Abstract

The goal of this work was to develop and validate a spectrally resolved photoacoustic imaging method, namely multi-spectral photoacoustic elasticity tomography (PAET) for quantifying the physiological parameters and elastic modulus of biological tissues. We theoretically and experimentally examined the PAET imaging method using simulations and in vitro experimental tests. Our simulation and in vitro experimental results indicated that the reconstructions were quantitatively accurate in terms of sizes, the physiological and elastic properties of the targets.

© 2016 Optical Society of America

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References

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  1. L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).
  2. G. Paltauf and H. Schmidt-Kloiber, “Pulsed optoacoustic characterization of layered media,” J. Appl. Phys. 88(3), 1624–1631 (2000).
    [Crossref]
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    [Crossref]
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    [Crossref]
  9. J. T. Oh, M. L. Li, H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Three-dimensional imaging of skin melanoma in vivo by dual-wavelength photoacoustic microscopy,” J. Biomed. Opt. 11(3), 034032 (2006).
    [Crossref] [PubMed]
  10. A. Agarwal, S. Huang, M. O’donnell, K. C. Day, M. Day, N. Kotov, and S. Ashkenazi, “Targeted gold nanorod contrast agent for prostate cancer detection by photoacoustic imaging,” J. Appl. Phys. 102(6), 064701 (2007).
    [Crossref]
  11. X. Wang, W. W. Roberts, P. L. Carson, D. P. Wood, and J. B. Fowlkes, “Photoacoustic tomography: a potential new tool for prostate cancer,” Biomed. Opt. Express 1(4), 1117–1126 (2010).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  14. M. S. Singh and H. Jiang, “Elastic property attributes to photoacoustic signals: an experimental phantom study,” Opt. Lett. 39(13), 3970–3973 (2014).
    [Crossref] [PubMed]
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  16. Z. Yuan and H Jiang, “Quantitative photoacoustic tomography: recovery of optical absorption coefficient maps of heterogeneous medium,” Appl. Phys. Lett. 88, 231101 (2006).
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    [Crossref] [PubMed]
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    [PubMed]
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  23. http//omlc.ogi.edu/spectra/index.html .
  24. J. P. Ritz, A. Roggan, C. Isbert, G. Müller, H. J. Buhr, and C. T. Germer, “Optical properties of native and coagulated porcine liver tissue between 400 and 2400 nm,” Lasers Surg. Med. 29(3), 205–212 (2001).
    [Crossref] [PubMed]

2016 (1)

Y. Liu, H. Jiang, and Z. Yuan, “Two-scheme for quantitative photoacoustic tomography based on Monte Carlo simulation,” Med. Phys. 43(7), 1–11 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (2)

M. S. Singh and H. Jiang, “Elastic property attributes to photoacoustic signals: an experimental phantom study,” Opt. Lett. 39(13), 3970–3973 (2014).
[Crossref] [PubMed]

Z. Yuan, X. Li, and L. Xi, “Listening to light scattering in turbid media: quantitative optical scattering imaging using photoacoustic measurements with one-wavelength illumination,” J. Opt. 16, 065301 (2014).

2010 (3)

2009 (1)

2008 (1)

J. Shah, S. Park, S. Aglyamov, T. Larson, L. Ma, K. Sokolov, K. Johnston, T. Milner, and S. Y. Emelianov, “Photoacoustic imaging and temperature measurement for photothermal cancer therapy,” J. Biomed. Opt. 13(3), 034024 (2008).
[Crossref] [PubMed]

2007 (2)

S. Yang, D. Xing, Y. Lao, D. Yang, L. Zeng, L. Xiang, and W. R. Chen, “Noninvasive monitoring of traumatic brain injury and post-traumatic rehabilitation with laser-induced photoacoustic imaging,” Appl. Phys. Lett. 90(24), 243902 (2007).
[Crossref]

A. Agarwal, S. Huang, M. O’donnell, K. C. Day, M. Day, N. Kotov, and S. Ashkenazi, “Targeted gold nanorod contrast agent for prostate cancer detection by photoacoustic imaging,” J. Appl. Phys. 102(6), 064701 (2007).
[Crossref]

2006 (5)

2005 (1)

J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(3), 031912 (2005).
[Crossref] [PubMed]

2001 (1)

J. P. Ritz, A. Roggan, C. Isbert, G. Müller, H. J. Buhr, and C. T. Germer, “Optical properties of native and coagulated porcine liver tissue between 400 and 2400 nm,” Lasers Surg. Med. 29(3), 205–212 (2001).
[Crossref] [PubMed]

2000 (1)

G. Paltauf and H. Schmidt-Kloiber, “Pulsed optoacoustic characterization of layered media,” J. Appl. Phys. 88(3), 1624–1631 (2000).
[Crossref]

1997 (1)

Agarwal, A.

