Abstract

Photoacoustic tomography is a promising imaging modality offering high ultrasonic resolution with intrinsic optical contrast. However, quantification in photoacoustic imaging is challenging. We present an algorithm for quantitative photoacoustic estimation of optical absorption and diffusion coefficients based on minimizing an error function between measured photoacoustic channel data and a calculated forward model with a multiple-illumination pattern. Unlike many other algorithms, the proposed method does not require the erroneous assumption of ideal tomographic reconstruction of initial pressures and to our knowledge is the first demonstration of the efficacy of multiple-illumination photoacoustic tomography requiring only transducer channel data. Simulations show promise for numerically robust optical property estimation as illustrated by well-conditioned Hessian singular values in 2D examples.

© 2012 OSA

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt.15(2), 021311 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. G. Bal and K. Ren, “Multi-source quantitative photoacoustic tomography in a diffusive regime,” Inverse Probl.27(7), 075003 (2011).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. R. J. Zemp, “Quantitative photoacoustic tomography with multiple optical sources,” Appl. Opt.49(18), 3566–3572 (2010).
    [CrossRef] [PubMed]
  15. P. Shao, B. Cox, and R. J. Zemp, “Estimating optical absorption, scattering, and Grueneisen distributions with multiple-illumination photoacoustic tomography,” Appl. Opt.50(19), 3145–3154 (2011).
    [CrossRef] [PubMed]
  16. L. V. Wang and H.-I. Wu, Biomedical Optics: Principles and Imaging, (Wiley, 2007).
  17. B. Cox, T. Tarvainen, and S. Arridge, in Contemporary Mathematics (Book News Inc., 2011), pp. 1–12.
  18. H. Gao, H. Zhang, and S. Osher, “Bregman methods in quantitative photoacoustic tomography,” CAM Report 10–42, (July 2010).

2012

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt.17(6), 061202 (2012).
[CrossRef] [PubMed]

G. Bal and K. Ren, “On multi-spectral quantitative photoacoustic tomography in diffusive regime,” Inverse Probl.28(2), 025010 (2012).
[CrossRef]

2011

2010

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt.15(2), 021311 (2010).
[CrossRef] [PubMed]

R. J. Zemp, “Quantitative photoacoustic tomography with multiple optical sources,” Appl. Opt.49(18), 3566–3572 (2010).
[CrossRef] [PubMed]

2009

B. T. Cox, S. R. Arridge, and P. C. Beard, “Estimating chromophore distributions from multiwavelength photoacoustic images,” J. Opt. Soc. Am. A26(2), 443–455 (2009).
[CrossRef] [PubMed]

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K.-H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95(1), 013703 (2009).
[CrossRef]

2008

2007

2006

B. T. Cox, S. R. Arridge, K. P. Köstli, and P. C. Beard, “Two-dimensional quantitative photoacoustic image reconstruction of absorption distributions in scattering media by use of a simple iterative method,” Appl. Opt.45(8), 1866–1875 (2006).
[CrossRef] [PubMed]

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

2005

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 Pt 1), 031912 (2005).
[CrossRef] [PubMed]

2003

M. Xu and L. V. Wang, “Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5 Pt 2), 056605 (2003).
[CrossRef] [PubMed]

Arridge, S. R.

Bagchi, S.

Bal, G.

G. Bal and K. Ren, “On multi-spectral quantitative photoacoustic tomography in diffusive regime,” Inverse Probl.28(2), 025010 (2012).
[CrossRef]

G. Bal and K. Ren, “Multi-source quantitative photoacoustic tomography in a diffusive regime,” Inverse Probl.27(7), 075003 (2011).
[CrossRef]

Banerjee, B.

Beard, P. C.

Cox, B.

Cox, B. T.

Englmeier, K.-H.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K.-H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95(1), 013703 (2009).
[CrossRef]

Guo, Z.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt.15(2), 021311 (2010).
[CrossRef] [PubMed]

Jetzfellner, T.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K.-H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95(1), 013703 (2009).
[CrossRef]

Jiang, H. B.

L. Yin, Q. Wang, Q. Zhang, and H. B. Jiang, “Tomographic imaging of absolute optical absorption coefficient in turbid media using combined photoacoustic and diffusing light measurements,” Opt. Lett.32(17), 2556–2558 (2007).
[CrossRef] [PubMed]

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

Köstli, K. P.

Laufer, J. G.

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt.17(6), 061202 (2012).
[CrossRef] [PubMed]

Li, C.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt.15(2), 021311 (2010).
[CrossRef] [PubMed]

Ntziachristos, V.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K.-H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95(1), 013703 (2009).
[CrossRef]

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 Pt 1), 031912 (2005).
[CrossRef] [PubMed]

Razansky, D.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K.-H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95(1), 013703 (2009).
[CrossRef]

Ren, K.

