. S. Cohen, and X. Yang, “Growth of melanoma brain tumors monitored by photoacoustic microscopy,” J. Biomed. Opt. 15(4), 040510 (2010). [CrossRef] [PubMed]
13. L. Xi, S. R. Grobmyer, L. Wu, R. Chen, G. Zhou, L. G. Gutwein, J. Sun, W. Liao, Q. Zhou, H. Xie, and H. Jiang, “Evaluation of breast tumor margins in vivo with intraoperative photoacoustic imaging,” Opt. Express 20(8), 8726–8731 (2012). [CrossRef] [PubMed]
14. J. Xia, G. Li, L. Wang, M. Nasiriavanaki, K. Maslov, J. A. Engelbach, J. R. Garbow, and L. V. Wang, “Wide-field two-dimensional multifocal optical-resolution photoacoustic-computed microscopy,” Opt. Lett. 38(24), 5236–5239 (2013). [CrossRef] [PubMed]
15. J. Yao, L. Wang, J. M. Yang, K. I. Maslov, T. T. Wong, L. Li, C. H. Huang, J. Zou, and L. V. Wang, “High-speed label-free functional photoacoustic microscopy of mouse brain in action,” Nat. Methods 12(5), 407–410 (2015). [CrossRef] [PubMed]
17. L. Xi, C. Duan, H. Xie, and H. Jiang, “Combining Optical-resolution Photoacoustic Microscopy with Optical Coherence Tomography in a Miniature Probe,” in Biomedical Optics 2014, OSA Technical Digest (online) (Optical Society of America, 2014), paper BS3A.62.
18. G. Wissmeyer, D. Soliman, R. Shnaiderman, A. Rosenthal, and V. Ntziachristos, “All-optical optoacoustic microscope based on wideband pulse interferometry,” Opt. Lett. 41(9), 1953–1956 (2016). [CrossRef] [PubMed]
20. X. Gao, C. Tao, X. Wang, and X. Liu, “Quantitative imaging of microvasculature in deep tissue with a spectrum-based photo-acoustic microscopy,” Opt. Lett. 40(6), 970–973 (2015). [CrossRef] [PubMed]
21. D. Wang, Y. Wang, W. Wang, D. Luo, U. Chitgupi, J. Geng, Y. Zhou, L. Wang, J. F. Lovell, and J. Xia, “Deep tissue photoacoustic computed tomography with a fast and compact laser system,” Biomed. Opt. Express 8(1), 112–123 (2016). [CrossRef] [PubMed]
22. R. Cheng, J. Shao, X. Gao, C. Tao, J. Ge, and X. Liu, “Noninvasive assessment of early dental lesion using a dual-contrast phototacoustic tomography,” Sci. Rep. 6(1), 21798 (2016). [CrossRef] [PubMed]
23. S. Wang, C. Tao, X. Gao, X. Wang, and X. Liu, “Quantitatively photoacoustic examination of abnormal particles hidden in a mixture of particles with non-uniform sizes,” Opt. Express 23(25), 32253 (2015). [CrossRef]
24. L. Liu, C. Tao, X. Liu, M. Deng, S. Wang, and J. Liu, “Photoacoustic tomography from weak and noisy signals by using a pulse decomposition algorithm in the time-domain,” Opt. Express 23(21), 26969–26977 (2015). [CrossRef] [PubMed]
25. X. Jin, C. Li, and L. V. Wang, “Effects of acoustic heterogeneities on transcranial brain imaging with microwave-induced thermoacoustic tomography,” Med. Phys. 35(7), 3205–3214 (2008). [CrossRef] [PubMed]
26. J. Jose, R. G. Willemink, W. Steenbergen, C. H. Slump, T. G. van Leeuwen, and S. Manohar, “Speed-of-sound compensated photoacoustic tomography for accurate imaging,” Med. Phys. 39(12), 7262–7271 (2012). [CrossRef] [PubMed]
27. G. Paltauf, S. Gratt, K. Passler, R. Nuster, and P. Burgholzer, “Photoacoustic imaging with limited diffraction beam transducers,” Proc. SPIE 7177, 77170S (2009). [CrossRef]
29. R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, T. G. van Leeuwen, and F. F. M. de Mul, “Photoacoustic imaging of blood vessels with a double-ring sensor featuring a narrow angular aperture,” J. Biomed. Opt. 9(6), 1327–1335 (2004). [CrossRef] [PubMed]
30. K. Passler, R. Nuster, S. Gratt, P. Burgholzer, and G. Paltauf, “Piezoelectric annular array for large depth of field photoacoustic imaging,” Biomed. Opt. Express 2(9), 2655–2664 (2011). [CrossRef] [PubMed]
31. X. L. Dean-Ben, R. Ma, D. Razansky, and V. Ntziachristos, “Statistical approach for optoacoustic image reconstruction in the presence of strong acoustic heterogeneities,” IEEE Trans. Med. Imaging 30(2), 401–408 (2011). [CrossRef] [PubMed]
32. X. L. Deán-Ben, V. Ntziachristos, and D. Razansky, “Statistical optoacoustic image reconstruction using a-priori knowledge on the location of acoustic distortions,” Appl. Phys. Lett. 98(17), 171110 (2011). [CrossRef]
33. H. Jiang, Z. Yuan, and X. Gu, “Spatially varying optical and acoustic property reconstruction using finite-element-based photoacoustic tomography,” J. Opt. Soc. Am. A 23(4), 878–888 (2006). [CrossRef] [PubMed]
34. C. Yoon, J. Kang, S. Han, Y. Yoo, T. K. Song, and J. H. Chang, “Enhancement of photoacoustic image quality by sound speed correction: ex vivo evaluation,” Opt. Express 20(3), 3082–3090 (2012). [CrossRef] [PubMed]