A. Agarwal, S. Huang, M. O’donnell, K. C. Day, M. Day, N. Kotov, and S. Ashkenazi, “Targeted gold nanorod contrast agent for prostate cancer detection by photoacoustic imaging,” J. Appl. Phys. 102(6), 064701 (2007).
[Crossref]

Aglyamov, S.

J. Shah, S. Park, S. Aglyamov, T. Larson, L. Ma, K. Sokolov, K. Johnston, T. Milner, and S. Y. Emelianov, “Photoacoustic imaging and temperature measurement for photothermal cancer therapy,” J. Biomed. Opt. 13(3), 034024 (2008).
[Crossref] [PubMed]

Arridge, S.

Ashkenazi, S.

A. Agarwal, S. Huang, M. O’donnell, K. C. Day, M. Day, N. Kotov, and S. Ashkenazi, “Targeted gold nanorod contrast agent for prostate cancer detection by photoacoustic imaging,” J. Appl. Phys. 102(6), 064701 (2007).
[Crossref]

Azhari, H.

T. Glozman and H. Azhari, “A method for characterization of tissue elastic properties combining ultrasonic computed tomography with elastography,” J. Ultrasound Med. 29(3), 387–398 (2010).
[PubMed]

Beard, P.

Buhr, H. J.

J. P. Ritz, A. Roggan, C. Isbert, G. Müller, H. J. Buhr, and C. T. Germer, “Optical properties of native and coagulated porcine liver tissue between 400 and 2400 nm,” Lasers Surg. Med. 29(3), 205–212 (2001).
[Crossref] [PubMed]

Carson, P. L.

Chen, W. R.

S. Yang, D. Xing, Y. Lao, D. Yang, L. Zeng, L. Xiang, and W. R. Chen, “Noninvasive monitoring of traumatic brain injury and post-traumatic rehabilitation with laser-induced photoacoustic imaging,” Appl. Phys. Lett. 90(24), 243902 (2007).
[Crossref]

Cox, B.

Day, K. C.

A. Agarwal, S. Huang, M. O’donnell, K. C. Day, M. Day, N. Kotov, and S. Ashkenazi, “Targeted gold nanorod contrast agent for prostate cancer detection by photoacoustic imaging,” J. Appl. Phys. 102(6), 064701 (2007).
[Crossref]

Day, M.

A. Agarwal, S. Huang, M. O’donnell, K. C. Day, M. Day, N. Kotov, and S. Ashkenazi, “Targeted gold nanorod contrast agent for prostate cancer detection by photoacoustic imaging,” J. Appl. Phys. 102(6), 064701 (2007).
[Crossref]

Emelianov, S. Y.

J. Shah, S. Park, S. Aglyamov, T. Larson, L. Ma, K. Sokolov, K. Johnston, T. Milner, and S. Y. Emelianov, “Photoacoustic imaging and temperature measurement for photothermal cancer therapy,” J. Biomed. Opt. 13(3), 034024 (2008).
[Crossref] [PubMed]

Fowlkes, J. B.

Germer, C. T.

J. P. Ritz, A. Roggan, C. Isbert, G. Müller, H. J. Buhr, and C. T. Germer, “Optical properties of native and coagulated porcine liver tissue between 400 and 2400 nm,” Lasers Surg. Med. 29(3), 205–212 (2001).
[Crossref] [PubMed]

Glozman, T.

T. Glozman and H. Azhari, “A method for characterization of tissue elastic properties combining ultrasonic computed tomography with elastography,” J. Ultrasound Med. 29(3), 387–398 (2010).
[PubMed]

Gu, X.

Huang, S.

A. Agarwal, S. Huang, M. O’donnell, K. C. Day, M. Day, N. Kotov, and S. Ashkenazi, “Targeted gold nanorod contrast agent for prostate cancer detection by photoacoustic imaging,” J. Appl. Phys. 102(6), 064701 (2007).
[Crossref]

Isbert, C.

J. P. Ritz, A. Roggan, C. Isbert, G. Müller, H. J. Buhr, and C. T. Germer, “Optical properties of native and coagulated porcine liver tissue between 400 and 2400 nm,” Lasers Surg. Med. 29(3), 205–212 (2001).
[Crossref] [PubMed]

Jacques, S. L.