G. Bal and K. Ren, “On multi-spectral quantitative photoacoustic tomography in diffusive regime,” Inverse Probl.28(2), 025010 (2012).
[CrossRef]

G. Bal and K. Ren, “Multi-source quantitative photoacoustic tomography in a diffusive regime,” Inverse Probl.27(7), 075003 (2011).
[CrossRef]

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 Pt 1), 031912 (2005).
[CrossRef] [PubMed]

Rosenthal, A.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K.-H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95(1), 013703 (2009).
[CrossRef]

Roy, D.

Schulz, R.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K.-H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95(1), 013703 (2009).
[CrossRef]

Shao, P.

Song, L.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt.15(2), 021311 (2010).
[CrossRef] [PubMed]

Vasu, R. M.

Wang, L. V.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt.15(2), 021311 (2010).
[CrossRef] [PubMed]

L. V. Wang, “Tutorial on photoacoustic microscopy and computed tomography,” IEEE J. Sel. Top. Quantum Electron.14(1), 171–179 (2008).
[CrossRef]

M. Xu and L. V. Wang, “Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5 Pt 2), 056605 (2003).
[CrossRef] [PubMed]

Wang, Q.

Xu, M.

M. Xu and L. V. Wang, “Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5 Pt 2), 056605 (2003).
[CrossRef] [PubMed]

Yin, L.

Yuan, Z.

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

Zemp, R. J.

Zhang, Q.

Appl. Opt.

Appl. Phys. (Berl.)

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

Appl. Phys. Lett.

T. Jetzfellner, D. Razansky, A. Rosenthal, R. Schulz, K.-H. Englmeier, and V. Ntziachristos, “Performance of iterative optoacoustic tomography with experimental data,” Appl. Phys. Lett.95(1), 013703 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

L. V. Wang, “Tutorial on photoacoustic microscopy and computed tomography,” IEEE J. Sel. Top. Quantum Electron.14(1), 171–179 (2008).
[CrossRef]

Inverse Probl.

G. Bal and K. Ren, “On multi-spectral quantitative photoacoustic tomography in diffusive regime,” Inverse Probl.28(2), 025010 (2012).
[CrossRef]

G. Bal and K. Ren, “Multi-source quantitative photoacoustic tomography in a diffusive regime,” Inverse Probl.27(7), 075003 (2011).
[CrossRef]

J. Biomed. Opt.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt.15(2), 021311 (2010).
[CrossRef] [PubMed]

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt.17(6), 061202 (2012).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Opt. Lett.

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

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 Pt 1), 031912 (2005).
[CrossRef] [PubMed]

M. Xu and L. V. Wang, “Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5 Pt 2), 056605 (2003).
[CrossRef] [PubMed]

Other

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

B. Cox, T. Tarvainen, and S. Arridge, in Contemporary Mathematics (Book News Inc., 2011), pp. 1–12.

H. Gao, H. Zhang, and S. Osher, “Bregman methods in quantitative photoacoustic tomography,” CAM Report 10–42, (July 2010).

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Figures (5)

Fig. 1
Fig. 1

The 2-dimensional simulation setup (a) and true optical property model (b), (c). Four light sources are distributed on each side of the imaging object, with a 3-mm gap backward from the soft tissue surface. 64 detectors are circumferentially located around the object.

Fig. 2
Fig. 2

(a) Normalized optical fluence distribution from source on top of the object. (b) Optical fluence perturbations due to only absorption heterogeneities. (c) Fluence perturbations due to only diffusion coefficient distribution. (d) Total fluence perturbations. (e) Ultrasound transducer channel data due to the same light source displayed in different forms.

Fig. 3
Fig. 3

Simulation results with the ratio metric method and the proposed method with 4 illuminations surrounding the object. From top to bottom, absorption and diffusion coefficient distribution obtained with the ratiometric method described in [15], and the 1st, 3rd, 5th, and 10th iteration with the proposed method.

Fig. 4
Fig. 4

Log of relative errors between true model and recovered absorption and diffusion coefficient distributions with different iterations.

Fig. 5
Fig. 5

Singular values for different configurations. MIPAT with different source and detector count (1, 4 and 8 sources with 64 detectors and 16 detectors) are compared. Conditioning of CW-DOT with the same number of sources and detectors is also included for comparison.

Tables (1)

Tables Icon

Table 1 Condition Number for Different Configurations

Equations (8)

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p o = [ | p {111} 0 p {T11} 0 || p {1M1} 0 p {TM1} 0 || p {11S} 0 p {T1S} 0 || p {1MS} 0 p {TMS} 0 | ] T
p {τik} c = p o,k ( r i , t τ R i /c) 4π R i dr= f k ( r i ,u, t τ )
J ρj = J {τik}j = f k ( r i ,u, t τ ) u j = ( f k ( r i ,u, t τ ) E k )( E k u j )
[ B k ] j E k μ j = [ E k μ aj E k D j ] T
E k μ aj = δ j Φ k ( r )+ μ a ( r ) Φ k ( r ) μ aj
E k D j = μ a ( r ) Φ k ( r ) D j
Φ k ( r ) μ aj = ΔxΔy D 0 G 0 ( r , r j )Φ( r j , r )
Φ k ( r ) D j =ΔxΔy G 0 ( r , r j )ΔΦ( r j , r )

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