Jiang, H

Z. Yuan and H Jiang, “Quantitative photoacoustic tomography: recovery of optical absorption coefficient maps of heterogeneous medium,” Appl. Phys. Lett. 88, 231101 (2006).

Jiang, H.

Johnston, K.

J. Shah, S. Park, S. Aglyamov, T. Larson, L. Ma, K. Sokolov, K. Johnston, T. Milner, and S. Y. Emelianov, “Photoacoustic imaging and temperature measurement for photothermal cancer therapy,” J. Biomed. Opt. 13(3), 034024 (2008).
[Crossref] [PubMed]

Kostli, K.

Kotov, N.

A. Agarwal, S. Huang, M. O’donnell, K. C. Day, M. Day, N. Kotov, and S. Ashkenazi, “Targeted gold nanorod contrast agent for prostate cancer detection by photoacoustic imaging,” J. Appl. Phys. 102(6), 064701 (2007).
[Crossref]

Lao, Y.

S. Yang, D. Xing, Y. Lao, D. Yang, L. Zeng, L. Xiang, and W. R. Chen, “Noninvasive monitoring of traumatic brain injury and post-traumatic rehabilitation with laser-induced photoacoustic imaging,” Appl. Phys. Lett. 90(24), 243902 (2007).
[Crossref]

Larson, T.

J. Shah, S. Park, S. Aglyamov, T. Larson, L. Ma, K. Sokolov, K. Johnston, T. Milner, and S. Y. Emelianov, “Photoacoustic imaging and temperature measurement for photothermal cancer therapy,” J. Biomed. Opt. 13(3), 034024 (2008).
[Crossref] [PubMed]

Li, M. L.

J. T. Oh, M. L. Li, H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Three-dimensional imaging of skin melanoma in vivo by dual-wavelength photoacoustic microscopy,” J. Biomed. Opt. 11(3), 034032 (2006).
[Crossref] [PubMed]

Li, S.

Li, X.

Z. Yuan, X. Li, and L. Xi, “Listening to light scattering in turbid media: quantitative optical scattering imaging using photoacoustic measurements with one-wavelength illumination,” J. Opt. 16, 065301 (2014).

Liu, W.

Liu, Y.

Y. Liu, H. Jiang, and Z. Yuan, “Two-scheme for quantitative photoacoustic tomography based on Monte Carlo simulation,” Med. Phys. 43(7), 1–11 (2016).
[Crossref] [PubMed]

Ma, L.

J. Shah, S. Park, S. Aglyamov, T. Larson, L. Ma, K. Sokolov, K. Johnston, T. Milner, and S. Y. Emelianov, “Photoacoustic imaging and temperature measurement for photothermal cancer therapy,” J. Biomed. Opt. 13(3), 034024 (2008).
[Crossref] [PubMed]

Maslov, K.

J. T. Oh, M. L. Li, H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Three-dimensional imaging of skin melanoma in vivo by dual-wavelength photoacoustic microscopy,” J. Biomed. Opt. 11(3), 034032 (2006).
[Crossref] [PubMed]

Milner, T.

J. Shah, S. Park, S. Aglyamov, T. Larson, L. Ma, K. Sokolov, K. Johnston, T. Milner, and S. Y. Emelianov, “Photoacoustic imaging and temperature measurement for photothermal cancer therapy,” J. Biomed. Opt. 13(3), 034024 (2008).
[Crossref] [PubMed]

Montcel, B.

Müller, G.

J. P. Ritz, A. Roggan, C. Isbert, G. Müller, H. J. Buhr, and C. T. Germer, “Optical properties of native and coagulated porcine liver tissue between 400 and 2400 nm,” Lasers Surg. Med. 29(3), 205–212 (2001).
[Crossref] [PubMed]

Ntziachristos, V.

J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(3), 031912 (2005).
[Crossref] [PubMed]

O’donnell, M.

A. Agarwal, S. Huang, M. O’donnell, K. C. Day, M. Day, N. Kotov, and S. Ashkenazi, “Targeted gold nanorod contrast agent for prostate cancer detection by photoacoustic imaging,” J. Appl. Phys. 102(6), 064701 (2007).
[Crossref]

Oh, J. T.

J. T. Oh, M. L. Li, H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Three-dimensional imaging of skin melanoma in vivo by dual-wavelength photoacoustic microscopy,” J. Biomed. Opt. 11(3), 034032 (2006).
[Crossref] [PubMed]

Oraevsky, A. A.

Paltauf, G.

G. Paltauf and H. Schmidt-Kloiber, “Pulsed optoacoustic characterization of layered media,” J. Appl. Phys. 88(3), 1624–1631 (2000).
[Crossref]

Park, S.

J. Shah, S. Park, S. Aglyamov, T. Larson, L. Ma, K. Sokolov, K. Johnston, T. Milner, and S. Y. Emelianov, “Photoacoustic imaging and temperature measurement for photothermal cancer therapy,” J. Biomed. Opt. 13(3), 034024 (2008).
[Crossref] [PubMed]

Ripoll, J.

J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(3), 031912 (2005).
[Crossref] [PubMed]

Ritz, J. P.

J. P. Ritz, A. Roggan, C. Isbert, G. Müller, H. J. Buhr, and C. T. Germer, “Optical properties of native and coagulated porcine liver tissue between 400 and 2400 nm,” Lasers Surg. Med. 29(3), 205–212 (2001).
[Crossref] [PubMed]

Roberts, W. W.

Roggan, A.

J. P. Ritz, A. Roggan, C. Isbert, G. Müller, H. J. Buhr, and C. T. Germer, “Optical properties of native and coagulated porcine liver tissue between 400 and 2400 nm,” Lasers Surg. Med. 29(3), 205–212 (2001).
[Crossref] [PubMed]

Schmidt-Kloiber, H.

G. Paltauf and H. Schmidt-Kloiber, “Pulsed optoacoustic characterization of layered media,” J. Appl. Phys. 88(3), 1624–1631 (2000).
[Crossref]

Shah, J.

J. Shah, S. Park, S. Aglyamov, T. Larson, L. Ma, K. Sokolov, K. Johnston, T. Milner, and S. Y. Emelianov, “Photoacoustic imaging and temperature measurement for photothermal cancer therapy,” J. Biomed. Opt. 13(3), 034024 (2008).
[Crossref] [PubMed]

Singh, M. S.

Sokolov, K.

J. Shah, S. Park, S. Aglyamov, T. Larson, L. Ma, K. Sokolov, K. Johnston, T. Milner, and S. Y. Emelianov, “Photoacoustic imaging and temperature measurement for photothermal cancer therapy,” J. Biomed. Opt. 13(3), 034024 (2008).
[Crossref] [PubMed]

Stoica, G.

J. T. Oh, M. L. Li, H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Three-dimensional imaging of skin melanoma in vivo by dual-wavelength photoacoustic microscopy,” J. Biomed. Opt. 11(3), 034032 (2006).
[Crossref] [PubMed]

Tittel, F. K.

Vray, D.

Wang, L. V.

J. T. Oh, M. L. Li, H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Three-dimensional imaging of skin melanoma in vivo by dual-wavelength photoacoustic microscopy,” J. Biomed. Opt. 11(3), 034032 (2006).
[Crossref] [PubMed]

Wang, X.

Wood, D. P.

Xi, L.

Z. Yuan, X. Li, and L. Xi, “Listening to light scattering in turbid media: quantitative optical scattering imaging using photoacoustic measurements with one-wavelength illumination,” J. Opt. 16, 065301 (2014).

Xiang, L.

S. Yang, D. Xing, Y. Lao, D. Yang, L. Zeng, L. Xiang, and W. R. Chen, “Noninvasive monitoring of traumatic brain injury and post-traumatic rehabilitation with laser-induced photoacoustic imaging,” Appl. Phys. Lett. 90(24), 243902 (2007).
[Crossref]

Xing, D.

S. Yang, D. Xing, Y. Lao, D. Yang, L. Zeng, L. Xiang, and W. R. Chen, “Noninvasive monitoring of traumatic brain injury and post-traumatic rehabilitation with laser-induced photoacoustic imaging,” Appl. Phys. Lett. 90(24), 243902 (2007).
[Crossref]

Yang, D.

S. Yang, D. Xing, Y. Lao, D. Yang, L. Zeng, L. Xiang, and W. R. Chen, “Noninvasive monitoring of traumatic brain injury and post-traumatic rehabilitation with laser-induced photoacoustic imaging,” Appl. Phys. Lett. 90(24), 243902 (2007).
[Crossref]

Yang, S.

S. Yang, D. Xing, Y. Lao, D. Yang, L. Zeng, L. Xiang, and W. R. Chen, “Noninvasive monitoring of traumatic brain injury and post-traumatic rehabilitation with laser-induced photoacoustic imaging,” Appl. Phys. Lett. 90(24), 243902 (2007).
[Crossref]

Yuan, Z.

Zemp, R. J.

Zeng, L.

S. Yang, D. Xing, Y. Lao, D. Yang, L. Zeng, L. Xiang, and W. R. Chen, “Noninvasive monitoring of traumatic brain injury and post-traumatic rehabilitation with laser-induced photoacoustic imaging,” Appl. Phys. Lett. 90(24), 243902 (2007).
[Crossref]

Zhang, H. F.

J. T. Oh, M. L. Li, H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Three-dimensional imaging of skin melanoma in vivo by dual-wavelength photoacoustic microscopy,” J. Biomed. Opt. 11(3), 034032 (2006).
[Crossref] [PubMed]

Zhang, Q.

Appl. Opt. (3)

Appl. Phys. Lett. (2)

Z. Yuan and H Jiang, “Quantitative photoacoustic tomography: recovery of optical absorption coefficient maps of heterogeneous medium,” Appl. Phys. Lett. 88, 231101 (2006).

S. Yang, D. Xing, Y. Lao, D. Yang, L. Zeng, L. Xiang, and W. R. Chen, “Noninvasive monitoring of traumatic brain injury and post-traumatic rehabilitation with laser-induced photoacoustic imaging,” Appl. Phys. Lett. 90(24), 243902 (2007).
[Crossref]

Biomed. Opt. Express (2)

J. Appl. Phys. (2)

G. Paltauf and H. Schmidt-Kloiber, “Pulsed optoacoustic characterization of layered media,” J. Appl. Phys. 88(3), 1624–1631 (2000).
[Crossref]

A. Agarwal, S. Huang, M. O’donnell, K. C. Day, M. Day, N. Kotov, and S. Ashkenazi, “Targeted gold nanorod contrast agent for prostate cancer detection by photoacoustic imaging,” J. Appl. Phys. 102(6), 064701 (2007).
[Crossref]

J. Biomed. Opt. (2)

J. Shah, S. Park, S. Aglyamov, T. Larson, L. Ma, K. Sokolov, K. Johnston, T. Milner, and S. Y. Emelianov, “Photoacoustic imaging and temperature measurement for photothermal cancer therapy,” J. Biomed. Opt. 13(3), 034024 (2008).
[Crossref] [PubMed]

J. T. Oh, M. L. Li, H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Three-dimensional imaging of skin melanoma in vivo by dual-wavelength photoacoustic microscopy,” J. Biomed. Opt. 11(3), 034032 (2006).
[Crossref] [PubMed]

J. Opt. (1)

Z. Yuan, X. Li, and L. Xi, “Listening to light scattering in turbid media: quantitative optical scattering imaging using photoacoustic measurements with one-wavelength illumination,” J. Opt. 16, 065301 (2014).

J. Opt. Soc. Am. A (1)

J. Ultrasound Med. (1)

T. Glozman and H. Azhari, “A method for characterization of tissue elastic properties combining ultrasonic computed tomography with elastography,” J. Ultrasound Med. 29(3), 387–398 (2010).
[PubMed]

Lasers Surg. Med. (1)

J. P. Ritz, A. Roggan, C. Isbert, G. Müller, H. J. Buhr, and C. T. Germer, “Optical properties of native and coagulated porcine liver tissue between 400 and 2400 nm,” Lasers Surg. Med. 29(3), 205–212 (2001).
[Crossref] [PubMed]

Med. Phys. (1)

Y. Liu, H. Jiang, and Z. Yuan, “Two-scheme for quantitative photoacoustic tomography based on Monte Carlo simulation,” Med. Phys. 43(7), 1–11 (2016).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(3), 031912 (2005).
[Crossref] [PubMed]

Other (4)

C. Xu, P. Kumavor, A. Aguirre, and Q. Zhu, “Quantitative recovery of absorption coefficient using DOT-assisted photoacoustic tomography for breast imaging,” BsuD in OSA Biomedical Optics Topical Meeting, Miami, FL, 2010.
[Crossref]

F. A. Duck, Physical properties of tissues: a comprehensive reference book (Academic press, 2013).

http//omlc.ogi.edu/spectra/index.html .

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the PAT system. BS: beam splitter; PC: personal computer.

Fig. 2
Fig. 2

(a) Test geometry. The dimension units are in millimeters. (b) The exact (left column) and recovered (right column) images using 6 optical wavelengths. The first to the third rows of Fig. 2(b) denote the Hb, HBO2 and H2O, respectively. The axes (left and bottom) illustrate the spatial scale, in mm, whereas the color scale (right) denote HbO2 and HbR in μM, and H2O in percentage.

Fig. 3
Fig. 3

The exact (left side) and recovered (right side) K images using 6 optical wavelengths for the simulation test 1 based on the test geometry in Fig. 2(a). The axes (left and bottom) illustrate the spatial scale, in mm, whereas the color scale (right) denotes K in GPa.

Fig. 4
Fig. 4

Quantitative HbR (left) and K (right) images recovered by our multi-spectral PAET. The axes (left and bottom) illustrate the spatial scale, in mm, whereas the color scale (right) denote HbR in μM and K in GPa.

Fig. 5
Fig. 5

The Photograph of the chicken breast used for the first in vitro experimental test (a), the recovered HbR concentration image (b), the recovered K image (c), the HbR profile plotted along the center of the target (d), and the K profile plotted along the center of the target (e). The axes (left and bottom) illustrate the spatial scale, in mm, whereas the color scale (right) denote HbR in μM and K in GPa.

Fig. 6
Fig. 6

The Photograph of the porcine liver tissue used for the second in vitro experimental test (a), the recovered HbR concentrations image (b), the recovered K (c), the HbR profile plotted along the center of the target (d), and the K profile plotted along the center of the target (e). The axes (left and bottom) illustrate the spatial scale, in mm, whereas the color scale (right) denote HbR in μM and K in GPa.

Tables (5)

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Table 1 Chromophore Concentrations and K for the targets in simulation test 1

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Table 2 HbR concentration and K of the targets in simulation test 2

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Table 3 The reconstructed chromophore concentrations and K for the targets in simulation test 1

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Table 4 Optical properties and extinction coefficients of the chicken breast

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Table 5 Average longitudinal velocities for the different phantoms [21]

Equations (21)

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ρ(r) t V(r,t)=p(r,t).
V(r,t)= 1 ρ(r) v s 2 (r) t p(r,t)+β t T(r,t).
ρ(r) C p t T(r,t)=H(r,t).
ρ(r)( 1 ρ(r) p(r,t)) 1 v s 2 (r) 2 t 2 p(r,t)= β C p t H(r,t).
( 1 ρ(r) p(r,t)) 1 K 2 t 2 p(r,t)= β ρ C p t H(r,t).
2 p(r,t) ρ 0 K 2 t 2 p(r,t)= β C p t H(r,t).
P(r,ω)= + p(r,t)exp(iωt)dt .
2 p(r,ω)+ K 0 K k 0 2 p(r,ω)=i k 0 β C p v 0 Ψ( r ).
2 p(r,ω)+O k 0 2 p(r,ω)=i k 0 β C p v 0 Ψ( r ).
2 p(r,ω,λ)+O k 0 2 p(r,ω,λ)=i k 0 β C p v 0 μ(r,ω)Φ(r,λ)
μ a (λ)= i=1 ε i (λ) c i .
2 p(r,ω,λ)+O k 0 2 p(r,ω,λ)=i k 0 β C p v 0 i=1 ε i ( λ ) c i Φ( r,λ ).
Ap=B
( J T J+ξI)Δχ= J T ( p o p c ).
p o = ( p 1 o , p 2 o ,, p M o ) T | (ω,λ), p c = ( p 1 c , p 2 c ,, p M c ) T | (ω,λ) .
p i ( ω,λ ) ( c l ) ,j = k=1 N ( p i ( ω,λ ) Ψ k ( λ ) Ψ k ( λ ) μ a,j ( λ ) ε l ( λ ) ) (i=1,2...M;j=1,2...N;l=1,2...Chrom) .
Ψ k ( λ ) μ a j ( λ ) =( Φ j + μ a,j ( Φ j / μ a,j ) if (k=j) μ a,k ( Φ k / μ a,j ) if (kj) | ( λ ) .
D(r,λ)Φ(r,λ) μ a (r,λ)Φ( r,λ )=S(r,λ).
[ A ]{ p( ω,λ ) O j }=[ A O j ]{ p( ω,λ ) }.
[ Ψ ][ A ]=[ Δ d ].
[ Ψ ][ A ]{ p( λ ) O j }=[ Ψ ][ A O j ]{ p( λ ) }.

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